name string | atp_proof string | mizar_proof string | system string |
|---|---|---|---|
t75_bvfunc14 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t74_bvfunc14, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(... | reserve Y for non empty set,
G for Subset of PARTITIONS(Y),
A,B,C,D,E,F for a_partition of Y;
reserve Y for non empty set,
G for Subset of PARTITIONS(Y),
A, B, C, D, E, F, J, M for a_partition of Y,
x,x1,x2,x3,x4,x5,x6,x7,x8,x9 for set;
theorem
for G being Subset of PARTITIONS(Y), A,B,C,D,E,F,J,M,N being
a... | Convert the following ATP output trace into a readable Mizar proof. |
t62_pzfmisc1 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(d16_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_par... | reserve i, I for set,
f for Function,
x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;
theorem :: ZFMISC_1:119
x1 c= A & x2 c= B implies [|x1,x2|] c= [|A,B|]
proof
assume that
A1: x1 c= A and
A2: x2 c= B;
let i;
assume
A3: i in I;
then
A4: x1.i c= A.i by A1,PBOOLE:def 2;
x2.i c= B.i by A2,A3,PBO... | Convert the following ATP output trace into a readable Mizar proof. |
t2_funct_4 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t2_funct_4, conjecture, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>k3_relat_1(X2,X1)=k3_relat_1(X2,k5_relat_1(X1,k10_xtuple_0(X2))))), file('/scratch/mptp/predsminms1/t2_funct_4__0', t2_funct_4)).
fof(t53_relat_1... | reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2,X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
theorem
g*f = (g|rng f)*f
proof
x in dom(g*f) iff x in dom((g|rng f)*f)
proof
A1: dom(g|rng f) = dom g /\ rng f by RELAT_1:61;
thus x in dom(g*f) implies x in dom((g|rn... | Convert the following ATP output trace into a readable Mizar proof. |
t18_borsuk_5 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t18_borsuk_5, conjecture, ![X1]:(v1_rat_1(X1)=>![X2]:((v1_xreal_0(X2)&~(v1_rat_1(X2)))=>~(v1_rat_1(k2_xcmplx_0(X1,X2))))), file('/scratch/mptp/predsminms1/t18_borsuk_5__0', t18_borsuk_5)).
fof(fc4_borsuk_5, axiom, ![X1, X2]:((v1_rat_1(X1)&(v1_xreal_... | reserve x1, x2, x3, x4, x5, x6, x7 for set;
theorem
for a being rational number, b being irrational real number
holds a + b is irrational;
| Convert the following ATP output trace into a readable Mizar proof. |
t4_groupp_1 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t4_groupp_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(v7_ordinal1(X3)=>(k5_group_1(X1,X3,k2_group_1(X1,X2))=k1_group_1(X1)=>k5_group_1(X1,X3,X2)=k1_grou... | reserve G for Group,
a,b for Element of G,
m, n for Nat,
p for prime Nat;
theorem Th4:
a" |^ n = 1_G implies a |^ n = 1_G
proof
a"" = a;
hence thesis by Th3;
end;
| Convert the following ATP output trace into a readable Mizar proof. |
t34_cqc_the3 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(d5_cqc_the3, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>(r5_cqc_the3(X1,X2,X3)<=>(r1_cqc_the3(X1,X2,X3)&r1_cqc_the3(X1,X3,X2)))))), file('/scratch/mp... | reserve A for QC-alphabet;
reserve p, q, r, s, p1, q1 for Element of CQC-WFF(A),
X, Y, Z, X1, X2 for Subset of CQC-WFF(A),
h for QC-formula of A,
x, y for bound_QC-variable of A,
n for Element of NAT;
theorem
p |-| q & r |-| s implies p '&' r |-| q '&' s
proof
assume that
A1: p |-| q and
A2: r |-| s;
A3: q... | Convert the following ATP output trace into a readable Mizar proof. |
t10_lfuzzy_1 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(redefinition_r2_relset_1, axiom, ![X1, X2, X3, X4]:((m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(r2_relset_1(X1,X2,X3,X4)<=>X3=X4)), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', redefinitio... | reserve X, Y for non empty set;
theorem Th10:
for R,S being RMembership_Func of X,X holds R is symmetric & S
is symmetric implies converse max(R,S) = max(R,S)
proof
let R,S be RMembership_Func of X,X;
assume R is symmetric & S is symmetric;
then converse R = R & converse S =S by Def4;
hence thesis by FUZZY... | Convert the following ATP output trace into a readable Mizar proof. |
t36_yellow_3 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t36_yellow_3, conjecture, ![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v2_struct_0(X2))&(v5_orders_2(X2)&l1_orders_2(X2)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_... |
theorem Th36:
for S1, S2 being antisymmetric non empty RelStr for D1 being
Subset of S1, D2 being Subset of S2 for x being Element of S1, y being Element
of S2 st ex_inf_of D1,S1 & ex_inf_of D2,S2 & for b being Element of [:S1,S2:]
st b is_<=_than [:D1,D2:] holds [x,y] >= b holds (for c being Element of S1 st
c ... | Convert the following ATP output trace into a readable Mizar proof. |
t23_graph_5 | Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t23_graph_5, conjecture, ![X1, X2, X3]:((~(v2_struct_0(X3))&l1_graph_1(X3))=>![X4]:(m2_finseq_1(X4,u4_struct_0(X3))=>![X5]:(m2_finseq_1(X5,u4_struct_0(X3))=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,k8_finseq_1(u4_struct_0(X3),X4,X5)),X1)... | reserve n,m,i,j,k for Element of NAT,
x,y,e,X,V,U for set,
W,f,g for Function;
reserve p,q for FinSequence;
reserve G for Graph,
pe,qe for FinSequence of the carrier' of G;
theorem Th23:
vertices(pe^qe) \ X c= V implies vertices(pe) \ X c= V &
vertices(qe) \ X c= V
proof
A1: rng pe c= rng(pe^qe) & rng qe c= ... | Convert the following ATP output trace into a readable Mizar proof. |
t75_exchsort | "Proof found!\n# SZS status Theorem\n# SZS output start CNFRefutation\nfof(t12_funct_5, axiom, ![X1,(...TRUNCATED) | "reserve a,a1,a2,b,c,d for ordinal number,\n n,m,k for Nat,\n x,y,z,t,X,Y,Z for set;\nreserve f,g (...TRUNCATED) | Convert the following ATP output trace into a readable Mizar proof. |
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