TSTP Solution File: SET955+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET955+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:47 EDT 2024
% Result : Theorem 0.16s 0.37s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 4 unt; 0 def)
% Number of atoms : 233 ( 64 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 248 ( 84 ~; 116 |; 28 &)
% ( 16 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-5 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 171 ( 143 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C,D] :
( ! [E,F] :
( in(ordered_pair(E,F),cartesian_product2(A,B))
<=> in(ordered_pair(E,F),cartesian_product2(C,D)) )
=> cartesian_product2(A,B) = cartesian_product2(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C,D] :
( ! [E,F] :
( in(ordered_pair(E,F),cartesian_product2(A,B))
<=> in(ordered_pair(E,F),cartesian_product2(C,D)) )
=> cartesian_product2(A,B) = cartesian_product2(C,D) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
<=> ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ),
introduced(predicate_definition,[f3]) ).
fof(f15,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] : pd0_0(F,E,D,B,A) ) ),
inference(formula_renaming,[status(thm)],[f3,f14]) ).
fof(f16,plain,
! [A,B,C] :
( ( C != cartesian_product2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| pd0_0(sk0_1(D,C,B,A),sk0_0(D,C,B,A),D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ( ( ~ in(sk0_2(C,B,A),C)
| ! [E,F] : ~ pd0_0(F,E,sk0_2(C,B,A),B,A) )
& ( in(sk0_2(C,B,A),C)
| pd0_0(sk0_4(C,B,A),sk0_3(C,B,A),sk0_2(C,B,A),B,A) ) ) ) ),
inference(skolemization,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| pd0_0(sk0_1(X3,X0,X2,X1),sk0_0(X3,X0,X2,X1),X3,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f29,plain,
? [A,B,C,D] :
( ! [E,F] :
( in(ordered_pair(E,F),cartesian_product2(A,B))
<=> in(ordered_pair(E,F),cartesian_product2(C,D)) )
& cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
? [A,B,C,D] :
( ! [E,F] :
( ( ~ in(ordered_pair(E,F),cartesian_product2(A,B))
| in(ordered_pair(E,F),cartesian_product2(C,D)) )
& ( in(ordered_pair(E,F),cartesian_product2(A,B))
| ~ in(ordered_pair(E,F),cartesian_product2(C,D)) ) )
& cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f31,plain,
? [A,B,C,D] :
( ! [E,F] :
( ~ in(ordered_pair(E,F),cartesian_product2(A,B))
| in(ordered_pair(E,F),cartesian_product2(C,D)) )
& ! [E,F] :
( in(ordered_pair(E,F),cartesian_product2(A,B))
| ~ in(ordered_pair(E,F),cartesian_product2(C,D)) )
& cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
( ! [E,F] :
( ~ in(ordered_pair(E,F),cartesian_product2(sk0_7,sk0_8))
| in(ordered_pair(E,F),cartesian_product2(sk0_9,sk0_10)) )
& ! [E,F] :
( in(ordered_pair(E,F),cartesian_product2(sk0_7,sk0_8))
| ~ in(ordered_pair(E,F),cartesian_product2(sk0_9,sk0_10)) )
& cartesian_product2(sk0_7,sk0_8) != cartesian_product2(sk0_9,sk0_10) ),
inference(skolemization,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sk0_7,sk0_8))
| in(ordered_pair(X0,X1),cartesian_product2(sk0_9,sk0_10)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(sk0_7,sk0_8))
| ~ in(ordered_pair(X0,X1),cartesian_product2(sk0_9,sk0_10)) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
cartesian_product2(sk0_7,sk0_8) != cartesian_product2(sk0_9,sk0_10),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f36,plain,
! [A,B] :
( ? [C] :
( in(C,A)
<~> in(C,B) )
| A = B ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f37,plain,
! [A,B] :
( ? [C] :
( ( in(C,A)
| in(C,B) )
& ( ~ in(C,A)
| ~ in(C,B) ) )
| A = B ),
inference(NNF_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [A,B] :
( ( ( in(sk0_11(B,A),A)
| in(sk0_11(B,A),B) )
& ( ~ in(sk0_11(B,A),A)
| ~ in(sk0_11(B,A),B) ) )
| A = B ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( in(sk0_11(X0,X1),X1)
| in(sk0_11(X0,X1),X0)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ in(sk0_11(X0,X1),X1)
| ~ in(sk0_11(X0,X1),X0)
| X1 = X0 ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,plain,
! [A,B,D,E,F] :
( ( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f42,plain,
( ! [A,B,D,E,F] :
( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| X2 = ordered_pair(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ in(X0,cartesian_product2(X1,X2))
| pd0_0(sk0_1(X0,cartesian_product2(X1,X2),X2,X1),sk0_0(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f19]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ in(X0,cartesian_product2(X1,X2))
| X0 = ordered_pair(sk0_0(X0,cartesian_product2(X1,X2),X2,X1),sk0_1(X0,cartesian_product2(X1,X2),X2,X1)) ),
inference(resolution,[status(thm)],[f47,f45]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sk0_11(X0,cartesian_product2(X1,X2)) = ordered_pair(sk0_0(sk0_11(X0,cartesian_product2(X1,X2)),cartesian_product2(X1,X2),X2,X1),sk0_1(sk0_11(X0,cartesian_product2(X1,X2)),cartesian_product2(X1,X2),X2,X1))
| in(sk0_11(X0,cartesian_product2(X1,X2)),X0)
| cartesian_product2(X1,X2) = X0 ),
inference(resolution,[status(thm)],[f62,f39]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2))
| cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
inference(resolution,[status(thm)],[f63,f62]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_7,sk0_8))
| ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X2,X3),X3,X2)),cartesian_product2(sk0_9,sk0_10))
| cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
inference(paramodulation,[status(thm)],[f68,f34]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_7,sk0_8))
| ~ in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_9,sk0_10))
| cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0))
| cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
inference(paramodulation,[status(thm)],[f68,f76]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_7,sk0_8))
| ~ in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(sk0_9,sk0_10))
| cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(X2,X3)),cartesian_product2(X0,X1),X1,X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0))
| in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1))
| cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1) ),
inference(resolution,[status(thm)],[f80,f39]) ).
fof(f84,plain,
! [X0,X1] :
( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0))
| in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1)) ),
inference(duplicate_literals_removal,[status(esa)],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( in(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f62]) ).
fof(f86,plain,
! [X0,X1] :
( cartesian_product2(sk0_9,sk0_10) = cartesian_product2(X0,X1)
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(X0,X1),X1,X0))
| sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)) = ordered_pair(sk0_0(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(X0,X1),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) ),
inference(resolution,[status(thm)],[f85,f62]) ).
fof(f143,plain,
( spl0_2
<=> cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8) ),
introduced(split_symbol_definition) ).
fof(f144,plain,
( cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( spl0_3
<=> sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f148,plain,
( sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) != sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10))
| spl0_3 ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( spl0_4
<=> ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f150,plain,
( ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
| sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) != sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10))
| ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)) = sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)) ),
inference(equality_factoring,[status(esa)],[f86]) ).
fof(f153,plain,
( spl0_2
| ~ spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f152,f143,f146,f149]) ).
fof(f154,plain,
( $false
| spl0_3 ),
inference(trivial_equality_resolution,[status(esa)],[f148]) ).
fof(f155,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f35]) ).
fof(f157,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f165,plain,
( spl0_6
<=> in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f166,plain,
( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f173,plain,
( spl0_8
<=> in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f174,plain,
( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f183,plain,
( spl0_10
<=> in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_7,sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f185,plain,
( ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_7,sk0_8))
| spl0_10 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f191,plain,
( spl0_12
<=> in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_9,sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f193,plain,
( ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_9,sk0_10))
| spl0_12 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f196,plain,
( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_9,sk0_10))
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f150,f34]) ).
fof(f197,plain,
( spl0_6
| ~ spl0_12
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f196,f165,f191,f149]) ).
fof(f198,plain,
( ~ in(ordered_pair(sk0_0(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7),sk0_1(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8),sk0_8,sk0_7)),cartesian_product2(sk0_7,sk0_8))
| in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10))
| ~ spl0_4 ),
inference(paramodulation,[status(thm)],[f150,f33]) ).
fof(f199,plain,
( ~ spl0_10
| spl0_8
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f198,f183,f173,f149]) ).
fof(f200,plain,
( ~ in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_9,sk0_10))
| ~ spl0_4
| spl0_12 ),
inference(forward_demodulation,[status(thm)],[f150,f193]) ).
fof(f201,plain,
( ~ in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| ~ spl0_4
| spl0_10 ),
inference(forward_demodulation,[status(thm)],[f150,f185]) ).
fof(f210,plain,
( in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
| ~ spl0_4
| spl0_12 ),
inference(resolution,[status(thm)],[f200,f39]) ).
fof(f211,plain,
( spl0_6
| spl0_2
| ~ spl0_4
| spl0_12 ),
inference(split_clause,[status(thm)],[f210,f165,f143,f149,f191]) ).
fof(f212,plain,
( $false
| ~ spl0_4
| spl0_10
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f201]) ).
fof(f213,plain,
( ~ spl0_4
| spl0_10
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f231,plain,
( ~ in(sk0_11(cartesian_product2(sk0_7,sk0_8),cartesian_product2(sk0_9,sk0_10)),cartesian_product2(sk0_7,sk0_8))
| cartesian_product2(sk0_9,sk0_10) = cartesian_product2(sk0_7,sk0_8)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f174,f40]) ).
fof(f232,plain,
( ~ spl0_6
| spl0_2
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f231,f165,f143,f173]) ).
fof(f234,plain,
$false,
inference(sat_refutation,[status(thm)],[f153,f155,f157,f197,f199,f211,f213,f232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET955+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n003.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 21:50:03 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.34 % Drodi V3.6.0
% 0.16/0.37 % Refutation found
% 0.16/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.39 % Elapsed time: 0.053850 seconds
% 0.16/0.39 % CPU time: 0.280596 seconds
% 0.16/0.39 % Total memory used: 61.159 MB
% 0.16/0.39 % Net memory used: 61.003 MB
%------------------------------------------------------------------------------