%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET894+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:10:55 PM UTC 2026
% Result : Theorem 5.85s 1.33s
% Output : CNFRefutation 5.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of formulae : 69 ( 8 unt; 1 def)
% Number of atoms : 256 ( 111 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 276 ( 89 ~; 146 |; 33 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-5 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 267 ( 249 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B] : cartesian_product2(singleton(A),singleton(B)) = singleton(ordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B] : cartesian_product2(singleton(A),singleton(B)) = singleton(ordered_pair(A,B)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f16,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,definition,
! [A,B,D,E,F] :
( sP0_prd(F,E,D,B,A)
<=> ( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f24,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] : sP0_prd(F,E,D,B,A) ) ),
inference(formula_renaming,[status(thm)],[f4,f23]) ).
fof(f25,plain,
! [A,B,C] :
( ( ? [D] :
( ( ? [E,F] : sP0_prd(F,E,D,B,A)
| in(D,C) )
& ( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C = cartesian_product2(A,B) )
& ( ! [D] :
( ( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| in(D,C) )
& ( ? [E,F] : sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
( ! [A,B,C] :
( ? [D] :
( ( ? [E,F] : sP0_prd(F,E,D,B,A)
| in(D,C) )
& ( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C = cartesian_product2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| in(D,C) )
& ! [D] :
( ? [E,F] : sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
( ! [A,B,C] :
( ( ( sP0_prd(sK5_skl(C,B,A),sK4_skl(C,B,A),sK3_skl(C,B,A),B,A)
| in(sK3_skl(C,B,A),C) )
& ( ! [E,F] : ~ sP0_prd(F,E,sK3_skl(C,B,A),B,A)
| ~ in(sK3_skl(C,B,A),C) ) )
| C = cartesian_product2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| in(D,C) )
& ! [D] :
( sP0_prd(sK2_skl(D,C,B,A),sK1_skl(D,C,B,A),D,B,A)
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(E,sK1_skl(D,C,B,A)),skolemize(F,sK2_skl(D,C,B,A)),skolemize(D,sK3_skl(C,B,A)),skolemize(E,sK4_skl(C,B,A)),skolemize(F,sK5_skl(C,B,A))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( sP0_prd(sK2_skl(X3,X0,X2,X1),sK1_skl(X3,X0,X2,X1),X3,X2,X1)
| ~ in(X3,X0)
| X0 != cartesian_product2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X4,X5,X3,X2,X1)
| in(X3,X0)
| X0 != cartesian_product2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4] :
( ~ sP0_prd(X3,X4,sK3_skl(X0,X2,X1),X2,X1)
| ~ in(sK3_skl(X0,X2,X1),X0)
| X0 = cartesian_product2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( sP0_prd(sK5_skl(X0,X2,X1),sK4_skl(X0,X2,X1),sK3_skl(X0,X2,X1),X2,X1)
| in(sK3_skl(X0,X2,X1),X0)
| X0 = cartesian_product2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f34,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f48,plain,
? [A,B] : cartesian_product2(singleton(A),singleton(B)) != singleton(ordered_pair(A,B)),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f49,plain,
cartesian_product2(singleton(sK9_skl),singleton(sK10_skl)) != singleton(ordered_pair(sK9_skl,sK10_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(A,sK9_skl),skolemize(B,sK10_skl)],[f48]) ).
fof(f50,plain,
cartesian_product2(singleton(sK9_skl),singleton(sK10_skl)) != singleton(ordered_pair(sK9_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [A,B,D,E,F] :
( ( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A)
| sP0_prd(F,E,D,B,A) )
& ( ( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
( ! [A,B,D,E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A)
| sP0_prd(F,E,D,B,A) )
& ! [A,B,D,E,F] :
( ( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( X2 = ordered_pair(X1,X0)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f58,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f59,plain,
! [X0,X1,X2] :
( sP0_prd(sK2_skl(X0,cartesian_product2(X1,X2),X2,X1),sK1_skl(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4] :
( ~ sP0_prd(X3,X4,X0,X2,X1)
| in(X0,cartesian_product2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f90,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X2,X1),cartesian_product2(X1,X2))
| in(sK3_skl(X0,X2,X1),X0)
| X0 = cartesian_product2(X1,X2) ),
inference(resolution,[status(thm)],[f31,f60]) ).
fof(f96,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| sK3_skl(X0,X1,X2) = ordered_pair(sK4_skl(X0,X1,X2),sK5_skl(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f55,f31]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4] :
( in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK5_skl(X0,X1,X2),X4)
| ~ in(sK3_skl(X0,X1,X2),cartesian_product2(X3,X4)) ),
inference(paramodulation,[status(thm)],[f96,f37]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4] :
( in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK4_skl(X0,X1,X2),X3)
| ~ in(sK3_skl(X0,X1,X2),cartesian_product2(X3,X4)) ),
inference(paramodulation,[status(thm)],[f96,f36]) ).
fof(f103,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK5_skl(X0,X1,X2),X1) ),
inference(resolution,[status(thm)],[f99,f90]) ).
fof(f105,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK5_skl(X0,X1,X2),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f103]) ).
fof(f107,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK4_skl(X0,X1,X2),X2) ),
inference(resolution,[status(thm)],[f100,f90]) ).
fof(f109,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X1,X2),X0)
| X0 = cartesian_product2(X2,X1)
| in(sK4_skl(X0,X1,X2),X2) ),
inference(duplicate_literals_removal,[status(thm)],[f107]) ).
fof(f111,plain,
! [X0,X1,X2] :
( sK5_skl(X0,singleton(X2),X1) = X2
| in(sK3_skl(X0,singleton(X2),X1),X0)
| X0 = cartesian_product2(X1,singleton(X2)) ),
inference(resolution,[status(thm)],[f105,f57]) ).
fof(f113,plain,
! [X0,X1,X2] :
( sK4_skl(X0,X2,singleton(X1)) = X1
| in(sK3_skl(X0,X2,singleton(X1)),X0)
| X0 = cartesian_product2(singleton(X1),X2) ),
inference(resolution,[status(thm)],[f109,f57]) ).
fof(f117,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),singleton(X2),X1) = X0
| sK5_skl(singleton(X0),singleton(X2),X1) = X2
| singleton(X0) = cartesian_product2(X1,singleton(X2)) ),
inference(resolution,[status(thm)],[f111,f57]) ).
fof(f123,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),X2,singleton(X1)) = X0
| sK4_skl(singleton(X0),X2,singleton(X1)) = X1
| singleton(X0) = cartesian_product2(singleton(X1),X2) ),
inference(resolution,[status(thm)],[f113,f57]) ).
fof(f129,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),singleton(X1),X2) = X0
| singleton(X0) = cartesian_product2(X2,singleton(X1))
| in(sK3_skl(singleton(X0),singleton(X1),X2),singleton(X0))
| singleton(X0) = cartesian_product2(X2,singleton(X1))
| sK3_skl(singleton(X0),singleton(X1),X2) = ordered_pair(sK4_skl(singleton(X0),singleton(X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f117,f96]) ).
fof(f133,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),singleton(X1),X2) = X0
| in(sK3_skl(singleton(X0),singleton(X1),X2),singleton(X0))
| singleton(X0) = cartesian_product2(X2,singleton(X1))
| sK3_skl(singleton(X0),singleton(X1),X2) = ordered_pair(sK4_skl(singleton(X0),singleton(X1),X2),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f129]) ).
fof(f134,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),singleton(X1),X2) = X0
| singleton(X0) = cartesian_product2(X2,singleton(X1))
| sK3_skl(singleton(X0),singleton(X1),X2) = ordered_pair(sK4_skl(singleton(X0),singleton(X1),X2),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f57]) ).
fof(f147,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),singleton(X1),singleton(X2)) = X0
| singleton(X0) = cartesian_product2(singleton(X2),singleton(X1))
| sK3_skl(singleton(X0),singleton(X1),singleton(X2)) = X0
| singleton(X0) = cartesian_product2(singleton(X2),singleton(X1))
| sK3_skl(singleton(X0),singleton(X1),singleton(X2)) = ordered_pair(X2,X1) ),
inference(paramodulation,[status(thm)],[f123,f134]) ).
fof(f151,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),singleton(X1),singleton(X2)) = X0
| singleton(X0) = cartesian_product2(singleton(X2),singleton(X1))
| sK3_skl(singleton(X0),singleton(X1),singleton(X2)) = ordered_pair(X2,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f147]) ).
fof(f163,plain,
! [X0,X1,X2] :
( sK3_skl(singleton(X0),singleton(X2),singleton(X1)) = X0
| ordered_pair(X1,X2) != X0
| singleton(X0) = cartesian_product2(singleton(X1),singleton(X2)) ),
inference(equality_factoring,[status(thm)],[f151]) ).
fof(f180,plain,
! [X0,X1] :
( sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)) = ordered_pair(X0,X1)
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f163]) ).
fof(f195,plain,
! [X0,X1] :
( singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1))
| sP0_prd(sK5_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),sK4_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),ordered_pair(X0,X1),singleton(X1),singleton(X0))
| in(sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(paramodulation,[status(thm)],[f180,f31]) ).
fof(f206,plain,
! [X0,X1] :
( sP0_prd(sK5_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),sK4_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),ordered_pair(X0,X1),singleton(X1),singleton(X0))
| in(sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f195]) ).
fof(f369,plain,
! [X0,X1,X2] :
( ~ in(sK3_skl(X0,X2,X1),cartesian_product2(X1,X2))
| ~ in(sK3_skl(X0,X2,X1),X0)
| X0 = cartesian_product2(X1,X2) ),
inference(resolution,[status(thm)],[f30,f59]) ).
fof(f372,plain,
! [X0,X1,X2,X3] :
( singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1))
| ~ sP0_prd(X2,X3,ordered_pair(X0,X1),singleton(X1),singleton(X0))
| ~ in(sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(paramodulation,[status(thm)],[f180,f30]) ).
fof(f377,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X2,X3,ordered_pair(X0,X1),singleton(X1),singleton(X0))
| ~ in(sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f372]) ).
fof(f411,plain,
! [X0,X1] :
( singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1))
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X0),singleton(X1)))
| ~ in(sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(paramodulation,[status(thm)],[f180,f369]) ).
fof(f415,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X0),singleton(X1)))
| ~ in(sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f411]) ).
fof(f853,plain,
! [X0,X1,X2,X3] :
( singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1))
| ~ sP0_prd(X2,X3,ordered_pair(X0,X1),singleton(X1),singleton(X0))
| ~ in(ordered_pair(X0,X1),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(paramodulation,[status(thm)],[f180,f377]) ).
fof(f868,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X2,X3,ordered_pair(X0,X1),singleton(X1),singleton(X0))
| ~ in(ordered_pair(X0,X1),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f853]) ).
fof(f869,plain,
! [X0,X1] :
( in(sK3_skl(singleton(ordered_pair(X0,X1)),singleton(X1),singleton(X0)),singleton(ordered_pair(X0,X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f206,f870]) ).
fof(f870,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X2,X3,ordered_pair(X0,X1),singleton(X1),singleton(X0))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f868,f58]) ).
fof(f872,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X0),singleton(X1)))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f415,f869]) ).
fof(f874,plain,
! [X0,X1] :
( ~ in(X1,singleton(X1))
| ~ in(X0,singleton(X0))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(resolution,[status(thm)],[f872,f38]) ).
fof(f880,plain,
! [X0,X1] :
( ~ in(X1,singleton(X1))
| singleton(ordered_pair(X0,X1)) = cartesian_product2(singleton(X0),singleton(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f874,f58]) ).
fof(f881,plain,
~ in(sK10_skl,singleton(sK10_skl)),
inference(resolution,[status(thm)],[f880,f50]) ).
fof(f882,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f881,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET894+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:45:43 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 5.85/1.33 % Refutation found
% 5.85/1.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.85/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.85/1.35 % Elapsed time: 0.914285 seconds
% 5.85/1.35 % CPU time: 6.774636 seconds
% 5.85/1.35 % Total memory used: 168.043 MB
% 5.85/1.35 % Net memory used: 161.640 MB
%------------------------------------------------------------------------------