%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET951+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:11:02 PM UTC 2026
% Result : Theorem 57.39s 8.11s
% Output : CNFRefutation 57.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 81 ( 17 unt; 7 def)
% Number of atoms : 248 ( 54 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 280 ( 113 ~; 107 |; 46 &)
% ( 13 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-5 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 215 ( 189 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C,D,E] :
~ ( ! [F,G] :
~ ( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C,D,E] :
~ ( ! [F,G] :
~ ( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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(f19,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,f18]) ).
fof(f20,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)],[f19]) ).
fof(f21,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)],[f20]) ).
fof(f22,plain,
( ! [A,B,C] :
( ( ( sP0_prd(sK4_skl(C,B,A),sK3_skl(C,B,A),sK2_skl(C,B,A),B,A)
| in(sK2_skl(C,B,A),C) )
& ( ! [E,F] : ~ sP0_prd(F,E,sK2_skl(C,B,A),B,A)
| ~ in(sK2_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(sK1_skl(D,C,B,A),sK0_skl(D,C,B,A),D,B,A)
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(F,sK1_skl(D,C,B,A)),skolemize(D,sK2_skl(C,B,A)),skolemize(E,sK3_skl(C,B,A)),skolemize(F,sK4_skl(C,B,A))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( sP0_prd(sK1_skl(X3,X0,X2,X1),sK0_skl(X3,X0,X2,X1),X3,X2,X1)
| ~ in(X3,X0)
| X0 != cartesian_product2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f27,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [A,B,C] :
( ( ( ( in(sK5_skl(C,B,A),B)
& in(sK5_skl(C,B,A),A) )
| in(sK5_skl(C,B,A),C) )
& ( ~ in(sK5_skl(C,B,A),B)
| ~ in(sK5_skl(C,B,A),A)
| ~ in(sK5_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(D,sK5_skl(C,B,A))],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f44,plain,
? [A,B,C,D,E] :
( ! [F,G] :
( ~ in(G,set_intersection2(C,E))
| ~ in(F,set_intersection2(B,D))
| A != ordered_pair(F,G) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f45,plain,
? [A,B,C,D,E] :
( ! [G] :
( ~ in(G,set_intersection2(C,E))
| ! [F] :
( ~ in(F,set_intersection2(B,D))
| A != ordered_pair(F,G) ) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
( ! [G] :
( ~ in(G,set_intersection2(sK10_skl,sK12_skl))
| ! [F] :
( ~ in(F,set_intersection2(sK9_skl,sK11_skl))
| sK8_skl != ordered_pair(F,G) ) )
& in(sK8_skl,set_intersection2(cartesian_product2(sK9_skl,sK10_skl),cartesian_product2(sK11_skl,sK12_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl),skolemize(C,sK10_skl),skolemize(D,sK11_skl),skolemize(E,sK12_skl)],[f45]) ).
fof(f47,plain,
in(sK8_skl,set_intersection2(cartesian_product2(sK9_skl,sK10_skl),cartesian_product2(sK11_skl,sK12_skl))),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(X1,set_intersection2(sK10_skl,sK12_skl))
| sK8_skl != ordered_pair(X0,X1)
| ~ in(X0,set_intersection2(sK9_skl,sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
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) )
& ( ( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f53,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)],[f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4] :
( in(X1,X4)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( in(X0,X3)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4] :
( X2 = ordered_pair(X1,X0)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X2,X1))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f59,plain,
! [X0,X1,X2] :
( sP0_prd(sK1_skl(X0,cartesian_product2(X1,X2),X2,X1),sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f23]) ).
fof(f61,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f62,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f76,plain,
in(sK8_skl,cartesian_product2(sK11_skl,sK12_skl)),
inference(resolution,[status(thm)],[f47,f58]) ).
fof(f86,plain,
sP0_prd(sK1_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl),sK0_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl),sK8_skl,sK12_skl,sK11_skl),
inference(resolution,[status(thm)],[f76,f59]) ).
fof(f89,plain,
in(sK8_skl,cartesian_product2(sK9_skl,sK10_skl)),
inference(resolution,[status(thm)],[f61,f47]) ).
fof(f123,plain,
sK8_skl = ordered_pair(sK0_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl),sK1_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl)),
inference(resolution,[status(thm)],[f86,f56]) ).
fof(f124,plain,
in(sK0_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl),sK11_skl),
inference(resolution,[status(thm)],[f86,f54]) ).
fof(f125,plain,
in(sK1_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl),sK12_skl),
inference(resolution,[status(thm)],[f86,f55]) ).
fof(f222,plain,
! [X0,X1,X2] :
( in(sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f59,f54]) ).
fof(f223,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,cartesian_product2(X1,X2),X2,X1),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f59,f55]) ).
fof(f224,plain,
! [X0,X1,X2] :
( ~ in(X0,cartesian_product2(X1,X2))
| ordered_pair(sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),sK1_skl(X0,cartesian_product2(X1,X2),X2,X1)) = X0 ),
inference(resolution,[status(thm)],[f59,f56]) ).
fof(f385,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(X0,cartesian_product2(X1,X2),X2,X1),set_intersection2(X2,X3))
| ~ in(sK1_skl(X0,cartesian_product2(X1,X2),X2,X1),X3)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f223,f62]) ).
fof(f393,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),set_intersection2(X1,X3))
| ~ in(sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),X3) ),
inference(resolution,[status(thm)],[f222,f62]) ).
fof(f514,plain,
ordered_pair(sK0_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),sK1_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl)) = sK8_skl,
inference(resolution,[status(thm)],[f224,f89]) ).
fof(f4164,definition,
( sQ2_spl
<=> in(sK8_skl,cartesian_product2(sK11_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f4166,plain,
( sQ2_spl
| ~ in(sK8_skl,cartesian_product2(sK11_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f4164]) ).
fof(f4171,definition,
( sQ4_spl
<=> in(sK8_skl,cartesian_product2(sK9_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f4173,plain,
( sQ4_spl
| ~ in(sK8_skl,cartesian_product2(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f4171]) ).
fof(f4178,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4173,f89]) ).
fof(f4179,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f4178]) ).
fof(f4181,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4166,f76]) ).
fof(f4182,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f4181]) ).
fof(f5276,plain,
! [X0,X1] :
( sK1_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl) = X1
| sK8_skl != ordered_pair(X0,X1) ),
inference(paramodulation,[status(thm)],[f123,f51]) ).
fof(f5279,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK8_skl
| sK0_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl) = X0 ),
inference(paramodulation,[status(thm)],[f123,f50]) ).
fof(f5489,plain,
sK1_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl) = sK1_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),
inference(resolution,[status(thm)],[f5276,f514]) ).
fof(f5497,definition,
( sQ8_spl
<=> sK8_skl = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f5499,plain,
( sQ8_spl
| sK8_skl != sK8_skl ),
inference(component_clause,[status(thm)],[f5497]) ).
fof(f5508,plain,
( sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5499]) ).
fof(f5509,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f5508]) ).
fof(f5539,plain,
sK0_skl(sK8_skl,cartesian_product2(sK11_skl,sK12_skl),sK12_skl,sK11_skl) = sK0_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),
inference(resolution,[status(thm)],[f5279,f514]) ).
fof(f6575,plain,
in(sK1_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),sK12_skl),
inference(backward_demodulation,[status(thm)],[f5489,f125]) ).
fof(f6598,plain,
( in(sK1_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),set_intersection2(sK10_skl,sK12_skl))
| ~ in(sK8_skl,cartesian_product2(sK9_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f6575,f385]) ).
fof(f6602,definition,
( sQ19_spl
<=> in(sK1_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),set_intersection2(sK10_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f6603,plain,
( ~ sQ19_spl
| in(sK1_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),set_intersection2(sK10_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f6602]) ).
fof(f6605,plain,
( sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f6598,f4171,f6602]) ).
fof(f6903,plain,
! [X0] :
( ~ sQ19_spl
| sK8_skl != ordered_pair(X0,sK1_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl))
| ~ in(X0,set_intersection2(sK9_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f6603,f48]) ).
fof(f7476,definition,
! [X0] :
( sQ24_spl
<=> ~ in(sK8_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f7477,plain,
! [X0] :
( ~ sQ24_spl
| ~ in(sK8_skl,X0) ),
inference(component_clause,[status(thm)],[f7476]) ).
fof(f7504,plain,
( ~ sQ24_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f47,f7477]) ).
fof(f7507,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f7504]) ).
fof(f8653,plain,
in(sK0_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),sK11_skl),
inference(backward_demodulation,[status(thm)],[f5539,f124]) ).
fof(f8763,plain,
( ~ in(sK8_skl,cartesian_product2(sK9_skl,sK10_skl))
| in(sK0_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),set_intersection2(sK9_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f8653,f393]) ).
fof(f8767,definition,
( sQ30_spl
<=> in(sK0_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),set_intersection2(sK9_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f8768,plain,
( ~ sQ30_spl
| in(sK0_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),set_intersection2(sK9_skl,sK11_skl)) ),
inference(component_clause,[status(thm)],[f8767]) ).
fof(f8770,plain,
( ~ sQ4_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f8763,f8767,f4171]) ).
fof(f10073,plain,
( ~ sQ19_spl
| ~ in(sK0_skl(sK8_skl,cartesian_product2(sK9_skl,sK10_skl),sK10_skl,sK9_skl),set_intersection2(sK9_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f6903,f514]) ).
fof(f10075,plain,
( ~ sQ19_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10073,f8768]) ).
fof(f10076,plain,
( ~ sQ19_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f10075]) ).
fof(f10077,plain,
$false,
inference(sat_refutation,[status(thm)],[f4179,f4182,f5509,f6605,f7507,f8770,f10076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET951+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:44:50 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 57.39/8.11 % Refutation found
% 57.39/8.11 % SZS status Theorem for theBenchmark: Theorem is valid
% 57.39/8.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.53/8.69 % Elapsed time: 8.325062 seconds
% 4.53/8.69 % CPU time: 62.065013 seconds
% 4.53/8.69 % Total memory used: 435.885 MB
% 4.53/8.69 % Net memory used: 394.299 MB
%------------------------------------------------------------------------------