%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU137+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:19:20 PM UTC 2026
% Result : Theorem 0.14s 0.62s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 108 ( 12 unt; 12 def)
% Number of atoms : 331 ( 35 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 373 ( 150 ~; 162 |; 39 &)
% ( 18 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 159 ( 151 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f25,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f29,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_union2(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_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [A,B,C] :
( ( ( in(sK0_skl(C,B,A),B)
| in(sK0_skl(C,B,A),A)
| in(sK0_skl(C,B,A),C) )
& ( ( ~ in(sK0_skl(C,B,A),B)
& ~ in(sK0_skl(C,B,A),A) )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = set_union2(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_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X0,X2,X1),X1)
| ~ in(sK0_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X0,X2,X1),X2)
| ~ in(sK0_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f36,plain,
! [X0,X1,X2] :
( in(sK0_skl(X0,X2,X1),X2)
| in(sK0_skl(X0,X2,X1),X1)
| in(sK0_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f37,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f38,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,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_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f45,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_difference(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_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK2_skl(C,B,A),B)
& in(sK2_skl(C,B,A),A) )
| in(sK2_skl(C,B,A),C) )
& ( in(sK2_skl(C,B,A),B)
| ~ in(sK2_skl(C,B,A),A)
| ~ in(sK2_skl(C,B,A),C) ) )
| C = set_difference(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_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f60,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(thm)],[f12]) ).
fof(f61,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f75,plain,
? [A,B] :
( B != set_union2(A,set_difference(B,A))
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f76,plain,
( sK7_skl != set_union2(sK6_skl,set_difference(sK7_skl,sK6_skl))
& subset(sK6_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl)],[f75]) ).
fof(f77,plain,
subset(sK6_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
sK7_skl != set_union2(sK6_skl,set_difference(sK7_skl,sK6_skl)),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f88,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f33]) ).
fof(f91,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f47]) ).
fof(f93,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f49]) ).
fof(f101,plain,
! [X0,X1] : ~ in(set_union2(X0,X1),X0),
inference(resolution,[status(thm)],[f26,f89]) ).
fof(f111,plain,
( ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK6_skl)
| ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f34,f78]) ).
fof(f115,definition,
( sQ0_spl
<=> in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( sQ0_spl
| ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK7_skl) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
( sQ1_spl
<=> in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ1_spl
| in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f111,f115,f118]) ).
fof(f150,plain,
( sQ0_spl
| in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),set_difference(sK7_skl,sK6_skl))
| in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK6_skl)
| sK7_skl = set_union2(sK6_skl,set_difference(sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f117,f36]) ).
fof(f152,definition,
( sQ2_spl
<=> sK7_skl = set_union2(sK6_skl,set_difference(sK7_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ2_spl
| sK7_skl = set_union2(sK6_skl,set_difference(sK7_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ3_spl
<=> in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),set_difference(sK7_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ3_spl
| in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),set_difference(sK7_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f157,plain,
( sQ3_spl
| ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),set_difference(sK7_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ0_spl
| sQ3_spl
| sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f150,f152,f118,f155,f115]) ).
fof(f159,plain,
( ~ sQ3_spl
| ~ in(set_difference(sK7_skl,sK6_skl),sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl)) ),
inference(resolution,[status(thm)],[f156,f26]) ).
fof(f161,plain,
! [X0] :
( ~ sQ3_spl
| in(set_difference(sK7_skl,sK6_skl),X0)
| ~ in(set_difference(sK7_skl,sK6_skl),set_union2(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),X0)) ),
inference(resolution,[status(thm)],[f159,f88]) ).
fof(f163,plain,
( ~ sQ3_spl
| ~ in(set_difference(sK7_skl,sK6_skl),set_union2(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),set_difference(sK7_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f161,f26]) ).
fof(f274,plain,
( ~ sQ3_spl
| ~ in(set_difference(sK7_skl,sK6_skl),set_difference(sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f163,f90]) ).
fof(f280,plain,
( ~ sQ3_spl
| in(set_difference(sK7_skl,sK6_skl),sK6_skl)
| ~ in(set_difference(sK7_skl,sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f274,f93]) ).
fof(f282,definition,
( sQ8_spl
<=> in(set_difference(sK7_skl,sK6_skl),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f285,definition,
( sQ9_spl
<=> in(set_difference(sK7_skl,sK6_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ9_spl
| in(set_difference(sK7_skl,sK6_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( ~ sQ3_spl
| sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f280,f282,f285,f155]) ).
fof(f289,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f78]) ).
fof(f290,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f291,plain,
( ~ sQ9_spl
| ~ in(sK6_skl,set_difference(sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f286,f26]) ).
fof(f293,plain,
( ~ sQ9_spl
| in(sK6_skl,sK6_skl)
| ~ in(sK6_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f291,f93]) ).
fof(f295,definition,
( sQ10_spl
<=> in(sK6_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( sQ10_spl
| ~ in(sK6_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,definition,
( sQ11_spl
<=> in(sK6_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( ~ sQ11_spl
| in(sK6_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,plain,
( ~ sQ9_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f293,f295,f298,f285]) ).
fof(f302,plain,
( ~ sQ11_spl
| $false ),
inference(resolution,[status(thm)],[f299,f26]) ).
fof(f306,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f382,plain,
! [X0] :
( sQ10_spl
| in(sK6_skl,X0)
| ~ in(sK6_skl,set_union2(sK7_skl,X0)) ),
inference(resolution,[status(thm)],[f297,f88]) ).
fof(f389,plain,
! [X0] : ~ in(X0,X0),
inference(paramodulation,[status(thm)],[f61,f101]) ).
fof(f404,plain,
! [X0] :
( sQ10_spl
| ~ in(sK6_skl,set_difference(sK7_skl,X0)) ),
inference(resolution,[status(thm)],[f91,f297]) ).
fof(f441,plain,
( ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),set_difference(sK7_skl,sK6_skl))
| ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f35,f78]) ).
fof(f446,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f441,f115,f155]) ).
fof(f514,plain,
! [X0,X1] :
( sQ10_spl
| ~ in(sK6_skl,set_difference(set_difference(sK7_skl,X0),X1)) ),
inference(resolution,[status(thm)],[f404,f91]) ).
fof(f518,definition,
! [X0] :
( sQ15_spl
<=> in(sK6_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f519,plain,
! [X0] :
( ~ sQ15_spl
| in(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f526,plain,
! [X0,X1] :
( sQ10_spl
| in(sK6_skl,X1)
| ~ in(sK6_skl,set_difference(sK7_skl,X0)) ),
inference(resolution,[status(thm)],[f514,f93]) ).
fof(f532,definition,
! [X0] :
( sQ16_spl
<=> ~ in(sK6_skl,set_difference(sK7_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ10_spl
| sQ15_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f526,f532,f518,f295]) ).
fof(f544,plain,
( sQ10_spl
| ~ in(sK6_skl,set_union2(sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f382,f389]) ).
fof(f554,plain,
! [X0] :
( sQ10_spl
| ~ in(sK6_skl,set_difference(set_union2(sK7_skl,sK6_skl),X0)) ),
inference(resolution,[status(thm)],[f544,f91]) ).
fof(f557,plain,
( sQ10_spl
| ~ in(sK6_skl,set_union2(sK6_skl,sK7_skl)) ),
inference(paramodulation,[status(thm)],[f27,f544]) ).
fof(f563,plain,
! [X0] :
( sQ10_spl
| ~ in(sK6_skl,set_difference(set_union2(sK6_skl,sK7_skl),X0)) ),
inference(resolution,[status(thm)],[f557,f91]) ).
fof(f576,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),set_difference(sK7_skl,X0)) ),
inference(resolution,[status(thm)],[f117,f91]) ).
fof(f577,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),X0)
| ~ subset(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f117,f41]) ).
fof(f602,plain,
( sQ10_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f557,f519]) ).
fof(f642,plain,
( sQ10_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f643,plain,
( ~ sQ3_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f576]) ).
fof(f644,plain,
( ~ sQ3_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f706,plain,
! [X0] :
( sQ10_spl
| in(sK6_skl,X0)
| ~ in(sK6_skl,set_union2(sK6_skl,sK7_skl)) ),
inference(resolution,[status(thm)],[f563,f93]) ).
fof(f711,definition,
( sQ18_spl
<=> in(sK6_skl,set_union2(sK6_skl,sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( sQ10_spl
| sQ15_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f706,f711,f518,f295]) ).
fof(f715,plain,
! [X0] :
( sQ10_spl
| in(sK6_skl,X0)
| ~ in(sK6_skl,set_union2(sK7_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f554,f93]) ).
fof(f722,definition,
( sQ19_spl
<=> in(sK6_skl,set_union2(sK7_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( sQ10_spl
| sQ15_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f715,f722,f518,f295]) ).
fof(f756,plain,
( ~ sQ1_spl
| sQ0_spl
| ~ subset(sK6_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f577,f119]) ).
fof(f767,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f756,f77]) ).
fof(f768,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f777,plain,
( sQ3_spl
| in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK6_skl)
| ~ in(sK0_skl(sK7_skl,set_difference(sK7_skl,sK6_skl),sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f157,f93]) ).
fof(f782,plain,
( sQ3_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f777,f115,f118,f155]) ).
fof(f783,plain,
$false,
inference(sat_refutation,[status(thm)],[f121,f158,f288,f290,f301,f306,f446,f535,f642,f644,f714,f725,f768,f782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU137+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:50:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.62 % Refutation found
% 0.14/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.47/0.64 % Elapsed time: 0.266693 seconds
% 1.47/0.64 % CPU time: 1.754479 seconds
% 1.47/0.64 % Total memory used: 117.360 MB
% 1.47/0.64 % Net memory used: 114.482 MB
%------------------------------------------------------------------------------