%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU135+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 91 ( 11 unt; 11 def)
% Number of atoms : 289 ( 44 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 324 ( 126 ~; 143 |; 38 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 126 ( 120 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f54,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f55,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f64,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)],[f6]) ).
fof(f65,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)],[f64]) ).
fof(f66,plain,
( ! [A,B,C] :
( ( ( in(sK1_skl(C,B,A),B)
| in(sK1_skl(C,B,A),A)
| in(sK1_skl(C,B,A),C) )
& ( ( ~ in(sK1_skl(C,B,A),B)
& ~ in(sK1_skl(C,B,A),A) )
| ~ in(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f65]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ in(sK1_skl(X0,X2,X1),X1)
| ~ in(sK1_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ in(sK1_skl(X0,X2,X1),X2)
| ~ in(sK1_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f72,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X2)
| in(sK1_skl(X0,X2,X1),X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f89,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)],[f9]) ).
fof(f90,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)],[f89]) ).
fof(f91,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK4_skl(C,B,A),B)
& in(sK4_skl(C,B,A),A) )
| in(sK4_skl(C,B,A),C) )
& ( in(sK4_skl(C,B,A),B)
| ~ in(sK4_skl(C,B,A),A)
| ~ in(sK4_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,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f113,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f114,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f145,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f154,plain,
? [A,B] : set_union2(A,set_difference(B,A)) != set_union2(A,B),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f155,plain,
set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)) != set_union2(sK8_skl,sK9_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f154]) ).
fof(f156,plain,
set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)) != set_union2(sK8_skl,sK9_skl),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f186,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f192,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f92]) ).
fof(f194,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f223,plain,
( ~ subset(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)))
| ~ subset(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f58,f156]) ).
fof(f225,definition,
( sQ0_spl
<=> subset(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ0_spl
| ~ subset(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl)) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,definition,
( sQ1_spl
<=> subset(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ1_spl
| ~ subset(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl))) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f223,f225,f228]) ).
fof(f462,plain,
( sQ0_spl
| set_difference(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl)) != empty_set ),
inference(resolution,[status(thm)],[f115,f227]) ).
fof(f463,plain,
( sQ0_spl
| ~ subset(empty_set,set_difference(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl)))
| ~ subset(set_difference(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl)),empty_set) ),
inference(resolution,[status(thm)],[f462,f58]) ).
fof(f465,definition,
( sQ2_spl
<=> subset(set_difference(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f468,definition,
( sQ3_spl
<=> subset(empty_set,set_difference(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( sQ3_spl
| ~ subset(empty_set,set_difference(set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)),set_union2(sK8_skl,sK9_skl))) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f463,f465,f468,f225]) ).
fof(f473,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f145]) ).
fof(f474,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f475,plain,
( sQ1_spl
| set_difference(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl))) != empty_set ),
inference(resolution,[status(thm)],[f230,f115]) ).
fof(f476,plain,
( sQ1_spl
| ~ subset(empty_set,set_difference(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl))))
| ~ subset(set_difference(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl))),empty_set) ),
inference(resolution,[status(thm)],[f475,f58]) ).
fof(f478,definition,
( sQ4_spl
<=> subset(set_difference(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl))),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f481,definition,
( sQ5_spl
<=> subset(empty_set,set_difference(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ5_spl
| ~ subset(empty_set,set_difference(set_union2(sK8_skl,sK9_skl),set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)))) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f476,f478,f481,f228]) ).
fof(f486,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f145]) ).
fof(f487,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f583,plain,
( ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK8_skl)
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_union2(sK8_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f70,f156]) ).
fof(f596,definition,
( sQ12_spl
<=> in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_union2(sK8_skl,sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ12_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_union2(sK8_skl,sK9_skl)) ),
inference(component_clause,[status(thm)],[f596]) ).
fof(f599,definition,
( sQ13_spl
<=> in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( ~ sQ13_spl
| in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK8_skl) ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f601,plain,
( sQ13_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK8_skl) ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f602,plain,
( ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f583,f596,f599]) ).
fof(f604,plain,
( ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_difference(sK9_skl,sK8_skl))
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_union2(sK8_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f71,f156]) ).
fof(f614,definition,
( sQ15_spl
<=> in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_difference(sK9_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ15_spl
| in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_difference(sK9_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f616,plain,
( sQ15_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_difference(sK9_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,plain,
( ~ sQ15_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f604,f596,f614]) ).
fof(f709,plain,
( sQ12_spl
| in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_difference(sK9_skl,sK8_skl))
| in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK8_skl)
| set_union2(sK8_skl,sK9_skl) = set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)) ),
inference(resolution,[status(thm)],[f598,f72]) ).
fof(f710,plain,
( sQ12_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK9_skl) ),
inference(resolution,[status(thm)],[f598,f188]) ).
fof(f711,plain,
( sQ12_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK8_skl) ),
inference(resolution,[status(thm)],[f598,f187]) ).
fof(f715,definition,
( sQ17_spl
<=> set_union2(sK8_skl,sK9_skl) = set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f716,plain,
( ~ sQ17_spl
| set_union2(sK8_skl,sK9_skl) = set_union2(sK8_skl,set_difference(sK9_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f718,plain,
( sQ12_spl
| sQ15_spl
| sQ13_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f709,f715,f599,f614,f596]) ).
fof(f719,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f716,f156]) ).
fof(f720,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f719]) ).
fof(f721,plain,
( ~ sQ13_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f711]) ).
fof(f722,plain,
( ~ sQ13_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f721]) ).
fof(f738,plain,
! [X0] :
( sQ12_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_difference(sK9_skl,X0)) ),
inference(resolution,[status(thm)],[f710,f192]) ).
fof(f740,plain,
( ~ sQ15_spl
| sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f615,f738]) ).
fof(f741,plain,
( ~ sQ15_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f745,plain,
! [X0] :
( sQ13_spl
| in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),X0)
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_union2(sK8_skl,X0)) ),
inference(resolution,[status(thm)],[f601,f186]) ).
fof(f753,plain,
( sQ15_spl
| in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK8_skl)
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK9_skl) ),
inference(resolution,[status(thm)],[f616,f194]) ).
fof(f761,definition,
( sQ20_spl
<=> in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( sQ20_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),sK9_skl) ),
inference(component_clause,[status(thm)],[f761]) ).
fof(f764,plain,
( sQ15_spl
| sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f753,f761,f599,f614]) ).
fof(f868,plain,
( sQ20_spl
| sQ13_spl
| ~ in(sK1_skl(set_union2(sK8_skl,sK9_skl),set_difference(sK9_skl,sK8_skl),sK8_skl),set_union2(sK8_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f745,f763]) ).
fof(f878,plain,
( sQ20_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f868,f596,f599,f761]) ).
fof(f881,plain,
$false,
inference(sat_refutation,[status(thm)],[f231,f471,f474,f484,f487,f602,f617,f718,f720,f722,f741,f764,f878]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU135+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:52:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.50 % Refutation found
% 0.14/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.46/0.52 % Elapsed time: 0.139974 seconds
% 0.46/0.52 % CPU time: 0.783741 seconds
% 0.46/0.52 % Total memory used: 114.563 MB
% 0.46/0.52 % Net memory used: 112.943 MB
%------------------------------------------------------------------------------