%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET938+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 : n019.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 02:11:01 PM UTC 2026
% Result : Theorem 1.62s 0.85s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 9 unt; 5 def)
% Number of atoms : 238 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 268 ( 104 ~; 122 |; 30 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 141 ( 133 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [A,B] : subset(set_union2(powerset(set_difference(A,B)),powerset(set_difference(B,A))),powerset(symmetric_difference(A,B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [A,B] : subset(set_union2(powerset(set_difference(A,B)),powerset(set_difference(B,A))),powerset(symmetric_difference(A,B))),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f20,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
( ! [A,B] :
( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [A,B] :
( ( ( subset(sK0_skl(B,A),A)
| in(sK0_skl(B,A),B) )
& ( ~ subset(sK0_skl(B,A),A)
| ~ in(sK0_skl(B,A),B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
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_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)],[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_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)],[f27]) ).
fof(f29,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))],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f36,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f37,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)],[f36]) ).
fof(f38,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)],[f37]) ).
fof(f39,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_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,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f43,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f58,plain,
? [A,B] : ~ subset(set_union2(powerset(set_difference(A,B)),powerset(set_difference(B,A))),powerset(symmetric_difference(A,B))),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f59,plain,
~ subset(set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))),powerset(symmetric_difference(sK5_skl,sK6_skl))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f58]) ).
fof(f60,plain,
~ subset(set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))),powerset(symmetric_difference(sK5_skl,sK6_skl))),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f23]) ).
fof(f62,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f24]) ).
fof(f63,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,symmetric_difference(X1,X2)) ),
inference(paramodulation,[status(thm)],[f43,f64]) ).
fof(f137,plain,
! [X0,X1,X2] :
( in(sK2_skl(X2,set_union2(X0,X1)),X1)
| in(sK2_skl(X2,set_union2(X0,X1)),X0)
| subset(set_union2(X0,X1),X2) ),
inference(resolution,[status(thm)],[f41,f63]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(set_union2(X1,X2),X0),X2)
| subset(X0,set_union2(X1,X2)) ),
inference(resolution,[status(thm)],[f42,f65]) ).
fof(f143,plain,
! [X0,X1] :
( ~ subset(sK2_skl(powerset(X1),X0),X1)
| subset(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f42,f62]) ).
fof(f286,plain,
( in(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),powerset(set_difference(sK6_skl,sK5_skl)))
| in(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),powerset(set_difference(sK5_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f137,f60]) ).
fof(f292,definition,
( sQ0_spl
<=> in(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),powerset(set_difference(sK5_skl,sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( ~ sQ0_spl
| in(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),powerset(set_difference(sK5_skl,sK6_skl))) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ1_spl
<=> in(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),powerset(set_difference(sK6_skl,sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( ~ sQ1_spl
| in(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),powerset(set_difference(sK6_skl,sK5_skl))) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f286,f292,f295]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(set_union2(set_difference(X1,X2),set_difference(X2,X1)),X0),set_difference(X2,X1))
| subset(X0,symmetric_difference(X1,X2)) ),
inference(paramodulation,[status(thm)],[f43,f141]) ).
fof(f313,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(symmetric_difference(X1,X2),X0),set_difference(X2,X1))
| subset(X0,symmetric_difference(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f43,f309]) ).
fof(f315,plain,
( ~ sQ0_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f293,f61]) ).
fof(f317,plain,
! [X0] :
( ~ sQ0_spl
| in(X0,set_difference(sK5_skl,sK6_skl))
| ~ in(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))) ),
inference(resolution,[status(thm)],[f315,f40]) ).
fof(f434,plain,
! [X0] :
( ~ sQ0_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),X0)
| in(sK2_skl(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))),set_difference(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f317,f41]) ).
fof(f438,plain,
( ~ sQ0_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK5_skl,sK6_skl))
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f434,f42]) ).
fof(f442,definition,
( sQ2_spl
<=> subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK5_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ2_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK5_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f438,f442,f292]) ).
fof(f446,plain,
( ~ sQ1_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f296,f61]) ).
fof(f812,plain,
! [X0] :
( ~ sQ2_spl
| in(X0,set_difference(sK5_skl,sK6_skl))
| ~ in(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))) ),
inference(resolution,[status(thm)],[f443,f40]) ).
fof(f813,plain,
! [X0] :
( ~ sQ1_spl
| in(X0,set_difference(sK6_skl,sK5_skl))
| ~ in(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))) ),
inference(resolution,[status(thm)],[f446,f40]) ).
fof(f1092,plain,
! [X0] :
( ~ sQ2_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),X0)
| in(sK2_skl(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))),set_difference(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f812,f41]) ).
fof(f1153,plain,
! [X0] :
( ~ sQ1_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),X0)
| in(sK2_skl(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))),set_difference(sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f813,f41]) ).
fof(f1318,plain,
! [X0] :
( ~ sQ2_spl
| in(sK2_skl(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))),symmetric_difference(sK5_skl,sK6_skl))
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),X0) ),
inference(resolution,[status(thm)],[f1092,f121]) ).
fof(f1322,plain,
( ~ sQ1_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK6_skl,sK5_skl))
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f1153,f42]) ).
fof(f1326,definition,
( sQ3_spl
<=> subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK6_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1327,plain,
( ~ sQ3_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),set_difference(sK6_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f1326]) ).
fof(f1329,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1322,f1326,f295]) ).
fof(f1435,plain,
! [X0] :
( ~ sQ3_spl
| in(X0,set_difference(sK6_skl,sK5_skl))
| ~ in(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))) ),
inference(resolution,[status(thm)],[f1327,f40]) ).
fof(f1508,plain,
! [X0] :
( ~ sQ3_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),X0)
| in(sK2_skl(X0,sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))))),set_difference(sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f1435,f41]) ).
fof(f1547,plain,
( ~ sQ2_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),symmetric_difference(sK5_skl,sK6_skl))
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),symmetric_difference(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f1318,f42]) ).
fof(f1549,definition,
( sQ4_spl
<=> subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),symmetric_difference(sK5_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1550,plain,
( ~ sQ4_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),symmetric_difference(sK5_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f1549]) ).
fof(f1552,plain,
( ~ sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1547,f1549,f442]) ).
fof(f1675,plain,
( ~ sQ4_spl
| subset(set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl))),powerset(symmetric_difference(sK5_skl,sK6_skl))) ),
inference(resolution,[status(thm)],[f1550,f143]) ).
fof(f1677,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1675,f60]) ).
fof(f1678,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f1677]) ).
fof(f2660,plain,
( ~ sQ3_spl
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),symmetric_difference(sK5_skl,sK6_skl))
| subset(sK2_skl(powerset(symmetric_difference(sK5_skl,sK6_skl)),set_union2(powerset(set_difference(sK5_skl,sK6_skl)),powerset(set_difference(sK6_skl,sK5_skl)))),symmetric_difference(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f1508,f313]) ).
fof(f2666,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f2660,f1549,f1326]) ).
fof(f2669,plain,
$false,
inference(sat_refutation,[status(thm)],[f298,f445,f1329,f1552,f1678,f2666]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET938+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.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 05:44:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.62/0.85 % Refutation found
% 1.62/0.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.62/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.99/0.89 % Elapsed time: 0.517569 seconds
% 0.99/0.89 % CPU time: 3.656727 seconds
% 0.99/0.89 % Total memory used: 137.669 MB
% 0.99/0.89 % Net memory used: 132.604 MB
%------------------------------------------------------------------------------