%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU135+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 : n006.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 02:19:19 PM UTC 2026
% Result : Theorem 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 21
% Syntax : Number of formulae : 117 ( 8 unt; 16 def)
% Number of atoms : 372 ( 35 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 412 ( 157 ~; 194 |; 37 &)
% ( 22 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 17 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 157 ( 149 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f18,conjecture,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(negated_conjecture,[status(cth)],[f18]) ).
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(f33,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)],[f4]) ).
fof(f34,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)],[f33]) ).
fof(f35,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))],[f34]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,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)],[f35]) ).
fof(f40,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)],[f35]) ).
fof(f41,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)],[f35]) ).
fof(f42,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f43,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)],[f42]) ).
fof(f44,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)],[f43]) ).
fof(f45,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))],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,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)],[f6]) ).
fof(f50,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)],[f49]) ).
fof(f51,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))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f74,plain,
? [A,B] : set_union2(A,set_difference(B,A)) != set_union2(A,B),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f75,plain,
set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) != set_union2(sK5_skl,sK6_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f74]) ).
fof(f76,plain,
set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) != set_union2(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f89,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f38]) ).
fof(f92,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f94,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f124,plain,
( ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl)
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f39,f76]) ).
fof(f125,plain,
( ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK5_skl)
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_union2(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f39,f76]) ).
fof(f129,definition,
( sQ2_spl
<=> in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ2_spl
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl))) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ3_spl
<=> in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( ~ sQ3_spl
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f134,plain,
( sQ3_spl
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f124,f129,f132]) ).
fof(f136,definition,
( sQ4_spl
<=> in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_union2(sK5_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ4_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_union2(sK5_skl,sK6_skl)) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
( sQ5_spl
<=> in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ5_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f125,f136,f139]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ in(X0,sK0_skl(X0,X2,X1))
| in(sK0_skl(X0,X2,X1),X2)
| in(sK0_skl(X0,X2,X1),X1)
| X0 = set_union2(X1,X2) ),
inference(resolution,[status(thm)],[f41,f26]) ).
fof(f167,plain,
( sQ4_spl
| in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_difference(sK6_skl,sK5_skl))
| in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK5_skl)
| set_union2(sK5_skl,sK6_skl) = set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f138,f41]) ).
fof(f168,plain,
( sQ4_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK6_skl) ),
inference(resolution,[status(thm)],[f138,f91]) ).
fof(f169,plain,
( sQ4_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f138,f90]) ).
fof(f172,definition,
( sQ6_spl
<=> set_union2(sK5_skl,sK6_skl) = set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ6_spl
| set_union2(sK5_skl,sK6_skl) = set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ7_spl
<=> in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_difference(sK6_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ7_spl
| in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_difference(sK6_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( sQ7_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_difference(sK6_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ4_spl
| sQ7_spl
| sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f167,f172,f139,f175,f136]) ).
fof(f180,plain,
! [X0] :
( sQ4_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_difference(sK6_skl,X0)) ),
inference(resolution,[status(thm)],[f168,f92]) ).
fof(f181,plain,
( ~ sQ7_spl
| sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f176,f180]) ).
fof(f182,plain,
( ~ sQ7_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f184,plain,
! [X0] :
( sQ5_spl
| in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),X0)
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_union2(sK5_skl,X0)) ),
inference(resolution,[status(thm)],[f141,f89]) ).
fof(f190,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f76]) ).
fof(f191,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f192,plain,
( sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f169,f139,f136]) ).
fof(f204,plain,
( sQ2_spl
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK6_skl)
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl)
| set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) = set_union2(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f131,f41]) ).
fof(f205,plain,
( sQ2_spl
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_difference(sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f131,f91]) ).
fof(f206,plain,
( sQ2_spl
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f131,f90]) ).
fof(f209,definition,
( sQ10_spl
<=> in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( sQ2_spl
| sQ10_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f204,f172,f132,f209,f129]) ).
fof(f224,plain,
( sQ2_spl
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl)
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK6_skl) ),
inference(resolution,[status(thm)],[f205,f94]) ).
fof(f227,plain,
( sQ2_spl
| sQ3_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f224,f209,f132,f129]) ).
fof(f228,plain,
( ~ sQ3_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f206]) ).
fof(f229,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f232,plain,
( sQ3_spl
| ~ in(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl))
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK6_skl)
| set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) = set_union2(sK5_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f134,f155]) ).
fof(f233,plain,
! [X0] :
( sQ3_spl
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0)
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_union2(sK5_skl,X0)) ),
inference(resolution,[status(thm)],[f134,f89]) ).
fof(f234,plain,
! [X0] :
( sQ3_spl
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,X0)) ),
inference(resolution,[status(thm)],[f134,f92]) ).
fof(f235,definition,
( sQ11_spl
<=> in(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( sQ3_spl
| ~ sQ11_spl
| sQ10_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f232,f172,f209,f235,f132]) ).
fof(f247,plain,
! [X0,X1] :
( sQ3_spl
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_difference(set_difference(sK5_skl,X0),X1)) ),
inference(resolution,[status(thm)],[f234,f92]) ).
fof(f248,definition,
! [X0] :
( sQ12_spl
<=> in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f255,definition,
( sQ13_spl
<=> in(sK6_skl,sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ13_spl
| ~ in(sK6_skl,sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl)) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
! [X0] :
( sQ14_spl
<=> in(sK6_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f259,plain,
! [X0] :
( ~ sQ14_spl
| in(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f262,plain,
( ~ sQ14_spl
| $false ),
inference(resolution,[status(thm)],[f259,f26]) ).
fof(f266,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f268,plain,
! [X0] :
( sQ13_spl
| ~ in(sK6_skl,set_difference(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0)) ),
inference(resolution,[status(thm)],[f257,f92]) ).
fof(f271,plain,
! [X0,X1] :
( sQ13_spl
| ~ in(sK6_skl,set_difference(set_difference(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0),X1)) ),
inference(resolution,[status(thm)],[f268,f92]) ).
fof(f283,plain,
! [X0,X1] :
( sQ3_spl
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X1)
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,X0)) ),
inference(resolution,[status(thm)],[f247,f94]) ).
fof(f286,definition,
! [X0] :
( sQ16_spl
<=> ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_difference(sK5_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ3_spl
| sQ12_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f283,f286,f248,f132]) ).
fof(f290,plain,
! [X0,X1] :
( sQ13_spl
| in(sK6_skl,X1)
| ~ in(sK6_skl,set_difference(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0)) ),
inference(resolution,[status(thm)],[f271,f94]) ).
fof(f293,definition,
! [X0] :
( sQ17_spl
<=> ~ in(sK6_skl,set_difference(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f294,plain,
! [X0] :
( ~ sQ17_spl
| ~ in(sK6_skl,set_difference(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0)) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,plain,
( sQ13_spl
| sQ14_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f290,f293,f258,f255]) ).
fof(f308,plain,
! [X0] :
( sQ3_spl
| ~ in(X0,sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl))
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_union2(sK5_skl,X0)) ),
inference(resolution,[status(thm)],[f233,f26]) ).
fof(f401,plain,
( sQ3_spl
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK6_skl)
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl)
| set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) = set_union2(sK5_skl,sK6_skl)
| ~ in(set_difference(sK6_skl,sK5_skl),sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f308,f41]) ).
fof(f409,definition,
( sQ23_spl
<=> in(set_difference(sK6_skl,sK5_skl),sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ10_spl
| sQ3_spl
| sQ6_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f401,f409,f172,f132,f209]) ).
fof(f518,plain,
( ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK6_skl)
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f40,f76]) ).
fof(f519,plain,
( ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_difference(sK6_skl,sK5_skl))
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_union2(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f40,f76]) ).
fof(f524,plain,
( ~ sQ10_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f518,f129,f209]) ).
fof(f525,plain,
( ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f519,f136,f175]) ).
fof(f538,plain,
! [X0] :
( sQ3_spl
| ~ in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),X0)
| ~ subset(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f46,f134]) ).
fof(f621,plain,
! [X0] :
( ~ sQ17_spl
| in(sK6_skl,X0)
| ~ in(sK6_skl,sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl)) ),
inference(resolution,[status(thm)],[f294,f94]) ).
fof(f625,plain,
( ~ sQ17_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f621,f255,f258,f293]) ).
fof(f632,plain,
( sQ7_spl
| in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK5_skl)
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK6_skl) ),
inference(resolution,[status(thm)],[f177,f94]) ).
fof(f637,definition,
( sQ28_spl
<=> in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( sQ28_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),sK6_skl) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,plain,
( sQ7_spl
| sQ5_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f632,f637,f139,f175]) ).
fof(f646,plain,
( sQ3_spl
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK6_skl)
| in(sK0_skl(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK6_skl,sK5_skl),sK5_skl)
| set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)) = set_union2(sK5_skl,sK6_skl)
| ~ subset(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK5_skl) ),
inference(resolution,[status(thm)],[f538,f41]) ).
fof(f661,definition,
( sQ31_spl
<=> subset(set_union2(sK5_skl,set_difference(sK6_skl,sK5_skl)),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f664,plain,
( sQ10_spl
| sQ3_spl
| sQ6_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f646,f661,f172,f132,f209]) ).
fof(f748,plain,
( sQ5_spl
| sQ28_spl
| ~ in(sK0_skl(set_union2(sK5_skl,sK6_skl),set_difference(sK6_skl,sK5_skl),sK5_skl),set_union2(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f639,f184]) ).
fof(f752,plain,
( sQ5_spl
| sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f748,f136,f637,f139]) ).
fof(f753,plain,
$false,
inference(sat_refutation,[status(thm)],[f135,f142,f178,f182,f191,f192,f212,f227,f229,f238,f266,f289,f296,f412,f524,f525,f625,f640,f664,f752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU135+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:51:58 UTC 2026
% 0.11/0.36 % 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
% 0.14/0.51 % Elapsed time: 0.141131 seconds
% 0.14/0.51 % CPU time: 0.833987 seconds
% 0.14/0.51 % Total memory used: 114.769 MB
% 0.14/0.51 % Net memory used: 112.577 MB
%------------------------------------------------------------------------------