%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET986+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 02:11:06 PM UTC 2026
% Result : Theorem 268.84s 34.68s
% Output : CNFRefutation 185.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 79
% Syntax : Number of formulae : 367 ( 61 unt; 69 def)
% Number of atoms : 931 ( 122 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 995 ( 431 ~; 429 |; 53 &)
% ( 78 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 73 ( 71 usr; 70 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 380 ( 370 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> 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,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(set_difference(B,singleton(A)),singleton(A)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(set_difference(B,singleton(A)),singleton(A)) = B ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,axiom,
! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f32,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(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) )
& ! [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)],[f32]) ).
fof(f34,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))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ in(sK1_skl(X2,X1,X0),X0)
| ~ in(sK1_skl(X2,X1,X0),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ in(sK1_skl(X0,X1,X2),X0)
| X0 = set_union2(X2,X1)
| ~ in(sK1_skl(X0,X1,X2),X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f40,plain,
! [X0,X1,X2] :
( set_union2(X2,X1) = X0
| in(sK1_skl(X0,X1,X2),X0)
| in(sK1_skl(X0,X1,X2),X2)
| in(sK1_skl(X0,X1,X2),X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f41,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f42,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)],[f41]) ).
fof(f43,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)],[f42]) ).
fof(f44,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))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,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)],[f7]) ).
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) )
& ! [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)],[f48]) ).
fof(f50,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK3_skl(C,B,A),B)
& in(sK3_skl(C,B,A),A) )
| in(sK3_skl(C,B,A),C) )
& ( in(sK3_skl(C,B,A),B)
| ~ in(sK3_skl(C,B,A),A)
| ~ in(sK3_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,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f63,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(thm)],[f10]) ).
fof(f64,plain,
! [X0] : X0 = set_union2(X0,X0),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f69,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f70,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
? [A,B] :
( set_union2(set_difference(B,singleton(A)),singleton(A)) != B
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f72,plain,
( set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) != sK7_skl
& in(sK6_skl,sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl)],[f71]) ).
fof(f73,plain,
in(sK6_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) != sK7_skl,
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [A,B,C] :
( ( A = C
| ~ in(A,B)
| in(A,set_difference(B,singleton(C))) )
& ( ( A != C
& in(A,B) )
| ~ in(A,set_difference(B,singleton(C))) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f76,plain,
( ! [A,B,C] :
( A = C
| ~ in(A,B)
| in(A,set_difference(B,singleton(C))) )
& ! [A,B,C] :
( ( A != C
& in(A,B) )
| ~ in(A,set_difference(B,singleton(C))) ) ),
inference(miniscoping,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( X0 != X2
| ~ in(X0,set_difference(X1,singleton(X2))) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_difference(X2,singleton(X1)))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_union2(X2,X1))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f35]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f82,plain,
! [X0,X1] :
( X1 = X0
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,X2)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f87,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ in(X0,set_difference(X2,X1))
| ~ in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f89,plain,
! [X0,X1] : ~ in(X0,set_difference(X1,singleton(X0))),
inference(destructive_equality_resolution,[status(thm)],[f78]) ).
fof(f102,plain,
( ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK6_skl)) ),
inference(resolution,[status(thm)],[f74,f39]) ).
fof(f104,plain,
set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) != sK7_skl,
inference(paramodulation,[status(thm)],[f19,f74]) ).
fof(f105,definition,
( sQ0_spl
<=> in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ0_spl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK6_skl)) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f107,plain,
( sQ0_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK6_skl)) ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
( sQ1_spl
<=> in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( sQ1_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f102,f105,f108]) ).
fof(f112,plain,
( ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK7_skl)
| ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(resolution,[status(thm)],[f104,f39]) ).
fof(f113,definition,
( sQ2_spl
<=> in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(sK7_skl,singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( sQ2_spl
| ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,definition,
( sQ3_spl
<=> in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( sQ3_spl
| ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK7_skl) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f112,f113,f116]) ).
fof(f120,plain,
( sQ0_spl
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(resolution,[status(thm)],[f107,f40]) ).
fof(f122,definition,
( sQ4_spl
<=> in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ4_spl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f124,plain,
( sQ4_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ5_spl
<=> set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ5_spl
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ0_spl
| sQ5_spl
| sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f120,f122,f108,f125,f105]) ).
fof(f129,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f74]) ).
fof(f130,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f133,plain,
( sQ2_spl
| ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK7_skl)
| in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK6_skl)) ),
inference(resolution,[status(thm)],[f115,f85]) ).
fof(f135,definition,
( sQ6_spl
<=> in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f138,definition,
( sQ7_spl
<=> set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ7_spl
| set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) = sK7_skl ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f142,definition,
( sQ8_spl
<=> sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( ~ sQ8_spl
| sK6_skl = sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f144,plain,
( sQ8_spl
| sK6_skl != sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f146,plain,
( sQ2_spl
| ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f133,f135,f116,f113]) ).
fof(f149,plain,
! [X0,X1] :
( ~ in(X0,sK2_skl(X1,X0))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f18,f46]) ).
fof(f153,plain,
~ in(sK7_skl,sK6_skl),
inference(resolution,[status(thm)],[f18,f73]) ).
fof(f154,plain,
! [X0,X1] : ~ in(set_union2(X0,X1),X0),
inference(resolution,[status(thm)],[f18,f81]) ).
fof(f162,plain,
! [X0,X1,X2] :
( in(sK1_skl(X1,X0,X2),X1)
| in(sK1_skl(X1,X0,X2),X2)
| X1 = set_union2(X2,X0)
| ~ in(X0,sK1_skl(X1,X0,X2)) ),
inference(resolution,[status(thm)],[f18,f40]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ~ in(set_union2(X1,X2),X0)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f18,f81]) ).
fof(f173,plain,
! [X0] : ~ in(X0,X0),
inference(factoring,[status(thm)],[f18]) ).
fof(f184,plain,
! [X0] :
( ~ in(sK7_skl,set_union2(X0,sK6_skl))
| in(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f153,f80]) ).
fof(f187,plain,
~ in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK7_skl)),
inference(resolution,[status(thm)],[f82,f104]) ).
fof(f188,plain,
~ in(sK7_skl,singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)))),
inference(resolution,[status(thm)],[f82,f74]) ).
fof(f189,plain,
~ in(sK7_skl,singleton(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))),
inference(resolution,[status(thm)],[f82,f104]) ).
fof(f190,plain,
~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK7_skl)),
inference(resolution,[status(thm)],[f82,f74]) ).
fof(f211,plain,
! [X0] :
( ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(X0,singleton(sK7_skl)))
| in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),X0) ),
inference(resolution,[status(thm)],[f190,f80]) ).
fof(f215,plain,
~ in(sK7_skl,set_union2(sK7_skl,sK6_skl)),
inference(resolution,[status(thm)],[f184,f173]) ).
fof(f219,plain,
! [X0] :
( ~ in(sK7_skl,set_union2(X0,sK6_skl))
| ~ in(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f184,f18]) ).
fof(f228,plain,
! [X0] :
( in(sK7_skl,X0)
| ~ in(sK7_skl,set_union2(X0,singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))))) ),
inference(resolution,[status(thm)],[f188,f80]) ).
fof(f251,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f104]) ).
fof(f252,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f253,plain,
! [X0] :
( ~ in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(X0,singleton(sK7_skl)))
| in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0) ),
inference(resolution,[status(thm)],[f187,f80]) ).
fof(f261,definition,
( sQ15_spl
<=> in(sK6_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ15_spl
| ~ in(sK6_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f265,definition,
( sQ16_spl
<=> in(sK6_skl,set_difference(sK7_skl,singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( ~ sQ16_spl
| in(sK6_skl,set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f284,plain,
! [X0] : ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),singleton(X0))),
inference(resolution,[status(thm)],[f77,f190]) ).
fof(f285,plain,
! [X0] : ~ in(sK7_skl,set_difference(singleton(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))),singleton(X0))),
inference(resolution,[status(thm)],[f77,f189]) ).
fof(f286,plain,
! [X0] : ~ in(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),singleton(X0))),
inference(resolution,[status(thm)],[f77,f188]) ).
fof(f328,definition,
! [X0] :
( sQ18_spl
<=> in(sK7_skl,singleton(X0)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f329,plain,
! [X0] :
( ~ sQ18_spl
| in(sK7_skl,singleton(X0)) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
( sQ19_spl
<=> in(sK7_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f335,definition,
! [X0] :
( sQ20_spl
<=> sK7_skl = X0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f336,plain,
! [X0] :
( ~ sQ20_spl
| sK7_skl = X0 ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f358,definition,
( sQ23_spl
<=> in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ in(sK7_skl,sK6_skl)
| ~ in(sK6_skl,sK7_skl) ),
inference(paramodulation,[status(thm)],[f64,f219]) ).
fof(f375,plain,
( ~ sQ19_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f372,f261,f331]) ).
fof(f376,definition,
! [X0] :
( sQ25_spl
<=> ~ in(X0,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f377,plain,
! [X0] :
( ~ sQ25_spl
| ~ in(X0,sK7_skl) ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f380,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f73]) ).
fof(f381,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f384,plain,
! [X0] :
( ~ in(sK7_skl,singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))))
| sK7_skl = X0 ),
inference(resolution,[status(thm)],[f286,f79]) ).
fof(f386,plain,
! [X0,X1] : ~ in(sK7_skl,set_difference(set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),singleton(X0)),singleton(X1))),
inference(resolution,[status(thm)],[f286,f77]) ).
fof(f390,definition,
( sQ26_spl
<=> in(sK7_skl,singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ26_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f384,f335,f390]) ).
fof(f395,plain,
( ~ sQ20_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f74,f336]) ).
fof(f435,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f454,plain,
( ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK6_skl))
| ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK7_skl) ),
inference(resolution,[status(thm)],[f38,f104]) ).
fof(f455,plain,
( ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl)))
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl) ),
inference(resolution,[status(thm)],[f38,f74]) ).
fof(f459,plain,
( ~ sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f455,f108,f122]) ).
fof(f460,plain,
( ~ sQ6_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f454,f116,f135]) ).
fof(f463,plain,
! [X0,X1] : ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(set_difference(singleton(sK7_skl),singleton(X0)),X1)),
inference(resolution,[status(thm)],[f84,f284]) ).
fof(f464,plain,
! [X0] : ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),X0)),
inference(resolution,[status(thm)],[f84,f190]) ).
fof(f467,plain,
! [X0] : ~ in(sK7_skl,set_difference(set_union2(sK7_skl,sK6_skl),X0)),
inference(resolution,[status(thm)],[f84,f215]) ).
fof(f470,plain,
! [X0] : ~ in(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),X0)),
inference(resolution,[status(thm)],[f84,f188]) ).
fof(f471,plain,
! [X0] : ~ in(sK7_skl,set_difference(sK6_skl,X0)),
inference(resolution,[status(thm)],[f84,f153]) ).
fof(f479,plain,
! [X0,X1,X2] : ~ in(set_union2(set_union2(X0,X1),X2),X0),
inference(resolution,[status(thm)],[f154,f81]) ).
fof(f523,plain,
! [X0,X1] : ~ in(sK7_skl,set_difference(set_difference(sK6_skl,X0),X1)),
inference(resolution,[status(thm)],[f471,f84]) ).
fof(f526,definition,
! [X0] :
( sQ27_spl
<=> in(sK7_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f527,plain,
! [X0] :
( ~ sQ27_spl
| in(sK7_skl,X0) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f532,plain,
! [X0] :
( sQ1_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,X0)) ),
inference(resolution,[status(thm)],[f110,f84]) ).
fof(f533,plain,
! [X0] :
( sQ1_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(X0,sK7_skl))
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0) ),
inference(resolution,[status(thm)],[f110,f80]) ).
fof(f534,definition,
( sQ28_spl
<=> in(singleton(sK6_skl),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f558,plain,
! [X0,X1] :
( ~ in(sK7_skl,set_difference(sK6_skl,X1))
| sK7_skl = X0 ),
inference(resolution,[status(thm)],[f523,f79]) ).
fof(f560,plain,
! [X0,X1,X2] : ~ in(sK7_skl,set_difference(set_difference(set_difference(sK6_skl,X0),X1),X2)),
inference(resolution,[status(thm)],[f523,f84]) ).
fof(f562,definition,
! [X1] :
( sQ30_spl
<=> ~ in(sK7_skl,set_difference(sK6_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f566,plain,
( sQ30_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f558,f335,f562]) ).
fof(f569,plain,
! [X0] :
( ~ in(sK7_skl,set_union2(sK7_skl,sK6_skl))
| sK7_skl = X0 ),
inference(resolution,[status(thm)],[f467,f79]) ).
fof(f573,definition,
( sQ31_spl
<=> in(sK7_skl,set_union2(sK7_skl,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( ~ sQ31_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f569,f335,f573]) ).
fof(f580,plain,
! [X0] :
( sQ3_spl
| ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(sK7_skl,X0)) ),
inference(resolution,[status(thm)],[f118,f84]) ).
fof(f597,plain,
! [X0] :
( ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK7_skl))
| in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),X0) ),
inference(resolution,[status(thm)],[f464,f85]) ).
fof(f598,plain,
! [X0,X1] : ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(set_difference(singleton(sK7_skl),X0),X1)),
inference(resolution,[status(thm)],[f464,f84]) ).
fof(f599,plain,
! [X0,X1] :
( in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),X0)
| ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(X0,set_difference(singleton(sK7_skl),X1))) ),
inference(resolution,[status(thm)],[f464,f80]) ).
fof(f602,definition,
! [X0] :
( sQ32_spl
<=> in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),X0) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f603,plain,
! [X0] :
( ~ sQ32_spl
| in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),X0) ),
inference(component_clause,[status(thm)],[f602]) ).
fof(f605,plain,
( ~ sQ23_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f597,f602,f358]) ).
fof(f611,plain,
! [X0,X1] : ~ in(sK7_skl,set_difference(set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),X0),X1)),
inference(resolution,[status(thm)],[f470,f84]) ).
fof(f612,plain,
! [X0,X1] :
( ~ in(sK7_skl,set_union2(X0,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),X1)))
| in(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f470,f80]) ).
fof(f625,plain,
( sQ4_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK6_skl)) ),
inference(resolution,[status(thm)],[f124,f85]) ).
fof(f633,plain,
( sQ4_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f625,f105,f108,f122]) ).
fof(f705,plain,
! [X0] :
( sQ1_spl
| ~ subset(X0,sK7_skl)
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0) ),
inference(resolution,[status(thm)],[f45,f110]) ).
fof(f724,plain,
! [X0] :
( ~ subset(X0,sK6_skl)
| ~ in(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f45,f153]) ).
fof(f726,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X0)
| ~ in(X3,X2)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(resolution,[status(thm)],[f45,f88]) ).
fof(f729,plain,
! [X0,X1,X2] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f45,f18]) ).
fof(f741,plain,
( ~ sQ4_spl
| sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f532]) ).
fof(f743,plain,
( sQ1_spl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)
| sK7_skl = set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))
| ~ in(singleton(sK6_skl),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(resolution,[status(thm)],[f532,f162]) ).
fof(f751,plain,
( sQ1_spl
| sQ5_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f743,f534,f125,f108]) ).
fof(f752,plain,
( ~ sQ4_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f741]) ).
fof(f778,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ subset(singleton(sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f705,f106]) ).
fof(f783,plain,
( sQ1_spl
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl)))
| ~ subset(singleton(sK6_skl),sK7_skl) ),
inference(resolution,[status(thm)],[f705,f40]) ).
fof(f792,definition,
( sQ37_spl
<=> subset(sK7_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f794,plain,
( sQ37_spl
| ~ subset(sK7_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f792]) ).
fof(f797,definition,
( sQ38_spl
<=> subset(singleton(sK6_skl),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f800,plain,
( sQ5_spl
| sQ1_spl
| sQ4_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f783,f797,f122,f108,f125]) ).
fof(f855,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ in(sK2_skl(sK7_skl,singleton(sK6_skl)),sK7_skl) ),
inference(resolution,[status(thm)],[f778,f47]) ).
fof(f861,definition,
( sQ48_spl
<=> set_union2(sK7_skl,sK7_skl) = set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f862,plain,
( ~ sQ48_spl
| set_union2(sK7_skl,sK7_skl) = set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f861]) ).
fof(f869,plain,
( ~ sQ48_spl
| sK7_skl = set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(forward_demodulation,[status(thm)],[f64,f862]) ).
fof(f870,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f869,f104]) ).
fof(f871,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f870]) ).
fof(f886,definition,
( sQ50_spl
<=> set_union2(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f887,plain,
( ~ sQ50_spl
| set_union2(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) = sK7_skl ),
inference(component_clause,[status(thm)],[f886]) ).
fof(f894,plain,
( ~ sQ50_spl
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl ),
inference(forward_demodulation,[status(thm)],[f64,f887]) ).
fof(f895,plain,
( ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f894,f74]) ).
fof(f896,plain,
~ sQ50_spl,
inference(contradiction_clause,[status(thm)],[f895]) ).
fof(f908,definition,
( sQ53_spl
<=> sK7_skl = set_union2(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f909,plain,
( ~ sQ53_spl
| sK7_skl = set_union2(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(component_clause,[status(thm)],[f908]) ).
fof(f913,plain,
( ~ sQ53_spl
| sK7_skl = set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) ),
inference(forward_demodulation,[status(thm)],[f64,f909]) ).
fof(f914,plain,
( ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f913,f104]) ).
fof(f915,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f914]) ).
fof(f924,definition,
( sQ54_spl
<=> set_union2(sK7_skl,sK7_skl) = set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f925,plain,
( ~ sQ54_spl
| set_union2(sK7_skl,sK7_skl) = set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f934,plain,
( ~ sQ54_spl
| sK7_skl = set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f64,f925]) ).
fof(f935,plain,
( ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f934,f74]) ).
fof(f936,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f935]) ).
fof(f1047,plain,
! [X0] :
( ~ sQ0_spl
| sQ1_spl
| ~ in(sK2_skl(sK7_skl,singleton(sK6_skl)),set_difference(sK7_skl,X0)) ),
inference(resolution,[status(thm)],[f855,f84]) ).
fof(f1122,plain,
! [X0,X1,X2,X3] :
( ~ subset(X3,X0)
| ~ in(set_union2(X1,X2),X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f169,f45]) ).
fof(f1253,plain,
! [X0,X1,X2] :
( ~ in(sK7_skl,set_difference(set_difference(sK6_skl,X1),X2))
| sK7_skl = X0 ),
inference(resolution,[status(thm)],[f560,f79]) ).
fof(f1258,definition,
! [X1,X2] :
( sQ62_spl
<=> ~ in(sK7_skl,set_difference(set_difference(sK6_skl,X1),X2)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1262,plain,
( sQ62_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1253,f335,f1258]) ).
fof(f1266,plain,
! [X0] :
( ~ in(sK7_skl,singleton(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))))
| sK7_skl = X0 ),
inference(resolution,[status(thm)],[f285,f79]) ).
fof(f1271,definition,
( sQ63_spl
<=> in(sK7_skl,singleton(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1275,plain,
( ~ sQ63_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1266,f335,f1271]) ).
fof(f1296,plain,
! [X0] :
( ~ in(sK7_skl,X0)
| ~ in(X0,sK2_skl(sK6_skl,X0)) ),
inference(resolution,[status(thm)],[f149,f724]) ).
fof(f1311,plain,
( sQ1_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(sK2_skl(sK6_skl,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))),sK7_skl))
| ~ in(sK7_skl,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(resolution,[status(thm)],[f1296,f533]) ).
fof(f1322,definition,
( sQ66_spl
<=> in(sK7_skl,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1325,definition,
( sQ67_spl
<=> in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(sK2_skl(sK6_skl,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))),sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1328,plain,
( sQ1_spl
| ~ sQ67_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f1311,f1322,f1325,f108]) ).
fof(f1368,plain,
! [X0] :
( ~ sQ0_spl
| sQ1_spl
| ~ in(sK2_skl(sK7_skl,singleton(sK6_skl)),sK7_skl)
| sK2_skl(sK7_skl,singleton(sK6_skl)) = X0 ),
inference(resolution,[status(thm)],[f1047,f79]) ).
fof(f1373,definition,
! [X0] :
( sQ75_spl
<=> sK2_skl(sK7_skl,singleton(sK6_skl)) = X0 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1374,plain,
! [X0] :
( ~ sQ75_spl
| sK2_skl(sK7_skl,singleton(sK6_skl)) = X0 ),
inference(component_clause,[status(thm)],[f1373]) ).
fof(f1376,definition,
( sQ76_spl
<=> in(sK2_skl(sK7_skl,singleton(sK6_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1379,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ76_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f1368,f1373,f1376,f108,f105]) ).
fof(f1380,definition,
! [X0] :
( sQ77_spl
<=> in(sK2_skl(sK7_skl,singleton(sK6_skl)),X0) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1381,plain,
! [X0] :
( ~ sQ77_spl
| in(sK2_skl(sK7_skl,singleton(sK6_skl)),X0) ),
inference(component_clause,[status(thm)],[f1380]) ).
fof(f1669,definition,
! [X1] :
( sQ81_spl
<=> ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),singleton(X1))) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1747,plain,
! [X0,X1] :
( ~ in(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),singleton(X1)))
| sK7_skl = X0 ),
inference(resolution,[status(thm)],[f386,f79]) ).
fof(f1755,definition,
! [X1] :
( sQ83_spl
<=> ~ in(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),singleton(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1758,plain,
( sQ83_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1747,f335,f1755]) ).
fof(f1857,plain,
( sQ8_spl
| ~ in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK6_skl)) ),
inference(resolution,[status(thm)],[f144,f82]) ).
fof(f1880,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f794,f70]) ).
fof(f1881,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f1880]) ).
fof(f1882,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f89]) ).
fof(f1883,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f1882]) ).
fof(f1922,plain,
! [X0,X1] :
( ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),singleton(X1)))
| in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),X0) ),
inference(resolution,[status(thm)],[f463,f85]) ).
fof(f1929,plain,
( sQ81_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1922,f602,f1669]) ).
fof(f2009,definition,
! [X0] :
( sQ95_spl
<=> ~ in(sK7_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f2010,plain,
! [X0] :
( ~ sQ95_spl
| ~ in(sK7_skl,X0) ),
inference(component_clause,[status(thm)],[f2009]) ).
fof(f2158,plain,
( sQ3_spl
| set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) = sK7_skl
| in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK7_skl)
| in(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK6_skl)) ),
inference(resolution,[status(thm)],[f580,f40]) ).
fof(f2165,plain,
( sQ7_spl
| sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f2158,f135,f116,f138]) ).
fof(f2175,plain,
( ~ sQ95_spl
| $false ),
inference(resolution,[status(thm)],[f2010,f87]) ).
fof(f2185,plain,
~ sQ95_spl,
inference(contradiction_clause,[status(thm)],[f2175]) ).
fof(f2188,plain,
( ~ sQ25_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f73,f377]) ).
fof(f2216,plain,
~ in(sK7_skl,sK6_skl),
inference(resolution,[status(thm)],[f73,f18]) ).
fof(f2272,plain,
( ~ sQ27_spl
| $false ),
inference(resolution,[status(thm)],[f527,f89]) ).
fof(f2280,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f2272]) ).
fof(f2304,plain,
( ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f188,f329]) ).
fof(f2307,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f2304]) ).
fof(f2325,plain,
( ~ sQ32_spl
| $false ),
inference(resolution,[status(thm)],[f603,f154]) ).
fof(f2336,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f2325]) ).
fof(f3289,plain,
( ~ in(sK7_skl,set_union2(sK7_skl,singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)))))
| ~ subset(sK7_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f729,f228]) ).
fof(f3295,plain,
! [X0] :
( ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),X0)))
| ~ subset(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
inference(resolution,[status(thm)],[f729,f599]) ).
fof(f3297,plain,
( ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK7_skl)))
| ~ subset(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
inference(resolution,[status(thm)],[f729,f211]) ).
fof(f3299,plain,
( ~ in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK7_skl)))
| ~ subset(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(resolution,[status(thm)],[f729,f253]) ).
fof(f3306,plain,
( sQ1_spl
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl))
| ~ subset(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(resolution,[status(thm)],[f729,f533]) ).
fof(f3327,plain,
! [X0,X1,X2,X3] :
( set_union2(X2,X1) = X0
| in(sK1_skl(X0,X1,X2),X2)
| ~ subset(X3,sK1_skl(X0,X1,X2))
| ~ in(X1,X3)
| in(sK1_skl(X0,X1,X2),X0) ),
inference(resolution,[status(thm)],[f729,f40]) ).
fof(f3373,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))
| ~ subset(singleton(sK6_skl),X0) ),
inference(resolution,[status(thm)],[f729,f106]) ).
fof(f3393,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,sK1_skl(X0,X1,X2))
| X0 = set_union2(X2,X1)
| in(sK1_skl(X0,X1,X2),X0)
| ~ subset(X1,X3)
| in(sK1_skl(X0,X1,X2),X2) ),
inference(resolution,[status(thm)],[f729,f40]) ).
fof(f3424,definition,
( sQ102_spl
<=> subset(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f3426,plain,
( sQ102_spl
| ~ subset(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(component_clause,[status(thm)],[f3424]) ).
fof(f3427,definition,
( sQ103_spl
<=> in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f3430,plain,
( ~ sQ103_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f3299,f3424,f3427]) ).
fof(f3431,definition,
( sQ104_spl
<=> subset(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f3433,plain,
( sQ104_spl
| ~ subset(sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),sK1_skl(sK7_skl,set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f3431]) ).
fof(f3439,definition,
( sQ106_spl
<=> subset(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f3441,plain,
( sQ106_spl
| ~ subset(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(component_clause,[status(thm)],[f3439]) ).
fof(f3442,definition,
( sQ107_spl
<=> in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f3445,plain,
( sQ1_spl
| ~ sQ107_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f3306,f3439,f3442,f108]) ).
fof(f3447,definition,
( sQ108_spl
<=> subset(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f3449,plain,
( sQ108_spl
| ~ subset(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f3447]) ).
fof(f3450,definition,
! [X0] :
( sQ109_spl
<=> ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),X0))) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f3453,plain,
( sQ109_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f3295,f3447,f3450]) ).
fof(f3454,definition,
( sQ110_spl
<=> in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f3457,plain,
( ~ sQ110_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f3297,f3447,f3454]) ).
fof(f3458,definition,
( sQ111_spl
<=> in(sK7_skl,set_union2(sK7_skl,singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f3461,plain,
( ~ sQ111_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f3289,f792,f3458]) ).
fof(f3463,plain,
( sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3449,f70]) ).
fof(f3464,plain,
sQ108_spl,
inference(contradiction_clause,[status(thm)],[f3463]) ).
fof(f3465,plain,
( sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3426,f70]) ).
fof(f3466,plain,
sQ102_spl,
inference(contradiction_clause,[status(thm)],[f3465]) ).
fof(f3467,plain,
( sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3441,f70]) ).
fof(f3468,plain,
sQ106_spl,
inference(contradiction_clause,[status(thm)],[f3467]) ).
fof(f3469,plain,
( sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3433,f70]) ).
fof(f3470,plain,
sQ104_spl,
inference(contradiction_clause,[status(thm)],[f3469]) ).
fof(f3498,plain,
! [X0] :
( sQ1_spl
| ~ in(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))
| sK7_skl = set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)
| ~ subset(singleton(sK6_skl),X0) ),
inference(resolution,[status(thm)],[f3393,f532]) ).
fof(f3507,definition,
! [X0] :
( sQ115_spl
<=> ( ~ in(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))
| ~ subset(singleton(sK6_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f3510,plain,
( sQ5_spl
| sQ1_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f3498,f3507,f108,f125]) ).
fof(f3572,plain,
! [X0] :
( sQ1_spl
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl)))
| ~ subset(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))
| ~ in(singleton(sK6_skl),X0) ),
inference(resolution,[status(thm)],[f3327,f110]) ).
fof(f3581,definition,
! [X0] :
( sQ121_spl
<=> ( ~ subset(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))
| ~ in(singleton(sK6_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f3585,plain,
( sQ1_spl
| sQ5_spl
| sQ4_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f3572,f3581,f122,f125,f108]) ).
fof(f3629,plain,
! [X0,X1] :
( ~ subset(X0,set_difference(X1,sK7_skl))
| ~ in(sK6_skl,X0) ),
inference(resolution,[status(thm)],[f726,f73]) ).
fof(f3702,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(X0,X1,X2),X2)
| ~ subset(X1,set_difference(X3,X1))
| set_union2(X2,X1) = X0
| in(sK1_skl(X0,X1,X2),X0) ),
inference(resolution,[status(thm)],[f726,f40]) ).
fof(f3703,plain,
! [X0,X1,X2,X3,X4] :
( ~ subset(X3,set_difference(X4,X1))
| in(sK1_skl(X0,X1,X2),X0)
| in(sK1_skl(X0,X1,X2),X2)
| X0 = set_union2(X2,X1)
| ~ in(sK1_skl(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f726,f40]) ).
fof(f3791,plain,
! [X0,X1,X2,X3,X4] :
( in(sK1_skl(X3,X0,X4),X3)
| X3 = set_union2(X4,X0)
| ~ in(sK1_skl(X3,X0,X4),X2)
| in(sK1_skl(X3,X0,X4),X4)
| ~ subset(X0,set_difference(X1,X2)) ),
inference(resolution,[status(thm)],[f726,f40]) ).
fof(f3863,plain,
! [X0] :
( sQ1_spl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl)))
| ~ subset(singleton(sK6_skl),set_difference(X0,singleton(sK6_skl)))
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl ),
inference(resolution,[status(thm)],[f3702,f110]) ).
fof(f3876,definition,
! [X0] :
( sQ126_spl
<=> ~ subset(singleton(sK6_skl),set_difference(X0,singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f3884,plain,
( sQ1_spl
| sQ4_spl
| sQ126_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f3863,f125,f3876,f122,f108]) ).
fof(f3976,plain,
! [X0,X1] :
( sQ1_spl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK7_skl)
| sK7_skl = set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X1)
| ~ subset(singleton(sK6_skl),set_difference(X0,X1)) ),
inference(resolution,[status(thm)],[f3791,f532]) ).
fof(f4001,definition,
! [X0,X1] :
( sQ133_spl
<=> ( ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X1)
| ~ subset(singleton(sK6_skl),set_difference(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f4004,plain,
( sQ1_spl
| sQ5_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f3976,f4001,f125,f108]) ).
fof(f4013,plain,
! [X0,X1,X2,X3,X4,X5] :
( set_union2(set_difference(X2,X3),X1) = X0
| ~ subset(X4,set_difference(X5,X1))
| in(sK1_skl(X0,X1,set_difference(X2,X3)),X0)
| ~ in(sK1_skl(X0,X1,set_difference(X2,X3)),X4)
| ~ in(sK1_skl(X0,X1,set_difference(X2,X3)),X3) ),
inference(resolution,[status(thm)],[f3703,f88]) ).
fof(f4030,definition,
! [X0,X1] :
( sQ136_spl
<=> ( ~ subset(X0,set_difference(X1,singleton(sK6_skl)))
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f4949,plain,
! [X0,X1] :
( sQ1_spl
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl
| ~ subset(X0,set_difference(X1,singleton(sK6_skl)))
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0)
| ~ in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK6_skl)) ),
inference(resolution,[status(thm)],[f4013,f110]) ).
fof(f4963,plain,
( sQ1_spl
| sQ5_spl
| sQ136_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4949,f105,f4030,f125,f108]) ).
fof(f5143,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(singleton(sK7_skl),X0)))
| ~ subset(singleton(sK6_skl),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
inference(resolution,[status(thm)],[f3373,f599]) ).
fof(f5144,plain,
( ~ sQ0_spl
| ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK7_skl)))
| ~ subset(singleton(sK6_skl),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
inference(resolution,[status(thm)],[f3373,f211]) ).
fof(f5145,plain,
( ~ sQ0_spl
| ~ in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK7_skl)))
| ~ subset(singleton(sK6_skl),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(resolution,[status(thm)],[f3373,f253]) ).
fof(f5238,plain,
! [X0,X1] :
( ~ sQ0_spl
| set_union2(X1,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) = X0
| in(sK1_skl(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X1),X1)
| in(sK1_skl(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X1),X0)
| ~ subset(singleton(sK6_skl),sK1_skl(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X1)) ),
inference(resolution,[status(thm)],[f3373,f40]) ).
fof(f5276,definition,
( sQ152_spl
<=> subset(singleton(sK6_skl),set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f5279,definition,
( sQ153_spl
<=> in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f5282,plain,
( ~ sQ0_spl
| ~ sQ153_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5144,f5276,f5279,f105]) ).
fof(f5287,definition,
! [X0] :
( sQ155_spl
<=> ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(singleton(sK7_skl),X0))) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f5290,plain,
( ~ sQ0_spl
| sQ155_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f5143,f5276,f5287,f105]) ).
fof(f5291,definition,
( sQ156_spl
<=> subset(singleton(sK6_skl),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f5294,definition,
( sQ157_spl
<=> in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f5297,plain,
( ~ sQ0_spl
| ~ sQ157_spl
| ~ sQ156_spl ),
inference(split_clause,[status(thm)],[f5145,f5291,f5294,f105]) ).
fof(f5474,plain,
! [X0] :
( ~ sQ0_spl
| ~ subset(singleton(sK6_skl),sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0))
| set_union2(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) = sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))
| in(sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0),X0)
| ~ subset(singleton(sK6_skl),sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0)) ),
inference(resolution,[status(thm)],[f5238,f3373]) ).
fof(f5486,plain,
! [X0] :
( ~ sQ0_spl
| in(sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0),X0)
| set_union2(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) = sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))
| ~ subset(singleton(sK6_skl),sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f5474]) ).
fof(f5688,plain,
( ~ sQ0_spl
| ~ subset(singleton(sK6_skl),sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))))
| set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) = sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))
| ~ subset(singleton(sK6_skl),sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))) ),
inference(resolution,[status(thm)],[f5486,f3373]) ).
fof(f5700,definition,
( sQ160_spl
<=> subset(singleton(sK6_skl),sK1_skl(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f5703,definition,
( sQ161_spl
<=> set_union2(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) = sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f5706,plain,
( ~ sQ0_spl
| sQ161_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f5688,f5700,f5703,f105]) ).
fof(f6075,plain,
! [X0] : ~ in(sK6_skl,set_difference(X0,sK7_skl)),
inference(resolution,[status(thm)],[f3629,f70]) ).
fof(f6134,plain,
! [X0,X1] : ~ in(sK6_skl,set_difference(set_difference(X0,sK7_skl),X1)),
inference(resolution,[status(thm)],[f6075,f84]) ).
fof(f6268,plain,
! [X0,X1] :
( ~ in(sK6_skl,set_difference(X1,sK7_skl))
| sK6_skl = X0 ),
inference(resolution,[status(thm)],[f6134,f79]) ).
fof(f6278,definition,
! [X0] :
( sQ176_spl
<=> sK6_skl = X0 ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f6279,plain,
! [X0] :
( ~ sQ176_spl
| X0 = sK6_skl ),
inference(component_clause,[status(thm)],[f6278]) ).
fof(f6281,definition,
! [X1] :
( sQ177_spl
<=> ~ in(sK6_skl,set_difference(X1,sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f6284,plain,
( sQ177_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f6268,f6278,f6281]) ).
fof(f6285,definition,
! [X0] :
( sQ178_spl
<=> in(sK6_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f6286,plain,
! [X0] :
( ~ sQ178_spl
| in(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f6285]) ).
fof(f6517,plain,
! [X0] :
( ~ sQ176_spl
| ~ in(sK7_skl,X0) ),
inference(paramodulation,[status(thm)],[f6279,f2216]) ).
fof(f6566,plain,
( ~ sQ176_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f6517,f2009,f6278]) ).
fof(f6578,plain,
( ~ sQ178_spl
| $false ),
inference(resolution,[status(thm)],[f6286,f89]) ).
fof(f6595,plain,
~ sQ178_spl,
inference(contradiction_clause,[status(thm)],[f6578]) ).
fof(f7171,plain,
! [X0,X1] :
( ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),X1))
| in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),X0) ),
inference(resolution,[status(thm)],[f598,f85]) ).
fof(f7182,definition,
! [X1] :
( sQ199_spl
<=> ~ in(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)),set_difference(singleton(sK7_skl),X1)) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f7185,plain,
( sQ199_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f7171,f602,f7182]) ).
fof(f7418,plain,
! [X0,X1] :
( ~ in(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),X1))
| sK7_skl = X0 ),
inference(resolution,[status(thm)],[f611,f79]) ).
fof(f7430,definition,
! [X1] :
( sQ202_spl
<=> ~ in(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),X1)) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f7434,plain,
( sQ202_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f7418,f335,f7430]) ).
fof(f7483,plain,
! [X0] :
( ~ subset(sK7_skl,sK7_skl)
| ~ in(sK7_skl,set_union2(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),X0))) ),
inference(resolution,[status(thm)],[f612,f729]) ).
fof(f7496,definition,
! [X0] :
( sQ204_spl
<=> ~ in(sK7_skl,set_union2(sK7_skl,set_difference(singleton(set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl))),X0))) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f7499,plain,
( ~ sQ37_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f7483,f7496,f792]) ).
fof(f7548,definition,
( sQ207_spl
<=> subset(sK2_skl(singleton(sK7_skl),singleton(sK6_skl)),sK2_skl(singleton(sK7_skl),singleton(sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f7550,plain,
( sQ207_spl
| ~ subset(sK2_skl(singleton(sK7_skl),singleton(sK6_skl)),sK2_skl(singleton(sK7_skl),singleton(sK6_skl))) ),
inference(component_clause,[status(thm)],[f7548]) ).
fof(f7568,plain,
( sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1857,f135,f142]) ).
fof(f7569,plain,
( sQ207_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7550,f70]) ).
fof(f7570,plain,
sQ207_spl,
inference(contradiction_clause,[status(thm)],[f7569]) ).
fof(f7690,plain,
! [X0] :
( ~ sQ75_spl
| ~ sQ0_spl
| sQ1_spl
| ~ in(X0,sK7_skl) ),
inference(paramodulation,[status(thm)],[f1374,f855]) ).
fof(f7694,definition,
! [X0] :
( sQ212_spl
<=> in(X0,singleton(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f7695,plain,
! [X0] :
( ~ sQ212_spl
| in(X0,singleton(sK6_skl)) ),
inference(component_clause,[status(thm)],[f7694]) ).
fof(f7698,plain,
( ~ sQ75_spl
| ~ sQ0_spl
| sQ1_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f7690,f376,f108,f105,f1373]) ).
fof(f7699,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f2188]) ).
fof(f7771,plain,
( ~ sQ212_spl
| $false ),
inference(resolution,[status(thm)],[f7695,f479]) ).
fof(f7796,plain,
~ sQ212_spl,
inference(contradiction_clause,[status(thm)],[f7771]) ).
fof(f7823,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ77_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f855,f1381]) ).
fof(f7848,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ77_spl ),
inference(contradiction_clause,[status(thm)],[f7823]) ).
fof(f8695,plain,
( ~ in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(singleton(sK6_skl),singleton(sK7_skl)))
| ~ subset(singleton(sK6_skl),set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(resolution,[status(thm)],[f1122,f253]) ).
fof(f8841,plain,
! [X0,X1,X2,X3,X4] :
( in(sK1_skl(X1,X2,X3),X3)
| set_union2(X3,X2) = X1
| ~ in(set_union2(X2,X4),X0)
| in(sK1_skl(X1,X2,X3),X1)
| ~ subset(X0,sK1_skl(X1,X2,X3)) ),
inference(resolution,[status(thm)],[f1122,f40]) ).
fof(f8915,definition,
( sQ228_spl
<=> in(set_union2(singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_union2(singleton(sK6_skl),singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f8918,plain,
( ~ sQ228_spl
| ~ sQ156_spl ),
inference(split_clause,[status(thm)],[f8695,f5291,f8915]) ).
fof(f9379,plain,
! [X0,X1] :
( sQ1_spl
| in(sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl))),set_difference(sK7_skl,singleton(sK6_skl)))
| set_union2(set_difference(sK7_skl,singleton(sK6_skl)),singleton(sK6_skl)) = sK7_skl
| ~ in(set_union2(singleton(sK6_skl),X1),X0)
| ~ subset(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ),
inference(resolution,[status(thm)],[f8841,f110]) ).
fof(f9397,definition,
! [X0,X1] :
( sQ242_spl
<=> ( ~ in(set_union2(singleton(sK6_skl),X1),X0)
| ~ subset(X0,sK1_skl(sK7_skl,singleton(sK6_skl),set_difference(sK7_skl,singleton(sK6_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f9400,plain,
( sQ1_spl
| sQ4_spl
| sQ5_spl
| sQ242_spl ),
inference(split_clause,[status(thm)],[f9379,f9397,f125,f122,f108]) ).
fof(f10632,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ in(sK6_skl,sK7_skl) ),
inference(backward_demodulation,[status(thm)],[f143,f118]) ).
fof(f10739,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10632,f261,f142,f116]) ).
fof(f10784,plain,
$false,
inference(sat_refutation,[status(thm)],[f111,f119,f128,f130,f146,f252,f375,f381,f394,f435,f459,f460,f566,f576,f605,f633,f751,f752,f800,f871,f896,f915,f936,f1262,f1275,f1328,f1379,f1758,f1881,f1883,f1929,f2165,f2185,f2280,f2307,f2336,f3430,f3445,f3453,f3457,f3461,f3464,f3466,f3468,f3470,f3510,f3585,f3884,f4004,f4963,f5282,f5290,f5297,f5706,f6284,f6566,f6595,f7185,f7434,f7499,f7568,f7570,f7698,f7699,f7796,f7848,f8918,f9400,f10739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET986+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n014.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 05:46:05 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 268.84/34.68 % Refutation found
% 268.84/34.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 268.84/34.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 240.89/34.82 % Elapsed time: 34.266439 seconds
% 240.89/34.82 % CPU time: 270.055336 seconds
% 240.89/34.82 % Total memory used: 630.377 MB
% 240.89/34.82 % Net memory used: 549.962 MB
%------------------------------------------------------------------------------