%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET919+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:10:58 PM UTC 2026
% Result : Theorem 0.13s 6.13s
% Output : CNFRefutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 55
% Syntax : Number of formulae : 268 ( 31 unt; 47 def)
% Number of atoms : 799 ( 337 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 835 ( 304 ~; 427 |; 48 &)
% ( 53 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 50 ( 48 usr; 48 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 259 ( 247 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C] :
( in(A,B)
=> ( set_intersection2(unordered_pair(A,C),B) = singleton(A)
| ( A != C
& in(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C] :
( in(A,B)
=> ( set_intersection2(unordered_pair(A,C),B) = singleton(A)
| ( A != C
& in(C,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,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(f17,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)],[f16]) ).
fof(f18,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))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( sK0_skl(X0,X1) != X1
| ~ in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( sK0_skl(X0,X1) = X1
| in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [A,B,C] :
( ( ( sK1_skl(C,B,A) = B
| sK1_skl(C,B,A) = A
| in(sK1_skl(C,B,A),C) )
& ( ( sK1_skl(C,B,A) != B
& sK1_skl(C,B,A) != A )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
! [X0,X1,X2] :
( sK1_skl(X0,X2,X1) != X2
| ~ in(sK1_skl(X0,X2,X1),X0)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
! [X0,X1,X2] :
( sK1_skl(X0,X2,X1) = X2
| sK1_skl(X0,X2,X1) = X1
| in(sK1_skl(X0,X2,X1),X0)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
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_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
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_intersection2(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_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,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_intersection2(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_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f41,plain,
! [A] : set_intersection2(A,A) = A,
inference(miniscoping,[status(thm)],[f7]) ).
fof(f42,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f47,plain,
? [A,B,C] :
( set_intersection2(unordered_pair(A,C),B) != singleton(A)
& ( A = C
| ~ in(C,B) )
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f48,plain,
? [A,B] :
( ? [C] :
( set_intersection2(unordered_pair(A,C),B) != singleton(A)
& ( A = C
| ~ in(C,B) ) )
& in(A,B) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl) != singleton(sK5_skl)
& ( sK5_skl = sK7_skl
| ~ in(sK7_skl,sK6_skl) )
& in(sK5_skl,sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl)],[f48]) ).
fof(f50,plain,
in(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
( sK5_skl = sK7_skl
| ~ in(sK7_skl,sK6_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl) != singleton(sK5_skl),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,definition,
( sQ0_spl
<=> in(sK7_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f56,definition,
( sQ1_spl
<=> sK5_skl = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ1_spl
| sK5_skl = sK7_skl ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f53,f56]) ).
fof(f60,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f61,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f62,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f63,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f64,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f65,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f35]) ).
fof(f66,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f76,plain,
set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl) != singleton(sK5_skl),
inference(paramodulation,[status(thm)],[f14,f52]) ).
fof(f90,plain,
set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) != singleton(sK5_skl),
inference(paramodulation,[status(thm)],[f15,f52]) ).
fof(f108,plain,
! [X0,X1,X2] :
( in(sK0_skl(set_intersection2(X0,X1),X2),X1)
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f22,f66]) ).
fof(f109,plain,
! [X0,X1,X2] :
( in(sK0_skl(set_intersection2(X0,X1),X2),X0)
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f22,f65]) ).
fof(f110,plain,
! [X0,X1,X2] :
( sK0_skl(unordered_pair(X0,X1),X2) = X1
| sK0_skl(unordered_pair(X0,X1),X2) = X0
| sK0_skl(unordered_pair(X0,X1),X2) = X2
| unordered_pair(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f22,f62]) ).
fof(f112,plain,
! [X0,X1] :
( ~ in(X0,sK0_skl(X0,X1))
| sK0_skl(X0,X1) = X1
| X0 = singleton(X1) ),
inference(resolution,[status(thm)],[f22,f13]) ).
fof(f113,plain,
! [X0,X1,X2] :
( sK0_skl(X0,X1) = X1
| X0 = singleton(X1)
| ~ in(sK0_skl(X0,X1),X2)
| in(sK0_skl(X0,X1),set_intersection2(X2,X0)) ),
inference(resolution,[status(thm)],[f67,f22]) ).
fof(f114,plain,
! [X0] :
( ~ in(sK5_skl,X0)
| in(sK5_skl,set_intersection2(X0,sK6_skl)) ),
inference(resolution,[status(thm)],[f67,f50]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_intersection2(X1,unordered_pair(X2,X0))) ),
inference(resolution,[status(thm)],[f67,f64]) ).
fof(f117,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(X0,set_intersection2(X1,singleton(X0))) ),
inference(resolution,[status(thm)],[f67,f61]) ).
fof(f120,plain,
! [X0] : in(sK5_skl,set_intersection2(unordered_pair(sK5_skl,X0),sK6_skl)),
inference(resolution,[status(thm)],[f114,f63]) ).
fof(f121,plain,
in(sK5_skl,set_intersection2(singleton(sK5_skl),sK6_skl)),
inference(resolution,[status(thm)],[f114,f61]) ).
fof(f137,plain,
! [X0,X1] :
( sK0_skl(X0,X1) = X1
| X0 = singleton(X1)
| in(sK0_skl(X0,X1),set_intersection2(X0,singleton(sK0_skl(X0,X1)))) ),
inference(resolution,[status(thm)],[f117,f22]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( sK0_skl(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X2
| sK0_skl(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X1
| sK0_skl(set_intersection2(X0,unordered_pair(X1,X2)),X3) = X3
| set_intersection2(X0,unordered_pair(X1,X2)) = singleton(X3) ),
inference(resolution,[status(thm)],[f108,f62]) ).
fof(f149,plain,
! [X0,X1,X2] :
( in(sK0_skl(set_intersection2(X0,X1),X2),set_intersection2(X1,singleton(sK0_skl(set_intersection2(X0,X1),X2))))
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f108,f117]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( ~ in(sK0_skl(set_intersection2(X0,X1),X2),X3)
| in(sK0_skl(set_intersection2(X0,X1),X2),set_intersection2(X3,X1))
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f108,f67]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ in(X1,sK0_skl(set_intersection2(X0,X1),X2))
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f108,f13]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( sK0_skl(set_intersection2(unordered_pair(X0,X1),X2),X3) = X1
| sK0_skl(set_intersection2(unordered_pair(X0,X1),X2),X3) = X0
| sK0_skl(set_intersection2(unordered_pair(X0,X1),X2),X3) = X3
| set_intersection2(unordered_pair(X0,X1),X2) = singleton(X3) ),
inference(resolution,[status(thm)],[f109,f62]) ).
fof(f160,plain,
! [X0,X1,X2] :
( sK0_skl(set_intersection2(singleton(X0),X1),X2) = X0
| sK0_skl(set_intersection2(singleton(X0),X1),X2) = X2
| set_intersection2(singleton(X0),X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f109,f60]) ).
fof(f161,plain,
! [X0,X1,X2] :
( in(sK0_skl(set_intersection2(X0,X1),X2),set_intersection2(X0,singleton(sK0_skl(set_intersection2(X0,X1),X2))))
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f109,f117]) ).
fof(f162,plain,
! [X0,X1,X2,X3] :
( ~ in(sK0_skl(set_intersection2(X0,X1),X2),X3)
| in(sK0_skl(set_intersection2(X0,X1),X2),set_intersection2(X3,X0))
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f109,f67]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ in(X0,sK0_skl(set_intersection2(X0,X1),X2))
| sK0_skl(set_intersection2(X0,X1),X2) = X2
| set_intersection2(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f109,f13]) ).
fof(f220,plain,
! [X0,X1,X2] :
( sK1_skl(singleton(X0),X2,X1) = X0
| sK1_skl(singleton(X0),X2,X1) = X2
| sK1_skl(singleton(X0),X2,X1) = X1
| singleton(X0) = unordered_pair(X1,X2) ),
inference(resolution,[status(thm)],[f31,f60]) ).
fof(f240,plain,
! [X0] : in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(sK5_skl,X0))),
inference(paramodulation,[status(thm)],[f15,f120]) ).
fof(f273,plain,
! [X0] :
( sK0_skl(unordered_pair(sK7_skl,sK5_skl),X0) = sK5_skl
| sK0_skl(unordered_pair(sK7_skl,sK5_skl),X0) = sK7_skl
| sK0_skl(unordered_pair(sK7_skl,sK5_skl),X0) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f110,f76]) ).
fof(f274,plain,
! [X0] :
( sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK7_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK5_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = X0
| set_intersection2(sK6_skl,singleton(X0)) != singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f110,f90]) ).
fof(f275,plain,
! [X0] :
( sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK7_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK5_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f110,f52]) ).
fof(f390,plain,
! [X0] :
( sK0_skl(unordered_pair(sK7_skl,sK5_skl),X0) = sK5_skl
| sK7_skl != sK5_skl
| sK0_skl(unordered_pair(sK7_skl,sK5_skl),X0) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ),
inference(equality_factoring,[status(thm)],[f273]) ).
fof(f392,definition,
! [X0] :
( sQ2_spl
<=> ( sK0_skl(unordered_pair(sK7_skl,sK5_skl),X0) = sK5_skl
| sK0_skl(unordered_pair(sK7_skl,sK5_skl),X0) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f390,f392,f56]) ).
fof(f396,plain,
! [X0,X1] :
( in(sK5_skl,set_intersection2(set_intersection2(X0,unordered_pair(X1,sK5_skl)),sK6_skl))
| ~ in(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f115,f114]) ).
fof(f535,plain,
! [X0] :
( sK1_skl(singleton(X0),sK5_skl,sK7_skl) = X0
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = sK5_skl
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f220,f76]) ).
fof(f536,plain,
! [X0] :
( sK1_skl(singleton(X0),sK7_skl,sK5_skl) = X0
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK7_skl
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,singleton(X0)) != singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f220,f90]) ).
fof(f537,plain,
! [X0] :
( sK1_skl(singleton(X0),sK7_skl,sK5_skl) = X0
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK7_skl
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK5_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f220,f52]) ).
fof(f601,plain,
! [X0] :
( sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK5_skl
| sK7_skl != sK5_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = X0
| set_intersection2(sK6_skl,singleton(X0)) != singleton(sK5_skl) ),
inference(equality_factoring,[status(thm)],[f274]) ).
fof(f603,definition,
! [X0] :
( sQ3_spl
<=> ( sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK5_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = X0
| set_intersection2(sK6_skl,singleton(X0)) != singleton(sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f606,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f601,f603,f56]) ).
fof(f706,plain,
! [X0] :
( sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK5_skl
| sK7_skl != sK5_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ),
inference(equality_factoring,[status(thm)],[f275]) ).
fof(f708,definition,
! [X0] :
( sQ4_spl
<=> ( sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = sK5_skl
| sK0_skl(unordered_pair(sK5_skl,sK7_skl),X0) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f711,plain,
( ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f706,f708,f56]) ).
fof(f963,plain,
! [X0] :
( in(sK5_skl,sK6_skl)
| ~ in(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f396,f66]) ).
fof(f977,definition,
! [X0] :
( sQ5_spl
<=> ~ in(sK5_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f978,plain,
! [X0] :
( ~ sQ5_spl
| ~ in(sK5_skl,X0) ),
inference(component_clause,[status(thm)],[f977]) ).
fof(f980,definition,
( sQ6_spl
<=> in(sK5_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f983,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f963,f977,f980]) ).
fof(f1010,plain,
! [X0] :
( ~ sQ1_spl
| in(sK5_skl,set_intersection2(unordered_pair(sK7_skl,X0),sK6_skl)) ),
inference(backward_demodulation,[status(thm)],[f57,f120]) ).
fof(f1015,plain,
( ~ sQ1_spl
| in(sK5_skl,set_intersection2(singleton(sK7_skl),sK6_skl)) ),
inference(backward_demodulation,[status(thm)],[f57,f121]) ).
fof(f1021,plain,
( ~ sQ1_spl
| set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl) != singleton(sK7_skl) ),
inference(backward_demodulation,[status(thm)],[f57,f52]) ).
fof(f1062,plain,
! [X0] :
( ~ sQ1_spl
| in(sK7_skl,set_intersection2(unordered_pair(sK7_skl,X0),sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f57,f1010]) ).
fof(f1067,plain,
( ~ sQ1_spl
| in(sK7_skl,set_intersection2(singleton(sK7_skl),sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f57,f1015]) ).
fof(f1072,plain,
( ~ sQ1_spl
| set_intersection2(unordered_pair(sK7_skl,sK7_skl),sK6_skl) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f1021]) ).
fof(f1155,plain,
! [X0] : in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(X0,sK5_skl))),
inference(paramodulation,[status(thm)],[f14,f240]) ).
fof(f1229,plain,
! [X0] :
( ~ in(set_intersection2(X0,sK6_skl),sK5_skl)
| ~ in(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f114,f13]) ).
fof(f1390,definition,
! [X0] :
( sQ7_spl
<=> ~ in(sK7_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1391,plain,
! [X0] :
( ~ sQ7_spl
| ~ in(sK7_skl,X0) ),
inference(component_clause,[status(thm)],[f1390]) ).
fof(f1395,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1062,f1391]) ).
fof(f1418,plain,
( ~ sQ1_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1395]) ).
fof(f1422,plain,
set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) != singleton(sK5_skl),
inference(paramodulation,[status(thm)],[f15,f52]) ).
fof(f1423,plain,
set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) != singleton(sK5_skl),
inference(paramodulation,[status(thm)],[f15,f52]) ).
fof(f1427,plain,
set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl) != singleton(sK5_skl),
inference(paramodulation,[status(thm)],[f14,f52]) ).
fof(f1593,plain,
( ~ sQ1_spl
| set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)) != singleton(sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f1422]) ).
fof(f1594,plain,
( ~ sQ1_spl
| set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f1593]) ).
fof(f1710,definition,
( sQ8_spl
<=> in(sK6_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1877,plain,
( ~ sQ1_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)),sK7_skl) = sK7_skl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)),sK7_skl) = sK7_skl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)),sK7_skl) = sK7_skl ),
inference(resolution,[status(thm)],[f147,f1594]) ).
fof(f1962,definition,
( sQ9_spl
<=> sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)),sK7_skl) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1965,plain,
( ~ sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1877,f1962,f56]) ).
fof(f2013,plain,
( sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK7_skl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl ),
inference(resolution,[status(thm)],[f1423,f147]) ).
fof(f2018,plain,
set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)) != singleton(sK5_skl),
inference(paramodulation,[status(thm)],[f14,f1423]) ).
fof(f2019,definition,
( sQ10_spl
<=> sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f2020,plain,
( ~ sQ10_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl ),
inference(component_clause,[status(thm)],[f2019]) ).
fof(f2022,definition,
( sQ11_spl
<=> sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f2023,plain,
( ~ sQ11_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK7_skl ),
inference(component_clause,[status(thm)],[f2022]) ).
fof(f2025,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f2013,f2019,f2022]) ).
fof(f2075,plain,
( ~ sQ1_spl
| set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)) != singleton(sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f1422]) ).
fof(f2076,plain,
( ~ sQ1_spl
| set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f2075]) ).
fof(f2357,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = X0
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = sK5_skl
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f535]) ).
fof(f2358,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = X0
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = sK5_skl
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f2357]) ).
fof(f2359,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = X0
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK5_skl
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f2358]) ).
fof(f2360,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl(singleton(X0),sK5_skl,sK7_skl) = X0
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK7_skl
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f2359]) ).
fof(f2361,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = X0
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK7_skl
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK7_skl) ),
inference(forward_demodulation,[status(thm)],[f57,f2360]) ).
fof(f2362,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = X0
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK7_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f2361]) ).
fof(f2369,plain,
! [X0] :
( ~ sQ1_spl
| sK1_skl(singleton(X0),sK7_skl,sK7_skl) = X0
| sK7_skl != X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK7_skl) ),
inference(equality_factoring,[status(thm)],[f2362]) ).
fof(f2370,plain,
( ~ sQ1_spl
| sK1_skl(singleton(sK7_skl),sK7_skl,sK7_skl) = sK7_skl
| set_intersection2(singleton(sK7_skl),sK6_skl) != singleton(sK7_skl) ),
inference(destructive_equality_resolution,[status(thm)],[f2369]) ).
fof(f2516,definition,
( sQ12_spl
<=> set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)) = singleton(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f2517,plain,
( ~ sQ12_spl
| set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK7_skl)) = singleton(sK7_skl) ),
inference(component_clause,[status(thm)],[f2516]) ).
fof(f2557,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2517,f2076]) ).
fof(f2558,plain,
( ~ sQ12_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f2557]) ).
fof(f2603,definition,
( sQ22_spl
<=> set_intersection2(singleton(sK7_skl),sK6_skl) = singleton(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f2605,plain,
( sQ22_spl
| set_intersection2(singleton(sK7_skl),sK6_skl) != singleton(sK7_skl) ),
inference(component_clause,[status(thm)],[f2603]) ).
fof(f2606,definition,
( sQ23_spl
<=> sK1_skl(singleton(sK7_skl),sK7_skl,sK7_skl) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2607,plain,
( ~ sQ23_spl
| sK1_skl(singleton(sK7_skl),sK7_skl,sK7_skl) = sK7_skl ),
inference(component_clause,[status(thm)],[f2606]) ).
fof(f2609,plain,
( ~ sQ1_spl
| sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f2370,f2603,f2606,f56]) ).
fof(f2716,plain,
( ~ sQ23_spl
| sK1_skl(singleton(sK7_skl),sK7_skl,sK7_skl) != sK7_skl
| ~ in(sK7_skl,singleton(sK7_skl))
| singleton(sK7_skl) = unordered_pair(sK7_skl,sK7_skl) ),
inference(paramodulation,[status(thm)],[f2607,f30]) ).
fof(f2718,definition,
( sQ25_spl
<=> singleton(sK7_skl) = unordered_pair(sK7_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f2719,plain,
( ~ sQ25_spl
| singleton(sK7_skl) = unordered_pair(sK7_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f2718]) ).
fof(f2729,definition,
( sQ28_spl
<=> in(sK7_skl,singleton(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f2731,plain,
( sQ28_spl
| ~ in(sK7_skl,singleton(sK7_skl)) ),
inference(component_clause,[status(thm)],[f2729]) ).
fof(f2733,plain,
( ~ sQ23_spl
| ~ sQ28_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f2716,f2718,f2729,f2606]) ).
fof(f2735,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2731,f61]) ).
fof(f2736,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f2735]) ).
fof(f2738,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| set_intersection2(singleton(sK7_skl),sK6_skl) != singleton(sK7_skl) ),
inference(backward_demodulation,[status(thm)],[f2719,f1072]) ).
fof(f2952,plain,
( sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) = sK5_skl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) = sK7_skl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) = sK5_skl ),
inference(resolution,[status(thm)],[f2018,f147]) ).
fof(f2956,definition,
( sQ29_spl
<=> sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f2957,plain,
( ~ sQ29_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) = sK5_skl ),
inference(component_clause,[status(thm)],[f2956]) ).
fof(f2959,definition,
( sQ30_spl
<=> sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f2962,plain,
( sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f2952,f2956,f2959]) ).
fof(f2965,plain,
( ~ in(sK6_skl,sK5_skl)
| ~ in(sK5_skl,sK6_skl) ),
inference(paramodulation,[status(thm)],[f42,f1229]) ).
fof(f2966,definition,
( sQ31_spl
<=> in(sK6_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f2969,plain,
( ~ sQ31_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f2965,f980,f2966]) ).
fof(f2973,plain,
( ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f50,f978]) ).
fof(f2996,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f2973]) ).
fof(f3016,plain,
! [X0] :
( sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK5_skl
| sK7_skl != sK5_skl
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = X0
| set_intersection2(sK6_skl,singleton(X0)) != singleton(sK5_skl) ),
inference(equality_factoring,[status(thm)],[f536]) ).
fof(f3018,definition,
! [X0] :
( sQ32_spl
<=> ( sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK5_skl
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = X0
| set_intersection2(sK6_skl,singleton(X0)) != singleton(sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f3021,plain,
( ~ sQ1_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f3016,f3018,f56]) ).
fof(f3167,plain,
! [X0] :
( sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK5_skl
| sK7_skl != sK5_skl
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ),
inference(equality_factoring,[status(thm)],[f537]) ).
fof(f3169,definition,
! [X0] :
( sQ33_spl
<=> ( sK1_skl(singleton(X0),sK7_skl,sK5_skl) = sK5_skl
| sK1_skl(singleton(X0),sK7_skl,sK5_skl) = X0
| set_intersection2(singleton(X0),sK6_skl) != singleton(sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f3172,plain,
( ~ sQ1_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f3167,f3169,f56]) ).
fof(f3190,definition,
( sQ34_spl
<=> sK0_skl(set_intersection2(singleton(sK7_skl),sK6_skl),sK7_skl) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f3191,plain,
( ~ sQ34_spl
| sK0_skl(set_intersection2(singleton(sK7_skl),sK6_skl),sK7_skl) = sK7_skl ),
inference(component_clause,[status(thm)],[f3190]) ).
fof(f3236,plain,
( sK0_skl(set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl),sK5_skl) = sK5_skl
| sK0_skl(set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl),sK5_skl) = sK7_skl
| sK0_skl(set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl),sK5_skl) = sK5_skl ),
inference(resolution,[status(thm)],[f159,f1427]) ).
fof(f3237,plain,
( sK0_skl(set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK5_skl) = sK7_skl
| sK0_skl(set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK5_skl) = sK5_skl
| sK0_skl(set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK5_skl) = sK5_skl ),
inference(resolution,[status(thm)],[f159,f52]) ).
fof(f3349,definition,
( sQ44_spl
<=> sK0_skl(set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl),sK5_skl) = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f3350,plain,
( ~ sQ44_spl
| sK0_skl(set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl),sK5_skl) = sK5_skl ),
inference(component_clause,[status(thm)],[f3349]) ).
fof(f3352,definition,
( sQ45_spl
<=> sK0_skl(set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl),sK5_skl) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f3355,plain,
( sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f3236,f3349,f3352]) ).
fof(f3356,definition,
( sQ46_spl
<=> sK0_skl(set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK5_skl) = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f3357,plain,
( ~ sQ46_spl
| sK0_skl(set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK5_skl) = sK5_skl ),
inference(component_clause,[status(thm)],[f3356]) ).
fof(f3359,definition,
( sQ47_spl
<=> sK0_skl(set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK5_skl) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f3362,plain,
( sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f3237,f3356,f3359]) ).
fof(f3804,plain,
( ~ sQ34_spl
| sK0_skl(set_intersection2(singleton(sK7_skl),sK6_skl),sK7_skl) != sK7_skl
| ~ in(sK7_skl,set_intersection2(singleton(sK7_skl),sK6_skl))
| set_intersection2(singleton(sK7_skl),sK6_skl) = singleton(sK7_skl) ),
inference(paramodulation,[status(thm)],[f3191,f21]) ).
fof(f3851,definition,
( sQ60_spl
<=> in(sK7_skl,set_intersection2(singleton(sK7_skl),sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f3853,plain,
( sQ60_spl
| ~ in(sK7_skl,set_intersection2(singleton(sK7_skl),sK6_skl)) ),
inference(component_clause,[status(thm)],[f3851]) ).
fof(f3855,plain,
( ~ sQ34_spl
| ~ sQ60_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f3804,f2603,f3851,f3190]) ).
fof(f3865,plain,
( sQ22_spl
| sK0_skl(set_intersection2(singleton(sK7_skl),sK6_skl),sK7_skl) = sK7_skl
| sK0_skl(set_intersection2(singleton(sK7_skl),sK6_skl),sK7_skl) = sK7_skl ),
inference(resolution,[status(thm)],[f2605,f160]) ).
fof(f3871,plain,
( sQ22_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f3865,f3190,f2603]) ).
fof(f4388,plain,
( ~ sQ10_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) != sK5_skl
| ~ in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)))
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2020,f21]) ).
fof(f4389,definition,
( sQ64_spl
<=> set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl) = singleton(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f4390,plain,
( ~ sQ64_spl
| set_intersection2(unordered_pair(sK5_skl,sK7_skl),sK6_skl) = singleton(sK5_skl) ),
inference(component_clause,[status(thm)],[f4389]) ).
fof(f4396,definition,
( sQ66_spl
<=> set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f4397,plain,
( ~ sQ66_spl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(component_clause,[status(thm)],[f4396]) ).
fof(f4447,definition,
( sQ78_spl
<=> in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f4449,plain,
( sQ78_spl
| ~ in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl))) ),
inference(component_clause,[status(thm)],[f4447]) ).
fof(f4451,plain,
( ~ sQ10_spl
| ~ sQ78_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4388,f4396,f4447,f2019]) ).
fof(f4452,plain,
( ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4397,f1423]) ).
fof(f4453,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f4452]) ).
fof(f4617,plain,
( ~ sQ29_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) != sK5_skl
| ~ in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)))
| set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2957,f21]) ).
fof(f4618,definition,
( sQ79_spl
<=> set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl) = singleton(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f4619,plain,
( ~ sQ79_spl
| set_intersection2(unordered_pair(sK7_skl,sK5_skl),sK6_skl) = singleton(sK5_skl) ),
inference(component_clause,[status(thm)],[f4618]) ).
fof(f4625,definition,
( sQ81_spl
<=> set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)) = singleton(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f4626,plain,
( ~ sQ81_spl
| set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)) = singleton(sK5_skl) ),
inference(component_clause,[status(thm)],[f4625]) ).
fof(f4676,definition,
( sQ93_spl
<=> in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f4678,plain,
( sQ93_spl
| ~ in(sK5_skl,set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl))) ),
inference(component_clause,[status(thm)],[f4676]) ).
fof(f4680,plain,
( ~ sQ29_spl
| ~ sQ93_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f4617,f4625,f4676,f2956]) ).
fof(f4681,plain,
( ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4626,f2018]) ).
fof(f4682,plain,
~ sQ81_spl,
inference(contradiction_clause,[status(thm)],[f4681]) ).
fof(f4684,plain,
( ~ sQ46_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl ),
inference(paramodulation,[status(thm)],[f15,f3357]) ).
fof(f4711,plain,
( ~ sQ46_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f4684,f2019,f3356]) ).
fof(f4765,plain,
( ~ sQ44_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK5_skl) = sK5_skl ),
inference(paramodulation,[status(thm)],[f15,f3350]) ).
fof(f4790,plain,
( ~ sQ44_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f4765,f2956,f3349]) ).
fof(f4843,plain,
( ~ sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4619,f1427]) ).
fof(f4844,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f4843]) ).
fof(f4845,plain,
( sQ93_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4678,f1155]) ).
fof(f4846,plain,
sQ93_spl,
inference(contradiction_clause,[status(thm)],[f4845]) ).
fof(f4856,plain,
( ~ sQ11_spl
| ~ in(sK6_skl,sK7_skl)
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f163]) ).
fof(f4857,plain,
! [X0] :
( ~ sQ11_spl
| ~ in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),X0)
| in(sK7_skl,set_intersection2(X0,sK6_skl))
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f162]) ).
fof(f4858,plain,
( ~ sQ11_spl
| in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),set_intersection2(sK6_skl,singleton(sK7_skl)))
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f161]) ).
fof(f4859,plain,
( ~ sQ11_spl
| in(sK7_skl,set_intersection2(sK6_skl,singleton(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl))))
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f161]) ).
fof(f4861,plain,
( ~ sQ11_spl
| ~ in(unordered_pair(sK5_skl,sK7_skl),sK7_skl)
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f151]) ).
fof(f4862,plain,
! [X0] :
( ~ sQ11_spl
| ~ in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),X0)
| in(sK7_skl,set_intersection2(X0,unordered_pair(sK5_skl,sK7_skl)))
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f150]) ).
fof(f4863,plain,
( ~ sQ11_spl
| in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),set_intersection2(unordered_pair(sK5_skl,sK7_skl),singleton(sK7_skl)))
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f149]) ).
fof(f4864,plain,
( ~ sQ11_spl
| in(sK7_skl,set_intersection2(unordered_pair(sK5_skl,sK7_skl),singleton(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl))))
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f149]) ).
fof(f4865,plain,
( ~ sQ11_spl
| in(sK7_skl,sK6_skl)
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f109]) ).
fof(f4866,plain,
( ~ sQ11_spl
| in(sK7_skl,unordered_pair(sK5_skl,sK7_skl))
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f108]) ).
fof(f4867,plain,
( ~ sQ11_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl)
| in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),set_intersection2(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),singleton(sK7_skl))) ),
inference(paramodulation,[status(thm)],[f2023,f137]) ).
fof(f4868,plain,
( ~ sQ11_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl)
| in(sK7_skl,set_intersection2(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),singleton(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl)))) ),
inference(paramodulation,[status(thm)],[f2023,f137]) ).
fof(f4869,plain,
! [X0] :
( ~ sQ11_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl)
| ~ in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),X0)
| in(sK7_skl,set_intersection2(X0,set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)))) ),
inference(paramodulation,[status(thm)],[f2023,f113]) ).
fof(f4870,plain,
( ~ sQ11_spl
| ~ in(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK7_skl)
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f112]) ).
fof(f4871,plain,
( ~ sQ11_spl
| sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl) = sK5_skl
| in(sK7_skl,set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)))
| set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)) = singleton(sK5_skl) ),
inference(paramodulation,[status(thm)],[f2023,f22]) ).
fof(f4873,definition,
( sQ116_spl
<=> in(sK7_skl,unordered_pair(sK5_skl,sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f4877,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4856,f4396,f2019,f1710,f2022]) ).
fof(f4878,definition,
! [X0] :
( sQ117_spl
<=> ( ~ in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),X0)
| in(sK7_skl,set_intersection2(X0,sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f4881,plain,
( ~ sQ11_spl
| sQ117_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4857,f4396,f2019,f4878,f2022]) ).
fof(f4882,definition,
( sQ118_spl
<=> in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),set_intersection2(sK6_skl,singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f4885,plain,
( ~ sQ11_spl
| sQ118_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4858,f4396,f2019,f4882,f2022]) ).
fof(f4886,definition,
( sQ119_spl
<=> in(sK7_skl,set_intersection2(sK6_skl,singleton(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f4889,plain,
( ~ sQ11_spl
| sQ119_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4859,f4396,f2019,f4886,f2022]) ).
fof(f4891,definition,
( sQ120_spl
<=> in(unordered_pair(sK5_skl,sK7_skl),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f4894,plain,
( ~ sQ11_spl
| ~ sQ120_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4861,f4396,f2019,f4891,f2022]) ).
fof(f4895,definition,
! [X0] :
( sQ121_spl
<=> ( ~ in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),X0)
| in(sK7_skl,set_intersection2(X0,unordered_pair(sK5_skl,sK7_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f4898,plain,
( ~ sQ11_spl
| sQ121_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4862,f4396,f2019,f4895,f2022]) ).
fof(f4899,definition,
( sQ122_spl
<=> in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),set_intersection2(unordered_pair(sK5_skl,sK7_skl),singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f4902,plain,
( ~ sQ11_spl
| sQ122_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4863,f4396,f2019,f4899,f2022]) ).
fof(f4903,definition,
( sQ123_spl
<=> in(sK7_skl,set_intersection2(unordered_pair(sK5_skl,sK7_skl),singleton(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f4906,plain,
( ~ sQ11_spl
| sQ123_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4864,f4396,f2019,f4903,f2022]) ).
fof(f4907,plain,
( ~ sQ11_spl
| sQ0_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4865,f4396,f2019,f53,f2022]) ).
fof(f4908,plain,
( ~ sQ11_spl
| sQ116_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4866,f4396,f2019,f4873,f2022]) ).
fof(f4909,definition,
( sQ124_spl
<=> in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),set_intersection2(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),singleton(sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f4912,plain,
( ~ sQ11_spl
| sQ10_spl
| sQ66_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f4867,f4909,f4396,f2019,f2022]) ).
fof(f4913,definition,
( sQ125_spl
<=> in(sK7_skl,set_intersection2(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),singleton(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f4916,plain,
( ~ sQ11_spl
| sQ10_spl
| sQ66_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f4868,f4913,f4396,f2019,f2022]) ).
fof(f4917,definition,
! [X0] :
( sQ126_spl
<=> ( ~ in(sK0_skl(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK5_skl),X0)
| in(sK7_skl,set_intersection2(X0,set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f4920,plain,
( ~ sQ11_spl
| sQ10_spl
| sQ66_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f4869,f4917,f4396,f2019,f2022]) ).
fof(f4921,definition,
( sQ127_spl
<=> in(set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f4924,plain,
( ~ sQ11_spl
| ~ sQ127_spl
| sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4870,f4396,f2019,f4921,f2022]) ).
fof(f4925,definition,
( sQ128_spl
<=> in(sK7_skl,set_intersection2(sK6_skl,unordered_pair(sK5_skl,sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f4928,plain,
( ~ sQ11_spl
| sQ10_spl
| sQ128_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f4871,f4396,f4925,f2019,f2022]) ).
fof(f4930,plain,
( ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4390,f52]) ).
fof(f4931,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f4930]) ).
fof(f4932,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4449,f240]) ).
fof(f4933,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f4932]) ).
fof(f4963,plain,
( ~ sQ1_spl
| sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1067,f3853]) ).
fof(f4964,plain,
( ~ sQ1_spl
| sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f4963]) ).
fof(f4970,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f2738,f2603,f2718,f56]) ).
fof(f4977,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f395,f606,f711,f983,f1418,f1965,f2025,f2558,f2609,f2733,f2736,f2962,f2969,f2996,f3021,f3172,f3355,f3362,f3855,f3871,f4451,f4453,f4680,f4682,f4711,f4790,f4844,f4846,f4877,f4881,f4885,f4889,f4894,f4898,f4902,f4906,f4907,f4908,f4912,f4916,f4920,f4924,f4928,f4931,f4933,f4964,f4970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET919+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 05:43:55 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.13/6.13 % Refutation found
% 0.13/6.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/6.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.90/6.16 % Elapsed time: 0.785050 seconds
% 4.90/6.16 % CPU time: 5.956053 seconds
% 4.90/6.16 % Total memory used: 169.147 MB
% 4.90/6.16 % Net memory used: 159.372 MB
%------------------------------------------------------------------------------