%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU136+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:20 PM UTC 2026
% Result : Theorem 67.29s 8.96s
% Output : CNFRefutation 67.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 80
% Syntax : Number of formulae : 343 ( 32 unt; 64 def)
% Number of atoms : 1137 ( 241 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1256 ( 462 ~; 653 |; 66 &)
% ( 73 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 70 ( 68 usr; 65 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 801 ( 786 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
~ ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f60,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f61,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f66,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)],[f65]) ).
fof(f67,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))],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f73,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X1,X2),X2)
| set_union2(X2,X1) = X0
| in(sK1_skl(X0,X1,X2),X0)
| in(sK1_skl(X0,X1,X2),X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f81,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)],[f8]) ).
fof(f82,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)],[f81]) ).
fof(f83,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_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,[sK3_skl]),skolemize(D,sK3_skl(C,B,A))],[f82]) ).
fof(f88,plain,
! [X0,X1,X2] :
( in(sK3_skl(X0,X1,X2),X0)
| set_intersection2(X2,X1) = X0
| in(sK3_skl(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f89,plain,
! [X0,X1,X2] :
( in(sK3_skl(X2,X1,X0),X1)
| in(sK3_skl(X2,X1,X0),X2)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f90,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f91,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)],[f90]) ).
fof(f92,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK4_skl(C,B,A),B)
& in(sK4_skl(C,B,A),A) )
| in(sK4_skl(C,B,A),C) )
& ( in(sK4_skl(C,B,A),B)
| ~ in(sK4_skl(C,B,A),A)
| ~ in(sK4_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f91]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f96,plain,
! [X0,X1,X2] :
( set_difference(X2,X1) = X0
| in(sK4_skl(X0,X1,X2),X1)
| ~ in(sK4_skl(X0,X1,X2),X2)
| ~ in(sK4_skl(X0,X1,X2),X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f97,plain,
! [X0,X1,X2] :
( in(sK4_skl(X0,X2,X1),X0)
| in(sK4_skl(X0,X2,X1),X1)
| X0 = set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f98,plain,
! [X0,X1,X2] :
( in(sK4_skl(X2,X1,X0),X2)
| ~ in(sK4_skl(X2,X1,X0),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f103,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f110,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(thm)],[f18]) ).
fof(f111,plain,
! [X0] : X0 = set_union2(X0,X0),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f131,plain,
! [X0] : X0 = set_union2(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f141,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f142,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK7_skl(B,A),B)
| ~ in(sK7_skl(B,A),A) )
& ( in(sK7_skl(B,A),B)
| in(sK7_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(C,sK7_skl(B,A))],[f142]) ).
fof(f144,plain,
! [X0,X1] :
( in(sK7_skl(X0,X1),X0)
| X1 = X0
| in(sK7_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f151,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f152,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( set_difference(X0,X1) != empty_set
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f155,plain,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f156,plain,
! [X0] : X0 = set_difference(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f157,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f158,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f157]) ).
fof(f159,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ( in(sK8_skl(B,A),B)
& in(sK8_skl(B,A),A) )
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(C,sK8_skl(B,A))],[f158]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ~ disjoint(X2,X1)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f165,plain,
? [A,B] : set_difference(set_union2(A,B),B) != set_difference(A,B),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f166,plain,
set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl) != set_difference(sK9_skl,sK10_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(A,sK9_skl),skolemize(B,sK10_skl)],[f165]) ).
fof(f167,plain,
set_difference(sK9_skl,sK10_skl) != set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f168,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f176,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f177,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f176]) ).
fof(f178,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
fof(f186,plain,
! [X0,X1,X2] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ in(X0,set_difference(X2,X1))
| ~ in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f94]) ).
fof(f192,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f193,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f93]) ).
fof(f223,plain,
! [X0] : X0 = set_union2(empty_set,X0),
inference(paramodulation,[status(thm)],[f53,f131]) ).
fof(f226,plain,
set_difference(sK9_skl,sK10_skl) != set_difference(set_union2(sK10_skl,sK9_skl),sK10_skl),
inference(paramodulation,[status(thm)],[f53,f167]) ).
fof(f256,plain,
! [X0,X1,X2,X3] :
( X0 = set_union2(set_difference(X2,X3),X1)
| in(sK1_skl(X0,X1,set_difference(X2,X3)),X0)
| ~ in(sK1_skl(X0,X1,set_difference(X2,X3)),X3)
| in(sK1_skl(X0,X1,set_difference(X2,X3)),X1) ),
inference(resolution,[status(thm)],[f187,f73]) ).
fof(f258,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(set_difference(X0,X1),X2,X3),X1)
| in(sK1_skl(set_difference(X0,X1),X2,X3),X3)
| set_difference(X0,X1) = set_union2(X3,X2)
| in(sK1_skl(set_difference(X0,X1),X2,X3),X2) ),
inference(resolution,[status(thm)],[f187,f73]) ).
fof(f260,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(X0,set_difference(X1,X2),X3),X2)
| set_union2(X3,set_difference(X1,X2)) = X0
| in(sK1_skl(X0,set_difference(X1,X2),X3),X0)
| in(sK1_skl(X0,set_difference(X1,X2),X3),X3) ),
inference(resolution,[status(thm)],[f187,f73]) ).
fof(f267,plain,
! [X0,X1,X2,X3] :
( ~ in(sK4_skl(set_difference(X0,X1),X3,X2),X3)
| ~ in(sK4_skl(set_difference(X0,X1),X3,X2),X1)
| set_difference(X0,X1) = set_difference(X2,X3) ),
inference(resolution,[status(thm)],[f187,f98]) ).
fof(f631,plain,
! [X0,X1] :
( set_union2(empty_set,X1) = X0
| in(sK1_skl(X0,X1,empty_set),X0)
| in(sK1_skl(X0,X1,empty_set),X1) ),
inference(resolution,[status(thm)],[f192,f73]) ).
fof(f633,plain,
! [X0,X1] :
( empty_set = set_union2(X1,X0)
| in(sK1_skl(empty_set,X0,X1),X0)
| in(sK1_skl(empty_set,X0,X1),X1) ),
inference(resolution,[status(thm)],[f192,f73]) ).
fof(f635,plain,
! [X0,X1] :
( in(sK1_skl(X0,empty_set,X1),X1)
| set_union2(X1,empty_set) = X0
| in(sK1_skl(X0,empty_set,X1),X0) ),
inference(resolution,[status(thm)],[f192,f73]) ).
fof(f713,plain,
! [X0,X1] :
( in(sK1_skl(X0,empty_set,X1),X0)
| in(sK1_skl(X0,empty_set,X1),X1)
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f131,f635]) ).
fof(f714,plain,
! [X0,X1] :
( in(sK1_skl(X1,X0,empty_set),X0)
| in(sK1_skl(X1,X0,empty_set),X1)
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f223,f631]) ).
fof(f972,plain,
( ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK10_skl,sK9_skl)),sK10_skl)
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK10_skl,sK9_skl)),sK10_skl) ),
inference(resolution,[status(thm)],[f267,f226]) ).
fof(f973,plain,
( ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),sK10_skl)
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),sK10_skl) ),
inference(resolution,[status(thm)],[f267,f167]) ).
fof(f974,plain,
( ~ in(sK4_skl(set_difference(set_union2(sK10_skl,sK9_skl),sK10_skl),sK10_skl,sK9_skl),sK10_skl)
| ~ in(sK4_skl(set_difference(set_union2(sK10_skl,sK9_skl),sK10_skl),sK10_skl,sK9_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f267,f226]) ).
fof(f975,plain,
( ~ in(sK4_skl(set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl),sK10_skl,sK9_skl),sK10_skl)
| ~ in(sK4_skl(set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl),sK10_skl,sK9_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f267,f167]) ).
fof(f980,definition,
( sQ8_spl
<=> in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f982,plain,
( sQ8_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),sK10_skl) ),
inference(component_clause,[status(thm)],[f980]) ).
fof(f983,plain,
~ sQ8_spl,
inference(split_clause,[status(thm)],[f973,f980]) ).
fof(f986,definition,
( sQ9_spl
<=> in(sK4_skl(set_difference(set_union2(sK10_skl,sK9_skl),sK10_skl),sK10_skl,sK9_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f989,plain,
~ sQ9_spl,
inference(split_clause,[status(thm)],[f974,f986]) ).
fof(f990,definition,
( sQ10_spl
<=> in(sK4_skl(set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl),sK10_skl,sK9_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f993,plain,
~ sQ10_spl,
inference(split_clause,[status(thm)],[f975,f990]) ).
fof(f994,definition,
( sQ11_spl
<=> in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK10_skl,sK9_skl)),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f997,plain,
~ sQ11_spl,
inference(split_clause,[status(thm)],[f972,f994]) ).
fof(f1041,plain,
! [X0,X1,X2] :
( in(sK1_skl(X1,X2,X0),X1)
| in(sK1_skl(X1,X2,X0),X2)
| X1 = set_union2(X0,X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f178,f73]) ).
fof(f1043,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X1,X2),X1)
| ~ empty(X0)
| set_union2(X2,X1) = X0
| in(sK1_skl(X0,X1,X2),X2) ),
inference(resolution,[status(thm)],[f178,f73]) ).
fof(f1045,plain,
! [X0,X1,X2] :
( in(sK1_skl(X1,X0,X2),X2)
| in(sK1_skl(X1,X0,X2),X1)
| X1 = set_union2(X2,X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f178,f73]) ).
fof(f1093,plain,
! [X0,X1,X2] :
( ~ in(X1,set_difference(X0,X2))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f178,f195]) ).
fof(f1144,plain,
( sQ8_spl
| set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl) = set_difference(sK9_skl,sK10_skl)
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK9_skl,sK10_skl))
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_difference(sK9_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f982,f96]) ).
fof(f1149,plain,
! [X0] :
( sQ8_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK10_skl,X0))
| in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),X0) ),
inference(resolution,[status(thm)],[f982,f193]) ).
fof(f1153,definition,
( sQ12_spl
<=> in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_difference(sK9_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1155,plain,
( sQ12_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_difference(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f1153]) ).
fof(f1156,definition,
( sQ13_spl
<=> in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK9_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1157,plain,
( ~ sQ13_spl
| in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f1156]) ).
fof(f1158,plain,
( sQ13_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f1156]) ).
fof(f1159,definition,
( sQ14_spl
<=> set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl) = set_difference(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1160,plain,
( ~ sQ14_spl
| set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl) = set_difference(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f1159]) ).
fof(f1162,plain,
( sQ8_spl
| sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1144,f1153,f1156,f1159,f980]) ).
fof(f1164,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1160,f167]) ).
fof(f1165,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f1164]) ).
fof(f1371,definition,
( sQ20_spl
<=> set_difference(set_union2(sK10_skl,sK9_skl),sK10_skl) = set_difference(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1372,plain,
( ~ sQ20_spl
| set_difference(set_union2(sK10_skl,sK9_skl),sK10_skl) = set_difference(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f1371]) ).
fof(f1375,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1372,f226]) ).
fof(f1376,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f1375]) ).
fof(f1484,plain,
( sQ8_spl
| sQ12_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK10_skl,set_difference(sK9_skl,sK10_skl))) ),
inference(resolution,[status(thm)],[f1155,f1149]) ).
fof(f1503,plain,
( sQ8_spl
| sQ12_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK10_skl,sK9_skl)) ),
inference(forward_demodulation,[status(thm)],[f155,f1484]) ).
fof(f1504,definition,
( sQ30_spl
<=> in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1506,plain,
( sQ30_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f1504]) ).
fof(f1514,plain,
! [X0] :
( sQ30_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_difference(sK9_skl,X0)) ),
inference(resolution,[status(thm)],[f1506,f195]) ).
fof(f1541,plain,
( sQ30_spl
| in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK9_skl,sK10_skl))
| set_difference(sK9_skl,sK10_skl) = set_difference(set_union2(sK9_skl,sK10_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f1514,f97]) ).
fof(f1553,plain,
( sQ30_spl
| sQ13_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f1541,f1159,f1156,f1504]) ).
fof(f1716,plain,
! [X0,X1,X2] :
( set_union2(X2,set_difference(X0,X1)) = empty_set
| ~ empty(X0)
| in(sK1_skl(empty_set,set_difference(X0,X1),X2),X2) ),
inference(resolution,[status(thm)],[f1093,f633]) ).
fof(f1718,plain,
! [X0,X1,X2] :
( in(sK1_skl(empty_set,X2,set_difference(X0,X1)),X2)
| ~ empty(X0)
| set_union2(set_difference(X0,X1),X2) = empty_set ),
inference(resolution,[status(thm)],[f1093,f633]) ).
fof(f1727,plain,
! [X0,X1,X2,X3,X4] :
( ~ empty(X3)
| set_difference(X0,X1) = set_union2(set_difference(X3,X4),X2)
| in(sK1_skl(set_difference(X0,X1),X2,set_difference(X3,X4)),X2)
| ~ in(sK1_skl(set_difference(X0,X1),X2,set_difference(X3,X4)),X1) ),
inference(resolution,[status(thm)],[f1093,f258]) ).
fof(f1729,plain,
! [X0,X1,X2,X3,X4] :
( in(sK1_skl(set_difference(X1,X2),set_difference(X0,X3),X4),X4)
| set_union2(X4,set_difference(X0,X3)) = set_difference(X1,X2)
| ~ in(sK1_skl(set_difference(X1,X2),set_difference(X0,X3),X4),X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f258]) ).
fof(f1735,plain,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
| ~ empty(X0)
| in(sK1_skl(set_difference(X0,X1),empty_set,X2),X2) ),
inference(resolution,[status(thm)],[f1093,f713]) ).
fof(f1744,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sK1_skl(set_difference(X0,X1),set_difference(X2,X3),X4),X3)
| set_union2(X4,set_difference(X2,X3)) = set_difference(X0,X1)
| ~ empty(X0)
| in(sK1_skl(set_difference(X0,X1),set_difference(X2,X3),X4),X4) ),
inference(resolution,[status(thm)],[f1093,f260]) ).
fof(f1746,plain,
! [X0,X1,X2,X3,X4] :
( ~ empty(X3)
| in(sK1_skl(X0,set_difference(X1,X2),set_difference(X3,X4)),X0)
| X0 = set_union2(set_difference(X3,X4),set_difference(X1,X2))
| ~ in(sK1_skl(X0,set_difference(X1,X2),set_difference(X3,X4)),X2) ),
inference(resolution,[status(thm)],[f1093,f260]) ).
fof(f1750,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| in(sK1_skl(X0,set_difference(X1,X2),empty_set),X0)
| X0 = set_difference(X1,X2) ),
inference(resolution,[status(thm)],[f1093,f714]) ).
fof(f1752,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| set_difference(X0,X1) = X2
| in(sK1_skl(set_difference(X0,X1),X2,empty_set),X2) ),
inference(resolution,[status(thm)],[f1093,f714]) ).
fof(f1757,plain,
! [X0,X1,X2,X3,X4] :
( in(sK1_skl(set_difference(X0,X1),X2,set_difference(X3,X4)),X2)
| ~ empty(X0)
| set_union2(set_difference(X3,X4),X2) = set_difference(X0,X1)
| ~ in(sK1_skl(set_difference(X0,X1),X2,set_difference(X3,X4)),X4) ),
inference(resolution,[status(thm)],[f1093,f256]) ).
fof(f1759,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sK1_skl(X0,set_difference(X1,X2),set_difference(X3,X4)),X4)
| ~ empty(X1)
| X0 = set_union2(set_difference(X3,X4),set_difference(X1,X2))
| in(sK1_skl(X0,set_difference(X1,X2),set_difference(X3,X4)),X0) ),
inference(resolution,[status(thm)],[f1093,f256]) ).
fof(f1765,plain,
! [X0,X1,X2,X3] :
( set_union2(set_difference(X0,X3),X2) = X1
| ~ empty(X2)
| in(sK1_skl(X1,X2,set_difference(X0,X3)),X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f1045]) ).
fof(f1767,plain,
! [X0,X1,X2,X3] :
( set_difference(X0,X1) = set_union2(X3,X2)
| ~ empty(X2)
| in(sK1_skl(set_difference(X0,X1),X2,X3),X3)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f1045]) ).
fof(f1770,plain,
! [X0,X1,X2,X3] :
( ~ empty(X0)
| ~ empty(X2)
| in(sK1_skl(set_difference(X2,X3),X1,X0),X1)
| set_union2(X0,X1) = set_difference(X2,X3) ),
inference(resolution,[status(thm)],[f1093,f1041]) ).
fof(f1772,plain,
! [X0,X1,X2,X3] :
( ~ empty(X2)
| in(sK1_skl(X1,set_difference(X2,X3),X0),X1)
| X1 = set_union2(X0,set_difference(X2,X3))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f1041]) ).
fof(f1775,plain,
! [X0,X1,X2,X3] :
( ~ empty(X2)
| in(sK1_skl(X0,set_difference(X2,X3),X1),X1)
| X0 = set_union2(X1,set_difference(X2,X3))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f1043]) ).
fof(f1777,plain,
! [X0,X1,X2,X3] :
( ~ empty(X2)
| X0 = set_union2(set_difference(X2,X3),X1)
| in(sK1_skl(X0,X1,set_difference(X2,X3)),X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f1043]) ).
fof(f1779,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(X1,X2,set_difference(X0,X3)),X1)
| set_union2(set_difference(X0,X3),X2) = X1
| in(sK1_skl(X1,X2,set_difference(X0,X3)),X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f73]) ).
fof(f1781,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(set_difference(X0,X1),X2,X3),X3)
| set_difference(X0,X1) = set_union2(X3,X2)
| in(sK1_skl(set_difference(X0,X1),X2,X3),X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1093,f73]) ).
fof(f1783,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(X3,set_difference(X1,X2),X0),X3)
| ~ empty(X1)
| in(sK1_skl(X3,set_difference(X1,X2),X0),X0)
| set_union2(X0,set_difference(X1,X2)) = X3 ),
inference(resolution,[status(thm)],[f1093,f73]) ).
fof(f1797,plain,
! [X0,X1,X2,X3] :
( in(sK4_skl(set_difference(X0,X1),X3,X2),X2)
| ~ empty(X0)
| set_difference(X0,X1) = set_difference(X2,X3) ),
inference(resolution,[status(thm)],[f1093,f97]) ).
fof(f1799,plain,
! [X0,X1,X2,X3] :
( in(sK4_skl(X3,X2,set_difference(X0,X1)),X3)
| ~ empty(X0)
| set_difference(set_difference(X0,X1),X2) = X3 ),
inference(resolution,[status(thm)],[f1093,f97]) ).
fof(f1815,plain,
! [X0,X1,X2,X3] :
( ~ empty(X1)
| in(sK3_skl(X3,set_difference(X1,X2),X0),X3)
| set_intersection2(X0,set_difference(X1,X2)) = X3 ),
inference(resolution,[status(thm)],[f1093,f89]) ).
fof(f1817,plain,
! [X0,X1,X2,X3] :
( ~ empty(X2)
| in(sK3_skl(set_difference(X2,X3),X1,X0),X1)
| set_intersection2(X0,X1) = set_difference(X2,X3) ),
inference(resolution,[status(thm)],[f1093,f89]) ).
fof(f1820,plain,
! [X0,X1,X2,X3] :
( set_difference(X0,X1) = set_intersection2(X3,X2)
| ~ empty(X0)
| in(sK3_skl(set_difference(X0,X1),X2,X3),X3) ),
inference(resolution,[status(thm)],[f1093,f88]) ).
fof(f1822,plain,
! [X0,X1,X2,X3] :
( ~ empty(X2)
| set_intersection2(set_difference(X2,X3),X1) = X0
| in(sK3_skl(X0,X1,set_difference(X2,X3)),X0) ),
inference(resolution,[status(thm)],[f1093,f88]) ).
fof(f1830,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| in(sK7_skl(set_difference(X1,X2),X0),X0)
| X0 = set_difference(X1,X2) ),
inference(resolution,[status(thm)],[f1093,f144]) ).
fof(f1832,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| in(sK7_skl(X2,set_difference(X0,X1)),X2)
| set_difference(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f1093,f144]) ).
fof(f1844,plain,
! [X0] :
( ~ in(X0,empty_set)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1093]) ).
fof(f1850,definition,
( sQ35_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f1852,plain,
( sQ35_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f1850]) ).
fof(f1853,definition,
! [X0] :
( sQ36_spl
<=> ~ in(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f1856,plain,
( sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f1844,f1850,f1853]) ).
fof(f1861,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1852,f103]) ).
fof(f1862,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f1861]) ).
fof(f1867,plain,
! [X0,X1,X2] :
( ~ empty(empty_set)
| set_intersection2(set_difference(empty_set,X2),X1) = X0
| in(sK3_skl(X0,X1,empty_set),X0) ),
inference(paramodulation,[status(thm)],[f168,f1822]) ).
fof(f1869,definition,
! [X0,X1,X2] :
( sQ37_spl
<=> ( set_intersection2(set_difference(empty_set,X2),X1) = X0
| in(sK3_skl(X0,X1,empty_set),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1872,plain,
( ~ sQ35_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f1867,f1869,f1850]) ).
fof(f1880,plain,
! [X0,X1] :
( ~ empty(empty_set)
| in(sK7_skl(X1,empty_set),X1)
| set_difference(empty_set,X0) = X1 ),
inference(paramodulation,[status(thm)],[f168,f1832]) ).
fof(f1882,definition,
! [X0,X1] :
( sQ38_spl
<=> ( in(sK7_skl(X1,empty_set),X1)
| set_difference(empty_set,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1885,plain,
( ~ sQ35_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1880,f1882,f1850]) ).
fof(f1892,plain,
! [X0,X1,X2] :
( ~ empty(empty_set)
| in(sK1_skl(X0,empty_set,X1),X1)
| X0 = set_union2(X1,set_difference(empty_set,X2))
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f168,f1775]) ).
fof(f1895,definition,
! [X0,X1,X2] :
( sQ39_spl
<=> ( in(sK1_skl(X0,empty_set,X1),X1)
| X0 = set_union2(X1,set_difference(empty_set,X2))
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1898,plain,
( ~ sQ35_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f1892,f1895,f1850]) ).
fof(f1906,plain,
! [X0,X1] :
( ~ empty(empty_set)
| in(sK7_skl(empty_set,X0),X0)
| X0 = set_difference(empty_set,X1) ),
inference(paramodulation,[status(thm)],[f168,f1830]) ).
fof(f1909,definition,
! [X0,X1] :
( sQ40_spl
<=> ( in(sK7_skl(empty_set,X0),X0)
| X0 = set_difference(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1912,plain,
( ~ sQ35_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1906,f1909,f1850]) ).
fof(f1918,plain,
! [X0,X1] :
( ~ empty(empty_set)
| set_difference(empty_set,X1) = X0
| in(sK1_skl(empty_set,X0,empty_set),X0) ),
inference(paramodulation,[status(thm)],[f168,f1752]) ).
fof(f1921,definition,
! [X0,X1] :
( sQ41_spl
<=> ( set_difference(empty_set,X1) = X0
| in(sK1_skl(empty_set,X0,empty_set),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1924,plain,
( ~ sQ35_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1918,f1921,f1850]) ).
fof(f1930,plain,
! [X0,X1] :
( X0 = set_difference(empty_set,X1)
| ~ empty(empty_set)
| in(sK1_skl(empty_set,empty_set,X0),X0) ),
inference(paramodulation,[status(thm)],[f168,f1735]) ).
fof(f1932,definition,
! [X0,X1] :
( sQ42_spl
<=> ( X0 = set_difference(empty_set,X1)
| in(sK1_skl(empty_set,empty_set,X0),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1935,plain,
( ~ sQ35_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1930,f1932,f1850]) ).
fof(f1942,plain,
! [X0,X1] :
( ~ empty(empty_set)
| in(sK1_skl(X0,empty_set,empty_set),X0)
| X0 = set_difference(empty_set,X1) ),
inference(paramodulation,[status(thm)],[f168,f1750]) ).
fof(f1945,definition,
! [X0,X1] :
( sQ43_spl
<=> ( in(sK1_skl(X0,empty_set,empty_set),X0)
| X0 = set_difference(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1948,plain,
( ~ sQ35_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f1942,f1945,f1850]) ).
fof(f1962,plain,
! [X0,X1,X2] :
( set_difference(empty_set,X2) = set_intersection2(X1,X0)
| ~ empty(empty_set)
| in(sK3_skl(empty_set,X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f168,f1820]) ).
fof(f1965,definition,
! [X0,X1,X2] :
( sQ44_spl
<=> ( set_difference(empty_set,X2) = set_intersection2(X1,X0)
| in(sK3_skl(empty_set,X0,X1),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1968,plain,
( ~ sQ35_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f1962,f1965,f1850]) ).
fof(f1983,plain,
! [X0,X1,X2,X3,X4] :
( ~ empty(X1)
| ~ empty(X3)
| in(sK1_skl(X0,set_difference(X3,X4),set_difference(X1,X2)),X0)
| X0 = set_union2(set_difference(X1,X2),set_difference(X3,X4)) ),
inference(resolution,[status(thm)],[f1783,f1093]) ).
fof(f1989,plain,
! [X0,X1,X2,X3,X4] :
( ~ empty(X3)
| in(sK1_skl(set_difference(X3,X4),set_difference(X1,X2),X0),X0)
| ~ empty(X1)
| set_union2(X0,set_difference(X1,X2)) = set_difference(X3,X4) ),
inference(resolution,[status(thm)],[f1783,f1093]) ).
fof(f1992,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,set_difference(empty_set,X1),X0),X2)
| ~ empty(empty_set)
| in(sK1_skl(X2,empty_set,X0),X0)
| set_union2(X0,set_difference(empty_set,X1)) = X2 ),
inference(paramodulation,[status(thm)],[f168,f1783]) ).
fof(f1994,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,empty_set,X0),X2)
| ~ empty(empty_set)
| in(sK1_skl(X2,set_difference(empty_set,X1),X0),X0)
| set_union2(X0,set_difference(empty_set,X1)) = X2 ),
inference(paramodulation,[status(thm)],[f168,f1783]) ).
fof(f1996,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| X0 = set_union2(X0,set_difference(X1,X2))
| in(sK1_skl(X0,set_difference(X1,X2),X0),X0) ),
inference(factoring,[status(thm)],[f1783]) ).
fof(f2003,definition,
! [X0,X1,X2] :
( sQ45_spl
<=> ( in(sK1_skl(X2,set_difference(empty_set,X1),X0),X2)
| in(sK1_skl(X2,empty_set,X0),X0)
| set_union2(X0,set_difference(empty_set,X1)) = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f2006,plain,
( ~ sQ35_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1992,f2003,f1850]) ).
fof(f2007,definition,
! [X0,X1,X2] :
( sQ46_spl
<=> ( in(sK1_skl(X2,empty_set,X0),X2)
| in(sK1_skl(X2,set_difference(empty_set,X1),X0),X0)
| set_union2(X0,set_difference(empty_set,X1)) = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f2010,plain,
( ~ sQ35_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f1994,f2007,f1850]) ).
fof(f2021,plain,
! [X0,X1,X2] :
( ~ empty(empty_set)
| in(sK3_skl(empty_set,X1,X0),X1)
| set_intersection2(X0,X1) = set_difference(empty_set,X2) ),
inference(paramodulation,[status(thm)],[f168,f1817]) ).
fof(f2023,definition,
! [X0,X1,X2] :
( sQ47_spl
<=> ( in(sK3_skl(empty_set,X1,X0),X1)
| set_intersection2(X0,X1) = set_difference(empty_set,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f2026,plain,
( ~ sQ35_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f2021,f2023,f1850]) ).
fof(f2039,plain,
! [X0,X1,X2] :
( ~ empty(empty_set)
| in(sK3_skl(X2,empty_set,X0),X2)
| set_intersection2(X0,set_difference(empty_set,X1)) = X2 ),
inference(paramodulation,[status(thm)],[f168,f1815]) ).
fof(f2042,definition,
! [X0,X1,X2] :
( sQ48_spl
<=> ( in(sK3_skl(X2,empty_set,X0),X2)
| set_intersection2(X0,set_difference(empty_set,X1)) = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f2045,plain,
( ~ sQ35_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f2039,f2042,f1850]) ).
fof(f2052,plain,
! [X0,X1,X2] :
( in(sK4_skl(empty_set,X2,X1),X1)
| ~ empty(empty_set)
| set_difference(empty_set,X0) = set_difference(X1,X2) ),
inference(paramodulation,[status(thm)],[f168,f1797]) ).
fof(f2056,definition,
! [X0,X1,X2] :
( sQ49_spl
<=> ( in(sK4_skl(empty_set,X2,X1),X1)
| set_difference(empty_set,X0) = set_difference(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f2059,plain,
( ~ sQ35_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f2052,f2056,f1850]) ).
fof(f2065,plain,
! [X0,X1,X2] :
( in(sK4_skl(X2,X1,empty_set),X2)
| ~ empty(empty_set)
| set_difference(set_difference(empty_set,X0),X1) = X2 ),
inference(paramodulation,[status(thm)],[f168,f1799]) ).
fof(f2067,definition,
! [X0,X1,X2] :
( sQ50_spl
<=> ( in(sK4_skl(X2,X1,empty_set),X2)
| set_difference(set_difference(empty_set,X0),X1) = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f2070,plain,
( ~ sQ35_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f2065,f2067,f1850]) ).
fof(f2078,plain,
! [X0,X1] :
( ~ empty(empty_set)
| X0 = set_union2(X0,set_difference(empty_set,X1))
| in(sK1_skl(X0,empty_set,X0),X0) ),
inference(paramodulation,[status(thm)],[f168,f1996]) ).
fof(f2080,definition,
! [X0,X1] :
( sQ51_spl
<=> ( X0 = set_union2(X0,set_difference(empty_set,X1))
| in(sK1_skl(X0,empty_set,X0),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f2083,plain,
( ~ sQ35_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f2078,f2080,f1850]) ).
fof(f2091,plain,
! [X0,X1] :
( set_union2(X0,set_difference(empty_set,X1)) = empty_set
| ~ empty(empty_set)
| in(sK1_skl(empty_set,empty_set,X0),X0) ),
inference(paramodulation,[status(thm)],[f168,f1716]) ).
fof(f2094,definition,
! [X0,X1] :
( sQ52_spl
<=> ( set_union2(X0,set_difference(empty_set,X1)) = empty_set
| in(sK1_skl(empty_set,empty_set,X0),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f2097,plain,
( ~ sQ35_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f2091,f2094,f1850]) ).
fof(f2105,plain,
! [X0,X1] :
( in(sK1_skl(empty_set,X1,empty_set),X1)
| ~ empty(empty_set)
| set_union2(set_difference(empty_set,X0),X1) = empty_set ),
inference(paramodulation,[status(thm)],[f168,f1718]) ).
fof(f2109,definition,
! [X0,X1] :
( sQ53_spl
<=> ( in(sK1_skl(empty_set,X1,empty_set),X1)
| set_union2(set_difference(empty_set,X0),X1) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f2112,plain,
( ~ sQ35_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f2105,f2109,f1850]) ).
fof(f2119,plain,
! [X0,X1,X2] :
( set_difference(empty_set,X2) = set_union2(X1,X0)
| ~ empty(X0)
| in(sK1_skl(empty_set,X0,X1),X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1767]) ).
fof(f2123,definition,
! [X0,X1,X2] :
( sQ54_spl
<=> ( set_difference(empty_set,X2) = set_union2(X1,X0)
| ~ empty(X0)
| in(sK1_skl(empty_set,X0,X1),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f2126,plain,
( sQ54_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2119,f1850,f2123]) ).
fof(f2137,plain,
! [X0,X1,X2,X3,X4] :
( ~ empty(X3)
| set_union2(set_difference(X3,X4),X2) = set_difference(X0,X1)
| in(sK1_skl(set_difference(X0,X1),X2,set_difference(X3,X4)),X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f1781,f1093]) ).
fof(f2140,plain,
! [X0,X1,X2] :
( in(sK1_skl(set_difference(empty_set,X2),X0,X1),X1)
| set_difference(empty_set,X2) = set_union2(X1,X0)
| in(sK1_skl(empty_set,X0,X1),X0)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1781]) ).
fof(f2142,plain,
! [X0,X1,X2] :
( in(sK1_skl(empty_set,X1,X2),X2)
| set_difference(empty_set,X0) = set_union2(X2,X1)
| in(sK1_skl(set_difference(empty_set,X0),X1,X2),X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1781]) ).
fof(f2144,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = set_union2(X2,X2)
| in(sK1_skl(set_difference(X0,X1),X2,X2),X2)
| ~ empty(X0) ),
inference(factoring,[status(thm)],[f1781]) ).
fof(f2145,definition,
! [X0,X1,X2] :
( sQ55_spl
<=> ( in(sK1_skl(empty_set,X1,X2),X2)
| set_difference(empty_set,X0) = set_union2(X2,X1)
| in(sK1_skl(set_difference(empty_set,X0),X1,X2),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f2148,plain,
( sQ55_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2142,f1850,f2145]) ).
fof(f2152,plain,
! [X0,X1,X2] :
( in(sK1_skl(set_difference(X1,X2),X0,X0),X0)
| ~ empty(X1)
| X0 = set_difference(X1,X2) ),
inference(forward_demodulation,[status(thm)],[f111,f2144]) ).
fof(f2157,definition,
! [X0,X1,X2] :
( sQ56_spl
<=> ( in(sK1_skl(set_difference(empty_set,X2),X0,X1),X1)
| set_difference(empty_set,X2) = set_union2(X1,X0)
| in(sK1_skl(empty_set,X0,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f2160,plain,
( sQ56_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2140,f1850,f2157]) ).
fof(f2172,plain,
! [X0,X1] :
( in(sK1_skl(empty_set,X0,X0),X0)
| ~ empty(empty_set)
| X0 = set_difference(empty_set,X1) ),
inference(paramodulation,[status(thm)],[f168,f2152]) ).
fof(f2174,definition,
! [X0,X1] :
( sQ57_spl
<=> ( in(sK1_skl(empty_set,X0,X0),X0)
| X0 = set_difference(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f2177,plain,
( ~ sQ35_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f2172,f2174,f1850]) ).
fof(f2184,plain,
! [X0,X1,X2] :
( ~ empty(empty_set)
| in(sK1_skl(X1,empty_set,X0),X1)
| X1 = set_union2(X0,set_difference(empty_set,X2))
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f168,f1772]) ).
fof(f2187,definition,
! [X0,X1,X2] :
( sQ58_spl
<=> ( in(sK1_skl(X1,empty_set,X0),X1)
| X1 = set_union2(X0,set_difference(empty_set,X2))
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f2190,plain,
( ~ sQ35_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f2184,f2187,f1850]) ).
fof(f2197,plain,
! [X0,X1,X2] :
( ~ empty(empty_set)
| X0 = set_union2(set_difference(empty_set,X2),X1)
| in(sK1_skl(X0,X1,empty_set),X1)
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f168,f1777]) ).
fof(f2199,definition,
! [X0,X1,X2] :
( sQ59_spl
<=> ( X0 = set_union2(set_difference(empty_set,X2),X1)
| in(sK1_skl(X0,X1,empty_set),X1)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f2202,plain,
( ~ sQ35_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f2197,f2199,f1850]) ).
fof(f2211,plain,
! [X0,X1,X2] :
( set_union2(set_difference(empty_set,X2),X1) = X0
| ~ empty(X1)
| in(sK1_skl(X0,X1,empty_set),X0)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1765]) ).
fof(f2213,definition,
! [X0,X1,X2] :
( sQ60_spl
<=> ( set_union2(set_difference(empty_set,X2),X1) = X0
| ~ empty(X1)
| in(sK1_skl(X0,X1,empty_set),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2216,plain,
( sQ60_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2211,f1850,f2213]) ).
fof(f2224,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| ~ empty(empty_set)
| in(sK1_skl(empty_set,X1,X0),X1)
| set_union2(X0,X1) = set_difference(empty_set,X2) ),
inference(paramodulation,[status(thm)],[f168,f1770]) ).
fof(f2228,definition,
! [X0,X1,X2] :
( sQ61_spl
<=> ( ~ empty(X0)
| in(sK1_skl(empty_set,X1,X0),X1)
| set_union2(X0,X1) = set_difference(empty_set,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f2231,plain,
( ~ sQ35_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f2224,f2228,f1850]) ).
fof(f2237,plain,
! [X0,X1,X2,X3] :
( ~ empty(X1)
| ~ empty(empty_set)
| in(sK1_skl(X0,empty_set,set_difference(X1,X2)),X0)
| X0 = set_union2(set_difference(X1,X2),set_difference(empty_set,X3)) ),
inference(paramodulation,[status(thm)],[f168,f1983]) ).
fof(f2239,plain,
! [X0,X1,X2,X3] :
( ~ empty(empty_set)
| ~ empty(X2)
| in(sK1_skl(X0,set_difference(X2,X3),empty_set),X0)
| X0 = set_union2(set_difference(empty_set,X1),set_difference(X2,X3)) ),
inference(paramodulation,[status(thm)],[f168,f1983]) ).
fof(f2243,definition,
! [X0,X1,X2,X3] :
( sQ62_spl
<=> ( ~ empty(X2)
| in(sK1_skl(X0,set_difference(X2,X3),empty_set),X0)
| X0 = set_union2(set_difference(empty_set,X1),set_difference(X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2246,plain,
( ~ sQ35_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f2239,f2243,f1850]) ).
fof(f2247,definition,
! [X0,X1,X2,X3] :
( sQ63_spl
<=> ( ~ empty(X1)
| in(sK1_skl(X0,empty_set,set_difference(X1,X2)),X0)
| X0 = set_union2(set_difference(X1,X2),set_difference(empty_set,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2250,plain,
( ~ sQ35_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f2237,f2247,f1850]) ).
fof(f2261,plain,
! [X0,X1,X2,X3] :
( ~ empty(empty_set)
| set_difference(X0,X1) = set_union2(set_difference(empty_set,X3),X2)
| in(sK1_skl(set_difference(X0,X1),X2,empty_set),X2)
| ~ in(sK1_skl(set_difference(X0,X1),X2,set_difference(empty_set,X3)),X1) ),
inference(paramodulation,[status(thm)],[f168,f1727]) ).
fof(f2265,definition,
! [X0,X1,X2,X3] :
( sQ64_spl
<=> ( set_difference(X0,X1) = set_union2(set_difference(empty_set,X3),X2)
| in(sK1_skl(set_difference(X0,X1),X2,empty_set),X2)
| ~ in(sK1_skl(set_difference(X0,X1),X2,set_difference(empty_set,X3)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2268,plain,
( ~ sQ35_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f2261,f2265,f1850]) ).
fof(f2281,plain,
! [X0,X1,X2,X3] :
( ~ empty(empty_set)
| in(sK1_skl(empty_set,set_difference(X1,X2),X0),X0)
| ~ empty(X1)
| set_union2(X0,set_difference(X1,X2)) = set_difference(empty_set,X3) ),
inference(paramodulation,[status(thm)],[f168,f1989]) ).
fof(f2283,plain,
! [X0,X1,X2,X3] :
( ~ empty(X2)
| in(sK1_skl(set_difference(X2,X3),empty_set,X0),X0)
| ~ empty(empty_set)
| set_union2(X0,set_difference(empty_set,X1)) = set_difference(X2,X3) ),
inference(paramodulation,[status(thm)],[f168,f1989]) ).
fof(f2288,definition,
! [X0,X1,X2,X3] :
( sQ65_spl
<=> ( in(sK1_skl(empty_set,set_difference(X1,X2),X0),X0)
| ~ empty(X1)
| set_union2(X0,set_difference(X1,X2)) = set_difference(empty_set,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2291,plain,
( ~ sQ35_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f2281,f2288,f1850]) ).
fof(f2292,definition,
! [X0,X1,X2,X3] :
( sQ66_spl
<=> ( ~ empty(X2)
| in(sK1_skl(set_difference(X2,X3),empty_set,X0),X0)
| set_union2(X0,set_difference(empty_set,X1)) = set_difference(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2295,plain,
( ~ sQ35_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f2283,f2292,f1850]) ).
fof(f2305,plain,
! [X0,X1,X2,X3] :
( ~ empty(empty_set)
| in(sK1_skl(X0,set_difference(X1,X2),empty_set),X0)
| X0 = set_union2(set_difference(empty_set,X3),set_difference(X1,X2))
| ~ in(sK1_skl(X0,set_difference(X1,X2),set_difference(empty_set,X3)),X2) ),
inference(paramodulation,[status(thm)],[f168,f1746]) ).
fof(f2314,definition,
! [X0,X1,X2,X3] :
( sQ67_spl
<=> ( in(sK1_skl(X0,set_difference(X1,X2),empty_set),X0)
| X0 = set_union2(set_difference(empty_set,X3),set_difference(X1,X2))
| ~ in(sK1_skl(X0,set_difference(X1,X2),set_difference(empty_set,X3)),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2317,plain,
( ~ sQ35_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f2305,f2314,f1850]) ).
fof(f2329,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(set_difference(empty_set,X3),set_difference(X0,X1),X2),X1)
| set_union2(X2,set_difference(X0,X1)) = set_difference(empty_set,X3)
| ~ empty(empty_set)
| in(sK1_skl(empty_set,set_difference(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f168,f1744]) ).
fof(f2341,definition,
! [X0,X1,X2,X3] :
( sQ68_spl
<=> ( ~ in(sK1_skl(set_difference(empty_set,X3),set_difference(X0,X1),X2),X1)
| set_union2(X2,set_difference(X0,X1)) = set_difference(empty_set,X3)
| in(sK1_skl(empty_set,set_difference(X0,X1),X2),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2344,plain,
( ~ sQ35_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f2329,f2341,f1850]) ).
fof(f2351,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(X0,set_difference(empty_set,X3),set_difference(X1,X2)),X2)
| ~ empty(empty_set)
| X0 = set_union2(set_difference(X1,X2),set_difference(empty_set,X3))
| in(sK1_skl(X0,empty_set,set_difference(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f168,f1759]) ).
fof(f2360,definition,
! [X0,X1,X2,X3] :
( sQ69_spl
<=> ( ~ in(sK1_skl(X0,set_difference(empty_set,X3),set_difference(X1,X2)),X2)
| X0 = set_union2(set_difference(X1,X2),set_difference(empty_set,X3))
| in(sK1_skl(X0,empty_set,set_difference(X1,X2)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2363,plain,
( ~ sQ35_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f2351,f2360,f1850]) ).
fof(f2373,plain,
! [X0,X1,X2,X3] :
( ~ empty(X1)
| set_union2(set_difference(X1,X2),X0) = set_difference(empty_set,X3)
| in(sK1_skl(empty_set,X0,set_difference(X1,X2)),X0)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f2137]) ).
fof(f2375,plain,
! [X0,X1,X2,X3] :
( ~ empty(empty_set)
| set_union2(set_difference(empty_set,X3),X2) = set_difference(X0,X1)
| in(sK1_skl(set_difference(X0,X1),X2,empty_set),X2)
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f168,f2137]) ).
fof(f2380,definition,
! [X0,X1,X2,X3] :
( sQ70_spl
<=> ( ~ empty(X1)
| set_union2(set_difference(X1,X2),X0) = set_difference(empty_set,X3)
| in(sK1_skl(empty_set,X0,set_difference(X1,X2)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f2383,plain,
( sQ70_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2373,f1850,f2380]) ).
fof(f2384,definition,
! [X0,X1,X2,X3] :
( sQ71_spl
<=> ( set_union2(set_difference(empty_set,X3),X2) = set_difference(X0,X1)
| in(sK1_skl(set_difference(X0,X1),X2,empty_set),X2)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f2387,plain,
( ~ sQ35_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f2375,f2384,f1850]) ).
fof(f2403,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X1,set_difference(empty_set,X2)),X0)
| set_union2(set_difference(empty_set,X2),X1) = X0
| in(sK1_skl(X0,X1,empty_set),X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1779]) ).
fof(f2405,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X1,empty_set),X0)
| set_union2(set_difference(empty_set,X2),X1) = X0
| in(sK1_skl(X0,X1,set_difference(empty_set,X2)),X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1779]) ).
fof(f2407,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| X0 = set_union2(set_difference(X1,X2),X0)
| in(sK1_skl(X0,X0,set_difference(X1,X2)),X0) ),
inference(factoring,[status(thm)],[f1779]) ).
fof(f2408,definition,
! [X0,X1,X2] :
( sQ72_spl
<=> ( in(sK1_skl(X0,X1,set_difference(empty_set,X2)),X0)
| set_union2(set_difference(empty_set,X2),X1) = X0
| in(sK1_skl(X0,X1,empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f2411,plain,
( sQ72_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2403,f1850,f2408]) ).
fof(f2413,definition,
! [X0,X1,X2] :
( sQ73_spl
<=> ( in(sK1_skl(X0,X1,empty_set),X0)
| set_union2(set_difference(empty_set,X2),X1) = X0
| in(sK1_skl(X0,X1,set_difference(empty_set,X2)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f2416,plain,
( sQ73_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2405,f1850,f2413]) ).
fof(f2432,plain,
! [X0,X1] :
( ~ empty(empty_set)
| X0 = set_union2(set_difference(empty_set,X1),X0)
| in(sK1_skl(X0,X0,empty_set),X0) ),
inference(paramodulation,[status(thm)],[f168,f2407]) ).
fof(f2434,definition,
! [X0,X1] :
( sQ74_spl
<=> ( X0 = set_union2(set_difference(empty_set,X1),X0)
| in(sK1_skl(X0,X0,empty_set),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f2437,plain,
( ~ sQ35_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f2432,f2434,f1850]) ).
fof(f2445,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(empty_set,X1,set_difference(X2,X3)),X1)
| ~ empty(empty_set)
| set_union2(set_difference(X2,X3),X1) = set_difference(empty_set,X0)
| ~ in(sK1_skl(set_difference(empty_set,X0),X1,set_difference(X2,X3)),X3) ),
inference(paramodulation,[status(thm)],[f168,f1757]) ).
fof(f2455,definition,
! [X0,X1,X2,X3] :
( sQ75_spl
<=> ( in(sK1_skl(empty_set,X1,set_difference(X2,X3)),X1)
| set_union2(set_difference(X2,X3),X1) = set_difference(empty_set,X0)
| ~ in(sK1_skl(set_difference(empty_set,X0),X1,set_difference(X2,X3)),X3) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f2458,plain,
( ~ sQ35_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f2445,f2455,f1850]) ).
fof(f2475,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(set_difference(X0,X1),empty_set,X3),X3)
| set_union2(X3,set_difference(empty_set,X2)) = set_difference(X0,X1)
| ~ in(sK1_skl(set_difference(X0,X1),set_difference(empty_set,X2),X3),X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f1729]) ).
fof(f2482,definition,
! [X0,X1,X2,X3] :
( sQ76_spl
<=> ( in(sK1_skl(set_difference(X0,X1),empty_set,X3),X3)
| set_union2(X3,set_difference(empty_set,X2)) = set_difference(X0,X1)
| ~ in(sK1_skl(set_difference(X0,X1),set_difference(empty_set,X2),X3),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f2485,plain,
( sQ76_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2475,f1850,f2482]) ).
fof(f2614,plain,
( ~ sQ13_spl
| in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),set_union2(sK10_skl,sK9_skl)) ),
inference(paramodulation,[status(thm)],[f53,f1157]) ).
fof(f2615,plain,
( ~ sQ13_spl
| sQ8_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2614,f1503]) ).
fof(f2616,plain,
( ~ sQ13_spl
| sQ8_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f2615]) ).
fof(f2848,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sK1_skl(set_difference(X0,X1),X2,X3),X4)
| set_difference(X0,X1) = set_union2(X3,X2)
| ~ disjoint(X4,X3)
| ~ empty(X0)
| in(sK1_skl(set_difference(X0,X1),X2,X3),X2) ),
inference(resolution,[status(thm)],[f162,f1781]) ).
fof(f2850,plain,
! [X0,X1,X2,X3,X4] :
( ~ empty(X0)
| ~ in(sK1_skl(set_difference(X0,X1),X3,X2),X4)
| in(sK1_skl(set_difference(X0,X1),X3,X2),X2)
| ~ disjoint(X4,X3)
| set_difference(X0,X1) = set_union2(X2,X3) ),
inference(resolution,[status(thm)],[f162,f1781]) ).
fof(f2894,plain,
! [X0,X1,X2,X3,X4] :
( ~ empty(X2)
| ~ disjoint(X4,X0)
| in(sK1_skl(X0,set_difference(X2,X3),X1),X1)
| ~ in(sK1_skl(X0,set_difference(X2,X3),X1),X4)
| X0 = set_union2(X1,set_difference(X2,X3)) ),
inference(resolution,[status(thm)],[f162,f1783]) ).
fof(f2896,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sK1_skl(X0,set_difference(X1,X2),X3),X4)
| ~ disjoint(X4,X3)
| ~ empty(X1)
| X0 = set_union2(X3,set_difference(X1,X2))
| in(sK1_skl(X0,set_difference(X1,X2),X3),X0) ),
inference(resolution,[status(thm)],[f162,f1783]) ).
fof(f2920,plain,
! [X0,X1,X2,X3,X4] :
( set_union2(set_difference(X0,X4),X3) = X2
| ~ in(sK1_skl(X2,X3,set_difference(X0,X4)),X1)
| in(sK1_skl(X2,X3,set_difference(X0,X4)),X3)
| ~ disjoint(X1,X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f162,f1779]) ).
fof(f2922,plain,
! [X0,X1,X2,X3,X4] :
( X3 = set_union2(set_difference(X0,X4),X2)
| ~ in(sK1_skl(X3,X2,set_difference(X0,X4)),X1)
| in(sK1_skl(X3,X2,set_difference(X0,X4)),X3)
| ~ disjoint(X1,X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f162,f1779]) ).
fof(f3131,plain,
! [X0,X1,X2,X3,X4] :
( in(sK1_skl(set_difference(X0,X1),X2,X3),X2)
| ~ empty(X0)
| ~ disjoint(X3,X4)
| set_difference(X0,X1) = set_union2(X3,X2)
| ~ in(sK1_skl(set_difference(X0,X1),X2,X3),X4) ),
inference(resolution,[status(thm)],[f162,f1781]) ).
fof(f3133,plain,
! [X0,X1,X2,X3,X4] :
( ~ disjoint(X3,X4)
| ~ in(sK1_skl(set_difference(X0,X1),X3,X2),X4)
| in(sK1_skl(set_difference(X0,X1),X3,X2),X2)
| ~ empty(X0)
| set_difference(X0,X1) = set_union2(X2,X3) ),
inference(resolution,[status(thm)],[f162,f1781]) ).
fof(f3160,plain,
! [X0,X1,X2,X3,X4] :
( ~ disjoint(X0,X4)
| ~ empty(X1)
| ~ in(sK1_skl(X0,set_difference(X1,X2),X3),X4)
| set_union2(X3,set_difference(X1,X2)) = X0
| in(sK1_skl(X0,set_difference(X1,X2),X3),X3) ),
inference(resolution,[status(thm)],[f162,f1783]) ).
fof(f3162,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sK1_skl(X3,set_difference(X0,X4),X1),X2)
| in(sK1_skl(X3,set_difference(X0,X4),X1),X3)
| X3 = set_union2(X1,set_difference(X0,X4))
| ~ disjoint(X1,X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f162,f1783]) ).
fof(f3179,plain,
! [X0,X1,X2,X3,X4] :
( ~ disjoint(X0,X4)
| ~ empty(X2)
| ~ in(sK1_skl(X0,X1,set_difference(X2,X3)),X4)
| set_union2(set_difference(X2,X3),X1) = X0
| in(sK1_skl(X0,X1,set_difference(X2,X3)),X1) ),
inference(resolution,[status(thm)],[f162,f1779]) ).
fof(f3181,plain,
! [X0,X1,X2,X3,X4] :
( ~ disjoint(X3,X4)
| in(sK1_skl(X0,X3,set_difference(X1,X2)),X0)
| ~ empty(X1)
| ~ in(sK1_skl(X0,X3,set_difference(X1,X2)),X4)
| X0 = set_union2(set_difference(X1,X2),X3) ),
inference(resolution,[status(thm)],[f162,f1779]) ).
fof(f3491,plain,
! [X0,X1,X2,X3] :
( ~ empty(empty_set)
| ~ in(sK1_skl(set_difference(empty_set,X0),X2,X1),X3)
| in(sK1_skl(empty_set,X2,X1),X1)
| ~ disjoint(X3,X2)
| set_difference(empty_set,X0) = set_union2(X1,X2) ),
inference(paramodulation,[status(thm)],[f168,f2850]) ).
fof(f3496,definition,
! [X0,X1,X2,X3] :
( sQ78_spl
<=> ( ~ in(sK1_skl(set_difference(empty_set,X0),X2,X1),X3)
| in(sK1_skl(empty_set,X2,X1),X1)
| ~ disjoint(X3,X2)
| set_difference(empty_set,X0) = set_union2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f3499,plain,
( ~ sQ35_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f3491,f3496,f1850]) ).
fof(f3578,definition,
! [X0] :
( sQ79_spl
<=> ~ subset(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f3579,plain,
! [X0] :
( ~ sQ79_spl
| ~ subset(X0,empty_set) ),
inference(component_clause,[status(thm)],[f3578]) ).
fof(f3591,plain,
! [X0,X1,X2,X3] :
( set_union2(set_difference(empty_set,X3),X2) = X1
| ~ in(sK1_skl(X1,X2,set_difference(empty_set,X3)),X0)
| in(sK1_skl(X1,X2,empty_set),X2)
| ~ disjoint(X0,X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f2920]) ).
fof(f3593,definition,
! [X0,X1,X2,X3] :
( sQ80_spl
<=> ( set_union2(set_difference(empty_set,X3),X2) = X1
| ~ in(sK1_skl(X1,X2,set_difference(empty_set,X3)),X0)
| in(sK1_skl(X1,X2,empty_set),X2)
| ~ disjoint(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f3596,plain,
( sQ80_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f3591,f1850,f3593]) ).
fof(f3620,plain,
! [X0,X1,X2,X3] :
( ~ disjoint(X0,X3)
| ~ empty(empty_set)
| ~ in(sK1_skl(X0,X1,set_difference(empty_set,X2)),X3)
| set_union2(set_difference(empty_set,X2),X1) = X0
| in(sK1_skl(X0,X1,empty_set),X1) ),
inference(paramodulation,[status(thm)],[f168,f3179]) ).
fof(f3625,definition,
! [X0,X1,X2,X3] :
( sQ81_spl
<=> ( ~ disjoint(X0,X3)
| ~ in(sK1_skl(X0,X1,set_difference(empty_set,X2)),X3)
| set_union2(set_difference(empty_set,X2),X1) = X0
| in(sK1_skl(X0,X1,empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f3628,plain,
( ~ sQ35_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f3620,f3625,f1850]) ).
fof(f3719,plain,
! [X0,X1,X2,X3] :
( X2 = set_union2(set_difference(empty_set,X3),X1)
| ~ in(sK1_skl(X2,X1,set_difference(empty_set,X3)),X0)
| in(sK1_skl(X2,X1,empty_set),X2)
| ~ disjoint(X0,X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f2922]) ).
fof(f3723,definition,
! [X0,X1,X2,X3] :
( sQ84_spl
<=> ( X2 = set_union2(set_difference(empty_set,X3),X1)
| ~ in(sK1_skl(X2,X1,set_difference(empty_set,X3)),X0)
| in(sK1_skl(X2,X1,empty_set),X2)
| ~ disjoint(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f3726,plain,
( sQ84_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f3719,f1850,f3723]) ).
fof(f3920,plain,
! [X0,X1,X2,X3] :
( ~ empty(empty_set)
| ~ disjoint(X3,X0)
| in(sK1_skl(X0,empty_set,X1),X1)
| ~ in(sK1_skl(X0,set_difference(empty_set,X2),X1),X3)
| X0 = set_union2(X1,set_difference(empty_set,X2)) ),
inference(paramodulation,[status(thm)],[f168,f2894]) ).
fof(f3922,definition,
! [X0,X1,X2,X3] :
( sQ87_spl
<=> ( ~ disjoint(X3,X0)
| in(sK1_skl(X0,empty_set,X1),X1)
| ~ in(sK1_skl(X0,set_difference(empty_set,X2),X1),X3)
| X0 = set_union2(X1,set_difference(empty_set,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f3925,plain,
( ~ sQ35_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f3920,f3922,f1850]) ).
fof(f3957,plain,
! [X0,X1,X2,X3] :
( ~ disjoint(X2,X3)
| ~ in(sK1_skl(set_difference(empty_set,X0),X2,X1),X3)
| in(sK1_skl(empty_set,X2,X1),X1)
| ~ empty(empty_set)
| set_difference(empty_set,X0) = set_union2(X1,X2) ),
inference(paramodulation,[status(thm)],[f168,f3133]) ).
fof(f3962,definition,
! [X0,X1,X2,X3] :
( sQ88_spl
<=> ( ~ disjoint(X2,X3)
| ~ in(sK1_skl(set_difference(empty_set,X0),X2,X1),X3)
| in(sK1_skl(empty_set,X2,X1),X1)
| set_difference(empty_set,X0) = set_union2(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f3965,plain,
( ~ sQ35_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f3957,f3962,f1850]) ).
fof(f4032,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(X0,set_difference(empty_set,X2),X1),X3)
| ~ disjoint(X3,X1)
| ~ empty(empty_set)
| X0 = set_union2(X1,set_difference(empty_set,X2))
| in(sK1_skl(X0,empty_set,X1),X0) ),
inference(paramodulation,[status(thm)],[f168,f2896]) ).
fof(f4034,definition,
! [X0,X1,X2,X3] :
( sQ90_spl
<=> ( ~ in(sK1_skl(X0,set_difference(empty_set,X2),X1),X3)
| ~ disjoint(X3,X1)
| X0 = set_union2(X1,set_difference(empty_set,X2))
| in(sK1_skl(X0,empty_set,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f4037,plain,
( ~ sQ35_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f4032,f4034,f1850]) ).
fof(f4068,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(X2,set_difference(empty_set,X3),X0),X1)
| in(sK1_skl(X2,empty_set,X0),X2)
| X2 = set_union2(X0,set_difference(empty_set,X3))
| ~ disjoint(X0,X1)
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f168,f3162]) ).
fof(f4070,definition,
! [X0,X1,X2,X3] :
( sQ91_spl
<=> ( ~ in(sK1_skl(X2,set_difference(empty_set,X3),X0),X1)
| in(sK1_skl(X2,empty_set,X0),X2)
| X2 = set_union2(X0,set_difference(empty_set,X3))
| ~ disjoint(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f4073,plain,
( sQ91_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f4068,f1850,f4070]) ).
fof(f4110,plain,
! [X0,X1,X2,X3] :
( ~ disjoint(X0,X3)
| ~ empty(empty_set)
| ~ in(sK1_skl(X0,set_difference(empty_set,X2),X1),X3)
| set_union2(X1,set_difference(empty_set,X2)) = X0
| in(sK1_skl(X0,empty_set,X1),X1) ),
inference(paramodulation,[status(thm)],[f168,f3160]) ).
fof(f4113,definition,
! [X0,X1,X2,X3] :
( sQ93_spl
<=> ( ~ disjoint(X0,X3)
| ~ in(sK1_skl(X0,set_difference(empty_set,X2),X1),X3)
| set_union2(X1,set_difference(empty_set,X2)) = X0
| in(sK1_skl(X0,empty_set,X1),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f4116,plain,
( ~ sQ35_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f4110,f4113,f1850]) ).
fof(f4147,plain,
! [X0] :
( ~ sQ79_spl
| set_difference(X0,empty_set) != empty_set ),
inference(resolution,[status(thm)],[f3579,f153]) ).
fof(f4150,plain,
! [X0] :
( ~ sQ79_spl
| X0 != empty_set ),
inference(forward_demodulation,[status(thm)],[f156,f4147]) ).
fof(f4151,plain,
( ~ sQ79_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f4150]) ).
fof(f4152,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f4151]) ).
fof(f4170,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(set_difference(empty_set,X3),X0,X1),X2)
| set_difference(empty_set,X3) = set_union2(X1,X0)
| ~ disjoint(X2,X1)
| ~ empty(empty_set)
| in(sK1_skl(empty_set,X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f168,f2848]) ).
fof(f4172,definition,
! [X0,X1,X2,X3] :
( sQ94_spl
<=> ( ~ in(sK1_skl(set_difference(empty_set,X3),X0,X1),X2)
| set_difference(empty_set,X3) = set_union2(X1,X0)
| ~ disjoint(X2,X1)
| in(sK1_skl(empty_set,X0,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f4175,plain,
( ~ sQ35_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f4170,f4172,f1850]) ).
fof(f4238,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(empty_set,X1,X2),X1)
| ~ empty(empty_set)
| ~ disjoint(X2,X3)
| set_difference(empty_set,X0) = set_union2(X2,X1)
| ~ in(sK1_skl(set_difference(empty_set,X0),X1,X2),X3) ),
inference(paramodulation,[status(thm)],[f168,f3131]) ).
fof(f4243,definition,
! [X0,X1,X2,X3] :
( sQ95_spl
<=> ( in(sK1_skl(empty_set,X1,X2),X1)
| ~ disjoint(X2,X3)
| set_difference(empty_set,X0) = set_union2(X2,X1)
| ~ in(sK1_skl(set_difference(empty_set,X0),X1,X2),X3) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f4246,plain,
( ~ sQ35_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f4238,f4243,f1850]) ).
fof(f4375,plain,
! [X0,X1,X2,X3] :
( ~ disjoint(X2,X3)
| in(sK1_skl(X0,X2,empty_set),X0)
| ~ empty(empty_set)
| ~ in(sK1_skl(X0,X2,set_difference(empty_set,X1)),X3)
| X0 = set_union2(set_difference(empty_set,X1),X2) ),
inference(paramodulation,[status(thm)],[f168,f3181]) ).
fof(f4377,definition,
! [X0,X1,X2,X3] :
( sQ98_spl
<=> ( ~ disjoint(X2,X3)
| in(sK1_skl(X0,X2,empty_set),X0)
| ~ in(sK1_skl(X0,X2,set_difference(empty_set,X1)),X3)
| X0 = set_union2(set_difference(empty_set,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f4380,plain,
( ~ sQ35_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f4375,f4377,f1850]) ).
fof(f4845,plain,
( sQ13_spl
| ~ in(sK4_skl(set_difference(sK9_skl,sK10_skl),sK10_skl,set_union2(sK9_skl,sK10_skl)),sK9_skl) ),
inference(resolution,[status(thm)],[f1158,f186]) ).
fof(f4867,plain,
( sQ13_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f4845,f1504,f1156]) ).
fof(f4872,plain,
$false,
inference(sat_refutation,[status(thm)],[f983,f989,f993,f997,f1162,f1165,f1376,f1553,f1856,f1862,f1872,f1885,f1898,f1912,f1924,f1935,f1948,f1968,f2006,f2010,f2026,f2045,f2059,f2070,f2083,f2097,f2112,f2126,f2148,f2160,f2177,f2190,f2202,f2216,f2231,f2246,f2250,f2268,f2291,f2295,f2317,f2344,f2363,f2383,f2387,f2411,f2416,f2437,f2458,f2485,f2616,f3499,f3596,f3628,f3726,f3925,f3965,f4037,f4073,f4116,f4152,f4175,f4246,f4380,f4867]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU136+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:52:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 67.29/8.96 % Refutation found
% 67.29/8.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 67.29/8.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.11/9.15 % Elapsed time: 8.777590 seconds
% 4.11/9.15 % CPU time: 68.203488 seconds
% 4.11/9.15 % Total memory used: 371.044 MB
% 4.11/9.15 % Net memory used: 328.255 MB
%------------------------------------------------------------------------------