%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU236+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 : n013.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 02:19:50 PM UTC 2026
% Result : Theorem 31.48s 5.07s
% Output : CNFRefutation 26.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 293
% Syntax : Number of formulae : 1316 ( 113 unt; 237 def)
% Number of atoms : 3999 ( 535 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 4499 (1816 ~;2106 |; 248 &)
% ( 288 <=>; 40 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 251 ( 249 usr; 238 prp; 0-2 aty)
% Number of functors : 48 ( 48 usr; 9 con; 0-4 aty)
% Number of variables : 945 ( 885 !; 60 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( ( A = empty_set
=> ( B = set_meet(A)
<=> B = empty_set ) )
& ( A != empty_set
=> ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(D,A)
=> in(C,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,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(f35,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [A] :
( empty(A)
=> ( relation(relation_inverse(A))
& empty(relation_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [A] : ~ empty(succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f123,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f136,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f137,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f146,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f147,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f154,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f158,lemma,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f184,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,lemma,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
inference(negated_conjecture,[status(cth)],[f206]) ).
fof(f220,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f223,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f246,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f255,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f263,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f275,lemma,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f278,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f279,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f293,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f294,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f295,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f298,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f295]) ).
fof(f300,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f302,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f303,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f314,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f315,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f314]) ).
fof(f316,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f318,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f349,plain,
! [A] :
( ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f350,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| in(D,C) )
& ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| in(D,C) )
& ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f349]) ).
fof(f351,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| in(D,C) )
& ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| in(D,C) )
& ! [D] :
( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f350]) ).
fof(f352,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(apply(A,sK9_skl(C,B,A)),B)
& in(sK9_skl(C,B,A),relation_dom(A)) )
| in(sK9_skl(C,B,A),C) )
& ( ~ in(apply(A,sK9_skl(C,B,A)),B)
| ~ in(sK9_skl(C,B,A),relation_dom(A))
| ~ in(sK9_skl(C,B,A),C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| in(D,C) )
& ! [D] :
( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(D,sK9_skl(C,B,A))],[f351]) ).
fof(f353,plain,
! [X0,X1,X2,X3] :
( in(X3,relation_dom(X0))
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f354,plain,
! [X0,X1,X2,X3] :
( in(apply(X0,X3),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f355,plain,
! [X0,X1,X2,X3] :
( ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0))
| in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f357,plain,
! [X0,X1,X2] :
( in(sK9_skl(X1,X2,X0),relation_dom(X0))
| in(sK9_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f358,plain,
! [X0,X1,X2] :
( in(apply(X0,sK9_skl(X1,X2,X0)),X2)
| in(sK9_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f369,plain,
! [A] :
( ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f370,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f369]) ).
fof(f371,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f370]) ).
fof(f372,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK15_skl(C,B,A),B)
& in(ordered_pair(sK14_skl(C,B,A),sK15_skl(C,B,A)),A) )
| in(sK14_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK14_skl(C,B,A),E),A) )
| ~ in(sK14_skl(C,B,A),C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ( in(sK13_skl(D,C,B,A),B)
& in(ordered_pair(D,sK13_skl(D,C,B,A)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(E,sK13_skl(D,C,B,A)),skolemize(D,sK14_skl(C,B,A)),skolemize(E,sK15_skl(C,B,A))],[f371]) ).
fof(f373,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,sK13_skl(X3,X1,X2,X0)),X0)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f374,plain,
! [X0,X1,X2,X3] :
( in(sK13_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f389,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f397,plain,
! [A,B] :
( ( ( B = set_meet(A)
<=> B = empty_set )
| A != empty_set )
& ( ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(C,D)
| ~ in(D,A) ) ) )
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f398,plain,
! [A,B] :
( ( ( ( B != empty_set
| B = set_meet(A) )
& ( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ( ( ( ? [C] :
( ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| in(C,B) )
& ( ? [D] :
( ~ in(C,D)
& in(D,A) )
| ~ in(C,B) ) )
| B = set_meet(A) )
& ( ! [C] :
( ( ? [D] :
( ~ in(C,D)
& in(D,A) )
| in(C,B) )
& ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f397]) ).
fof(f399,plain,
( ! [A] :
( ( ! [B] :
( B != empty_set
| B = set_meet(A) )
& ! [B] :
( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ! [A] :
( ( ! [B] :
( ? [C] :
( ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| in(C,B) )
& ( ? [D] :
( ~ in(C,D)
& in(D,A) )
| ~ in(C,B) ) )
| B = set_meet(A) )
& ! [B] :
( ( ! [C] :
( ? [D] :
( ~ in(C,D)
& in(D,A) )
| in(C,B) )
& ! [C] :
( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(miniscoping,[status(thm)],[f398]) ).
fof(f400,plain,
( ! [A] :
( ( ! [B] :
( B != empty_set
| B = set_meet(A) )
& ! [B] :
( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ! [A] :
( ( ! [B] :
( ( ( ! [D] :
( in(sK21_skl(B,A),D)
| ~ in(D,A) )
| in(sK21_skl(B,A),B) )
& ( ( ~ in(sK21_skl(B,A),sK22_skl(B,A))
& in(sK22_skl(B,A),A) )
| ~ in(sK21_skl(B,A),B) ) )
| B = set_meet(A) )
& ! [B] :
( ( ! [C] :
( ( ~ in(C,sK20_skl(C,B,A))
& in(sK20_skl(C,B,A),A) )
| in(C,B) )
& ! [C] :
( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl]),skolemize(D,sK20_skl(C,B,A)),skolemize(C,sK21_skl(B,A)),skolemize(D,sK22_skl(B,A))],[f399]) ).
fof(f402,plain,
! [X0,X1,X2] :
( in(sK20_skl(X2,X1,X0),X0)
| in(X2,X1)
| X1 != set_meet(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f407,plain,
! [X0,X1] :
( X1 = empty_set
| X1 != set_meet(X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f409,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)],[f25]) ).
fof(f410,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)],[f409]) ).
fof(f411,plain,
( ! [A,B] :
( ( ( sK23_skl(B,A) = A
| in(sK23_skl(B,A),B) )
& ( sK23_skl(B,A) != A
| ~ in(sK23_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,[sK23_skl]),skolemize(C,sK23_skl(B,A))],[f410]) ).
fof(f412,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f411]) ).
fof(f416,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f417,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f416]) ).
fof(f418,plain,
( ! [A] :
( in(sK24_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(B,sK24_skl(A))],[f417]) ).
fof(f419,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
! [X0] :
( in(sK24_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f421,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f422,plain,
( ! [A,B] :
( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(miniscoping,[status(thm)],[f421]) ).
fof(f423,plain,
( ! [A,B] :
( ( ( subset(sK25_skl(B,A),A)
| in(sK25_skl(B,A),B) )
& ( ~ subset(sK25_skl(B,A),A)
| ~ in(sK25_skl(B,A),B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(C,sK25_skl(B,A))],[f422]) ).
fof(f425,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f428,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f429,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(NNF_transformation,[status(thm)],[f428]) ).
fof(f430,plain,
( ! [A] :
( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
( ! [A] :
( ( ~ subset(sK26_skl(A),A)
& in(sK26_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl]),skolemize(B,sK26_skl(A))],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f443,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f444,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(NNF_transformation,[status(thm)],[f443]) ).
fof(f445,plain,
( ! [A] :
( ( ! [B] :
( ~ empty(B)
| element(B,A) )
& ! [B] :
( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ! [A] :
( ( ! [B] :
( ~ in(B,A)
| element(B,A) )
& ! [B] :
( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(miniscoping,[status(thm)],[f444]) ).
fof(f446,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f445]) ).
fof(f459,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)],[f32]) ).
fof(f460,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)],[f459]) ).
fof(f461,plain,
( ! [A,B,C] :
( ( ( in(sK30_skl(C,B,A),B)
| in(sK30_skl(C,B,A),A)
| in(sK30_skl(C,B,A),C) )
& ( ( ~ in(sK30_skl(C,B,A),B)
& ~ in(sK30_skl(C,B,A),A) )
| ~ in(sK30_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,[sK30_skl]),skolemize(D,sK30_skl(C,B,A))],[f460]) ).
fof(f462,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f461]) ).
fof(f487,plain,
! [A] :
( ! [B] :
( ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f488,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f487]) ).
fof(f489,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK38_skl(B,A),sK39_skl(B,A)),B)
& in(ordered_pair(sK38_skl(B,A),sK39_skl(B,A)),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl]),skolemize(C,sK38_skl(B,A)),skolemize(D,sK39_skl(B,A))],[f488]) ).
fof(f491,plain,
! [X0,X1] :
( in(ordered_pair(sK38_skl(X1,X0),sK39_skl(X1,X0)),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f489]) ).
fof(f509,plain,
! [A] :
( ! [B,C] :
( ( ( C = apply(A,B)
<=> C = empty_set )
| in(B,relation_dom(A)) )
& ( ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f510,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f509]) ).
fof(f511,plain,
! [A] :
( ( ! [B] :
( ( ! [C] :
( C != empty_set
| C = apply(A,B) )
& ! [C] :
( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ! [B] :
( ( ! [C] :
( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ! [C] :
( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f510]) ).
fof(f512,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
| X2 != apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f511]) ).
fof(f513,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f511]) ).
fof(f514,plain,
! [X0,X1,X2] :
( X2 = empty_set
| X2 != apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f511]) ).
fof(f516,plain,
! [A] :
( ( ~ epsilon_connected(A)
| ~ epsilon_transitive(A)
| ordinal(A) )
& ( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f517,plain,
( ! [A] :
( ~ epsilon_connected(A)
| ~ epsilon_transitive(A)
| ordinal(A) )
& ! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ) ),
inference(miniscoping,[status(thm)],[f516]) ).
fof(f518,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f517]) ).
fof(f519,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f517]) ).
fof(f530,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f531,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(miniscoping,[status(thm)],[f530]) ).
fof(f532,plain,
( ! [A,B] :
( ( ( ( in(sK47_skl(B,A),A)
& in(sK46_skl(B,A),sK47_skl(B,A)) )
| in(sK46_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK46_skl(B,A),D) )
| ~ in(sK46_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK45_skl(C,B,A),A)
& in(C,sK45_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl,sK47_skl]),skolemize(D,sK45_skl(C,B,A)),skolemize(C,sK46_skl(B,A)),skolemize(D,sK47_skl(B,A))],[f531]) ).
fof(f535,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f532]) ).
fof(f548,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f549,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f548]) ).
fof(f550,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f549]) ).
fof(f551,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK50_skl(B,A) = apply(A,sK51_skl(B,A))
& in(sK51_skl(B,A),relation_dom(A)) )
| in(sK50_skl(B,A),B) )
& ( ! [D] :
( sK50_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK50_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK49_skl(C,B,A))
& in(sK49_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(D,sK49_skl(C,B,A)),skolemize(C,sK50_skl(B,A)),skolemize(D,sK51_skl(B,A))],[f550]) ).
fof(f552,plain,
! [X0,X1,X2] :
( in(sK49_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f551]) ).
fof(f553,plain,
! [X0,X1,X2] :
( X2 = apply(X0,sK49_skl(X2,X1,X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f551]) ).
fof(f554,plain,
! [X0,X1,X2,X3] :
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f551]) ).
fof(f556,plain,
! [X0,X1] :
( in(sK51_skl(X1,X0),relation_dom(X0))
| in(sK50_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f551]) ).
fof(f557,plain,
! [X0,X1] :
( sK50_skl(X1,X0) = apply(X0,sK51_skl(X1,X0))
| in(sK50_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f551]) ).
fof(f569,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f570,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f569]) ).
fof(f571,plain,
! [A] :
( ! [B] :
( ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f572,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ( ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B = relation_inverse(A) )
& ( ! [C,D] :
( ( ~ in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f571]) ).
fof(f573,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ( ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B = relation_inverse(A) )
& ( ( ! [C,D] :
( ~ in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f572]) ).
fof(f574,plain,
! [A] :
( ! [B] :
( ( ( ( ( in(ordered_pair(sK56_skl(B,A),sK55_skl(B,A)),A)
| in(ordered_pair(sK55_skl(B,A),sK56_skl(B,A)),B) )
& ( ~ in(ordered_pair(sK56_skl(B,A),sK55_skl(B,A)),A)
| ~ in(ordered_pair(sK55_skl(B,A),sK56_skl(B,A)),B) ) )
| B = relation_inverse(A) )
& ( ( ! [C,D] :
( ~ in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl]),skolemize(C,sK55_skl(B,A)),skolemize(D,sK56_skl(B,A))],[f573]) ).
fof(f575,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1)
| X1 != relation_inverse(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f574]) ).
fof(f583,plain,
! [A] :
( ( one_to_one(A)
<=> ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f584,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f583]) ).
fof(f585,plain,
! [A] :
( ( ( ( sK57_skl(A) != sK58_skl(A)
& apply(A,sK57_skl(A)) = apply(A,sK58_skl(A))
& in(sK58_skl(A),relation_dom(A))
& in(sK57_skl(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57_skl,sK58_skl]),skolemize(B,sK57_skl(A)),skolemize(C,sK58_skl(A))],[f584]) ).
fof(f586,plain,
! [X0,X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f585]) ).
fof(f622,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f623,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f622]) ).
fof(f628,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f646,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f647,plain,
! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f646]) ).
fof(f649,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f650,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f659,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f662,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f670,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f671,plain,
one_to_one(empty_set),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f673,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f674,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f675,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f679,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f103]) ).
fof(f680,plain,
! [A] :
( ! [B] : ~ empty(set_union2(A,B))
| empty(A) ),
inference(miniscoping,[status(thm)],[f679]) ).
fof(f681,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f680]) ).
fof(f685,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f105]) ).
fof(f687,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f685]) ).
fof(f688,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f685]) ).
fof(f689,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f685]) ).
fof(f729,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f771,plain,
( function(sK66_skl)
& relation(sK66_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(A,sK66_skl)],[f136]) ).
fof(f772,plain,
relation(sK66_skl),
inference(cnf_transformation,[status(thm)],[f771]) ).
fof(f773,plain,
function(sK66_skl),
inference(cnf_transformation,[status(thm)],[f771]) ).
fof(f774,plain,
( ordinal(sK67_skl)
& epsilon_connected(sK67_skl)
& epsilon_transitive(sK67_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(A,sK67_skl)],[f137]) ).
fof(f775,plain,
epsilon_transitive(sK67_skl),
inference(cnf_transformation,[status(thm)],[f774]) ).
fof(f776,plain,
epsilon_connected(sK67_skl),
inference(cnf_transformation,[status(thm)],[f774]) ).
fof(f777,plain,
ordinal(sK67_skl),
inference(cnf_transformation,[status(thm)],[f774]) ).
fof(f778,plain,
( relation(sK68_skl)
& empty(sK68_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68_skl]),skolemize(A,sK68_skl)],[f138]) ).
fof(f779,plain,
empty(sK68_skl),
inference(cnf_transformation,[status(thm)],[f778]) ).
fof(f802,plain,
! [A] :
( empty(sK74_skl(A))
& element(sK74_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74_skl]),skolemize(B,sK74_skl(A))],[f144]) ).
fof(f803,plain,
! [X0] : element(sK74_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f802]) ).
fof(f804,plain,
! [X0] : empty(sK74_skl(X0)),
inference(cnf_transformation,[status(thm)],[f802]) ).
fof(f807,plain,
( one_to_one(sK76_skl)
& function(sK76_skl)
& relation(sK76_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76_skl]),skolemize(A,sK76_skl)],[f146]) ).
fof(f808,plain,
relation(sK76_skl),
inference(cnf_transformation,[status(thm)],[f807]) ).
fof(f809,plain,
function(sK76_skl),
inference(cnf_transformation,[status(thm)],[f807]) ).
fof(f810,plain,
one_to_one(sK76_skl),
inference(cnf_transformation,[status(thm)],[f807]) ).
fof(f811,plain,
( ordinal(sK77_skl)
& epsilon_connected(sK77_skl)
& epsilon_transitive(sK77_skl)
& ~ empty(sK77_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77_skl]),skolemize(A,sK77_skl)],[f147]) ).
fof(f812,plain,
~ empty(sK77_skl),
inference(cnf_transformation,[status(thm)],[f811]) ).
fof(f813,plain,
epsilon_transitive(sK77_skl),
inference(cnf_transformation,[status(thm)],[f811]) ).
fof(f814,plain,
epsilon_connected(sK77_skl),
inference(cnf_transformation,[status(thm)],[f811]) ).
fof(f815,plain,
ordinal(sK77_skl),
inference(cnf_transformation,[status(thm)],[f811]) ).
fof(f819,plain,
( function(sK79_skl)
& relation_empty_yielding(sK79_skl)
& relation(sK79_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79_skl]),skolemize(A,sK79_skl)],[f149]) ).
fof(f820,plain,
relation(sK79_skl),
inference(cnf_transformation,[status(thm)],[f819]) ).
fof(f822,plain,
function(sK79_skl),
inference(cnf_transformation,[status(thm)],[f819]) ).
fof(f829,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f153]) ).
fof(f830,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f829]) ).
fof(f831,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f830]) ).
fof(f832,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f830]) ).
fof(f833,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f154]) ).
fof(f834,plain,
! [A] :
( ordinal_subset(A,A)
| ! [B] : ~ ordinal(B)
| ~ ordinal(A) ),
inference(miniscoping,[status(thm)],[f833]) ).
fof(f835,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f834]) ).
fof(f845,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f932,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f938,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f959,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f194]) ).
fof(f960,plain,
! [B] :
( ! [A] :
( ordinal(A)
| ~ in(A,B) )
| ~ ordinal(B) ),
inference(miniscoping,[status(thm)],[f959]) ).
fof(f961,plain,
! [X0,X1] :
( ordinal(X1)
| ~ in(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f960]) ).
fof(f962,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f195]) ).
fof(f963,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f962]) ).
fof(f980,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f995,plain,
? [A] :
( ? [B] :
( ( in(A,B)
<~> ordinal_subset(succ(A),B) )
& ordinal(B) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f207]) ).
fof(f996,plain,
? [A] :
( ? [B] :
( ( ~ ordinal_subset(succ(A),B)
| ~ in(A,B) )
& ( ordinal_subset(succ(A),B)
| in(A,B) )
& ordinal(B) )
& ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f995]) ).
fof(f997,plain,
( ( ~ ordinal_subset(succ(sK86_skl),sK87_skl)
| ~ in(sK86_skl,sK87_skl) )
& ( ordinal_subset(succ(sK86_skl),sK87_skl)
| in(sK86_skl,sK87_skl) )
& ordinal(sK87_skl)
& ordinal(sK86_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86_skl,sK87_skl]),skolemize(A,sK86_skl),skolemize(B,sK87_skl)],[f996]) ).
fof(f998,plain,
ordinal(sK86_skl),
inference(cnf_transformation,[status(thm)],[f997]) ).
fof(f999,plain,
ordinal(sK87_skl),
inference(cnf_transformation,[status(thm)],[f997]) ).
fof(f1000,plain,
( ordinal_subset(succ(sK86_skl),sK87_skl)
| in(sK86_skl,sK87_skl) ),
inference(cnf_transformation,[status(thm)],[f997]) ).
fof(f1001,plain,
( ~ ordinal_subset(succ(sK86_skl),sK87_skl)
| ~ in(sK86_skl,sK87_skl) ),
inference(cnf_transformation,[status(thm)],[f997]) ).
fof(f1042,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f220]) ).
fof(f1043,plain,
! [A,C] :
( ~ in(C,A)
| ! [B] :
( ~ in(B,C)
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f1042]) ).
fof(f1044,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1043]) ).
fof(f1055,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f223]) ).
fof(f1056,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f1055]) ).
fof(f1121,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f1122,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f1150,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f255]) ).
fof(f1151,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1150]) ).
fof(f1177,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f1216,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f1253,definition,
! [X0] :
( sQ0_spl
<=> ( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1256,definition,
! [X1] :
( sQ1_spl
<=> ~ ordinal(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1257,plain,
! [X0] :
( ~ sQ1_spl
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f1256]) ).
fof(f1259,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f835,f1253,f1256]) ).
fof(f1260,definition,
( sQ2_spl
<=> in(sK86_skl,sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1261,plain,
( ~ sQ2_spl
| in(sK86_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f1260]) ).
fof(f1263,definition,
( sQ3_spl
<=> ordinal_subset(succ(sK86_skl),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1264,plain,
( ~ sQ3_spl
| ordinal_subset(succ(sK86_skl),sK87_skl) ),
inference(component_clause,[status(thm)],[f1263]) ).
fof(f1265,plain,
( sQ3_spl
| ~ ordinal_subset(succ(sK86_skl),sK87_skl) ),
inference(component_clause,[status(thm)],[f1263]) ).
fof(f1266,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1000,f1260,f1263]) ).
fof(f1267,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1001,f1260,f1263]) ).
fof(f1271,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f316]) ).
fof(f1281,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f353]) ).
fof(f1282,plain,
! [X0,X1,X2] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f354]) ).
fof(f1283,plain,
! [X0,X1,X2] :
( ~ in(apply(X0,X1),X2)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f355]) ).
fof(f1287,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0)),X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f373]) ).
fof(f1288,plain,
! [X0,X1,X2] :
( in(sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f374]) ).
fof(f1293,plain,
! [X0,X1] :
( in(sK20_skl(X1,set_meet(X0),X0),X0)
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(destructive_equality_resolution,[status(thm)],[f402]) ).
fof(f1295,plain,
set_meet(empty_set) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f407]) ).
fof(f1297,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f412]) ).
fof(f1299,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f419]) ).
fof(f1301,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f425]) ).
fof(f1305,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f462]) ).
fof(f1313,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f512]) ).
fof(f1314,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f514]) ).
fof(f1320,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f535]) ).
fof(f1324,plain,
! [X0,X1] :
( in(sK49_skl(X1,relation_rng(X0),X0),relation_dom(X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f552]) ).
fof(f1325,plain,
! [X0,X1] :
( X1 = apply(X0,sK49_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f553]) ).
fof(f1326,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f554]) ).
fof(f1329,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f575]) ).
fof(f1360,plain,
! [X0] : ~ in(succ(X0),X0),
inference(resolution,[status(thm)],[f845,f279]) ).
fof(f1362,plain,
! [X0,X1] :
( ~ in(succ(X1),X0)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f1044,f845]) ).
fof(f1365,plain,
! [X0,X1] :
( ~ ordinal(X1)
| in(succ(X1),X0)
| X0 = succ(X1)
| in(X0,succ(X1))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f963,f689]) ).
fof(f1366,plain,
! [X0] :
( in(empty_set,X0)
| X0 = empty_set
| in(X0,empty_set)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f963,f675]) ).
fof(f1367,plain,
! [X0] :
( in(sK87_skl,X0)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f963,f999]) ).
fof(f1369,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ ordinal(X2)
| in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f963,f961]) ).
fof(f1375,definition,
( sQ4_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1377,plain,
( sQ4_spl
| ~ ordinal(empty_set) ),
inference(component_clause,[status(thm)],[f1375]) ).
fof(f1378,definition,
( sQ5_spl
<=> in(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1379,plain,
( ~ sQ5_spl
| in(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f1378]) ).
fof(f1381,definition,
( sQ6_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1388,plain,
( ~ sQ2_spl
| ~ in(sK87_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f1261,f279]) ).
fof(f1389,plain,
( sQ3_spl
| ~ subset(succ(sK86_skl),sK87_skl)
| ~ ordinal(sK87_skl)
| ~ ordinal(succ(sK86_skl)) ),
inference(resolution,[status(thm)],[f1265,f832]) ).
fof(f1391,definition,
( sQ7_spl
<=> ordinal(succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
( ~ sQ7_spl
| ordinal(succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f1391]) ).
fof(f1393,plain,
( sQ7_spl
| ~ ordinal(succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f1391]) ).
fof(f1394,definition,
( sQ8_spl
<=> ordinal(sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1396,plain,
( sQ8_spl
| ~ ordinal(sK87_skl) ),
inference(component_clause,[status(thm)],[f1394]) ).
fof(f1397,definition,
( sQ9_spl
<=> subset(succ(sK86_skl),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1398,plain,
( ~ sQ9_spl
| subset(succ(sK86_skl),sK87_skl) ),
inference(component_clause,[status(thm)],[f1397]) ).
fof(f1399,plain,
( sQ9_spl
| ~ subset(succ(sK86_skl),sK87_skl) ),
inference(component_clause,[status(thm)],[f1397]) ).
fof(f1400,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1389,f1391,f1394,f1397,f1263]) ).
fof(f1401,definition,
( sQ10_spl
<=> ordinal_subset(sK87_skl,succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1402,plain,
( ~ sQ10_spl
| ordinal_subset(sK87_skl,succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f1401]) ).
fof(f1403,plain,
( sQ10_spl
| ~ ordinal_subset(sK87_skl,succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f1401]) ).
fof(f1405,plain,
! [X0] :
( in(sK67_skl,X0)
| X0 = sK67_skl
| in(X0,sK67_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f777,f963]) ).
fof(f1406,plain,
ordinal(sK68_skl),
inference(resolution,[status(thm)],[f779,f298]) ).
fof(f1409,plain,
! [X0,X1] :
( ~ in(X1,sK87_skl)
| ~ in(X0,X1)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1367,f1044]) ).
fof(f1413,definition,
( sQ11_spl
<=> in(sK87_skl,sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1414,plain,
( ~ sQ11_spl
| in(sK87_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f1413]) ).
fof(f1415,plain,
( sQ11_spl
| ~ in(sK87_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f1413]) ).
fof(f1416,definition,
( sQ12_spl
<=> sK87_skl = sK87_skl ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1427,definition,
( sQ13_spl
<=> in(sK87_skl,sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1428,plain,
( ~ sQ13_spl
| in(sK87_skl,sK86_skl) ),
inference(component_clause,[status(thm)],[f1427]) ).
fof(f1430,definition,
( sQ14_spl
<=> sK87_skl = sK86_skl ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1431,plain,
( ~ sQ14_spl
| sK87_skl = sK86_skl ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1432,plain,
( sQ14_spl
| sK87_skl != sK86_skl ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1434,definition,
( sQ15_spl
<=> ordinal(sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1436,plain,
( sQ15_spl
| ~ ordinal(sK86_skl) ),
inference(component_clause,[status(thm)],[f1434]) ).
fof(f1437,definition,
( sQ16_spl
<=> in(sK86_skl,sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1438,plain,
( ~ sQ16_spl
| in(sK86_skl,sK86_skl) ),
inference(component_clause,[status(thm)],[f1437]) ).
fof(f1440,definition,
( sQ17_spl
<=> sK86_skl = sK86_skl ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f1445,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1396,f999]) ).
fof(f1446,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1445]) ).
fof(f1449,plain,
( ~ sQ13_spl
| ~ in(sK86_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f1428,f279]) ).
fof(f1452,plain,
! [X0] :
( sK87_skl = empty_set
| in(sK87_skl,empty_set)
| ~ ordinal(sK87_skl)
| ~ in(X0,empty_set)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1409,f1366]) ).
fof(f1461,definition,
! [X0] :
( sQ20_spl
<=> ( ~ in(X0,empty_set)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1464,definition,
( sQ21_spl
<=> in(sK87_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1465,plain,
( ~ sQ21_spl
| in(sK87_skl,empty_set) ),
inference(component_clause,[status(thm)],[f1464]) ).
fof(f1467,definition,
( sQ22_spl
<=> sK87_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1468,plain,
( ~ sQ22_spl
| sK87_skl = empty_set ),
inference(component_clause,[status(thm)],[f1467]) ).
fof(f1470,plain,
( sQ22_spl
| sQ21_spl
| ~ sQ8_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1452,f1461,f1394,f1464,f1467]) ).
fof(f1493,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1406,f1257]) ).
fof(f1496,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1493]) ).
fof(f1500,plain,
( ~ sQ11_spl
| ~ in(sK87_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f1414,f1044]) ).
fof(f1505,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1500,f1414]) ).
fof(f1506,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f1505]) ).
fof(f1508,definition,
( sQ23_spl
<=> epsilon_transitive(succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1509,plain,
( ~ sQ23_spl
| epsilon_transitive(succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f1508]) ).
fof(f1510,plain,
( sQ23_spl
| ~ epsilon_transitive(succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f1508]) ).
fof(f1511,definition,
( sQ24_spl
<=> epsilon_connected(succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1513,plain,
( sQ24_spl
| ~ epsilon_connected(succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f1511]) ).
fof(f1525,plain,
! [X0,X1] :
( ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f963,f294]) ).
fof(f1526,plain,
! [X0] :
( in(sK77_skl,X0)
| X0 = sK77_skl
| in(X0,sK77_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f815,f963]) ).
fof(f1542,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| in(sK87_skl,sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f1431,f1261]) ).
fof(f1543,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1542,f1415]) ).
fof(f1544,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1543]) ).
fof(f1545,plain,
! [X0] :
( in(sK86_skl,X0)
| X0 = sK86_skl
| in(X0,sK86_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f998,f963]) ).
fof(f1552,plain,
! [X0] :
( in(sK67_skl,X0)
| X0 = sK67_skl
| in(X0,sK67_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f777,f963]) ).
fof(f1553,plain,
( ~ sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1465,f1299]) ).
fof(f1554,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1553]) ).
fof(f1560,plain,
( sQ9_spl
| ~ ordinal_subset(succ(sK86_skl),sK87_skl)
| ~ ordinal(sK87_skl)
| ~ ordinal(succ(sK86_skl)) ),
inference(resolution,[status(thm)],[f1399,f831]) ).
fof(f1561,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1560,f1391,f1394,f1263,f1397]) ).
fof(f1576,definition,
( sQ25_spl
<=> in(empty_set,sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f1577,plain,
( ~ sQ25_spl
| in(empty_set,sK86_skl) ),
inference(component_clause,[status(thm)],[f1576]) ).
fof(f1579,definition,
( sQ26_spl
<=> empty_set = sK86_skl ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1580,plain,
( ~ sQ26_spl
| empty_set = sK86_skl ),
inference(component_clause,[status(thm)],[f1579]) ).
fof(f1589,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| in(sK87_skl,empty_set) ),
inference(backward_demodulation,[status(thm)],[f1580,f1428]) ).
fof(f1596,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1589,f1464,f1579,f1427]) ).
fof(f1597,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1377,f675]) ).
fof(f1598,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f1597]) ).
fof(f1609,plain,
( sQ7_spl
| ~ ordinal(sK86_skl) ),
inference(resolution,[status(thm)],[f689,f1393]) ).
fof(f1611,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1609,f998]) ).
fof(f1612,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1611]) ).
fof(f1635,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| subset(succ(sK87_skl),sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f1431,f1398]) ).
fof(f1642,plain,
! [X0] :
( ~ ordinal(X0)
| empty_set = succ(X0)
| in(empty_set,succ(X0))
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f1365,f1299]) ).
fof(f1652,definition,
! [X0] :
( sQ27_spl
<=> ( ~ ordinal(X0)
| empty_set = succ(X0)
| in(empty_set,succ(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
( sQ27_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1642,f1375,f1652]) ).
fof(f1665,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f300,f932]) ).
fof(f1670,plain,
! [X0] : sK74_skl(X0) = empty_set,
inference(resolution,[status(thm)],[f1151,f804]) ).
fof(f1691,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ subset(sK87_skl,succ(sK87_skl))
| sK87_skl = succ(sK87_skl) ),
inference(resolution,[status(thm)],[f318,f1635]) ).
fof(f1693,plain,
! [X0,X1] :
( ~ ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f318,f831]) ).
fof(f1695,definition,
( sQ28_spl
<=> sK87_skl = succ(sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1696,plain,
( ~ sQ28_spl
| sK87_skl = succ(sK87_skl) ),
inference(component_clause,[status(thm)],[f1695]) ).
fof(f1697,plain,
( sQ28_spl
| sK87_skl != succ(sK87_skl) ),
inference(component_clause,[status(thm)],[f1695]) ).
fof(f1698,definition,
( sQ29_spl
<=> subset(sK87_skl,succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1700,plain,
( sQ29_spl
| ~ subset(sK87_skl,succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f1698]) ).
fof(f1701,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f1691,f1695,f1698,f1430,f1397]) ).
fof(f1725,definition,
! [X0] :
( sQ30_spl
<=> ( in(sK86_skl,X0)
| X0 = sK86_skl
| in(X0,sK86_skl)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1729,definition,
! [X0] :
( sQ31_spl
<=> ( in(empty_set,X0)
| X0 = empty_set
| in(X0,empty_set)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1743,definition,
( sQ32_spl
<=> in(empty_set,sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1746,definition,
( sQ33_spl
<=> empty_set = sK67_skl ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1747,plain,
( ~ sQ33_spl
| empty_set = sK67_skl ),
inference(component_clause,[status(thm)],[f1746]) ).
fof(f1753,definition,
! [X1] :
( sQ35_spl
<=> ( in(sK67_skl,X1)
| X1 = sK67_skl
| in(X1,sK67_skl)
| ~ ordinal(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f1757,definition,
( sQ36_spl
<=> ordinal(sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f1759,plain,
( sQ36_spl
| ~ ordinal(sK67_skl) ),
inference(component_clause,[status(thm)],[f1757]) ).
fof(f1760,definition,
( sQ37_spl
<=> in(sK67_skl,sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1761,plain,
( ~ sQ37_spl
| in(sK67_skl,sK67_skl) ),
inference(component_clause,[status(thm)],[f1760]) ).
fof(f1763,definition,
( sQ38_spl
<=> sK67_skl = sK67_skl ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1777,plain,
succ(empty_set) = singleton(empty_set),
inference(paramodulation,[status(thm)],[f389,f1665]) ).
fof(f1802,plain,
! [X0,X1] :
( ~ ordinal(X0)
| in(sK87_skl,X1)
| X1 = sK87_skl
| in(X1,sK87_skl)
| ~ ordinal(X1)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1367,f1369]) ).
fof(f1811,definition,
( sQ39_spl
<=> in(empty_set,sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1815,definition,
! [X0] :
( sQ40_spl
<=> ( ~ ordinal(X0)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1816,plain,
! [X0] :
( ~ sQ40_spl
| ~ ordinal(X0)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f1815]) ).
fof(f1818,definition,
! [X1] :
( sQ41_spl
<=> ( in(sK87_skl,X1)
| X1 = sK87_skl
| in(X1,sK87_skl)
| ~ ordinal(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1821,plain,
( sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1802,f1815,f1818]) ).
fof(f1824,plain,
! [X0] :
( ~ sQ40_spl
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1816]) ).
fof(f1928,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1436,f998]) ).
fof(f1929,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1928]) ).
fof(f1952,plain,
! [X0] :
( ~ ordinal(empty_set)
| in(singleton(empty_set),X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f1777,f1365]) ).
fof(f1954,plain,
( epsilon_transitive(singleton(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f1777,f687]) ).
fof(f1955,plain,
( epsilon_connected(singleton(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f1777,f688]) ).
fof(f1956,plain,
( ordinal(singleton(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f1777,f689]) ).
fof(f1962,definition,
! [X0] :
( sQ44_spl
<=> ( in(singleton(empty_set),X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1965,plain,
( ~ sQ4_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f1952,f1962,f1375]) ).
fof(f1966,definition,
( sQ45_spl
<=> epsilon_transitive(singleton(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1967,plain,
( ~ sQ45_spl
| epsilon_transitive(singleton(empty_set)) ),
inference(component_clause,[status(thm)],[f1966]) ).
fof(f1969,plain,
( sQ45_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1954,f1375,f1966]) ).
fof(f1970,definition,
( sQ46_spl
<=> epsilon_connected(singleton(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1973,plain,
( sQ46_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1955,f1375,f1970]) ).
fof(f1974,definition,
( sQ47_spl
<=> ordinal(singleton(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1975,plain,
( ~ sQ47_spl
| ordinal(singleton(empty_set)) ),
inference(component_clause,[status(thm)],[f1974]) ).
fof(f1977,plain,
( sQ47_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1956,f1375,f1974]) ).
fof(f1980,plain,
! [X0] :
( in(empty_set,X0)
| X0 = empty_set
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1366,f1299]) ).
fof(f1981,plain,
( empty_set = empty_set
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f1980,f1299]) ).
fof(f1989,plain,
( sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1981,f1375,f1381]) ).
fof(f1990,definition,
! [X0] :
( sQ48_spl
<=> ( ~ ordinal(X0)
| X0 = empty_set
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1991,plain,
! [X0] :
( ~ sQ48_spl
| ~ ordinal(X0)
| X0 = empty_set
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f1990]) ).
fof(f2009,plain,
! [X0] : subset(X0,succ(X0)),
inference(paramodulation,[status(thm)],[f389,f1177]) ).
fof(f2039,definition,
( sQ49_spl
<=> ordinal(succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f2040,plain,
( ~ sQ49_spl
| ordinal(succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f2039]) ).
fof(f2041,plain,
( sQ49_spl
| ~ ordinal(succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f2039]) ).
fof(f2061,definition,
( sQ51_spl
<=> epsilon_transitive(sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f2062,plain,
( ~ sQ51_spl
| epsilon_transitive(sK86_skl) ),
inference(component_clause,[status(thm)],[f2061]) ).
fof(f2065,definition,
( sQ52_spl
<=> epsilon_connected(sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f2132,plain,
empty(relation_inverse(empty_set)),
inference(resolution,[status(thm)],[f647,f649]) ).
fof(f2136,plain,
relation_inverse(empty_set) = empty_set,
inference(resolution,[status(thm)],[f2132,f1151]) ).
fof(f2139,definition,
( sQ54_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f2141,plain,
( sQ54_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f2139]) ).
fof(f2164,plain,
! [X0] :
( ~ sQ45_spl
| ~ epsilon_connected(singleton(empty_set))
| in(singleton(empty_set),X0)
| X0 = singleton(empty_set)
| in(X0,singleton(empty_set))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1525,f1967]) ).
fof(f2166,plain,
! [X0] :
( ~ epsilon_connected(sK77_skl)
| in(sK77_skl,X0)
| X0 = sK77_skl
| in(X0,sK77_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1525,f813]) ).
fof(f2170,definition,
! [X0] :
( sQ55_spl
<=> ( in(singleton(empty_set),X0)
| X0 = singleton(empty_set)
| in(X0,singleton(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f2173,plain,
( ~ sQ45_spl
| ~ sQ46_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f2164,f2170,f1970,f1966]) ).
fof(f2174,definition,
! [X0] :
( sQ56_spl
<=> ( in(sK77_skl,X0)
| X0 = sK77_skl
| in(X0,sK77_skl)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f2177,definition,
( sQ57_spl
<=> epsilon_connected(sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f2179,plain,
( sQ57_spl
| ~ epsilon_connected(sK77_skl) ),
inference(component_clause,[status(thm)],[f2177]) ).
fof(f2180,plain,
( ~ sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f2166,f2174,f2177]) ).
fof(f2181,definition,
( sQ58_spl
<=> epsilon_connected(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f2183,plain,
( sQ58_spl
| ~ epsilon_connected(empty_set) ),
inference(component_clause,[status(thm)],[f2181]) ).
fof(f2194,definition,
( sQ59_spl
<=> in(empty_set,sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
( ~ sQ59_spl
| in(empty_set,sK77_skl) ),
inference(component_clause,[status(thm)],[f2194]) ).
fof(f2197,definition,
( sQ60_spl
<=> empty_set = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2198,plain,
( ~ sQ60_spl
| empty_set = sK77_skl ),
inference(component_clause,[status(thm)],[f2197]) ).
fof(f2199,plain,
( sQ60_spl
| empty_set != sK77_skl ),
inference(component_clause,[status(thm)],[f2197]) ).
fof(f2205,definition,
( sQ62_spl
<=> ordinal(sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2207,plain,
( sQ62_spl
| ~ ordinal(sK77_skl) ),
inference(component_clause,[status(thm)],[f2205]) ).
fof(f2208,definition,
( sQ63_spl
<=> in(sK77_skl,sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2209,plain,
( ~ sQ63_spl
| in(sK77_skl,sK77_skl) ),
inference(component_clause,[status(thm)],[f2208]) ).
fof(f2210,plain,
( sQ63_spl
| ~ in(sK77_skl,sK77_skl) ),
inference(component_clause,[status(thm)],[f2208]) ).
fof(f2211,definition,
( sQ64_spl
<=> sK77_skl = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2226,plain,
( ~ sQ60_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f2198,f812]) ).
fof(f2229,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2226,f649]) ).
fof(f2230,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f2229]) ).
fof(f2267,plain,
! [X0,X1] :
( in(X0,relation_dom(sK79_skl))
| ~ in(X0,relation_inverse_image(sK79_skl,X1))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1281,f822]) ).
fof(f2268,plain,
! [X0,X1] :
( in(X0,relation_dom(sK76_skl))
| ~ in(X0,relation_inverse_image(sK76_skl,X1))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1281,f809]) ).
fof(f2269,plain,
! [X0,X1] :
( in(X0,relation_dom(sK66_skl))
| ~ in(X0,relation_inverse_image(sK66_skl,X1))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1281,f773]) ).
fof(f2270,plain,
! [X0,X1] :
( in(X0,relation_dom(empty_set))
| ~ in(X0,relation_inverse_image(empty_set,X1))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1281,f670]) ).
fof(f2274,definition,
( sQ65_spl
<=> relation(sK79_skl) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2276,plain,
( sQ65_spl
| ~ relation(sK79_skl) ),
inference(component_clause,[status(thm)],[f2274]) ).
fof(f2277,definition,
! [X0,X1] :
( sQ66_spl
<=> ( in(X0,relation_dom(sK79_skl))
| ~ in(X0,relation_inverse_image(sK79_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2280,plain,
( sQ66_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f2267,f2274,f2277]) ).
fof(f2281,definition,
( sQ67_spl
<=> relation(sK76_skl) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2283,plain,
( sQ67_spl
| ~ relation(sK76_skl) ),
inference(component_clause,[status(thm)],[f2281]) ).
fof(f2284,definition,
! [X0,X1] :
( sQ68_spl
<=> ( in(X0,relation_dom(sK76_skl))
| ~ in(X0,relation_inverse_image(sK76_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2287,plain,
( sQ68_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f2268,f2281,f2284]) ).
fof(f2288,definition,
( sQ69_spl
<=> relation(sK66_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2290,plain,
( sQ69_spl
| ~ relation(sK66_skl) ),
inference(component_clause,[status(thm)],[f2288]) ).
fof(f2291,definition,
! [X0,X1] :
( sQ70_spl
<=> ( in(X0,relation_dom(sK66_skl))
| ~ in(X0,relation_inverse_image(sK66_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f2294,plain,
( sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f2269,f2288,f2291]) ).
fof(f2295,definition,
! [X0,X1] :
( sQ71_spl
<=> ( in(X0,relation_dom(empty_set))
| ~ in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f2296,plain,
! [X0,X1] :
( ~ sQ71_spl
| in(X0,relation_dom(empty_set))
| ~ in(X0,relation_inverse_image(empty_set,X1)) ),
inference(component_clause,[status(thm)],[f2295]) ).
fof(f2298,plain,
( sQ71_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2270,f2139,f2295]) ).
fof(f2300,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2141,f650]) ).
fof(f2301,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f2300]) ).
fof(f2302,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2290,f772]) ).
fof(f2303,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f2302]) ).
fof(f2304,plain,
( sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2283,f808]) ).
fof(f2305,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f2304]) ).
fof(f2306,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2276,f820]) ).
fof(f2307,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f2306]) ).
fof(f2308,plain,
! [X0,X1] :
( ~ sQ71_spl
| in(X0,empty_set)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ),
inference(forward_demodulation,[status(thm)],[f1121,f2296]) ).
fof(f2309,plain,
! [X0,X1] :
( ~ sQ71_spl
| ~ in(X0,relation_inverse_image(empty_set,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2308,f1299]) ).
fof(f2330,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f1670,f803]) ).
fof(f2331,plain,
( ~ sQ47_spl
| ordinal(powerset(empty_set)) ),
inference(backward_demodulation,[status(thm)],[f938,f1975]) ).
fof(f2333,plain,
( ~ sQ45_spl
| epsilon_transitive(powerset(empty_set)) ),
inference(backward_demodulation,[status(thm)],[f938,f1967]) ).
fof(f2334,plain,
succ(empty_set) = powerset(empty_set),
inference(backward_demodulation,[status(thm)],[f938,f1777]) ).
fof(f2347,plain,
powerset(empty_set) != empty_set,
inference(paramodulation,[status(thm)],[f938,f729]) ).
fof(f2349,plain,
succ(empty_set) = set_union2(empty_set,powerset(empty_set)),
inference(paramodulation,[status(thm)],[f938,f389]) ).
fof(f2350,definition,
( sQ72_spl
<=> ordinal(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f2354,plain,
succ(empty_set) = powerset(empty_set),
inference(forward_demodulation,[status(thm)],[f1665,f2349]) ).
fof(f2356,plain,
! [X0] :
( ~ sQ45_spl
| ~ epsilon_connected(powerset(empty_set))
| in(powerset(empty_set),X0)
| X0 = powerset(empty_set)
| in(X0,powerset(empty_set))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f2333,f1525]) ).
fof(f2357,definition,
! [X0] :
( sQ73_spl
<=> ( in(powerset(empty_set),X0)
| X0 = powerset(empty_set)
| in(X0,powerset(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f2360,definition,
( sQ74_spl
<=> epsilon_connected(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f2363,plain,
( ~ sQ45_spl
| ~ sQ74_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f2356,f2357,f2360,f1966]) ).
fof(f2365,plain,
! [X0,X1] :
( in(apply(sK79_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK79_skl,X1))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1282,f822]) ).
fof(f2366,plain,
! [X0,X1] :
( in(apply(sK76_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK76_skl,X1))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1282,f809]) ).
fof(f2367,plain,
! [X0,X1] :
( in(apply(sK66_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK66_skl,X1))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1282,f773]) ).
fof(f2368,plain,
! [X0,X1] :
( in(apply(empty_set,X0),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1282,f670]) ).
fof(f2371,definition,
! [X0,X1] :
( sQ75_spl
<=> ( in(apply(sK79_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK79_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f2374,plain,
( sQ75_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f2365,f2274,f2371]) ).
fof(f2375,definition,
! [X0,X1] :
( sQ76_spl
<=> ( in(apply(sK76_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK76_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f2378,plain,
( sQ76_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f2366,f2281,f2375]) ).
fof(f2379,definition,
! [X0,X1] :
( sQ77_spl
<=> ( in(apply(sK66_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK66_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( sQ77_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f2367,f2288,f2379]) ).
fof(f2383,definition,
! [X0,X1] :
( sQ78_spl
<=> ( in(apply(empty_set,X0),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f2386,plain,
( sQ78_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2368,f2139,f2383]) ).
fof(f2389,plain,
! [X0,X1] :
( ~ in(apply(sK79_skl,X0),X1)
| ~ in(X0,relation_dom(sK79_skl))
| in(X0,relation_inverse_image(sK79_skl,X1))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1283,f822]) ).
fof(f2390,plain,
! [X0,X1] :
( ~ in(apply(sK76_skl,X0),X1)
| ~ in(X0,relation_dom(sK76_skl))
| in(X0,relation_inverse_image(sK76_skl,X1))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1283,f809]) ).
fof(f2391,plain,
! [X0,X1] :
( ~ in(apply(sK66_skl,X0),X1)
| ~ in(X0,relation_dom(sK66_skl))
| in(X0,relation_inverse_image(sK66_skl,X1))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1283,f773]) ).
fof(f2392,plain,
! [X0,X1] :
( ~ in(apply(empty_set,X0),X1)
| ~ in(X0,relation_dom(empty_set))
| in(X0,relation_inverse_image(empty_set,X1))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1283,f670]) ).
fof(f2396,definition,
! [X0,X1] :
( sQ79_spl
<=> ( ~ in(apply(sK79_skl,X0),X1)
| ~ in(X0,relation_dom(sK79_skl))
| in(X0,relation_inverse_image(sK79_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f2399,plain,
( sQ79_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f2389,f2274,f2396]) ).
fof(f2400,definition,
! [X0,X1] :
( sQ80_spl
<=> ( ~ in(apply(sK76_skl,X0),X1)
| ~ in(X0,relation_dom(sK76_skl))
| in(X0,relation_inverse_image(sK76_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f2403,plain,
( sQ80_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f2390,f2281,f2400]) ).
fof(f2404,definition,
! [X0,X1] :
( sQ81_spl
<=> ( ~ in(apply(sK66_skl,X0),X1)
| ~ in(X0,relation_dom(sK66_skl))
| in(X0,relation_inverse_image(sK66_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f2407,plain,
( sQ81_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f2391,f2288,f2404]) ).
fof(f2408,definition,
! [X0,X1] :
( sQ82_spl
<=> ( ~ in(apply(empty_set,X0),X1)
| ~ in(X0,relation_dom(empty_set))
| in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f2411,plain,
( sQ82_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2392,f2139,f2408]) ).
fof(f2414,plain,
( ~ sQ47_spl
| ~ sQ40_spl
| powerset(empty_set) = sK87_skl
| in(powerset(empty_set),sK87_skl) ),
inference(resolution,[status(thm)],[f1824,f2331]) ).
fof(f2415,plain,
( ~ sQ40_spl
| sK77_skl = sK87_skl
| in(sK77_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f1824,f815]) ).
fof(f2417,plain,
( ~ sQ40_spl
| sK86_skl = sK87_skl
| in(sK86_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f1824,f998]) ).
fof(f2418,plain,
( ~ sQ7_spl
| ~ sQ40_spl
| succ(sK86_skl) = sK87_skl
| in(succ(sK86_skl),sK87_skl) ),
inference(resolution,[status(thm)],[f1824,f1392]) ).
fof(f2424,definition,
( sQ83_spl
<=> in(powerset(empty_set),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f2425,plain,
( ~ sQ83_spl
| in(powerset(empty_set),sK87_skl) ),
inference(component_clause,[status(thm)],[f2424]) ).
fof(f2427,definition,
( sQ84_spl
<=> powerset(empty_set) = sK87_skl ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f2428,plain,
( ~ sQ84_spl
| powerset(empty_set) = sK87_skl ),
inference(component_clause,[status(thm)],[f2427]) ).
fof(f2429,plain,
( sQ84_spl
| powerset(empty_set) != sK87_skl ),
inference(component_clause,[status(thm)],[f2427]) ).
fof(f2430,plain,
( ~ sQ47_spl
| ~ sQ40_spl
| sQ84_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f2414,f2424,f2427,f1815,f1974]) ).
fof(f2431,definition,
( sQ85_spl
<=> in(sK77_skl,sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f2432,plain,
( ~ sQ85_spl
| in(sK77_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f2431]) ).
fof(f2433,plain,
( sQ85_spl
| ~ in(sK77_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f2431]) ).
fof(f2434,definition,
( sQ86_spl
<=> sK77_skl = sK87_skl ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f2435,plain,
( ~ sQ86_spl
| sK77_skl = sK87_skl ),
inference(component_clause,[status(thm)],[f2434]) ).
fof(f2437,plain,
( ~ sQ40_spl
| sQ86_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f2415,f2431,f2434,f1815]) ).
fof(f2439,plain,
( ~ sQ40_spl
| sQ14_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2417,f1260,f1430,f1815]) ).
fof(f2440,definition,
( sQ87_spl
<=> in(succ(sK86_skl),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f2441,plain,
( ~ sQ87_spl
| in(succ(sK86_skl),sK87_skl) ),
inference(component_clause,[status(thm)],[f2440]) ).
fof(f2443,definition,
( sQ88_spl
<=> succ(sK86_skl) = sK87_skl ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f2444,plain,
( ~ sQ88_spl
| succ(sK86_skl) = sK87_skl ),
inference(component_clause,[status(thm)],[f2443]) ).
fof(f2445,plain,
( sQ88_spl
| succ(sK86_skl) != sK87_skl ),
inference(component_clause,[status(thm)],[f2443]) ).
fof(f2446,plain,
( ~ sQ7_spl
| ~ sQ40_spl
| sQ88_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f2418,f2440,f2443,f1815,f1391]) ).
fof(f2452,plain,
( ~ sQ85_spl
| ~ in(sK87_skl,sK77_skl) ),
inference(resolution,[status(thm)],[f2432,f279]) ).
fof(f2457,plain,
( ~ sQ86_spl
| epsilon_transitive(sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f2435,f813]) ).
fof(f2458,plain,
( ~ sQ86_spl
| epsilon_connected(sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f2435,f814]) ).
fof(f2460,plain,
! [X0] :
( ~ sQ86_spl
| ~ epsilon_connected(sK87_skl)
| in(sK87_skl,X0)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f2457,f1525]) ).
fof(f2461,definition,
( sQ89_spl
<=> epsilon_connected(sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f2463,plain,
( sQ89_spl
| ~ epsilon_connected(sK87_skl) ),
inference(component_clause,[status(thm)],[f2461]) ).
fof(f2464,plain,
( ~ sQ86_spl
| ~ sQ89_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2460,f1818,f2461,f2434]) ).
fof(f2493,plain,
! [X0] :
( ~ ordinal_subset(X0,empty_set)
| ~ ordinal(empty_set)
| ~ ordinal(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f1056,f831]) ).
fof(f2495,definition,
! [X0] :
( sQ90_spl
<=> ( ~ ordinal_subset(X0,empty_set)
| ~ ordinal(X0)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f2496,plain,
! [X0] :
( ~ sQ90_spl
| ~ ordinal_subset(X0,empty_set)
| ~ ordinal(X0)
| X0 = empty_set ),
inference(component_clause,[status(thm)],[f2495]) ).
fof(f2498,plain,
( ~ sQ4_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f2493,f2495,f1375]) ).
fof(f2515,plain,
! [X0] :
( ~ ordinal(empty_set)
| in(powerset(empty_set),X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f2334,f1365]) ).
fof(f2517,plain,
( epsilon_transitive(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f2334,f687]) ).
fof(f2518,plain,
( epsilon_connected(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f2334,f688]) ).
fof(f2519,plain,
( ordinal(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f2334,f689]) ).
fof(f2526,definition,
! [X0] :
( sQ91_spl
<=> ( in(powerset(empty_set),X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f2529,plain,
( ~ sQ4_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f2515,f2526,f1375]) ).
fof(f2530,definition,
( sQ92_spl
<=> epsilon_transitive(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f2533,plain,
( sQ92_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2517,f1375,f2530]) ).
fof(f2534,plain,
( sQ74_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2518,f1375,f2360]) ).
fof(f2535,plain,
( sQ72_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2519,f1375,f2350]) ).
fof(f2539,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK79_skl),relation_dom(sK79_skl))
| in(sK9_skl(X0,X1,sK79_skl),X0)
| X0 = relation_inverse_image(sK79_skl,X1)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f357,f822]) ).
fof(f2540,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK76_skl),relation_dom(sK76_skl))
| in(sK9_skl(X0,X1,sK76_skl),X0)
| X0 = relation_inverse_image(sK76_skl,X1)
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f357,f809]) ).
fof(f2541,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK66_skl),relation_dom(sK66_skl))
| in(sK9_skl(X0,X1,sK66_skl),X0)
| X0 = relation_inverse_image(sK66_skl,X1)
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f357,f773]) ).
fof(f2542,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f357,f670]) ).
fof(f2546,definition,
! [X0,X1] :
( sQ93_spl
<=> ( in(sK9_skl(X0,X1,sK79_skl),relation_dom(sK79_skl))
| in(sK9_skl(X0,X1,sK79_skl),X0)
| X0 = relation_inverse_image(sK79_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f2549,plain,
( sQ93_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f2539,f2274,f2546]) ).
fof(f2550,definition,
! [X0,X1] :
( sQ94_spl
<=> ( in(sK9_skl(X0,X1,sK76_skl),relation_dom(sK76_skl))
| in(sK9_skl(X0,X1,sK76_skl),X0)
| X0 = relation_inverse_image(sK76_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f2553,plain,
( sQ94_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f2540,f2281,f2550]) ).
fof(f2554,definition,
! [X0,X1] :
( sQ95_spl
<=> ( in(sK9_skl(X0,X1,sK66_skl),relation_dom(sK66_skl))
| in(sK9_skl(X0,X1,sK66_skl),X0)
| X0 = relation_inverse_image(sK66_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f2557,plain,
( sQ95_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f2541,f2288,f2554]) ).
fof(f2558,definition,
! [X0,X1] :
( sQ96_spl
<=> ( in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f2561,plain,
( sQ96_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2542,f2139,f2558]) ).
fof(f2566,plain,
! [X0,X1] :
( in(apply(sK79_skl,sK9_skl(X0,X1,sK79_skl)),X1)
| in(sK9_skl(X0,X1,sK79_skl),X0)
| X0 = relation_inverse_image(sK79_skl,X1)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f358,f822]) ).
fof(f2567,plain,
! [X0,X1] :
( in(apply(sK76_skl,sK9_skl(X0,X1,sK76_skl)),X1)
| in(sK9_skl(X0,X1,sK76_skl),X0)
| X0 = relation_inverse_image(sK76_skl,X1)
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f358,f809]) ).
fof(f2568,plain,
! [X0,X1] :
( in(apply(sK66_skl,sK9_skl(X0,X1,sK66_skl)),X1)
| in(sK9_skl(X0,X1,sK66_skl),X0)
| X0 = relation_inverse_image(sK66_skl,X1)
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f358,f773]) ).
fof(f2569,plain,
! [X0,X1] :
( in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f358,f670]) ).
fof(f2572,definition,
! [X0,X1] :
( sQ97_spl
<=> ( in(apply(sK79_skl,sK9_skl(X0,X1,sK79_skl)),X1)
| in(sK9_skl(X0,X1,sK79_skl),X0)
| X0 = relation_inverse_image(sK79_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f2575,plain,
( sQ97_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f2566,f2274,f2572]) ).
fof(f2576,definition,
! [X0,X1] :
( sQ98_spl
<=> ( in(apply(sK76_skl,sK9_skl(X0,X1,sK76_skl)),X1)
| in(sK9_skl(X0,X1,sK76_skl),X0)
| X0 = relation_inverse_image(sK76_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f2579,plain,
( sQ98_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f2567,f2281,f2576]) ).
fof(f2580,definition,
! [X0,X1] :
( sQ99_spl
<=> ( in(apply(sK66_skl,sK9_skl(X0,X1,sK66_skl)),X1)
| in(sK9_skl(X0,X1,sK66_skl),X0)
| X0 = relation_inverse_image(sK66_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f2583,plain,
( sQ99_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f2568,f2288,f2580]) ).
fof(f2584,definition,
! [X0,X1] :
( sQ100_spl
<=> ( in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f2587,plain,
( sQ100_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2569,f2139,f2584]) ).
fof(f2603,plain,
( ~ sQ45_spl
| ~ sQ84_spl
| epsilon_transitive(sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f2428,f2333]) ).
fof(f2606,plain,
( ~ sQ84_spl
| sK87_skl = singleton(empty_set) ),
inference(backward_demodulation,[status(thm)],[f2428,f938]) ).
fof(f2610,plain,
( ~ sQ84_spl
| ~ empty(sK87_skl) ),
inference(paramodulation,[status(thm)],[f2428,f662]) ).
fof(f2611,plain,
! [X0] :
( ~ sQ45_spl
| ~ sQ84_spl
| ~ epsilon_connected(sK87_skl)
| in(sK87_skl,X0)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f2603,f1525]) ).
fof(f2612,plain,
( ~ sQ45_spl
| ~ sQ84_spl
| ~ sQ89_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2611,f1818,f2461,f2427,f1966]) ).
fof(f2619,definition,
! [X0] :
( sQ101_spl
<=> ( in(succ(sK86_skl),X0)
| X0 = succ(sK86_skl)
| in(X0,succ(sK86_skl))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f2643,plain,
( sQ9_spl
| ~ sQ88_spl
| ~ subset(sK87_skl,sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f2444,f1399]) ).
fof(f2656,plain,
( ~ sQ88_spl
| epsilon_connected(sK87_skl)
| ~ ordinal(sK86_skl) ),
inference(paramodulation,[status(thm)],[f2444,f688]) ).
fof(f2660,plain,
( ~ sQ88_spl
| ~ in(sK87_skl,sK86_skl) ),
inference(paramodulation,[status(thm)],[f2444,f1360]) ).
fof(f2661,plain,
( ~ sQ88_spl
| in(sK86_skl,sK87_skl) ),
inference(paramodulation,[status(thm)],[f2444,f845]) ).
fof(f2663,plain,
( sQ9_spl
| ~ sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2643,f1271]) ).
fof(f2664,plain,
( sQ9_spl
| ~ sQ88_spl ),
inference(contradiction_clause,[status(thm)],[f2663]) ).
fof(f2686,plain,
( ~ sQ28_spl
| in(sK87_skl,sK87_skl) ),
inference(paramodulation,[status(thm)],[f1696,f845]) ).
fof(f2692,definition,
( sQ105_spl
<=> epsilon_transitive(sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f2693,plain,
( ~ sQ105_spl
| epsilon_transitive(sK87_skl) ),
inference(component_clause,[status(thm)],[f2692]) ).
fof(f2694,plain,
( sQ105_spl
| ~ epsilon_transitive(sK87_skl) ),
inference(component_clause,[status(thm)],[f2692]) ).
fof(f2699,plain,
( ~ sQ28_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f2686,f1413,f1695]) ).
fof(f2700,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1700,f2009]) ).
fof(f2701,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f2700]) ).
fof(f2760,plain,
( in(sK87_skl,sK86_skl)
| sK86_skl = sK87_skl
| in(sK86_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f1367,f998]) ).
fof(f2761,plain,
( ~ sQ47_spl
| in(sK87_skl,powerset(empty_set))
| powerset(empty_set) = sK87_skl
| in(powerset(empty_set),sK87_skl) ),
inference(resolution,[status(thm)],[f1367,f2331]) ).
fof(f2762,plain,
( in(sK87_skl,sK77_skl)
| sK77_skl = sK87_skl
| in(sK77_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f1367,f815]) ).
fof(f2763,plain,
( in(sK87_skl,sK87_skl)
| sK87_skl = sK87_skl
| in(sK87_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f1367,f999]) ).
fof(f2764,plain,
( ~ sQ7_spl
| in(sK87_skl,succ(sK86_skl))
| succ(sK86_skl) = sK87_skl
| in(succ(sK86_skl),sK87_skl) ),
inference(resolution,[status(thm)],[f1367,f1392]) ).
fof(f2770,plain,
( sQ13_spl
| sQ14_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2760,f1260,f1430,f1427]) ).
fof(f2771,definition,
( sQ106_spl
<=> in(sK87_skl,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f2772,plain,
( ~ sQ106_spl
| in(sK87_skl,powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f2771]) ).
fof(f2774,plain,
( ~ sQ47_spl
| sQ106_spl
| sQ84_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f2761,f2424,f2427,f2771,f1974]) ).
fof(f2775,definition,
( sQ107_spl
<=> in(sK87_skl,sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f2776,plain,
( ~ sQ107_spl
| in(sK87_skl,sK77_skl) ),
inference(component_clause,[status(thm)],[f2775]) ).
fof(f2778,plain,
( sQ107_spl
| sQ86_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f2762,f2431,f2434,f2775]) ).
fof(f2779,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f2763,f1413,f1416]) ).
fof(f2780,definition,
( sQ108_spl
<=> in(sK87_skl,succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f2781,plain,
( ~ sQ108_spl
| in(sK87_skl,succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f2780]) ).
fof(f2783,plain,
( ~ sQ7_spl
| sQ108_spl
| sQ88_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f2764,f2440,f2443,f2780,f1391]) ).
fof(f2786,plain,
! [X0] :
( ~ sQ107_spl
| ~ ordinal(sK77_skl)
| in(sK87_skl,X0)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f2776,f1369]) ).
fof(f2791,plain,
( ~ sQ107_spl
| ~ sQ62_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2786,f1818,f2205,f2775]) ).
fof(f2792,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2207,f815]) ).
fof(f2793,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f2792]) ).
fof(f2795,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2183,f674]) ).
fof(f2796,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f2795]) ).
fof(f2797,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2179,f814]) ).
fof(f2798,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f2797]) ).
fof(f2800,plain,
! [X0] :
( ~ sQ48_spl
| X0 = empty_set
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1991]) ).
fof(f2804,plain,
! [X0] :
( ~ sQ105_spl
| ~ epsilon_connected(sK87_skl)
| in(sK87_skl,X0)
| X0 = sK87_skl
| in(X0,sK87_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f2693,f1525]) ).
fof(f2805,plain,
( ~ sQ105_spl
| ~ sQ89_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2804,f1818,f2461,f2692]) ).
fof(f2806,plain,
! [X0] :
( ~ sQ51_spl
| ~ epsilon_connected(sK86_skl)
| in(sK86_skl,X0)
| X0 = sK86_skl
| in(X0,sK86_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f2062,f1525]) ).
fof(f2807,plain,
( ~ sQ51_spl
| ~ sQ52_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f2806,f1725,f2065,f2061]) ).
fof(f2816,plain,
( in(sK87_skl,sK67_skl)
| sK67_skl = sK87_skl
| in(sK67_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f777,f1367]) ).
fof(f2818,definition,
( sQ109_spl
<=> in(sK67_skl,sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f2819,plain,
( ~ sQ109_spl
| in(sK67_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f2818]) ).
fof(f2820,plain,
( sQ109_spl
| ~ in(sK67_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f2818]) ).
fof(f2821,definition,
( sQ110_spl
<=> sK67_skl = sK87_skl ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f2822,plain,
( ~ sQ110_spl
| sK67_skl = sK87_skl ),
inference(component_clause,[status(thm)],[f2821]) ).
fof(f2824,definition,
( sQ111_spl
<=> in(sK87_skl,sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f2827,plain,
( sQ111_spl
| sQ110_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f2816,f2818,f2821,f2824]) ).
fof(f2828,plain,
! [X0] :
( ~ epsilon_connected(sK67_skl)
| in(sK67_skl,X0)
| X0 = sK67_skl
| in(X0,sK67_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f775,f1525]) ).
fof(f2829,definition,
( sQ112_spl
<=> epsilon_connected(sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f2831,plain,
( sQ112_spl
| ~ epsilon_connected(sK67_skl) ),
inference(component_clause,[status(thm)],[f2829]) ).
fof(f2832,plain,
( ~ sQ112_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f2828,f1753,f2829]) ).
fof(f2833,plain,
( sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2831,f776]) ).
fof(f2834,plain,
sQ112_spl,
inference(contradiction_clause,[status(thm)],[f2833]) ).
fof(f2835,plain,
( sQ89_spl
| ~ sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2463,f2458]) ).
fof(f2836,plain,
( sQ89_spl
| ~ sQ86_spl ),
inference(contradiction_clause,[status(thm)],[f2835]) ).
fof(f2883,plain,
( sQ49_spl
| ~ ordinal(sK87_skl) ),
inference(resolution,[status(thm)],[f2041,f689]) ).
fof(f2887,plain,
( sQ49_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2883,f1394,f2039]) ).
fof(f2888,definition,
( sQ115_spl
<=> epsilon_transitive(succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f2889,plain,
( ~ sQ115_spl
| epsilon_transitive(succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f2888]) ).
fof(f2890,plain,
( sQ115_spl
| ~ epsilon_transitive(succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f2888]) ).
fof(f2891,definition,
( sQ116_spl
<=> epsilon_connected(succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f2893,plain,
( sQ116_spl
| ~ epsilon_connected(succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f2891]) ).
fof(f2896,plain,
( sQ23_spl
| ~ ordinal(succ(sK86_skl)) ),
inference(resolution,[status(thm)],[f1510,f518]) ).
fof(f2899,plain,
( sQ23_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2896,f1391,f1508]) ).
fof(f2902,plain,
( ~ sQ47_spl
| ~ sQ48_spl
| powerset(empty_set) = empty_set ),
inference(resolution,[status(thm)],[f2800,f2331]) ).
fof(f2911,plain,
( ~ sQ47_spl
| ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2902,f2347]) ).
fof(f2912,plain,
( ~ sQ47_spl
| ~ sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f2911]) ).
fof(f2914,plain,
( sQ24_spl
| ~ ordinal(succ(sK86_skl)) ),
inference(resolution,[status(thm)],[f1513,f519]) ).
fof(f2917,plain,
( sQ24_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2914,f1391,f1511]) ).
fof(f2984,plain,
( sQ116_spl
| ~ ordinal(succ(sK87_skl)) ),
inference(resolution,[status(thm)],[f2893,f519]) ).
fof(f2987,plain,
( sQ116_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f2984,f2039,f2891]) ).
fof(f2989,plain,
( sQ115_spl
| ~ ordinal(succ(sK87_skl)) ),
inference(resolution,[status(thm)],[f2890,f518]) ).
fof(f2992,plain,
( sQ115_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f2989,f2039,f2888]) ).
fof(f2993,plain,
( ~ sQ49_spl
| in(sK87_skl,succ(sK87_skl))
| succ(sK87_skl) = sK87_skl
| in(succ(sK87_skl),sK87_skl) ),
inference(resolution,[status(thm)],[f2040,f1367]) ).
fof(f2995,definition,
( sQ117_spl
<=> in(succ(sK87_skl),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f2996,plain,
( ~ sQ117_spl
| in(succ(sK87_skl),sK87_skl) ),
inference(component_clause,[status(thm)],[f2995]) ).
fof(f2998,definition,
( sQ118_spl
<=> in(sK87_skl,succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f3001,plain,
( ~ sQ49_spl
| sQ118_spl
| sQ28_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f2993,f2995,f1695,f2998,f2039]) ).
fof(f3002,plain,
( ~ sQ117_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2996,f1360]) ).
fof(f3003,plain,
~ sQ117_spl,
inference(contradiction_clause,[status(thm)],[f3002]) ).
fof(f3016,plain,
! [X0] :
( ~ sQ23_spl
| ~ epsilon_connected(succ(sK86_skl))
| in(succ(sK86_skl),X0)
| X0 = succ(sK86_skl)
| in(X0,succ(sK86_skl))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1509,f1525]) ).
fof(f3017,plain,
( ~ sQ23_spl
| ~ sQ24_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f3016,f2619,f1511,f1508]) ).
fof(f3018,plain,
( ~ sQ84_spl
| succ(empty_set) = sK87_skl ),
inference(backward_demodulation,[status(thm)],[f2428,f2354]) ).
fof(f3024,plain,
( ~ sQ84_spl
| element(empty_set,sK87_skl) ),
inference(paramodulation,[status(thm)],[f2428,f2330]) ).
fof(f3026,plain,
( ~ sQ84_spl
| union(sK87_skl) = empty_set ),
inference(paramodulation,[status(thm)],[f2428,f1216]) ).
fof(f3033,plain,
! [X0] :
( ~ sQ115_spl
| ~ epsilon_connected(succ(sK87_skl))
| in(succ(sK87_skl),X0)
| X0 = succ(sK87_skl)
| in(X0,succ(sK87_skl))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f2889,f1525]) ).
fof(f3034,definition,
! [X0] :
( sQ119_spl
<=> ( in(succ(sK87_skl),X0)
| X0 = succ(sK87_skl)
| in(X0,succ(sK87_skl))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f3037,plain,
( ~ sQ115_spl
| ~ sQ116_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f3033,f3034,f2891,f2888]) ).
fof(f3045,plain,
! [X0] :
( ~ sQ84_spl
| ~ ordinal(empty_set)
| in(sK87_skl,X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f3018,f1365]) ).
fof(f3048,plain,
( ~ sQ84_spl
| epsilon_connected(sK87_skl)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f3018,f688]) ).
fof(f3056,definition,
! [X0] :
( sQ120_spl
<=> ( in(sK87_skl,X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f3059,plain,
( ~ sQ84_spl
| ~ sQ4_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f3045,f3056,f1375,f2427]) ).
fof(f3061,plain,
( ~ sQ84_spl
| sQ89_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3048,f1375,f2461,f2427]) ).
fof(f3109,definition,
( sQ121_spl
<=> relation(identity_relation(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f3111,plain,
( sQ121_spl
| ~ relation(identity_relation(sK87_skl)) ),
inference(component_clause,[status(thm)],[f3109]) ).
fof(f3121,plain,
( sQ121_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3111,f628]) ).
fof(f3122,plain,
sQ121_spl,
inference(contradiction_clause,[status(thm)],[f3121]) ).
fof(f3162,plain,
( ~ sQ87_spl
| ~ in(sK87_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f2441,f1362]) ).
fof(f3167,plain,
( ~ sQ87_spl
| ~ in(sK87_skl,succ(sK86_skl)) ),
inference(resolution,[status(thm)],[f2441,f279]) ).
fof(f3169,plain,
( ~ sQ87_spl
| ~ sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3167,f2781]) ).
fof(f3170,plain,
( ~ sQ87_spl
| ~ sQ108_spl ),
inference(contradiction_clause,[status(thm)],[f3169]) ).
fof(f3175,plain,
( ~ sQ83_spl
| ~ in(sK87_skl,powerset(empty_set)) ),
inference(resolution,[status(thm)],[f2425,f279]) ).
fof(f3177,plain,
( ~ sQ83_spl
| ~ sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3175,f2772]) ).
fof(f3178,plain,
( ~ sQ83_spl
| ~ sQ106_spl ),
inference(contradiction_clause,[status(thm)],[f3177]) ).
fof(f3179,plain,
( ~ sQ10_spl
| ~ ordinal(succ(sK86_skl))
| ~ ordinal(sK87_skl)
| ~ subset(succ(sK86_skl),sK87_skl)
| succ(sK86_skl) = sK87_skl ),
inference(resolution,[status(thm)],[f1693,f1402]) ).
fof(f3183,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f3179,f2443,f1397,f1394,f1391,f1401]) ).
fof(f3217,plain,
! [X0] :
( ~ sQ71_spl
| relation_inverse_image(empty_set,X0) = empty_set ),
inference(resolution,[status(thm)],[f420,f2309]) ).
fof(f3220,plain,
! [X0] :
( sK24_skl(singleton(X0)) = X0
| singleton(X0) = empty_set ),
inference(resolution,[status(thm)],[f420,f1297]) ).
fof(f3224,plain,
! [X0,X1] :
( ~ in(X1,sK24_skl(X0))
| ~ in(X0,X1)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f420,f1044]) ).
fof(f3226,plain,
! [X0] :
( ~ in(X0,sK24_skl(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f420,f279]) ).
fof(f3227,plain,
! [X0] : sK24_skl(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f3220,f729]) ).
fof(f3228,plain,
sK24_skl(powerset(empty_set)) = empty_set,
inference(paramodulation,[status(thm)],[f938,f3227]) ).
fof(f3231,plain,
! [X0,X1] :
( ~ sQ71_spl
| in(sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3217,f1288]) ).
fof(f3232,plain,
! [X0,X1] :
( ~ sQ71_spl
| in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3217,f1287]) ).
fof(f3233,definition,
! [X0,X1] :
( sQ124_spl
<=> ( in(sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f3236,plain,
( ~ sQ71_spl
| sQ124_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3231,f2139,f3233,f2295]) ).
fof(f3237,definition,
! [X0,X1] :
( sQ125_spl
<=> ( in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f3240,plain,
( ~ sQ71_spl
| sQ125_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3232,f2139,f3237,f2295]) ).
fof(f3243,plain,
( in(empty_set,powerset(empty_set))
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f3228,f420]) ).
fof(f3244,definition,
( sQ126_spl
<=> powerset(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f3245,plain,
( ~ sQ126_spl
| powerset(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f3244]) ).
fof(f3247,definition,
( sQ127_spl
<=> in(empty_set,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f3250,plain,
( sQ127_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f3243,f3244,f3247]) ).
fof(f3251,plain,
( ~ sQ126_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3245,f2347]) ).
fof(f3252,plain,
~ sQ126_spl,
inference(contradiction_clause,[status(thm)],[f3251]) ).
fof(f3280,plain,
( ~ sQ13_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1449,f1260,f1427]) ).
fof(f3287,plain,
( ~ sQ108_spl
| ~ sQ26_spl
| in(sK87_skl,succ(empty_set)) ),
inference(backward_demodulation,[status(thm)],[f1580,f2781]) ).
fof(f3290,plain,
( sQ9_spl
| ~ sQ26_spl
| ~ subset(succ(empty_set),sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f1580,f1399]) ).
fof(f3299,plain,
( ~ sQ25_spl
| ~ sQ26_spl
| in(empty_set,empty_set) ),
inference(backward_demodulation,[status(thm)],[f1580,f1577]) ).
fof(f3303,plain,
( sQ3_spl
| ~ sQ26_spl
| ~ ordinal_subset(succ(empty_set),sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f1580,f1265]) ).
fof(f3308,plain,
( ~ sQ108_spl
| ~ sQ26_spl
| in(sK87_skl,powerset(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f2334,f3287]) ).
fof(f3310,plain,
( sQ9_spl
| ~ sQ26_spl
| ~ subset(powerset(empty_set),sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f2334,f3290]) ).
fof(f3315,plain,
( ~ sQ25_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3299,f1299]) ).
fof(f3316,plain,
( ~ sQ25_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f3315]) ).
fof(f3433,plain,
( ~ in(powerset(empty_set),empty_set)
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f3228,f3226]) ).
fof(f3435,definition,
( sQ131_spl
<=> in(powerset(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f3438,plain,
( ~ sQ131_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f3433,f3244,f3435]) ).
fof(f3475,plain,
! [X0] :
( ~ empty(X0)
| empty(empty_set) ),
inference(paramodulation,[status(thm)],[f1665,f681]) ).
fof(f3481,definition,
( sQ132_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f3484,definition,
! [X0] :
( sQ133_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f3485,plain,
! [X0] :
( ~ sQ133_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f3484]) ).
fof(f3487,plain,
( sQ133_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f3475,f3481,f3484]) ).
fof(f3503,definition,
! [X0] :
( sQ134_spl
<=> in(X0,set_meet(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f3504,plain,
! [X0] :
( ~ sQ134_spl
| in(X0,set_meet(empty_set)) ),
inference(component_clause,[status(thm)],[f3503]) ).
fof(f3513,plain,
! [X0] :
( ~ sQ134_spl
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1295,f3504]) ).
fof(f3514,plain,
( ~ sQ134_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3513,f1299]) ).
fof(f3515,plain,
~ sQ134_spl,
inference(contradiction_clause,[status(thm)],[f3514]) ).
fof(f3540,plain,
( in(sK86_skl,sK86_skl)
| sK86_skl = sK86_skl
| in(sK86_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f1545,f998]) ).
fof(f3541,plain,
( ~ sQ47_spl
| in(sK86_skl,powerset(empty_set))
| powerset(empty_set) = sK86_skl
| in(powerset(empty_set),sK86_skl) ),
inference(resolution,[status(thm)],[f1545,f2331]) ).
fof(f3543,plain,
( in(sK86_skl,sK77_skl)
| sK77_skl = sK86_skl
| in(sK77_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f1545,f815]) ).
fof(f3545,plain,
( ~ sQ7_spl
| in(sK86_skl,succ(sK86_skl))
| succ(sK86_skl) = sK86_skl
| in(succ(sK86_skl),sK86_skl) ),
inference(resolution,[status(thm)],[f1545,f1392]) ).
fof(f3552,plain,
( sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f3540,f1437,f1440]) ).
fof(f3553,definition,
( sQ138_spl
<=> in(powerset(empty_set),sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f3554,plain,
( ~ sQ138_spl
| in(powerset(empty_set),sK86_skl) ),
inference(component_clause,[status(thm)],[f3553]) ).
fof(f3556,definition,
( sQ139_spl
<=> powerset(empty_set) = sK86_skl ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f3557,plain,
( ~ sQ139_spl
| powerset(empty_set) = sK86_skl ),
inference(component_clause,[status(thm)],[f3556]) ).
fof(f3559,definition,
( sQ140_spl
<=> in(sK86_skl,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f3560,plain,
( ~ sQ140_spl
| in(sK86_skl,powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f3559]) ).
fof(f3562,plain,
( ~ sQ47_spl
| sQ140_spl
| sQ139_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f3541,f3553,f3556,f3559,f1974]) ).
fof(f3563,definition,
( sQ141_spl
<=> in(sK67_skl,sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f3564,plain,
( ~ sQ141_spl
| in(sK67_skl,sK86_skl) ),
inference(component_clause,[status(thm)],[f3563]) ).
fof(f3566,definition,
( sQ142_spl
<=> sK67_skl = sK86_skl ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f3567,plain,
( ~ sQ142_spl
| sK67_skl = sK86_skl ),
inference(component_clause,[status(thm)],[f3566]) ).
fof(f3569,definition,
( sQ143_spl
<=> in(sK86_skl,sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f3570,plain,
( ~ sQ143_spl
| in(sK86_skl,sK67_skl) ),
inference(component_clause,[status(thm)],[f3569]) ).
fof(f3573,definition,
( sQ144_spl
<=> in(sK77_skl,sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f3574,plain,
( ~ sQ144_spl
| in(sK77_skl,sK86_skl) ),
inference(component_clause,[status(thm)],[f3573]) ).
fof(f3576,definition,
( sQ145_spl
<=> sK77_skl = sK86_skl ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f3577,plain,
( ~ sQ145_spl
| sK77_skl = sK86_skl ),
inference(component_clause,[status(thm)],[f3576]) ).
fof(f3578,plain,
( sQ145_spl
| sK77_skl != sK86_skl ),
inference(component_clause,[status(thm)],[f3576]) ).
fof(f3579,definition,
( sQ146_spl
<=> in(sK86_skl,sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f3580,plain,
( ~ sQ146_spl
| in(sK86_skl,sK77_skl) ),
inference(component_clause,[status(thm)],[f3579]) ).
fof(f3582,plain,
( sQ146_spl
| sQ145_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f3543,f3573,f3576,f3579]) ).
fof(f3584,definition,
( sQ147_spl
<=> in(succ(sK86_skl),sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f3585,plain,
( ~ sQ147_spl
| in(succ(sK86_skl),sK86_skl) ),
inference(component_clause,[status(thm)],[f3584]) ).
fof(f3587,definition,
( sQ148_spl
<=> succ(sK86_skl) = sK86_skl ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f3588,plain,
( ~ sQ148_spl
| succ(sK86_skl) = sK86_skl ),
inference(component_clause,[status(thm)],[f3587]) ).
fof(f3590,definition,
( sQ149_spl
<=> in(sK86_skl,succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f3593,plain,
( ~ sQ7_spl
| sQ149_spl
| sQ148_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f3545,f3584,f3587,f3590,f1391]) ).
fof(f3598,definition,
( sQ151_spl
<=> in(sK86_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f3599,plain,
( ~ sQ151_spl
| in(sK86_skl,empty_set) ),
inference(component_clause,[status(thm)],[f3598]) ).
fof(f3603,plain,
( ~ sQ151_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3599,f1299]) ).
fof(f3604,plain,
~ sQ151_spl,
inference(contradiction_clause,[status(thm)],[f3603]) ).
fof(f3607,plain,
( ~ sQ147_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3585,f1360]) ).
fof(f3608,plain,
~ sQ147_spl,
inference(contradiction_clause,[status(thm)],[f3607]) ).
fof(f3610,plain,
( sQ3_spl
| ~ sQ26_spl
| ~ ordinal_subset(powerset(empty_set),sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f2334,f3303]) ).
fof(f3611,plain,
( ~ sQ59_spl
| ~ sQ145_spl
| in(empty_set,sK86_skl) ),
inference(backward_demodulation,[status(thm)],[f3577,f2195]) ).
fof(f3619,plain,
( ~ sQ59_spl
| ~ sQ145_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f3611,f1576,f3576,f2194]) ).
fof(f3622,plain,
( ~ sQ87_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3162,f1427,f2440]) ).
fof(f3632,plain,
( ~ sQ88_spl
| sQ89_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2656,f1434,f2461,f2443]) ).
fof(f3635,plain,
( ~ sQ88_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2660,f1427,f2443]) ).
fof(f3636,plain,
( ~ sQ88_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2661,f1260,f2443]) ).
fof(f3678,definition,
( sQ153_spl
<=> empty_set = succ(sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f3679,plain,
( ~ sQ153_spl
| empty_set = succ(sK86_skl) ),
inference(component_clause,[status(thm)],[f3678]) ).
fof(f3681,definition,
( sQ154_spl
<=> subset(empty_set,succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f3683,plain,
( sQ154_spl
| ~ subset(empty_set,succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f3681]) ).
fof(f3685,plain,
( sQ154_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3683,f980]) ).
fof(f3686,plain,
sQ154_spl,
inference(contradiction_clause,[status(thm)],[f3685]) ).
fof(f3687,plain,
( ~ sQ133_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f649,f3485]) ).
fof(f3688,plain,
~ sQ133_spl,
inference(contradiction_clause,[status(thm)],[f3687]) ).
fof(f3692,plain,
! [X0] :
( in(sK77_skl,X0)
| X0 = sK77_skl
| in(X0,sK77_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f815,f963]) ).
fof(f3719,plain,
( ~ sQ3_spl
| ~ ordinal(sK87_skl)
| ~ ordinal(succ(sK86_skl))
| ~ subset(sK87_skl,succ(sK86_skl))
| sK87_skl = succ(sK86_skl) ),
inference(resolution,[status(thm)],[f1264,f1693]) ).
fof(f3720,definition,
( sQ155_spl
<=> subset(sK87_skl,succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f3722,plain,
( sQ155_spl
| ~ subset(sK87_skl,succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f3720]) ).
fof(f3723,plain,
( ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ155_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f3719,f2443,f3720,f1391,f1394,f1263]) ).
fof(f3727,plain,
( ~ sQ16_spl
| ~ in(sK86_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f1438,f1044]) ).
fof(f3733,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3727,f1438]) ).
fof(f3734,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f3733]) ).
fof(f3755,plain,
( ~ sQ148_spl
| in(sK86_skl,sK86_skl) ),
inference(paramodulation,[status(thm)],[f3588,f845]) ).
fof(f3764,plain,
( ~ sQ148_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f3755,f1437,f3587]) ).
fof(f3765,plain,
! [X0] :
( ~ sQ146_spl
| ~ ordinal(sK77_skl)
| in(sK86_skl,X0)
| X0 = sK86_skl
| in(X0,sK86_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f3580,f1369]) ).
fof(f3770,plain,
( ~ sQ146_spl
| ~ sQ62_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f3765,f1725,f2205,f3579]) ).
fof(f3789,plain,
( ~ sQ110_spl
| ~ sQ22_spl
| sK67_skl = empty_set ),
inference(backward_demodulation,[status(thm)],[f1468,f2822]) ).
fof(f3791,plain,
( ~ sQ143_spl
| ~ sQ110_spl
| ~ sQ22_spl
| in(sK86_skl,empty_set) ),
inference(forward_demodulation,[status(thm)],[f3789,f3570]) ).
fof(f3792,plain,
( ~ sQ143_spl
| ~ sQ110_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3791,f1299]) ).
fof(f3793,plain,
( ~ sQ143_spl
| ~ sQ110_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f3792]) ).
fof(f3824,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| in(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f1301,f831]) ).
fof(f3825,plain,
! [X0] : in(X0,powerset(X0)),
inference(resolution,[status(thm)],[f1301,f1271]) ).
fof(f3830,plain,
( ~ sQ141_spl
| ~ sQ110_spl
| in(sK87_skl,sK86_skl) ),
inference(forward_demodulation,[status(thm)],[f2822,f3564]) ).
fof(f3838,plain,
( ~ sQ139_spl
| sK86_skl = singleton(empty_set) ),
inference(backward_demodulation,[status(thm)],[f3557,f938]) ).
fof(f3895,plain,
( ~ sQ153_spl
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f3679,f659]) ).
fof(f3912,plain,
( ~ sQ153_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3895,f649]) ).
fof(f3913,plain,
~ sQ153_spl,
inference(contradiction_clause,[status(thm)],[f3912]) ).
fof(f3926,plain,
! [X0] :
( X0 = empty_set
| ~ in(X0,empty_set)
| ~ epsilon_transitive(empty_set) ),
inference(resolution,[status(thm)],[f432,f1056]) ).
fof(f3929,definition,
( sQ157_spl
<=> epsilon_transitive(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f3931,plain,
( sQ157_spl
| ~ epsilon_transitive(empty_set) ),
inference(component_clause,[status(thm)],[f3929]) ).
fof(f3932,definition,
! [X0] :
( sQ158_spl
<=> ( X0 = empty_set
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f3935,plain,
( sQ158_spl
| ~ sQ157_spl ),
inference(split_clause,[status(thm)],[f3926,f3929,f3932]) ).
fof(f3936,plain,
( sQ157_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3931,f673]) ).
fof(f3937,plain,
sQ157_spl,
inference(contradiction_clause,[status(thm)],[f3936]) ).
fof(f3975,plain,
! [X0] : ~ in(powerset(succ(X0)),X0),
inference(resolution,[status(thm)],[f3825,f1362]) ).
fof(f4001,plain,
! [X0] :
( ~ sQ140_spl
| ~ ordinal(powerset(empty_set))
| in(sK86_skl,X0)
| X0 = sK86_skl
| in(X0,sK86_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f3560,f1369]) ).
fof(f4006,plain,
( ~ sQ140_spl
| ~ sQ72_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f4001,f1725,f2350,f3559]) ).
fof(f4024,plain,
( ~ sQ9_spl
| ~ subset(sK87_skl,succ(sK86_skl))
| sK87_skl = succ(sK86_skl) ),
inference(resolution,[status(thm)],[f1398,f318]) ).
fof(f4025,plain,
( ~ sQ9_spl
| ~ sQ155_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f4024,f2443,f3720,f1397]) ).
fof(f4035,plain,
( sQ10_spl
| ~ subset(sK87_skl,succ(sK86_skl))
| ~ ordinal(succ(sK86_skl))
| ~ ordinal(sK87_skl) ),
inference(resolution,[status(thm)],[f1403,f832]) ).
fof(f4037,plain,
( sQ10_spl
| ~ sQ155_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4035,f1394,f1391,f3720,f1401]) ).
fof(f4058,definition,
! [X1] :
( sQ159_spl
<=> ~ ordinal(powerset(X1)) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f4059,plain,
! [X0] :
( ~ sQ159_spl
| ~ ordinal(powerset(X0)) ),
inference(component_clause,[status(thm)],[f4058]) ).
fof(f4062,plain,
( ~ sQ47_spl
| ~ sQ159_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2331,f4059]) ).
fof(f4065,plain,
( ~ sQ47_spl
| ~ sQ159_spl ),
inference(contradiction_clause,[status(thm)],[f4062]) ).
fof(f4078,plain,
( sQ155_spl
| ~ in(sK87_skl,succ(sK86_skl))
| ~ epsilon_transitive(succ(sK86_skl)) ),
inference(resolution,[status(thm)],[f3722,f432]) ).
fof(f4081,plain,
( sQ155_spl
| ~ sQ108_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f4078,f1508,f2780,f3720]) ).
fof(f4253,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1379,f1299]) ).
fof(f4254,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f4253]) ).
fof(f4284,plain,
! [X0,X1] :
( in(X0,singleton(X1))
| in(X0,X1)
| ~ in(X0,succ(X1)) ),
inference(paramodulation,[status(thm)],[f389,f1305]) ).
fof(f4318,plain,
( sQ9_spl
| ~ in(succ(sK86_skl),sK87_skl)
| ~ epsilon_transitive(sK87_skl) ),
inference(resolution,[status(thm)],[f1399,f432]) ).
fof(f4321,plain,
( sQ9_spl
| ~ sQ87_spl
| ~ sQ105_spl ),
inference(split_clause,[status(thm)],[f4318,f2692,f2440,f1397]) ).
fof(f4324,plain,
( sQ105_spl
| ~ ordinal(sK87_skl) ),
inference(resolution,[status(thm)],[f2694,f518]) ).
fof(f4325,plain,
( sQ105_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4324,f1394,f2692]) ).
fof(f4362,plain,
( ~ sQ108_spl
| ~ in(succ(sK86_skl),sK87_skl) ),
inference(resolution,[status(thm)],[f2781,f279]) ).
fof(f4366,plain,
( ~ sQ47_spl
| in(sK77_skl,powerset(empty_set))
| powerset(empty_set) = sK77_skl
| in(powerset(empty_set),sK77_skl) ),
inference(resolution,[status(thm)],[f1526,f2331]) ).
fof(f4368,plain,
( in(sK77_skl,sK77_skl)
| sK77_skl = sK77_skl
| in(sK77_skl,sK77_skl) ),
inference(resolution,[status(thm)],[f1526,f815]) ).
fof(f4370,plain,
( ~ sQ7_spl
| in(sK77_skl,succ(sK86_skl))
| succ(sK86_skl) = sK77_skl
| in(succ(sK86_skl),sK77_skl) ),
inference(resolution,[status(thm)],[f1526,f1392]) ).
fof(f4371,plain,
( ~ sQ49_spl
| in(sK77_skl,succ(sK87_skl))
| succ(sK87_skl) = sK77_skl
| in(succ(sK87_skl),sK77_skl) ),
inference(resolution,[status(thm)],[f1526,f2040]) ).
fof(f4376,definition,
( sQ160_spl
<=> in(powerset(empty_set),sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f4377,plain,
( ~ sQ160_spl
| in(powerset(empty_set),sK77_skl) ),
inference(component_clause,[status(thm)],[f4376]) ).
fof(f4379,definition,
( sQ161_spl
<=> powerset(empty_set) = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f4380,plain,
( ~ sQ161_spl
| powerset(empty_set) = sK77_skl ),
inference(component_clause,[status(thm)],[f4379]) ).
fof(f4381,plain,
( sQ161_spl
| powerset(empty_set) != sK77_skl ),
inference(component_clause,[status(thm)],[f4379]) ).
fof(f4382,definition,
( sQ162_spl
<=> in(sK77_skl,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f4383,plain,
( ~ sQ162_spl
| in(sK77_skl,powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f4382]) ).
fof(f4385,plain,
( ~ sQ47_spl
| sQ162_spl
| sQ161_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f4366,f4376,f4379,f4382,f1974]) ).
fof(f4387,plain,
( sQ64_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f4368,f2208,f2211]) ).
fof(f4389,definition,
( sQ163_spl
<=> in(succ(sK86_skl),sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f4390,plain,
( ~ sQ163_spl
| in(succ(sK86_skl),sK77_skl) ),
inference(component_clause,[status(thm)],[f4389]) ).
fof(f4392,definition,
( sQ164_spl
<=> succ(sK86_skl) = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f4393,plain,
( ~ sQ164_spl
| succ(sK86_skl) = sK77_skl ),
inference(component_clause,[status(thm)],[f4392]) ).
fof(f4395,definition,
( sQ165_spl
<=> in(sK77_skl,succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f4396,plain,
( ~ sQ165_spl
| in(sK77_skl,succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f4395]) ).
fof(f4398,plain,
( ~ sQ7_spl
| sQ165_spl
| sQ164_spl
| sQ163_spl ),
inference(split_clause,[status(thm)],[f4370,f4389,f4392,f4395,f1391]) ).
fof(f4399,definition,
( sQ166_spl
<=> in(succ(sK87_skl),sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f4400,plain,
( ~ sQ166_spl
| in(succ(sK87_skl),sK77_skl) ),
inference(component_clause,[status(thm)],[f4399]) ).
fof(f4402,definition,
( sQ167_spl
<=> succ(sK87_skl) = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f4403,plain,
( ~ sQ167_spl
| succ(sK87_skl) = sK77_skl ),
inference(component_clause,[status(thm)],[f4402]) ).
fof(f4405,definition,
( sQ168_spl
<=> in(sK77_skl,succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f4406,plain,
( ~ sQ168_spl
| in(sK77_skl,succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f4405]) ).
fof(f4408,plain,
( ~ sQ49_spl
| sQ168_spl
| sQ167_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f4371,f4399,f4402,f4405,f2039]) ).
fof(f4409,definition,
( sQ169_spl
<=> in(sK77_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f4410,plain,
( ~ sQ169_spl
| in(sK77_skl,empty_set) ),
inference(component_clause,[status(thm)],[f4409]) ).
fof(f4413,plain,
( ~ sQ169_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4410,f1299]) ).
fof(f4414,plain,
~ sQ169_spl,
inference(contradiction_clause,[status(thm)],[f4413]) ).
fof(f4418,plain,
( ~ sQ63_spl
| ~ in(sK77_skl,sK77_skl) ),
inference(resolution,[status(thm)],[f2209,f1044]) ).
fof(f4424,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4418,f2209]) ).
fof(f4425,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f4424]) ).
fof(f4428,plain,
( sQ28_spl
| ~ sQ167_spl
| sK87_skl != sK77_skl ),
inference(backward_demodulation,[status(thm)],[f4403,f1697]) ).
fof(f4450,plain,
( ~ sQ167_spl
| ~ in(sK77_skl,sK87_skl) ),
inference(paramodulation,[status(thm)],[f4403,f1360]) ).
fof(f4459,definition,
( sQ171_spl
<=> epsilon_transitive(sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f4465,plain,
( ~ sQ167_spl
| ~ sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4450,f2432]) ).
fof(f4466,plain,
( ~ sQ167_spl
| ~ sQ85_spl ),
inference(contradiction_clause,[status(thm)],[f4465]) ).
fof(f4474,plain,
( sQ88_spl
| ~ sQ164_spl
| sK77_skl != sK87_skl ),
inference(backward_demodulation,[status(thm)],[f4393,f2445]) ).
fof(f4500,plain,
( sQ88_spl
| ~ sQ164_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f4474,f2434,f4392,f2443]) ).
fof(f4509,plain,
( ~ sQ161_spl
| sK77_skl = singleton(empty_set) ),
inference(backward_demodulation,[status(thm)],[f4380,f938]) ).
fof(f4510,plain,
( ~ sQ161_spl
| sK24_skl(sK77_skl) = empty_set ),
inference(backward_demodulation,[status(thm)],[f4380,f3228]) ).
fof(f4517,plain,
( ~ sQ138_spl
| ~ sQ161_spl
| in(sK77_skl,sK86_skl) ),
inference(backward_demodulation,[status(thm)],[f4380,f3554]) ).
fof(f4520,plain,
( sQ84_spl
| ~ sQ161_spl
| sK77_skl != sK87_skl ),
inference(backward_demodulation,[status(thm)],[f4380,f2429]) ).
fof(f4529,plain,
( sQ84_spl
| ~ sQ161_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f4520,f2434,f4379,f2427]) ).
fof(f4579,plain,
( ~ sQ144_spl
| ~ sQ86_spl
| in(sK87_skl,sK86_skl) ),
inference(forward_demodulation,[status(thm)],[f2435,f3574]) ).
fof(f4580,plain,
( ~ sQ144_spl
| ~ sQ86_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4579,f1388]) ).
fof(f4581,plain,
( ~ sQ144_spl
| ~ sQ86_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f4580]) ).
fof(f4584,plain,
( ~ sQ84_spl
| sK24_skl(sK87_skl) = empty_set ),
inference(paramodulation,[status(thm)],[f2606,f3227]) ).
fof(f4730,plain,
( ~ sQ84_spl
| in(empty_set,sK87_skl)
| empty(sK87_skl) ),
inference(resolution,[status(thm)],[f3024,f446]) ).
fof(f4731,definition,
( sQ173_spl
<=> empty(sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f4732,plain,
( ~ sQ173_spl
| empty(sK87_skl) ),
inference(component_clause,[status(thm)],[f4731]) ).
fof(f4734,plain,
( ~ sQ84_spl
| sQ39_spl
| sQ173_spl ),
inference(split_clause,[status(thm)],[f4730,f4731,f1811,f2427]) ).
fof(f4735,plain,
( ~ sQ173_spl
| ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4732,f2610]) ).
fof(f4736,plain,
( ~ sQ173_spl
| ~ sQ84_spl ),
inference(contradiction_clause,[status(thm)],[f4735]) ).
fof(f4739,plain,
( sQ161_spl
| ~ sQ84_spl
| sK87_skl != sK77_skl ),
inference(forward_demodulation,[status(thm)],[f2428,f4381]) ).
fof(f4810,plain,
( ~ sQ166_spl
| ~ in(sK77_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f4400,f1362]) ).
fof(f4818,plain,
( ~ sQ166_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f4810,f2431,f4399]) ).
fof(f4822,plain,
( sQ161_spl
| ~ sQ84_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f4739,f2434,f2427,f4379]) ).
fof(f4823,plain,
( ~ sQ161_spl
| ~ sQ84_spl
| sK87_skl = sK77_skl ),
inference(forward_demodulation,[status(thm)],[f2428,f4380]) ).
fof(f4826,plain,
( ~ sQ138_spl
| ~ sQ161_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f4517,f3573,f4379,f3553]) ).
fof(f4827,plain,
( ~ sQ166_spl
| ~ sQ86_spl
| in(succ(sK87_skl),sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f2435,f4400]) ).
fof(f4837,plain,
( ~ sQ166_spl
| ~ sQ86_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f4827,f2995,f2434,f4399]) ).
fof(f4858,definition,
( sQ174_spl
<=> in(sK67_skl,sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f4861,definition,
( sQ175_spl
<=> sK67_skl = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f4862,plain,
( ~ sQ175_spl
| sK67_skl = sK77_skl ),
inference(component_clause,[status(thm)],[f4861]) ).
fof(f4864,definition,
( sQ176_spl
<=> in(sK77_skl,sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f4865,plain,
( ~ sQ176_spl
| in(sK77_skl,sK67_skl) ),
inference(component_clause,[status(thm)],[f4864]) ).
fof(f4873,plain,
! [X0] :
( ~ sQ90_spl
| ordinal_subset(empty_set,X0)
| ~ ordinal(X0)
| ~ ordinal(empty_set)
| ~ ordinal(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f2496,f303]) ).
fof(f4875,plain,
! [X0] :
( ~ sQ90_spl
| ~ subset(X0,empty_set)
| ~ ordinal(empty_set)
| ~ ordinal(X0)
| ~ ordinal(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f2496,f832]) ).
fof(f4876,definition,
! [X0] :
( sQ177_spl
<=> ( ordinal_subset(empty_set,X0)
| ~ ordinal(X0)
| ~ ordinal(X0)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f4879,plain,
( ~ sQ90_spl
| ~ sQ4_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f4873,f4876,f1375,f2495]) ).
fof(f4881,definition,
! [X0] :
( sQ178_spl
<=> ( ~ subset(X0,empty_set)
| ~ ordinal(X0)
| ~ ordinal(X0)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f4884,plain,
( ~ sQ90_spl
| ~ sQ4_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f4875,f4881,f1375,f2495]) ).
fof(f4952,plain,
( ~ sQ109_spl
| ~ sQ175_spl
| in(sK77_skl,sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f4862,f2819]) ).
fof(f4953,plain,
( ~ sQ109_spl
| ~ sQ175_spl
| sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4952,f2433]) ).
fof(f4954,plain,
( ~ sQ109_spl
| ~ sQ175_spl
| sQ85_spl ),
inference(contradiction_clause,[status(thm)],[f4953]) ).
fof(f4955,plain,
( ~ sQ141_spl
| ~ sQ110_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f3830,f1427,f2821,f3563]) ).
fof(f4995,plain,
! [X0] :
( X0 = empty_set
| in(ordered_pair(sK38_skl(empty_set,X0),sK39_skl(empty_set,X0)),X0)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f491,f1056]) ).
fof(f4998,definition,
! [X0] :
( sQ179_spl
<=> ( X0 = empty_set
| in(ordered_pair(sK38_skl(empty_set,X0),sK39_skl(empty_set,X0)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f5001,plain,
( ~ sQ54_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f4995,f4998,f2139]) ).
fof(f5059,plain,
( in(sK67_skl,sK77_skl)
| sK77_skl = sK67_skl
| in(sK77_skl,sK67_skl) ),
inference(resolution,[status(thm)],[f1552,f815]) ).
fof(f5061,plain,
( in(sK67_skl,sK86_skl)
| sK86_skl = sK67_skl
| in(sK86_skl,sK67_skl) ),
inference(resolution,[status(thm)],[f1552,f998]) ).
fof(f5063,plain,
( ~ sQ49_spl
| in(sK67_skl,succ(sK87_skl))
| succ(sK87_skl) = sK67_skl
| in(succ(sK87_skl),sK67_skl) ),
inference(resolution,[status(thm)],[f1552,f2040]) ).
fof(f5069,plain,
( sQ174_spl
| sQ175_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f5059,f4864,f4861,f4858]) ).
fof(f5071,plain,
( sQ141_spl
| sQ142_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f5061,f3569,f3566,f3563]) ).
fof(f5075,definition,
( sQ181_spl
<=> succ(sK86_skl) = sK67_skl ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f5076,plain,
( ~ sQ181_spl
| succ(sK86_skl) = sK67_skl ),
inference(component_clause,[status(thm)],[f5075]) ).
fof(f5082,definition,
( sQ183_spl
<=> in(succ(sK87_skl),sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f5083,plain,
( ~ sQ183_spl
| in(succ(sK87_skl),sK67_skl) ),
inference(component_clause,[status(thm)],[f5082]) ).
fof(f5085,definition,
( sQ184_spl
<=> succ(sK87_skl) = sK67_skl ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f5086,plain,
( ~ sQ184_spl
| succ(sK87_skl) = sK67_skl ),
inference(component_clause,[status(thm)],[f5085]) ).
fof(f5088,definition,
( sQ185_spl
<=> in(sK67_skl,succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f5091,plain,
( ~ sQ49_spl
| sQ185_spl
| sQ184_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f5063,f5082,f5085,f5088,f2039]) ).
fof(f5092,definition,
( sQ186_spl
<=> in(sK67_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f5093,plain,
( ~ sQ186_spl
| in(sK67_skl,empty_set) ),
inference(component_clause,[status(thm)],[f5092]) ).
fof(f5096,plain,
( ~ sQ186_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5093,f1299]) ).
fof(f5097,plain,
~ sQ186_spl,
inference(contradiction_clause,[status(thm)],[f5096]) ).
fof(f5110,plain,
( ~ sQ175_spl
| ~ sQ33_spl
| empty_set = sK77_skl ),
inference(forward_demodulation,[status(thm)],[f1747,f4862]) ).
fof(f5111,plain,
( ~ sQ175_spl
| ~ sQ33_spl
| sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5110,f2199]) ).
fof(f5112,plain,
( ~ sQ175_spl
| ~ sQ33_spl
| sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f5111]) ).
fof(f5120,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1759,f777]) ).
fof(f5121,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f5120]) ).
fof(f5221,plain,
( in(sK67_skl,sK67_skl)
| sK67_skl = sK67_skl
| in(sK67_skl,sK67_skl) ),
inference(resolution,[status(thm)],[f1405,f777]) ).
fof(f5231,plain,
( sQ38_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f5221,f1760,f1763]) ).
fof(f5242,plain,
( ~ sQ37_spl
| ~ in(sK67_skl,sK67_skl) ),
inference(resolution,[status(thm)],[f1761,f1044]) ).
fof(f5248,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5242,f1761]) ).
fof(f5249,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f5248]) ).
fof(f5273,plain,
( ~ sQ184_spl
| ~ in(sK67_skl,sK87_skl) ),
inference(paramodulation,[status(thm)],[f5086,f1360]) ).
fof(f5285,plain,
( ~ sQ184_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f5273,f2818,f5085]) ).
fof(f5289,plain,
( ~ sQ108_spl
| ~ sQ181_spl
| ~ in(sK67_skl,sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f5076,f4362]) ).
fof(f5316,plain,
( ~ sQ108_spl
| ~ sQ181_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f5289,f2818,f5075,f2780]) ).
fof(f5434,plain,
( in(empty_set,sK67_skl)
| sK67_skl = empty_set ),
inference(resolution,[status(thm)],[f1980,f777]) ).
fof(f5435,plain,
( in(empty_set,sK77_skl)
| sK77_skl = empty_set ),
inference(resolution,[status(thm)],[f1980,f815]) ).
fof(f5436,plain,
( in(empty_set,sK87_skl)
| sK87_skl = empty_set ),
inference(resolution,[status(thm)],[f1980,f999]) ).
fof(f5437,plain,
( in(empty_set,sK86_skl)
| sK86_skl = empty_set ),
inference(resolution,[status(thm)],[f1980,f998]) ).
fof(f5438,plain,
( ~ sQ7_spl
| in(empty_set,succ(sK86_skl))
| succ(sK86_skl) = empty_set ),
inference(resolution,[status(thm)],[f1980,f1392]) ).
fof(f5439,plain,
( ~ sQ49_spl
| in(empty_set,succ(sK87_skl))
| succ(sK87_skl) = empty_set ),
inference(resolution,[status(thm)],[f1980,f2040]) ).
fof(f5444,plain,
( sQ32_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f5434,f1746,f1743]) ).
fof(f5445,plain,
( sQ59_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f5435,f2197,f2194]) ).
fof(f5446,plain,
( sQ39_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f5436,f1467,f1811]) ).
fof(f5447,plain,
( sQ25_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f5437,f1579,f1576]) ).
fof(f5448,definition,
( sQ190_spl
<=> in(empty_set,succ(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f5449,plain,
( ~ sQ190_spl
| in(empty_set,succ(sK86_skl)) ),
inference(component_clause,[status(thm)],[f5448]) ).
fof(f5451,plain,
( ~ sQ7_spl
| sQ190_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f5438,f3678,f5448,f1391]) ).
fof(f5452,definition,
( sQ191_spl
<=> succ(sK87_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f5453,plain,
( ~ sQ191_spl
| succ(sK87_skl) = empty_set ),
inference(component_clause,[status(thm)],[f5452]) ).
fof(f5455,definition,
( sQ192_spl
<=> in(empty_set,succ(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f5456,plain,
( ~ sQ192_spl
| in(empty_set,succ(sK87_skl)) ),
inference(component_clause,[status(thm)],[f5455]) ).
fof(f5458,plain,
( ~ sQ49_spl
| sQ192_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f5439,f5452,f5455,f2039]) ).
fof(f5503,plain,
( ~ sQ191_spl
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f5453,f659]) ).
fof(f5522,plain,
( ~ sQ191_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5503,f649]) ).
fof(f5523,plain,
~ sQ191_spl,
inference(contradiction_clause,[status(thm)],[f5522]) ).
fof(f5580,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK79_skl,X0)),sK79_skl)
| ~ in(X0,relation_dom(sK79_skl))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1313,f822]) ).
fof(f5581,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK76_skl,X0)),sK76_skl)
| ~ in(X0,relation_dom(sK76_skl))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1313,f809]) ).
fof(f5582,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK66_skl,X0)),sK66_skl)
| ~ in(X0,relation_dom(sK66_skl))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1313,f773]) ).
fof(f5583,plain,
! [X0] :
( in(ordered_pair(X0,apply(empty_set,X0)),empty_set)
| ~ in(X0,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1313,f670]) ).
fof(f5586,definition,
! [X0] :
( sQ193_spl
<=> ( in(ordered_pair(X0,apply(sK79_skl,X0)),sK79_skl)
| ~ in(X0,relation_dom(sK79_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f5589,plain,
( sQ193_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f5580,f2274,f5586]) ).
fof(f5590,definition,
! [X0] :
( sQ194_spl
<=> ( in(ordered_pair(X0,apply(sK76_skl,X0)),sK76_skl)
| ~ in(X0,relation_dom(sK76_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f5593,plain,
( sQ194_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f5581,f2281,f5590]) ).
fof(f5594,definition,
! [X0] :
( sQ195_spl
<=> ( in(ordered_pair(X0,apply(sK66_skl,X0)),sK66_skl)
| ~ in(X0,relation_dom(sK66_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f5597,plain,
( sQ195_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f5582,f2288,f5594]) ).
fof(f5598,definition,
! [X0] :
( sQ196_spl
<=> ( in(ordered_pair(X0,apply(empty_set,X0)),empty_set)
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f5601,plain,
( sQ196_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f5583,f2139,f5598]) ).
fof(f5608,plain,
( sQ109_spl
| ~ sQ142_spl
| ~ in(sK86_skl,sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f3567,f2820]) ).
fof(f5609,plain,
( sQ109_spl
| ~ sQ142_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5608,f1261]) ).
fof(f5610,plain,
( sQ109_spl
| ~ sQ142_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f5609]) ).
fof(f5613,plain,
( sQ3_spl
| ~ sQ26_spl
| ~ subset(powerset(empty_set),sK87_skl)
| ~ ordinal(sK87_skl)
| ~ ordinal(powerset(empty_set)) ),
inference(resolution,[status(thm)],[f3610,f832]) ).
fof(f5614,definition,
( sQ197_spl
<=> ordinal_subset(sK87_skl,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f5615,plain,
( ~ sQ197_spl
| ordinal_subset(sK87_skl,powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f5614]) ).
fof(f5616,plain,
( sQ197_spl
| ~ ordinal_subset(sK87_skl,powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f5614]) ).
fof(f5618,definition,
( sQ198_spl
<=> subset(powerset(empty_set),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f5620,plain,
( sQ198_spl
| ~ subset(powerset(empty_set),sK87_skl) ),
inference(component_clause,[status(thm)],[f5618]) ).
fof(f5621,plain,
( sQ3_spl
| ~ sQ26_spl
| ~ sQ198_spl
| ~ sQ8_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5613,f2350,f1394,f5618,f1579,f1263]) ).
fof(f5629,plain,
( sQ3_spl
| ~ sQ26_spl
| ~ ordinal_subset(succ(empty_set),sK87_skl) ),
inference(backward_demodulation,[status(thm)],[f1580,f1265]) ).
fof(f5652,plain,
( sQ3_spl
| ~ sQ26_spl
| ~ subset(succ(empty_set),sK87_skl)
| ~ ordinal(sK87_skl)
| ~ ordinal(succ(empty_set)) ),
inference(resolution,[status(thm)],[f5629,f832]) ).
fof(f5653,definition,
( sQ199_spl
<=> ordinal(succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f5654,plain,
( ~ sQ199_spl
| ordinal(succ(empty_set)) ),
inference(component_clause,[status(thm)],[f5653]) ).
fof(f5655,plain,
( sQ199_spl
| ~ ordinal(succ(empty_set)) ),
inference(component_clause,[status(thm)],[f5653]) ).
fof(f5656,definition,
( sQ200_spl
<=> ordinal_subset(sK87_skl,succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f5657,plain,
( ~ sQ200_spl
| ordinal_subset(sK87_skl,succ(empty_set)) ),
inference(component_clause,[status(thm)],[f5656]) ).
fof(f5660,definition,
( sQ201_spl
<=> subset(succ(empty_set),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f5662,plain,
( sQ201_spl
| ~ subset(succ(empty_set),sK87_skl) ),
inference(component_clause,[status(thm)],[f5660]) ).
fof(f5663,plain,
( sQ3_spl
| ~ sQ26_spl
| ~ sQ201_spl
| ~ sQ8_spl
| ~ sQ199_spl ),
inference(split_clause,[status(thm)],[f5652,f5653,f1394,f5660,f1579,f1263]) ).
fof(f5685,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK79_skl)
| X1 = apply(sK79_skl,X0)
| ~ in(X0,relation_dom(sK79_skl))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f513,f822]) ).
fof(f5686,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK76_skl)
| X1 = apply(sK76_skl,X0)
| ~ in(X0,relation_dom(sK76_skl))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f513,f809]) ).
fof(f5687,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK66_skl)
| X1 = apply(sK66_skl,X0)
| ~ in(X0,relation_dom(sK66_skl))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f513,f773]) ).
fof(f5688,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),empty_set)
| X1 = apply(empty_set,X0)
| ~ in(X0,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f513,f670]) ).
fof(f5691,definition,
! [X0,X1] :
( sQ202_spl
<=> ( ~ in(ordered_pair(X0,X1),sK79_skl)
| X1 = apply(sK79_skl,X0)
| ~ in(X0,relation_dom(sK79_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f5694,plain,
( sQ202_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f5685,f2274,f5691]) ).
fof(f5695,definition,
! [X0,X1] :
( sQ203_spl
<=> ( ~ in(ordered_pair(X0,X1),sK76_skl)
| X1 = apply(sK76_skl,X0)
| ~ in(X0,relation_dom(sK76_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f5698,plain,
( sQ203_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f5686,f2281,f5695]) ).
fof(f5699,definition,
! [X0,X1] :
( sQ204_spl
<=> ( ~ in(ordered_pair(X0,X1),sK66_skl)
| X1 = apply(sK66_skl,X0)
| ~ in(X0,relation_dom(sK66_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f5702,plain,
( sQ204_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f5687,f2288,f5699]) ).
fof(f5703,definition,
! [X0,X1] :
( sQ205_spl
<=> ( ~ in(ordered_pair(X0,X1),empty_set)
| X1 = apply(empty_set,X0)
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f5706,plain,
( sQ205_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f5688,f2139,f5703]) ).
fof(f5709,plain,
! [X0] :
( apply(sK79_skl,X0) = empty_set
| in(X0,relation_dom(sK79_skl))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1314,f822]) ).
fof(f5710,plain,
! [X0] :
( apply(sK76_skl,X0) = empty_set
| in(X0,relation_dom(sK76_skl))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1314,f809]) ).
fof(f5711,plain,
! [X0] :
( apply(sK66_skl,X0) = empty_set
| in(X0,relation_dom(sK66_skl))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1314,f773]) ).
fof(f5712,plain,
! [X0] :
( apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1314,f670]) ).
fof(f5715,definition,
! [X0] :
( sQ206_spl
<=> ( apply(sK79_skl,X0) = empty_set
| in(X0,relation_dom(sK79_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f5718,plain,
( sQ206_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f5709,f2274,f5715]) ).
fof(f5719,definition,
! [X0] :
( sQ207_spl
<=> ( apply(sK76_skl,X0) = empty_set
| in(X0,relation_dom(sK76_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f5722,plain,
( sQ207_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f5710,f2281,f5719]) ).
fof(f5723,definition,
! [X0] :
( sQ208_spl
<=> ( apply(sK66_skl,X0) = empty_set
| in(X0,relation_dom(sK66_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f5726,plain,
( sQ208_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f5711,f2288,f5723]) ).
fof(f5727,definition,
! [X0] :
( sQ209_spl
<=> ( apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f5728,plain,
! [X0] :
( ~ sQ209_spl
| apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f5727]) ).
fof(f5730,plain,
( sQ209_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f5712,f2139,f5727]) ).
fof(f5731,plain,
! [X0] :
( ~ sQ209_spl
| apply(empty_set,X0) = empty_set
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1121,f5728]) ).
fof(f5732,plain,
! [X0] :
( ~ sQ209_spl
| apply(empty_set,X0) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f5731,f1299]) ).
fof(f5797,plain,
( ~ sQ176_spl
| ~ sQ110_spl
| in(sK77_skl,sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f2822,f4865]) ).
fof(f5798,plain,
( ~ sQ176_spl
| ~ sQ110_spl
| sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5797,f2433]) ).
fof(f5799,plain,
( ~ sQ176_spl
| ~ sQ110_spl
| sQ85_spl ),
inference(contradiction_clause,[status(thm)],[f5798]) ).
fof(f5875,plain,
( sQ199_spl
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f5655,f689]) ).
fof(f5878,plain,
( sQ199_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5875,f1375,f5653]) ).
fof(f5879,definition,
( sQ210_spl
<=> epsilon_transitive(succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f5880,plain,
( ~ sQ210_spl
| epsilon_transitive(succ(empty_set)) ),
inference(component_clause,[status(thm)],[f5879]) ).
fof(f5881,plain,
( sQ210_spl
| ~ epsilon_transitive(succ(empty_set)) ),
inference(component_clause,[status(thm)],[f5879]) ).
fof(f5882,definition,
( sQ211_spl
<=> epsilon_connected(succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f5884,plain,
( sQ211_spl
| ~ epsilon_connected(succ(empty_set)) ),
inference(component_clause,[status(thm)],[f5882]) ).
fof(f6050,plain,
( sQ211_spl
| ~ ordinal(succ(empty_set)) ),
inference(resolution,[status(thm)],[f5884,f519]) ).
fof(f6052,plain,
( sQ211_spl
| ~ sQ199_spl ),
inference(split_clause,[status(thm)],[f6050,f5653,f5882]) ).
fof(f6055,plain,
( sQ210_spl
| ~ ordinal(succ(empty_set)) ),
inference(resolution,[status(thm)],[f5881,f518]) ).
fof(f6057,plain,
( sQ210_spl
| ~ sQ199_spl ),
inference(split_clause,[status(thm)],[f6055,f5653,f5879]) ).
fof(f6058,plain,
( ~ sQ199_spl
| in(empty_set,succ(empty_set))
| succ(empty_set) = empty_set ),
inference(resolution,[status(thm)],[f5654,f1980]) ).
fof(f6059,plain,
( ~ sQ199_spl
| in(sK87_skl,succ(empty_set))
| succ(empty_set) = sK87_skl
| in(succ(empty_set),sK87_skl) ),
inference(resolution,[status(thm)],[f5654,f1367]) ).
fof(f6061,definition,
( sQ214_spl
<=> succ(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f6062,plain,
( ~ sQ214_spl
| succ(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f6061]) ).
fof(f6064,definition,
( sQ215_spl
<=> in(empty_set,succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f6067,plain,
( ~ sQ199_spl
| sQ215_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f6058,f6061,f6064,f5653]) ).
fof(f6068,definition,
( sQ216_spl
<=> in(succ(empty_set),sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f6071,definition,
( sQ217_spl
<=> succ(empty_set) = sK87_skl ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f6072,plain,
( ~ sQ217_spl
| succ(empty_set) = sK87_skl ),
inference(component_clause,[status(thm)],[f6071]) ).
fof(f6073,plain,
( sQ217_spl
| succ(empty_set) != sK87_skl ),
inference(component_clause,[status(thm)],[f6071]) ).
fof(f6074,definition,
( sQ218_spl
<=> in(sK87_skl,succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f6075,plain,
( ~ sQ218_spl
| in(sK87_skl,succ(empty_set)) ),
inference(component_clause,[status(thm)],[f6074]) ).
fof(f6077,plain,
( ~ sQ199_spl
| sQ218_spl
| sQ217_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f6059,f6068,f6071,f6074,f5653]) ).
fof(f6079,plain,
! [X0] :
( ~ sQ210_spl
| ~ epsilon_connected(succ(empty_set))
| in(succ(empty_set),X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f5880,f1525]) ).
fof(f6080,definition,
! [X0] :
( sQ219_spl
<=> ( in(succ(empty_set),X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f6083,plain,
( ~ sQ210_spl
| ~ sQ211_spl
| sQ219_spl ),
inference(split_clause,[status(thm)],[f6079,f6080,f5882,f5879]) ).
fof(f6089,plain,
( ~ sQ214_spl
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f6062,f659]) ).
fof(f6106,plain,
( ~ sQ214_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6089,f649]) ).
fof(f6107,plain,
~ sQ214_spl,
inference(contradiction_clause,[status(thm)],[f6106]) ).
fof(f6170,plain,
! [X0] :
( ~ sQ217_spl
| ~ ordinal(empty_set)
| in(sK87_skl,X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f6072,f1365]) ).
fof(f6173,plain,
( ~ sQ217_spl
| epsilon_connected(sK87_skl)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f6072,f688]) ).
fof(f6179,plain,
( ~ sQ217_spl
| ~ sQ4_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f6170,f3056,f1375,f6071]) ).
fof(f6181,plain,
( ~ sQ217_spl
| sQ89_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f6173,f1375,f2461,f6071]) ).
fof(f6202,plain,
( ~ sQ163_spl
| ~ in(sK77_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f4390,f1362]) ).
fof(f6212,plain,
( ~ sQ163_spl
| ~ sQ144_spl ),
inference(split_clause,[status(thm)],[f6202,f3573,f4389]) ).
fof(f6214,plain,
! [X0] :
( ~ sQ162_spl
| ~ in(X0,sK77_skl)
| in(X0,union(powerset(empty_set))) ),
inference(resolution,[status(thm)],[f4383,f1320]) ).
fof(f6223,plain,
! [X0] :
( ~ sQ162_spl
| ~ in(X0,sK77_skl)
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1216,f6214]) ).
fof(f6224,plain,
! [X0] :
( ~ sQ162_spl
| ~ in(X0,sK77_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6223,f1299]) ).
fof(f6252,plain,
( ~ sQ199_spl
| in(sK77_skl,succ(empty_set))
| succ(empty_set) = sK77_skl
| in(succ(empty_set),sK77_skl) ),
inference(resolution,[status(thm)],[f3692,f5654]) ).
fof(f6264,definition,
( sQ220_spl
<=> in(succ(empty_set),sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f6265,plain,
( ~ sQ220_spl
| in(succ(empty_set),sK77_skl) ),
inference(component_clause,[status(thm)],[f6264]) ).
fof(f6267,definition,
( sQ221_spl
<=> succ(empty_set) = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f6268,plain,
( ~ sQ221_spl
| succ(empty_set) = sK77_skl ),
inference(component_clause,[status(thm)],[f6267]) ).
fof(f6269,plain,
( sQ221_spl
| succ(empty_set) != sK77_skl ),
inference(component_clause,[status(thm)],[f6267]) ).
fof(f6270,definition,
( sQ222_spl
<=> in(sK77_skl,succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f6271,plain,
( ~ sQ222_spl
| in(sK77_skl,succ(empty_set)) ),
inference(component_clause,[status(thm)],[f6270]) ).
fof(f6273,plain,
( ~ sQ199_spl
| sQ222_spl
| sQ221_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f6252,f6264,f6267,f6270,f5653]) ).
fof(f6292,plain,
! [X0] :
( ~ sQ221_spl
| ~ ordinal(empty_set)
| in(sK77_skl,X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f6268,f1365]) ).
fof(f6294,plain,
( ~ sQ221_spl
| epsilon_transitive(sK77_skl)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f6268,f687]) ).
fof(f6301,definition,
! [X0] :
( sQ223_spl
<=> ( in(sK77_skl,X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f6304,plain,
( ~ sQ221_spl
| ~ sQ4_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f6292,f6301,f1375,f6267]) ).
fof(f6305,plain,
( ~ sQ221_spl
| sQ171_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f6294,f1375,f4459,f6267]) ).
fof(f6435,plain,
( sQ221_spl
| powerset(empty_set) != sK77_skl ),
inference(backward_demodulation,[status(thm)],[f2334,f6269]) ).
fof(f6440,plain,
( sQ217_spl
| powerset(empty_set) != sK87_skl ),
inference(backward_demodulation,[status(thm)],[f2334,f6073]) ).
fof(f6525,plain,
! [X0] :
( ~ in(X0,empty_set)
| ~ in(powerset(empty_set),X0)
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f3228,f3224]) ).
fof(f6528,definition,
! [X0] :
( sQ227_spl
<=> ( ~ in(X0,empty_set)
| ~ in(powerset(empty_set),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f6531,plain,
( sQ227_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f6525,f3244,f6528]) ).
fof(f6534,plain,
( ~ sQ183_spl
| ~ in(sK67_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f5083,f1362]) ).
fof(f6544,plain,
( ~ sQ183_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f6534,f2818,f5082]) ).
fof(f6729,plain,
! [X0] :
( ~ sQ143_spl
| ~ ordinal(sK67_skl)
| in(sK86_skl,X0)
| X0 = sK86_skl
| in(X0,sK86_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f3570,f1369]) ).
fof(f6734,plain,
( ~ sQ143_spl
| ~ sQ36_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f6729,f1725,f1757,f3569]) ).
fof(f6751,plain,
! [X0] :
( ~ sQ192_spl
| ~ ordinal(succ(sK87_skl))
| in(empty_set,X0)
| X0 = empty_set
| in(X0,empty_set)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f5456,f1369]) ).
fof(f6756,plain,
( ~ sQ192_spl
| ~ sQ49_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f6751,f1729,f2039,f5455]) ).
fof(f6759,plain,
! [X0] :
( ~ sQ106_spl
| ~ in(X0,sK87_skl)
| in(X0,union(powerset(empty_set))) ),
inference(resolution,[status(thm)],[f2772,f1320]) ).
fof(f6769,plain,
! [X0] :
( ~ sQ106_spl
| ~ in(X0,sK87_skl)
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1216,f6759]) ).
fof(f6770,plain,
! [X0] :
( ~ sQ106_spl
| ~ in(X0,sK87_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6769,f1299]) ).
fof(f6772,plain,
( sQ217_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f6440,f2427,f6071]) ).
fof(f6774,plain,
( ~ sQ84_spl
| sK87_skl = powerset(empty_set) ),
inference(forward_demodulation,[status(thm)],[f938,f2606]) ).
fof(f6778,plain,
( ~ sQ139_spl
| sK86_skl = powerset(empty_set) ),
inference(forward_demodulation,[status(thm)],[f938,f3838]) ).
fof(f6781,plain,
( ~ sQ217_spl
| powerset(empty_set) = sK87_skl ),
inference(forward_demodulation,[status(thm)],[f2334,f6072]) ).
fof(f6789,plain,
! [X0] :
( in(sK49_skl(X0,relation_rng(sK79_skl),sK79_skl),relation_dom(sK79_skl))
| ~ in(X0,relation_rng(sK79_skl))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1324,f822]) ).
fof(f6790,plain,
! [X0] :
( in(sK49_skl(X0,relation_rng(sK76_skl),sK76_skl),relation_dom(sK76_skl))
| ~ in(X0,relation_rng(sK76_skl))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1324,f809]) ).
fof(f6791,plain,
! [X0] :
( in(sK49_skl(X0,relation_rng(sK66_skl),sK66_skl),relation_dom(sK66_skl))
| ~ in(X0,relation_rng(sK66_skl))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1324,f773]) ).
fof(f6792,plain,
! [X0] :
( in(sK49_skl(X0,relation_rng(empty_set),empty_set),relation_dom(empty_set))
| ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1324,f670]) ).
fof(f6797,definition,
! [X0] :
( sQ228_spl
<=> ( in(sK49_skl(X0,relation_rng(sK79_skl),sK79_skl),relation_dom(sK79_skl))
| ~ in(X0,relation_rng(sK79_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f6800,plain,
( sQ228_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f6789,f2274,f6797]) ).
fof(f6801,definition,
! [X0] :
( sQ229_spl
<=> ( in(sK49_skl(X0,relation_rng(sK76_skl),sK76_skl),relation_dom(sK76_skl))
| ~ in(X0,relation_rng(sK76_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f6804,plain,
( sQ229_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f6790,f2281,f6801]) ).
fof(f6805,definition,
! [X0] :
( sQ230_spl
<=> ( in(sK49_skl(X0,relation_rng(sK66_skl),sK66_skl),relation_dom(sK66_skl))
| ~ in(X0,relation_rng(sK66_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f6808,plain,
( sQ230_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f6791,f2288,f6805]) ).
fof(f6809,definition,
! [X0] :
( sQ231_spl
<=> ( in(sK49_skl(X0,relation_rng(empty_set),empty_set),relation_dom(empty_set))
| ~ in(X0,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f6812,plain,
( sQ231_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6792,f2139,f6809]) ).
fof(f6817,plain,
! [X0] :
( X0 = apply(sK79_skl,sK49_skl(X0,relation_rng(sK79_skl),sK79_skl))
| ~ in(X0,relation_rng(sK79_skl))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1325,f822]) ).
fof(f6818,plain,
! [X0] :
( X0 = apply(sK76_skl,sK49_skl(X0,relation_rng(sK76_skl),sK76_skl))
| ~ in(X0,relation_rng(sK76_skl))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1325,f809]) ).
fof(f6819,plain,
! [X0] :
( X0 = apply(sK66_skl,sK49_skl(X0,relation_rng(sK66_skl),sK66_skl))
| ~ in(X0,relation_rng(sK66_skl))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1325,f773]) ).
fof(f6820,plain,
! [X0] :
( X0 = apply(empty_set,sK49_skl(X0,relation_rng(empty_set),empty_set))
| ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1325,f670]) ).
fof(f6824,definition,
! [X0] :
( sQ232_spl
<=> ( X0 = apply(sK79_skl,sK49_skl(X0,relation_rng(sK79_skl),sK79_skl))
| ~ in(X0,relation_rng(sK79_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f6827,plain,
( sQ232_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f6817,f2274,f6824]) ).
fof(f6828,definition,
! [X0] :
( sQ233_spl
<=> ( X0 = apply(sK76_skl,sK49_skl(X0,relation_rng(sK76_skl),sK76_skl))
| ~ in(X0,relation_rng(sK76_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f6831,plain,
( sQ233_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f6818,f2281,f6828]) ).
fof(f6832,definition,
! [X0] :
( sQ234_spl
<=> ( X0 = apply(sK66_skl,sK49_skl(X0,relation_rng(sK66_skl),sK66_skl))
| ~ in(X0,relation_rng(sK66_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f6835,plain,
( sQ234_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f6819,f2288,f6832]) ).
fof(f6836,definition,
! [X0] :
( sQ235_spl
<=> ( X0 = apply(empty_set,sK49_skl(X0,relation_rng(empty_set),empty_set))
| ~ in(X0,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f6839,plain,
( sQ235_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6820,f2139,f6836]) ).
fof(f6845,plain,
( ~ sQ160_spl
| ~ sQ84_spl
| in(sK87_skl,sK77_skl) ),
inference(backward_demodulation,[status(thm)],[f6774,f4377]) ).
fof(f6858,plain,
( ~ sQ160_spl
| ~ sQ84_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f6845,f2775,f2427,f4376]) ).
fof(f6860,plain,
( sQ221_spl
| ~ sQ161_spl ),
inference(split_clause,[status(thm)],[f6435,f4379,f6267]) ).
fof(f6861,plain,
( ~ sQ161_spl
| ~ sQ84_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f4823,f2434,f2427,f4379]) ).
fof(f6865,plain,
( ~ sQ161_spl
| ~ sQ84_spl
| sK87_skl = sK77_skl ),
inference(forward_demodulation,[status(thm)],[f6774,f4380]) ).
fof(f6869,plain,
( ~ sQ109_spl
| ~ sQ106_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2819,f6770]) ).
fof(f6870,plain,
( ~ sQ85_spl
| ~ sQ106_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2432,f6770]) ).
fof(f6890,plain,
( ~ sQ109_spl
| ~ sQ106_spl ),
inference(contradiction_clause,[status(thm)],[f6869]) ).
fof(f6891,plain,
( ~ sQ85_spl
| ~ sQ106_spl ),
inference(contradiction_clause,[status(thm)],[f6870]) ).
fof(f6902,plain,
( ~ sQ59_spl
| ~ sQ162_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2195,f6224]) ).
fof(f6921,plain,
( ~ sQ59_spl
| ~ sQ162_spl ),
inference(contradiction_clause,[status(thm)],[f6902]) ).
fof(f6922,plain,
( sQ28_spl
| ~ sQ167_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f4428,f2434,f4402,f1695]) ).
fof(f6923,plain,
( ~ sQ161_spl
| ~ sQ139_spl
| sK86_skl = sK77_skl ),
inference(forward_demodulation,[status(thm)],[f6778,f4380]) ).
fof(f6924,plain,
( ~ sQ161_spl
| ~ sQ139_spl
| sQ145_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6923,f3578]) ).
fof(f6925,plain,
( ~ sQ161_spl
| ~ sQ139_spl
| sQ145_spl ),
inference(contradiction_clause,[status(thm)],[f6924]) ).
fof(f6955,plain,
( ~ sQ145_spl
| ~ sQ161_spl
| ~ sQ84_spl
| sK87_skl = sK86_skl ),
inference(forward_demodulation,[status(thm)],[f6865,f3577]) ).
fof(f6956,plain,
( ~ sQ145_spl
| ~ sQ161_spl
| ~ sQ84_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6955,f1432]) ).
fof(f6957,plain,
( ~ sQ145_spl
| ~ sQ161_spl
| ~ sQ84_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f6956]) ).
fof(f6987,plain,
! [X0] :
( ~ sQ84_spl
| ~ in(X0,empty_set)
| ~ in(sK87_skl,X0)
| sK87_skl = empty_set ),
inference(paramodulation,[status(thm)],[f4584,f3224]) ).
fof(f6990,definition,
! [X0] :
( sQ236_spl
<=> ( ~ in(X0,empty_set)
| ~ in(sK87_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f6993,plain,
( ~ sQ84_spl
| sQ236_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f6987,f1467,f6990,f2427]) ).
fof(f6997,plain,
! [X0] :
( ~ in(X0,relation_dom(sK79_skl))
| in(apply(sK79_skl,X0),relation_rng(sK79_skl))
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f1326,f822]) ).
fof(f6998,plain,
! [X0] :
( ~ in(X0,relation_dom(sK76_skl))
| in(apply(sK76_skl,X0),relation_rng(sK76_skl))
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f1326,f809]) ).
fof(f6999,plain,
! [X0] :
( ~ in(X0,relation_dom(sK66_skl))
| in(apply(sK66_skl,X0),relation_rng(sK66_skl))
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f1326,f773]) ).
fof(f7000,plain,
! [X0] :
( ~ in(X0,relation_dom(empty_set))
| in(apply(empty_set,X0),relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1326,f670]) ).
fof(f7004,definition,
! [X0] :
( sQ237_spl
<=> ( ~ in(X0,relation_dom(sK79_skl))
| in(apply(sK79_skl,X0),relation_rng(sK79_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f7007,plain,
( sQ237_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f6997,f2274,f7004]) ).
fof(f7008,definition,
! [X0] :
( sQ238_spl
<=> ( ~ in(X0,relation_dom(sK76_skl))
| in(apply(sK76_skl,X0),relation_rng(sK76_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f7011,plain,
( sQ238_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f6998,f2281,f7008]) ).
fof(f7012,definition,
! [X0] :
( sQ239_spl
<=> ( ~ in(X0,relation_dom(sK66_skl))
| in(apply(sK66_skl,X0),relation_rng(sK66_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f7015,plain,
( sQ239_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f6999,f2288,f7012]) ).
fof(f7016,definition,
! [X0] :
( sQ240_spl
<=> ( ~ in(X0,relation_dom(empty_set))
| in(apply(empty_set,X0),relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f7019,plain,
( sQ240_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7000,f2139,f7016]) ).
fof(f7024,plain,
! [X0] :
( in(sK51_skl(X0,sK79_skl),relation_dom(sK79_skl))
| in(sK50_skl(X0,sK79_skl),X0)
| X0 = relation_rng(sK79_skl)
| ~ relation(sK79_skl) ),
inference(resolution,[status(thm)],[f556,f822]) ).
fof(f7025,plain,
! [X0] :
( in(sK51_skl(X0,sK76_skl),relation_dom(sK76_skl))
| in(sK50_skl(X0,sK76_skl),X0)
| X0 = relation_rng(sK76_skl)
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f556,f809]) ).
fof(f7026,plain,
! [X0] :
( in(sK51_skl(X0,sK66_skl),relation_dom(sK66_skl))
| in(sK50_skl(X0,sK66_skl),X0)
| X0 = relation_rng(sK66_skl)
| ~ relation(sK66_skl) ),
inference(resolution,[status(thm)],[f556,f773]) ).
fof(f7027,plain,
! [X0] :
( in(sK51_skl(X0,empty_set),relation_dom(empty_set))
| in(sK50_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f556,f670]) ).
fof(f7031,definition,
! [X0] :
( sQ241_spl
<=> ( in(sK51_skl(X0,sK79_skl),relation_dom(sK79_skl))
| in(sK50_skl(X0,sK79_skl),X0)
| X0 = relation_rng(sK79_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f7034,plain,
( sQ241_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f7024,f2274,f7031]) ).
fof(f7035,definition,
! [X0] :
( sQ242_spl
<=> ( in(sK51_skl(X0,sK76_skl),relation_dom(sK76_skl))
| in(sK50_skl(X0,sK76_skl),X0)
| X0 = relation_rng(sK76_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f7038,plain,
( sQ242_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f7025,f2281,f7035]) ).
fof(f7039,definition,
! [X0] :
( sQ243_spl
<=> ( in(sK51_skl(X0,sK66_skl),relation_dom(sK66_skl))
| in(sK50_skl(X0,sK66_skl),X0)
| X0 = relation_rng(sK66_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f7042,plain,
( sQ243_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f7026,f2288,f7039]) ).
fof(f7043,definition,
! [X0] :
( sQ244_spl
<=> ( in(sK51_skl(X0,empty_set),relation_dom(empty_set))
| in(sK50_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f7046,plain,
( sQ244_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7027,f2139,f7043]) ).
fof(f7075,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(X0,sK86_skl)
| in(X0,union(sK87_skl)) ),
inference(resolution,[status(thm)],[f1261,f1320]) ).
fof(f7084,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ84_spl
| ~ in(X0,sK86_skl)
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f3026,f7075]) ).
fof(f7085,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ84_spl
| ~ in(X0,sK86_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7084,f1299]) ).
fof(f7087,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ84_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1577,f7085]) ).
fof(f7099,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ84_spl
| in(X0,set_meet(sK86_skl))
| sK86_skl = empty_set ),
inference(resolution,[status(thm)],[f7085,f1293]) ).
fof(f7105,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ84_spl ),
inference(contradiction_clause,[status(thm)],[f7087]) ).
fof(f7108,definition,
! [X0] :
( sQ245_spl
<=> in(X0,set_meet(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f7109,plain,
! [X0] :
( ~ sQ245_spl
| in(X0,set_meet(sK86_skl)) ),
inference(component_clause,[status(thm)],[f7108]) ).
fof(f7111,plain,
( ~ sQ2_spl
| ~ sQ84_spl
| sQ245_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f7099,f1579,f7108,f2427,f1260]) ).
fof(f7118,plain,
( sQ9_spl
| ~ sQ26_spl
| ~ sQ84_spl
| ~ subset(sK87_skl,sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f2428,f3310]) ).
fof(f7119,plain,
( sQ9_spl
| ~ sQ26_spl
| ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7118,f1271]) ).
fof(f7120,plain,
( sQ9_spl
| ~ sQ26_spl
| ~ sQ84_spl ),
inference(contradiction_clause,[status(thm)],[f7119]) ).
fof(f7157,plain,
! [X0] :
( ~ sQ209_spl
| sK50_skl(X0,empty_set) = empty_set
| in(sK50_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f5732,f557]) ).
fof(f7158,definition,
( sQ247_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f7160,plain,
( sQ247_spl
| ~ function(empty_set) ),
inference(component_clause,[status(thm)],[f7158]) ).
fof(f7161,definition,
! [X0] :
( sQ248_spl
<=> ( sK50_skl(X0,empty_set) = empty_set
| in(sK50_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f7164,plain,
( ~ sQ209_spl
| sQ248_spl
| ~ sQ247_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7157,f2139,f7158,f7161,f5727]) ).
fof(f7165,plain,
( sQ247_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7160,f670]) ).
fof(f7166,plain,
sQ247_spl,
inference(contradiction_clause,[status(thm)],[f7165]) ).
fof(f7251,plain,
( ~ sQ221_spl
| ~ sQ145_spl
| succ(empty_set) = sK86_skl ),
inference(forward_demodulation,[status(thm)],[f3577,f6268]) ).
fof(f7262,plain,
! [X0] :
( ~ sQ221_spl
| ~ sQ145_spl
| ~ ordinal(empty_set)
| in(sK86_skl,X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f7251,f1365]) ).
fof(f7264,plain,
( ~ sQ221_spl
| ~ sQ145_spl
| epsilon_transitive(sK86_skl)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f7251,f687]) ).
fof(f7265,plain,
( ~ sQ221_spl
| ~ sQ145_spl
| epsilon_connected(sK86_skl)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f7251,f688]) ).
fof(f7272,definition,
! [X0] :
( sQ251_spl
<=> ( in(sK86_skl,X0)
| X0 = succ(empty_set)
| in(X0,succ(empty_set))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f7275,plain,
( ~ sQ221_spl
| ~ sQ145_spl
| ~ sQ4_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f7262,f7272,f1375,f3576,f6267]) ).
fof(f7276,plain,
( ~ sQ221_spl
| ~ sQ145_spl
| sQ51_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f7264,f1375,f2061,f3576,f6267]) ).
fof(f7277,plain,
( ~ sQ221_spl
| ~ sQ145_spl
| sQ52_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f7265,f1375,f2065,f3576,f6267]) ).
fof(f7279,plain,
( ~ sQ108_spl
| ~ sQ26_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f3308,f2771,f1579,f2780]) ).
fof(f7358,plain,
! [X0] :
( ~ sQ161_spl
| X0 = empty_set
| ~ in(X0,sK77_skl) ),
inference(paramodulation,[status(thm)],[f4509,f1297]) ).
fof(f7372,plain,
( ~ sQ10_spl
| ~ ordinal(succ(sK86_skl))
| ~ ordinal(sK87_skl)
| in(sK87_skl,powerset(succ(sK86_skl))) ),
inference(resolution,[status(thm)],[f3824,f1402]) ).
fof(f7376,definition,
( sQ252_spl
<=> in(sK87_skl,powerset(succ(sK86_skl))) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f7379,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f7372,f7376,f1394,f1391,f1401]) ).
fof(f7447,definition,
( sQ253_spl
<=> empty(sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f7448,plain,
( ~ sQ253_spl
| empty(sK77_skl) ),
inference(component_clause,[status(thm)],[f7447]) ).
fof(f7451,plain,
( ~ sQ253_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7448,f812]) ).
fof(f7452,plain,
~ sQ253_spl,
inference(contradiction_clause,[status(thm)],[f7451]) ).
fof(f7475,plain,
( relation_field(empty_set) = set_union2(empty_set,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1121,f570]) ).
fof(f7477,plain,
( relation_field(empty_set) = set_union2(relation_dom(empty_set),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1122,f570]) ).
fof(f7481,definition,
( sQ254_spl
<=> relation_field(empty_set) = set_union2(empty_set,relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f7484,plain,
( sQ254_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7475,f2139,f7481]) ).
fof(f7488,definition,
( sQ255_spl
<=> relation_field(empty_set) = set_union2(relation_dom(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f7491,plain,
( sQ255_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7477,f2139,f7488]) ).
fof(f7496,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),relation_inverse(X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1329,f623]) ).
fof(f7497,plain,
! [X0,X1] :
( in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2136,f7496]) ).
fof(f7498,definition,
! [X0,X1] :
( sQ256_spl
<=> ( in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f7501,plain,
( sQ256_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7497,f2139,f7498]) ).
fof(f7514,plain,
! [X0] :
( ~ sQ161_spl
| ~ in(X0,empty_set)
| ~ in(sK77_skl,X0)
| sK77_skl = empty_set ),
inference(paramodulation,[status(thm)],[f4510,f3224]) ).
fof(f7517,definition,
! [X0] :
( sQ257_spl
<=> ( ~ in(X0,empty_set)
| ~ in(sK77_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f7520,plain,
( ~ sQ161_spl
| sQ257_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f7514,f2197,f7517,f4379]) ).
fof(f7578,plain,
( ~ sQ245_spl
| $false ),
inference(resolution,[status(thm)],[f7109,f3975]) ).
fof(f7650,plain,
~ sQ245_spl,
inference(contradiction_clause,[status(thm)],[f7578]) ).
fof(f7651,plain,
( ~ sQ197_spl
| ~ sQ161_spl
| ordinal_subset(sK87_skl,sK77_skl) ),
inference(forward_demodulation,[status(thm)],[f4380,f5615]) ).
fof(f7652,plain,
( ~ sQ197_spl
| ~ sQ161_spl
| ~ ordinal(sK77_skl)
| ~ ordinal(sK87_skl)
| in(sK87_skl,powerset(sK77_skl)) ),
inference(resolution,[status(thm)],[f7651,f3824]) ).
fof(f7653,plain,
( ~ sQ197_spl
| ~ sQ161_spl
| ~ ordinal(sK77_skl)
| ~ ordinal(sK87_skl)
| ~ subset(sK77_skl,sK87_skl)
| sK77_skl = sK87_skl ),
inference(resolution,[status(thm)],[f7651,f1693]) ).
fof(f7654,definition,
( sQ258_spl
<=> in(sK87_skl,powerset(sK77_skl)) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f7657,plain,
( ~ sQ197_spl
| ~ sQ161_spl
| ~ sQ62_spl
| ~ sQ8_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f7652,f7654,f1394,f2205,f4379,f5614]) ).
fof(f7658,definition,
( sQ259_spl
<=> subset(sK77_skl,sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f7659,plain,
( ~ sQ259_spl
| subset(sK77_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f7658]) ).
fof(f7660,plain,
( sQ259_spl
| ~ subset(sK77_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f7658]) ).
fof(f7661,plain,
( ~ sQ197_spl
| ~ sQ161_spl
| ~ sQ62_spl
| ~ sQ8_spl
| ~ sQ259_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f7653,f2434,f7658,f1394,f2205,f4379,f5614]) ).
fof(f7664,plain,
( sQ259_spl
| ~ in(sK77_skl,sK87_skl)
| ~ epsilon_transitive(sK87_skl) ),
inference(resolution,[status(thm)],[f7660,f432]) ).
fof(f7666,plain,
( sQ259_spl
| ~ ordinal_subset(sK77_skl,sK87_skl)
| ~ ordinal(sK87_skl)
| ~ ordinal(sK77_skl) ),
inference(resolution,[status(thm)],[f7660,f831]) ).
fof(f7674,plain,
( sQ259_spl
| ~ sQ85_spl
| ~ sQ105_spl ),
inference(split_clause,[status(thm)],[f7664,f2692,f2431,f7658]) ).
fof(f7675,definition,
( sQ262_spl
<=> ordinal_subset(sK77_skl,sK87_skl) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f7676,plain,
( ~ sQ262_spl
| ordinal_subset(sK77_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f7675]) ).
fof(f7677,plain,
( sQ262_spl
| ~ ordinal_subset(sK77_skl,sK87_skl) ),
inference(component_clause,[status(thm)],[f7675]) ).
fof(f7678,plain,
( sQ259_spl
| ~ sQ262_spl
| ~ sQ8_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f7666,f2205,f1394,f7675,f7658]) ).
fof(f7679,plain,
( sQ197_spl
| ~ sQ161_spl
| ~ ordinal_subset(sK87_skl,sK77_skl) ),
inference(forward_demodulation,[status(thm)],[f4380,f5616]) ).
fof(f7702,definition,
! [X1] :
( sQ264_spl
<=> ~ ordinal(set_union2(sK87_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f7703,plain,
! [X0] :
( ~ sQ264_spl
| ~ ordinal(set_union2(sK87_skl,X0)) ),
inference(component_clause,[status(thm)],[f7702]) ).
fof(f7706,plain,
( sQ262_spl
| ordinal_subset(sK87_skl,sK77_skl)
| ~ ordinal(sK77_skl)
| ~ ordinal(sK87_skl) ),
inference(resolution,[status(thm)],[f7677,f303]) ).
fof(f7707,plain,
( sQ262_spl
| ~ subset(sK77_skl,sK87_skl)
| ~ ordinal(sK87_skl)
| ~ ordinal(sK77_skl) ),
inference(resolution,[status(thm)],[f7677,f832]) ).
fof(f7708,definition,
( sQ265_spl
<=> ordinal_subset(sK87_skl,sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f7711,plain,
( sQ262_spl
| sQ265_spl
| ~ sQ62_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7706,f1394,f2205,f7708,f7675]) ).
fof(f7712,plain,
( sQ262_spl
| ~ sQ259_spl
| ~ sQ8_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f7707,f2205,f1394,f7658,f7675]) ).
fof(f7726,plain,
( ~ sQ259_spl
| ~ subset(sK87_skl,sK77_skl)
| sK87_skl = sK77_skl ),
inference(resolution,[status(thm)],[f7659,f318]) ).
fof(f7727,definition,
( sQ266_spl
<=> subset(sK87_skl,sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f7729,plain,
( sQ266_spl
| ~ subset(sK87_skl,sK77_skl) ),
inference(component_clause,[status(thm)],[f7727]) ).
fof(f7730,plain,
( ~ sQ259_spl
| ~ sQ266_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f7726,f2434,f7727,f7658]) ).
fof(f7732,plain,
( sQ197_spl
| ~ sQ161_spl
| ~ subset(sK87_skl,sK77_skl)
| ~ ordinal(sK77_skl)
| ~ ordinal(sK87_skl) ),
inference(resolution,[status(thm)],[f7679,f832]) ).
fof(f7734,plain,
( sQ197_spl
| ~ sQ161_spl
| ~ sQ266_spl
| ~ sQ62_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7732,f1394,f2205,f7727,f4379,f5614]) ).
fof(f7783,plain,
( ~ sQ262_spl
| ~ ordinal(sK87_skl)
| ~ ordinal(sK77_skl)
| in(sK77_skl,powerset(sK87_skl)) ),
inference(resolution,[status(thm)],[f7676,f3824]) ).
fof(f7785,definition,
( sQ267_spl
<=> in(sK77_skl,powerset(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f7788,plain,
( ~ sQ262_spl
| ~ sQ8_spl
| ~ sQ62_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f7783,f7785,f2205,f1394,f7675]) ).
fof(f7792,plain,
( sQ266_spl
| ~ in(sK87_skl,sK77_skl)
| ~ epsilon_transitive(sK77_skl) ),
inference(resolution,[status(thm)],[f7729,f432]) ).
fof(f7794,plain,
( sQ266_spl
| ~ ordinal_subset(sK87_skl,sK77_skl)
| ~ ordinal(sK77_skl)
| ~ ordinal(sK87_skl) ),
inference(resolution,[status(thm)],[f7729,f831]) ).
fof(f7799,plain,
( sQ266_spl
| ~ sQ107_spl
| ~ sQ171_spl ),
inference(split_clause,[status(thm)],[f7792,f4459,f2775,f7727]) ).
fof(f7800,plain,
( sQ266_spl
| ~ sQ265_spl
| ~ sQ62_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f7794,f1394,f2205,f7708,f7727]) ).
fof(f7820,plain,
! [X0,X1] :
( X0 = X1
| apply(sK76_skl,X0) != apply(sK76_skl,X1)
| ~ in(X1,relation_dom(sK76_skl))
| ~ in(X0,relation_dom(sK76_skl))
| ~ function(sK76_skl)
| ~ relation(sK76_skl) ),
inference(resolution,[status(thm)],[f586,f810]) ).
fof(f7821,plain,
! [X0,X1] :
( X0 = X1
| apply(empty_set,X0) != apply(empty_set,X1)
| ~ in(X1,relation_dom(empty_set))
| ~ in(X0,relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f586,f671]) ).
fof(f7822,definition,
( sQ269_spl
<=> function(sK76_skl) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f7824,plain,
( sQ269_spl
| ~ function(sK76_skl) ),
inference(component_clause,[status(thm)],[f7822]) ).
fof(f7825,definition,
! [X0,X1] :
( sQ270_spl
<=> ( X0 = X1
| apply(sK76_skl,X0) != apply(sK76_skl,X1)
| ~ in(X1,relation_dom(sK76_skl))
| ~ in(X0,relation_dom(sK76_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f7828,plain,
( sQ270_spl
| ~ sQ269_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f7820,f2281,f7822,f7825]) ).
fof(f7829,definition,
! [X0,X1] :
( sQ271_spl
<=> ( X0 = X1
| apply(empty_set,X0) != apply(empty_set,X1)
| ~ in(X1,relation_dom(empty_set))
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f7832,plain,
( sQ271_spl
| ~ sQ247_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7821,f2139,f7158,f7829]) ).
fof(f7838,plain,
( sQ269_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7824,f809]) ).
fof(f7839,plain,
sQ269_spl,
inference(contradiction_clause,[status(thm)],[f7838]) ).
fof(f7867,definition,
! [X1] :
( sQ272_spl
<=> ~ ordinal(set_union2(X1,sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f7868,plain,
! [X0] :
( ~ sQ272_spl
| ~ ordinal(set_union2(X0,sK87_skl)) ),
inference(component_clause,[status(thm)],[f7867]) ).
fof(f7897,plain,
( ~ sQ264_spl
| ~ ordinal(succ(sK87_skl)) ),
inference(paramodulation,[status(thm)],[f389,f7703]) ).
fof(f7902,plain,
( ~ sQ264_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f7897,f2039,f7702]) ).
fof(f7908,plain,
! [X0] :
( ~ sQ272_spl
| ~ ordinal(set_union2(sK87_skl,X0)) ),
inference(paramodulation,[status(thm)],[f300,f7868]) ).
fof(f7912,plain,
( ~ sQ272_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f7908,f7702,f7867]) ).
fof(f7914,plain,
( sQ198_spl
| ~ sQ161_spl
| ~ subset(sK77_skl,sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f4380,f5620]) ).
fof(f7915,plain,
( sQ198_spl
| ~ sQ161_spl
| ~ sQ259_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7914,f7659]) ).
fof(f7916,plain,
( sQ198_spl
| ~ sQ161_spl
| ~ sQ259_spl ),
inference(contradiction_clause,[status(thm)],[f7915]) ).
fof(f7918,plain,
( sQ201_spl
| ~ sQ221_spl
| ~ subset(sK77_skl,sK87_skl) ),
inference(forward_demodulation,[status(thm)],[f6268,f5662]) ).
fof(f7919,plain,
( sQ201_spl
| ~ sQ221_spl
| ~ sQ259_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7918,f7659]) ).
fof(f7920,plain,
( sQ201_spl
| ~ sQ221_spl
| ~ sQ259_spl ),
inference(contradiction_clause,[status(thm)],[f7919]) ).
fof(f7922,plain,
( ~ sQ200_spl
| ~ sQ221_spl
| ordinal_subset(sK87_skl,sK77_skl) ),
inference(forward_demodulation,[status(thm)],[f6268,f5657]) ).
fof(f7923,plain,
( ~ sQ200_spl
| ~ sQ221_spl
| sQ197_spl
| ~ sQ161_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7922,f7679]) ).
fof(f7924,plain,
( ~ sQ200_spl
| ~ sQ221_spl
| sQ197_spl
| ~ sQ161_spl ),
inference(contradiction_clause,[status(thm)],[f7923]) ).
fof(f7936,plain,
( ~ sQ218_spl
| ~ sQ221_spl
| in(sK87_skl,sK77_skl) ),
inference(forward_demodulation,[status(thm)],[f6268,f6075]) ).
fof(f7937,plain,
( ~ sQ218_spl
| ~ sQ221_spl
| ~ sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7936,f2452]) ).
fof(f7938,plain,
( ~ sQ218_spl
| ~ sQ221_spl
| ~ sQ85_spl ),
inference(contradiction_clause,[status(thm)],[f7937]) ).
fof(f7939,plain,
( ~ sQ217_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f6781,f2427,f6071]) ).
fof(f7959,plain,
( ~ sQ222_spl
| ~ sQ221_spl
| in(sK77_skl,sK77_skl) ),
inference(forward_demodulation,[status(thm)],[f6268,f6271]) ).
fof(f7960,plain,
( ~ sQ222_spl
| ~ sQ221_spl
| sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7959,f2210]) ).
fof(f7961,plain,
( ~ sQ222_spl
| ~ sQ221_spl
| sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f7960]) ).
fof(f7963,plain,
( ~ sQ220_spl
| ~ sQ221_spl
| in(sK77_skl,sK77_skl) ),
inference(forward_demodulation,[status(thm)],[f6268,f6265]) ).
fof(f7964,plain,
( ~ sQ220_spl
| ~ sQ221_spl
| sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7963,f2210]) ).
fof(f7965,plain,
( ~ sQ220_spl
| ~ sQ221_spl
| sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f7964]) ).
fof(f7999,plain,
( ~ sQ108_spl
| in(sK87_skl,singleton(sK86_skl))
| in(sK87_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f4284,f2781]) ).
fof(f8010,plain,
( ~ sQ190_spl
| in(empty_set,singleton(sK86_skl))
| in(empty_set,sK86_skl) ),
inference(resolution,[status(thm)],[f4284,f5449]) ).
fof(f8021,definition,
( sQ274_spl
<=> in(sK87_skl,singleton(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f8022,plain,
( ~ sQ274_spl
| in(sK87_skl,singleton(sK86_skl)) ),
inference(component_clause,[status(thm)],[f8021]) ).
fof(f8024,plain,
( ~ sQ108_spl
| sQ274_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f7999,f1427,f8021,f2780]) ).
fof(f8035,definition,
( sQ277_spl
<=> in(empty_set,singleton(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f8038,plain,
( ~ sQ190_spl
| sQ277_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f8010,f1576,f8035,f5448]) ).
fof(f8073,plain,
( ~ sQ168_spl
| in(sK77_skl,singleton(sK87_skl))
| in(sK77_skl,sK87_skl) ),
inference(resolution,[status(thm)],[f4406,f4284]) ).
fof(f8084,definition,
( sQ278_spl
<=> in(sK77_skl,singleton(sK87_skl)) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f8087,plain,
( ~ sQ168_spl
| sQ278_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f8073,f2431,f8084,f4405]) ).
fof(f8097,plain,
( ~ sQ165_spl
| in(sK77_skl,singleton(sK86_skl))
| in(sK77_skl,sK86_skl) ),
inference(resolution,[status(thm)],[f4396,f4284]) ).
fof(f8108,definition,
( sQ279_spl
<=> in(sK77_skl,singleton(sK86_skl)) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f8111,plain,
( ~ sQ165_spl
| sQ279_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f8097,f3573,f8108,f4395]) ).
fof(f8181,plain,
! [X0] :
( ~ sQ161_spl
| in(X0,set_meet(sK77_skl))
| sK77_skl = empty_set
| sK20_skl(X0,set_meet(sK77_skl),sK77_skl) = empty_set ),
inference(resolution,[status(thm)],[f7358,f1293]) ).
fof(f8182,plain,
( ~ sQ161_spl
| sK77_skl = empty_set
| sK24_skl(sK77_skl) = empty_set ),
inference(resolution,[status(thm)],[f7358,f420]) ).
fof(f8185,plain,
! [X0] :
( ~ sQ161_spl
| ~ ordinal(X0)
| sK77_skl = succ(X0)
| in(sK77_skl,succ(X0))
| ~ ordinal(sK77_skl)
| succ(X0) = empty_set ),
inference(resolution,[status(thm)],[f7358,f1365]) ).
fof(f8190,definition,
! [X0] :
( sQ280_spl
<=> ( in(X0,set_meet(sK77_skl))
| sK20_skl(X0,set_meet(sK77_skl),sK77_skl) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f8193,plain,
( ~ sQ161_spl
| sQ60_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f8181,f8190,f2197,f4379]) ).
fof(f8194,definition,
( sQ281_spl
<=> sK24_skl(sK77_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f8197,plain,
( ~ sQ161_spl
| sQ60_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f8182,f8194,f2197,f4379]) ).
fof(f8198,definition,
! [X0] :
( sQ282_spl
<=> ( ~ ordinal(X0)
| sK77_skl = succ(X0)
| in(sK77_skl,succ(X0))
| succ(X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f8201,plain,
( ~ sQ161_spl
| ~ sQ62_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f8185,f8198,f2205,f4379]) ).
fof(f8386,plain,
( ~ sQ274_spl
| sK87_skl = sK86_skl ),
inference(resolution,[status(thm)],[f8022,f1297]) ).
fof(f8397,plain,
( ~ sQ274_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f8386,f1430,f8021]) ).
fof(f8402,plain,
$false,
inference(sat_refutation,[status(thm)],[f1259,f1266,f1267,f1400,f1446,f1470,f1496,f1506,f1544,f1554,f1561,f1596,f1598,f1612,f1655,f1701,f1821,f1929,f1965,f1969,f1973,f1977,f1989,f2173,f2180,f2230,f2280,f2287,f2294,f2298,f2301,f2303,f2305,f2307,f2363,f2374,f2378,f2382,f2386,f2399,f2403,f2407,f2411,f2430,f2437,f2439,f2446,f2464,f2498,f2529,f2533,f2534,f2535,f2549,f2553,f2557,f2561,f2575,f2579,f2583,f2587,f2612,f2664,f2699,f2701,f2770,f2774,f2778,f2779,f2783,f2791,f2793,f2796,f2798,f2805,f2807,f2827,f2832,f2834,f2836,f2887,f2899,f2912,f2917,f2987,f2992,f3001,f3003,f3017,f3037,f3059,f3061,f3122,f3170,f3178,f3183,f3236,f3240,f3250,f3252,f3280,f3316,f3438,f3487,f3515,f3552,f3562,f3582,f3593,f3604,f3608,f3619,f3622,f3632,f3635,f3636,f3686,f3688,f3723,f3734,f3764,f3770,f3793,f3913,f3935,f3937,f4006,f4025,f4037,f4065,f4081,f4254,f4321,f4325,f4385,f4387,f4398,f4408,f4414,f4425,f4466,f4500,f4529,f4581,f4734,f4736,f4818,f4822,f4826,f4837,f4879,f4884,f4954,f4955,f5001,f5069,f5071,f5091,f5097,f5112,f5121,f5231,f5249,f5285,f5316,f5444,f5445,f5446,f5447,f5451,f5458,f5523,f5589,f5593,f5597,f5601,f5610,f5621,f5663,f5694,f5698,f5702,f5706,f5718,f5722,f5726,f5730,f5799,f5878,f6052,f6057,f6067,f6077,f6083,f6107,f6179,f6181,f6212,f6273,f6304,f6305,f6531,f6544,f6734,f6756,f6772,f6800,f6804,f6808,f6812,f6827,f6831,f6835,f6839,f6858,f6860,f6861,f6890,f6891,f6921,f6922,f6925,f6957,f6993,f7007,f7011,f7015,f7019,f7034,f7038,f7042,f7046,f7105,f7111,f7120,f7164,f7166,f7275,f7276,f7277,f7279,f7379,f7452,f7484,f7491,f7501,f7520,f7650,f7657,f7661,f7674,f7678,f7711,f7712,f7730,f7734,f7788,f7799,f7800,f7828,f7832,f7839,f7902,f7912,f7916,f7920,f7924,f7938,f7939,f7961,f7965,f8024,f8038,f8087,f8111,f8193,f8197,f8201,f8397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU236+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n013.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 06:01:05 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.52 % Drodi V4.1.1
% 31.48/5.07 % Refutation found
% 31.48/5.07 % SZS status Theorem for theBenchmark: Theorem is valid
% 31.48/5.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.65/5.12 % Elapsed time: 4.660066 seconds
% 26.65/5.12 % CPU time: 35.695697 seconds
% 26.65/5.12 % Total memory used: 247.207 MB
% 26.65/5.12 % Net memory used: 226.802 MB
%------------------------------------------------------------------------------