%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU243+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 : n005.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 02:19:52 PM UTC 2026
% Result : Theorem 12.57s 2.25s
% Output : CNFRefutation 12.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 359
% Syntax : Number of formulae : 1411 ( 108 unt; 297 def)
% Number of atoms : 5454 ( 810 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 7097 (3054 ~;3253 |; 376 &)
% ( 369 <=>; 44 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 314 ( 312 usr; 298 prp; 0-2 aty)
% Number of functors : 72 ( 72 usr; 7 con; 0-4 aty)
% Number of variables : 2499 (2392 !; 107 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( empty(A)
=> relation(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(f14,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,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_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,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(f25,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,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(f29,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,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(f35,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,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(f40,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(f41,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( ! [D] :
~ ( disjoint(fiber(A,D),C)
& in(D,C) )
& C != empty_set
& subset(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,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(f46,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,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(f51,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(f56,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [A] :
( empty(A)
=> ( relation(relation_inverse(A))
& empty(relation_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f106,axiom,
! [A] : ~ empty(succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,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(f115,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,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(f120,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f122,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f130,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f137,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f153,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f163,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f165,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f166,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f175,lemma,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f185,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f204,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f219,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f220,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f264,conjecture,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f265,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
inference(negated_conjecture,[status(cth)],[f264]) ).
fof(f266,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f275,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f278,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f283,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f295,lemma,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f296,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f298,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f299,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f302,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f303,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f307,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f308,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f320,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f334,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(f335,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)],[f334]) ).
fof(f336,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f338,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f339,plain,
! [A] :
( ! [B,C] :
( ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f340,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f339]) ).
fof(f341,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f340]) ).
fof(f342,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ( ( in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
& in(sK2_skl(B,C,A),B) )
| in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) )
& ( ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
| ~ in(sK2_skl(B,C,A),B)
| ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(D,sK2_skl(B,C,A)),skolemize(E,sK3_skl(B,C,A))],[f341]) ).
fof(f346,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X0)
| ~ in(sK2_skl(X2,X1,X0),X2)
| ~ in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f348,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f359,plain,
! [A,B] :
( ! [C] :
( ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f360,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f359]) ).
fof(f361,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f360]) ).
fof(f362,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( ( ( in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),B)
& in(sK8_skl(A,C,B),A) )
| in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),C) )
& ( ~ in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),B)
| ~ in(sK8_skl(A,C,B),A)
| ~ in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(D,sK7_skl(A,C,B)),skolemize(E,sK8_skl(A,C,B))],[f361]) ).
fof(f366,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X0)
| ~ in(sK8_skl(X2,X1,X0),X2)
| ~ in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X1)
| X1 = relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f368,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X1)
| X1 = relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f373,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)],[f19]) ).
fof(f374,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)],[f373]) ).
fof(f375,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)],[f374]) ).
fof(f376,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))],[f375]) ).
fof(f377,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)],[f376]) ).
fof(f378,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)],[f376]) ).
fof(f379,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)],[f376]) ).
fof(f380,plain,
! [X0,X1,X2] :
( ~ in(apply(X0,sK9_skl(X1,X2,X0)),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)],[f376]) ).
fof(f381,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)],[f376]) ).
fof(f382,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)],[f376]) ).
fof(f383,plain,
! [A] :
( ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f384,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f384]) ).
fof(f386,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK12_skl(C,B,A),B)
& in(ordered_pair(sK12_skl(C,B,A),sK11_skl(C,B,A)),A) )
| in(sK11_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,sK11_skl(C,B,A)),A) )
| ~ in(sK11_skl(C,B,A),C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ( in(sK10_skl(D,C,B,A),B)
& in(ordered_pair(sK10_skl(D,C,B,A),D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(E,sK10_skl(D,C,B,A)),skolemize(D,sK11_skl(C,B,A)),skolemize(E,sK12_skl(C,B,A))],[f385]) ).
fof(f387,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK10_skl(X3,X1,X2,X0),X3),X0)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f389,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f390,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,sK11_skl(X1,X2,X0)),X0)
| ~ in(sK11_skl(X1,X2,X0),X1)
| X1 = relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f393,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)],[f21]) ).
fof(f394,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)],[f393]) ).
fof(f395,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)],[f394]) ).
fof(f396,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))],[f395]) ).
fof(f397,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)],[f396]) ).
fof(f398,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)],[f396]) ).
fof(f399,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X0)
| in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f400,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(sK14_skl(X1,X2,X0),X3),X0)
| ~ in(sK14_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f421,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f422,plain,
! [A] :
( relation(A)
<=> ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f423,plain,
! [A] :
( ( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(NNF_transformation,[status(thm)],[f422]) ).
fof(f424,plain,
( ! [A] :
( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ! [A] :
( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(miniscoping,[status(thm)],[f423]) ).
fof(f425,plain,
( ! [A] :
( ( ! [C,D] : sK19_skl(A) != ordered_pair(C,D)
& in(sK19_skl(A),A) )
| relation(A) )
& ! [A] :
( ! [B] :
( B = ordered_pair(sK17_skl(B,A),sK18_skl(B,A))
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(C,sK17_skl(B,A)),skolemize(D,sK18_skl(B,A)),skolemize(B,sK19_skl(A))],[f424]) ).
fof(f426,plain,
! [X0,X1] :
( X1 = ordered_pair(sK17_skl(X1,X0),sK18_skl(X1,X0))
| ~ in(X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f425]) ).
fof(f427,plain,
! [X0] :
( in(sK19_skl(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[status(thm)],[f425]) ).
fof(f436,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)],[f28]) ).
fof(f437,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)],[f436]) ).
fof(f438,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)],[f437]) ).
fof(f439,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(sK22_skl(B,A),D)
| ~ in(D,A) )
| in(sK22_skl(B,A),B) )
& ( ( ~ in(sK22_skl(B,A),sK23_skl(B,A))
& in(sK23_skl(B,A),A) )
| ~ in(sK22_skl(B,A),B) ) )
| B = set_meet(A) )
& ! [B] :
( ( ! [C] :
( ( ~ in(C,sK21_skl(C,B,A))
& in(sK21_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,[sK21_skl,sK22_skl,sK23_skl]),skolemize(D,sK21_skl(C,B,A)),skolemize(C,sK22_skl(B,A)),skolemize(D,sK23_skl(B,A))],[f438]) ).
fof(f441,plain,
! [X0,X1,X2] :
( in(sK21_skl(X2,X1,X0),X0)
| in(X2,X1)
| X1 != set_meet(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f443,plain,
! [X0,X1] :
( in(sK23_skl(X1,X0),X0)
| ~ in(sK22_skl(X1,X0),X1)
| X1 = set_meet(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f448,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)],[f29]) ).
fof(f449,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)],[f448]) ).
fof(f450,plain,
( ! [A,B] :
( ( ( sK24_skl(B,A) = A
| in(sK24_skl(B,A),B) )
& ( sK24_skl(B,A) != A
| ~ in(sK24_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,[sK24_skl]),skolemize(C,sK24_skl(B,A))],[f449]) ).
fof(f451,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f450]) ).
fof(f452,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f450]) ).
fof(f453,plain,
! [X0,X1] :
( sK24_skl(X0,X1) != X1
| ~ in(sK24_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f450]) ).
fof(f455,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f456,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f455]) ).
fof(f457,plain,
( ! [A] :
( in(sK25_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(B,sK25_skl(A))],[f456]) ).
fof(f458,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f457]) ).
fof(f459,plain,
! [X0] :
( in(sK25_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f457]) ).
fof(f460,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)],[f31]) ).
fof(f461,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)],[f460]) ).
fof(f462,plain,
( ! [A,B] :
( ( ( subset(sK26_skl(B,A),A)
| in(sK26_skl(B,A),B) )
& ( ~ subset(sK26_skl(B,A),A)
| ~ in(sK26_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,[sK26_skl]),skolemize(C,sK26_skl(B,A))],[f461]) ).
fof(f463,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f462]) ).
fof(f464,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f462]) ).
fof(f474,plain,
! [A] :
( ! [B] :
( ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f475,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A = B )
& ( ! [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f474]) ).
fof(f476,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A = B )
& ( ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f475]) ).
fof(f477,plain,
! [A] :
( ! [B] :
( ( ( ( ( in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),B)
| in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),A) )
& ( ~ in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),B)
| ~ in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),A) ) )
| A = B )
& ( ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl,sK29_skl]),skolemize(C,sK28_skl(B,A)),skolemize(D,sK29_skl(B,A))],[f476]) ).
fof(f480,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK28_skl(X1,X0),sK29_skl(X1,X0)),X1)
| ~ in(ordered_pair(sK28_skl(X1,X0),sK29_skl(X1,X0)),X0)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f481,plain,
! [X0,X1] :
( in(ordered_pair(sK28_skl(X1,X0),sK29_skl(X1,X0)),X1)
| in(ordered_pair(sK28_skl(X1,X0),sK29_skl(X1,X0)),X0)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f482,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f483,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)],[f482]) ).
fof(f484,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)],[f483]) ).
fof(f485,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f484]) ).
fof(f489,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f490,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f489]) ).
fof(f491,plain,
( ! [A,B,C] :
( ( ( sK30_skl(C,B,A) = B
| sK30_skl(C,B,A) = A
| in(sK30_skl(C,B,A),C) )
& ( ( sK30_skl(C,B,A) != B
& sK30_skl(C,B,A) != A )
| ~ in(sK30_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl]),skolemize(D,sK30_skl(C,B,A))],[f490]) ).
fof(f493,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f491]) ).
fof(f494,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f491]) ).
fof(f495,plain,
! [X0,X1,X2] :
( sK30_skl(X0,X2,X1) != X1
| ~ in(sK30_skl(X0,X2,X1),X0)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f491]) ).
fof(f496,plain,
! [X0,X1,X2] :
( sK30_skl(X0,X2,X1) != X2
| ~ in(sK30_skl(X0,X2,X1),X0)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f491]) ).
fof(f498,plain,
! [A] :
( ( well_founded_relation(A)
<=> ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f499,plain,
! [A] :
( ( ( ? [B] :
( ! [C] :
( ~ disjoint(fiber(A,C),B)
| ~ in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) )
| well_founded_relation(A) )
& ( ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f498]) ).
fof(f500,plain,
! [A] :
( ( ( ( ! [C] :
( ~ disjoint(fiber(A,C),sK32_skl(A))
| ~ in(C,sK32_skl(A)) )
& sK32_skl(A) != empty_set
& subset(sK32_skl(A),relation_field(A)) )
| well_founded_relation(A) )
& ( ! [B] :
( ( disjoint(fiber(A,sK31_skl(B,A)),B)
& in(sK31_skl(B,A),B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31_skl,sK32_skl]),skolemize(C,sK31_skl(B,A)),skolemize(B,sK32_skl(A))],[f499]) ).
fof(f501,plain,
! [X0,X1] :
( in(sK31_skl(X1,X0),X1)
| X1 = empty_set
| ~ subset(X1,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f500]) ).
fof(f502,plain,
! [X0,X1] :
( disjoint(fiber(X0,sK31_skl(X1,X0)),X1)
| X1 = empty_set
| ~ subset(X1,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f500]) ).
fof(f503,plain,
! [X0] :
( subset(sK32_skl(X0),relation_field(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f500]) ).
fof(f504,plain,
! [X0] :
( sK32_skl(X0) != empty_set
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f500]) ).
fof(f505,plain,
! [X0,X1] :
( ~ disjoint(fiber(X0,X1),sK32_skl(X0))
| ~ in(X1,sK32_skl(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f500]) ).
fof(f506,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)],[f37]) ).
fof(f507,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)],[f506]) ).
fof(f508,plain,
( ! [A,B,C] :
( ( ( in(sK33_skl(C,B,A),B)
| in(sK33_skl(C,B,A),A)
| in(sK33_skl(C,B,A),C) )
& ( ( ~ in(sK33_skl(C,B,A),B)
& ~ in(sK33_skl(C,B,A),A) )
| ~ in(sK33_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,[sK33_skl]),skolemize(D,sK33_skl(C,B,A))],[f507]) ).
fof(f510,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f511,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f512,plain,
! [X0,X1,X2] :
( ~ in(sK33_skl(X0,X2,X1),X1)
| ~ in(sK33_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f513,plain,
! [X0,X1,X2] :
( ~ in(sK33_skl(X0,X2,X1),X2)
| ~ in(sK33_skl(X0,X2,X1),X0)
| X0 = set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f534,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)],[f40]) ).
fof(f535,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)],[f534]) ).
fof(f536,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK41_skl(B,A),sK42_skl(B,A)),B)
& in(ordered_pair(sK41_skl(B,A),sK42_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,[sK41_skl,sK42_skl]),skolemize(C,sK41_skl(B,A)),skolemize(D,sK42_skl(B,A))],[f535]) ).
fof(f537,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f536]) ).
fof(f538,plain,
! [X0,X1] :
( in(ordered_pair(sK41_skl(X1,X0),sK42_skl(X1,X0)),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f536]) ).
fof(f539,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK41_skl(X1,X0),sK42_skl(X1,X0)),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f536]) ).
fof(f540,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f541,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f540]) ).
fof(f542,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f541]) ).
fof(f543,plain,
( ! [A,B] :
( ( ~ in(sK43_skl(B,A),B)
& in(sK43_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(C,sK43_skl(B,A))],[f542]) ).
fof(f544,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f543]) ).
fof(f546,plain,
! [X0,X1] :
( ~ in(sK43_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f543]) ).
fof(f547,plain,
! [A] :
( ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f548,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) )
| is_well_founded_in(A,B) )
& ( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f547]) ).
fof(f549,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) )
| is_well_founded_in(A,B) )
& ! [B] :
( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f548]) ).
fof(f550,plain,
! [A] :
( ( ! [B] :
( ( ! [D] :
( ~ disjoint(fiber(A,D),sK45_skl(B,A))
| ~ in(D,sK45_skl(B,A)) )
& sK45_skl(B,A) != empty_set
& subset(sK45_skl(B,A),B) )
| is_well_founded_in(A,B) )
& ! [B] :
( ! [C] :
( ( disjoint(fiber(A,sK44_skl(C,B,A)),C)
& in(sK44_skl(C,B,A),C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl,sK45_skl]),skolemize(D,sK44_skl(C,B,A)),skolemize(C,sK45_skl(B,A))],[f549]) ).
fof(f551,plain,
! [X0,X1,X2] :
( in(sK44_skl(X2,X1,X0),X2)
| X2 = empty_set
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
fof(f552,plain,
! [X0,X1,X2] :
( disjoint(fiber(X0,sK44_skl(X2,X1,X0)),X2)
| X2 = empty_set
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
fof(f553,plain,
! [X0,X1] :
( subset(sK45_skl(X1,X0),X1)
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
fof(f554,plain,
! [X0,X1] :
( sK45_skl(X1,X0) != empty_set
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
fof(f555,plain,
! [X0,X1,X2] :
( ~ disjoint(fiber(X0,X2),sK45_skl(X1,X0))
| ~ in(X2,sK45_skl(X1,X0))
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
fof(f556,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f557,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f556]) ).
fof(f558,plain,
( ! [A,B,C] :
( ( ( ( in(sK46_skl(C,B,A),B)
& in(sK46_skl(C,B,A),A) )
| in(sK46_skl(C,B,A),C) )
& ( ~ in(sK46_skl(C,B,A),B)
| ~ in(sK46_skl(C,B,A),A)
| ~ in(sK46_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl]),skolemize(D,sK46_skl(C,B,A))],[f557]) ).
fof(f561,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f558]) ).
fof(f562,plain,
! [X0,X1,X2] :
( ~ in(sK46_skl(X0,X2,X1),X2)
| ~ in(sK46_skl(X0,X2,X1),X1)
| ~ in(sK46_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f558]) ).
fof(f565,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)],[f44]) ).
fof(f566,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)],[f565]) ).
fof(f567,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)],[f566]) ).
fof(f568,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)],[f567]) ).
fof(f569,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)],[f567]) ).
fof(f570,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)],[f567]) ).
fof(f577,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f578,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f577]) ).
fof(f579,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f578]) ).
fof(f580,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK48_skl(B,A),sK49_skl(B,A)),A)
| in(sK48_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK48_skl(B,A),D),A)
| ~ in(sK48_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK47_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl]),skolemize(D,sK47_skl(C,B,A)),skolemize(C,sK48_skl(B,A)),skolemize(D,sK49_skl(B,A))],[f579]) ).
fof(f581,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK47_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f580]) ).
fof(f582,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f580]) ).
fof(f583,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK48_skl(X1,X0),X2),X0)
| ~ in(sK48_skl(X1,X0),X1)
| X1 = relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f580]) ).
fof(f596,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)],[f49]) ).
fof(f597,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)],[f596]) ).
fof(f598,plain,
( ! [A,B] :
( ( ( ( in(sK54_skl(B,A),A)
& in(sK53_skl(B,A),sK54_skl(B,A)) )
| in(sK53_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK53_skl(B,A),D) )
| ~ in(sK53_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK52_skl(C,B,A),A)
& in(C,sK52_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(D,sK52_skl(C,B,A)),skolemize(C,sK53_skl(B,A)),skolemize(D,sK54_skl(B,A))],[f597]) ).
fof(f600,plain,
! [X0,X1,X2] :
( in(sK52_skl(X2,X0,X1),X1)
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f598]) ).
fof(f614,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)],[f51]) ).
fof(f615,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)],[f614]) ).
fof(f616,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)],[f615]) ).
fof(f617,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK57_skl(B,A) = apply(A,sK58_skl(B,A))
& in(sK58_skl(B,A),relation_dom(A)) )
| in(sK57_skl(B,A),B) )
& ( ! [D] :
( sK57_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK57_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,sK56_skl(C,B,A))
& in(sK56_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,[sK56_skl,sK57_skl,sK58_skl]),skolemize(D,sK56_skl(C,B,A)),skolemize(C,sK57_skl(B,A)),skolemize(D,sK58_skl(B,A))],[f616]) ).
fof(f618,plain,
! [X0,X1,X2] :
( in(sK56_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f617]) ).
fof(f619,plain,
! [X0,X1,X2] :
( X2 = apply(X0,sK56_skl(X2,X1,X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f617]) ).
fof(f620,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)],[f617]) ).
fof(f639,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f640,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f639]) ).
fof(f717,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f718,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f717]) ).
fof(f723,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f736,plain,
! [A] : element(sK76_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76_skl]),skolemize(B,sK76_skl(A))],[f100]) ).
fof(f737,plain,
! [X0] : element(sK76_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f736]) ).
fof(f741,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f102]) ).
fof(f742,plain,
! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f741]) ).
fof(f744,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f745,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f754,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f765,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f770,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f774,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f115]) ).
fof(f775,plain,
! [A] :
( ! [B] : ~ empty(set_union2(A,B))
| empty(A) ),
inference(miniscoping,[status(thm)],[f774]) ).
fof(f776,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f775]) ).
fof(f780,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f117]) ).
fof(f782,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f780]) ).
fof(f784,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f780]) ).
fof(f788,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f120]) ).
fof(f789,plain,
! [A] :
( ! [B] : ~ empty(set_union2(B,A))
| empty(A) ),
inference(miniscoping,[status(thm)],[f788]) ).
fof(f790,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f789]) ).
fof(f795,plain,
! [A] :
( ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f122]) ).
fof(f796,plain,
! [X0] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f795]) ).
fof(f797,plain,
! [X0] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f795]) ).
fof(f798,plain,
! [X0] :
( ordinal(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f795]) ).
fof(f816,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(thm)],[f130]) ).
fof(f817,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f816]) ).
fof(f818,plain,
! [A] : set_intersection2(A,A) = A,
inference(miniscoping,[status(thm)],[f131]) ).
fof(f819,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f818]) ).
fof(f834,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f900,plain,
( function(sK86_skl)
& relation(sK86_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86_skl]),skolemize(A,sK86_skl)],[f153]) ).
fof(f901,plain,
relation(sK86_skl),
inference(cnf_transformation,[status(thm)],[f900]) ).
fof(f902,plain,
function(sK86_skl),
inference(cnf_transformation,[status(thm)],[f900]) ).
fof(f928,plain,
( relation(sK93_skl)
& ~ empty(sK93_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93_skl]),skolemize(A,sK93_skl)],[f160]) ).
fof(f930,plain,
relation(sK93_skl),
inference(cnf_transformation,[status(thm)],[f928]) ).
fof(f936,plain,
( one_to_one(sK96_skl)
& function(sK96_skl)
& relation(sK96_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96_skl]),skolemize(A,sK96_skl)],[f163]) ).
fof(f937,plain,
relation(sK96_skl),
inference(cnf_transformation,[status(thm)],[f936]) ).
fof(f938,plain,
function(sK96_skl),
inference(cnf_transformation,[status(thm)],[f936]) ).
fof(f945,plain,
( relation_empty_yielding(sK98_skl)
& relation(sK98_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98_skl]),skolemize(A,sK98_skl)],[f165]) ).
fof(f946,plain,
relation(sK98_skl),
inference(cnf_transformation,[status(thm)],[f945]) ).
fof(f948,plain,
( function(sK99_skl)
& relation_empty_yielding(sK99_skl)
& relation(sK99_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99_skl]),skolemize(A,sK99_skl)],[f166]) ).
fof(f949,plain,
relation(sK99_skl),
inference(cnf_transformation,[status(thm)],[f948]) ).
fof(f951,plain,
function(sK99_skl),
inference(cnf_transformation,[status(thm)],[f948]) ).
fof(f974,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f1004,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( in(powerset(C),B)
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f185]) ).
fof(f1005,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( in(powerset(C),B)
| ~ in(C,B) )
& ! [D] :
( in(D,B)
| ! [C] :
( ~ subset(D,C)
| ~ in(C,B) ) )
& in(A,B) ),
inference(miniscoping,[status(thm)],[f1004]) ).
fof(f1006,plain,
! [A] :
( ! [C] :
( in(C,sK100_skl(A))
| are_equipotent(C,sK100_skl(A))
| ~ subset(C,sK100_skl(A)) )
& ! [C] :
( in(powerset(C),sK100_skl(A))
| ~ in(C,sK100_skl(A)) )
& ! [D] :
( in(D,sK100_skl(A))
| ! [C] :
( ~ subset(D,C)
| ~ in(C,sK100_skl(A)) ) )
& in(A,sK100_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100_skl]),skolemize(B,sK100_skl(A))],[f1005]) ).
fof(f1007,plain,
! [X0] : in(X0,sK100_skl(X0)),
inference(cnf_transformation,[status(thm)],[f1006]) ).
fof(f1061,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f1067,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f1109,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f1110,plain,
! [A,B,C] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f220]) ).
fof(f1111,plain,
! [C] :
( ! [A,B] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f1110]) ).
fof(f1112,plain,
! [X0,X1,X2] :
( in(X1,relation_field(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1111]) ).
fof(f1113,plain,
! [X0,X1,X2] :
( in(X2,relation_field(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1111]) ).
fof(f1259,plain,
? [A] :
( ( well_founded_relation(A)
<~> is_well_founded_in(A,relation_field(A)) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f265]) ).
fof(f1260,plain,
? [A] :
( ( ~ is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A) )
& ( is_well_founded_in(A,relation_field(A))
| well_founded_relation(A) )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f1259]) ).
fof(f1261,plain,
( ( ~ is_well_founded_in(sK117_skl,relation_field(sK117_skl))
| ~ well_founded_relation(sK117_skl) )
& ( is_well_founded_in(sK117_skl,relation_field(sK117_skl))
| well_founded_relation(sK117_skl) )
& relation(sK117_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117_skl]),skolemize(A,sK117_skl)],[f1260]) ).
fof(f1262,plain,
relation(sK117_skl),
inference(cnf_transformation,[status(thm)],[f1261]) ).
fof(f1263,plain,
( is_well_founded_in(sK117_skl,relation_field(sK117_skl))
| well_founded_relation(sK117_skl) ),
inference(cnf_transformation,[status(thm)],[f1261]) ).
fof(f1264,plain,
( ~ is_well_founded_in(sK117_skl,relation_field(sK117_skl))
| ~ well_founded_relation(sK117_skl) ),
inference(cnf_transformation,[status(thm)],[f1261]) ).
fof(f1265,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f1266,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f1294,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f275]) ).
fof(f1295,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1294]) ).
fof(f1301,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f278]) ).
fof(f1302,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1301]) ).
fof(f1303,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1301]) ).
fof(f1321,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f1360,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f295]) ).
fof(f1361,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f296]) ).
fof(f1362,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [D] :
( in(D,B)
| ! [C] :
( ~ subset(D,C)
| ~ in(C,B) ) )
& in(A,B) ),
inference(miniscoping,[status(thm)],[f1361]) ).
fof(f1363,plain,
! [A] :
( ! [C] :
( in(C,sK120_skl(A))
| are_equipotent(C,sK120_skl(A))
| ~ subset(C,sK120_skl(A)) )
& ! [C] :
( ( ! [E] :
( in(E,sK121_skl(C,A))
| ~ subset(E,C) )
& in(sK121_skl(C,A),sK120_skl(A)) )
| ~ in(C,sK120_skl(A)) )
& ! [D] :
( in(D,sK120_skl(A))
| ! [C] :
( ~ subset(D,C)
| ~ in(C,sK120_skl(A)) ) )
& in(A,sK120_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120_skl,sK121_skl]),skolemize(B,sK120_skl(A)),skolemize(D,sK121_skl(C,A))],[f1362]) ).
fof(f1364,plain,
! [X0] : in(X0,sK120_skl(X0)),
inference(cnf_transformation,[status(thm)],[f1363]) ).
fof(f1404,definition,
( sQ2_spl
<=> well_founded_relation(sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
( ~ sQ2_spl
| well_founded_relation(sK117_skl) ),
inference(component_clause,[status(thm)],[f1404]) ).
fof(f1406,plain,
( sQ2_spl
| ~ well_founded_relation(sK117_skl) ),
inference(component_clause,[status(thm)],[f1404]) ).
fof(f1407,definition,
( sQ3_spl
<=> is_well_founded_in(sK117_skl,relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1408,plain,
( ~ sQ3_spl
| is_well_founded_in(sK117_skl,relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f1407]) ).
fof(f1409,plain,
( sQ3_spl
| ~ is_well_founded_in(sK117_skl,relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f1407]) ).
fof(f1410,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1263,f1404,f1407]) ).
fof(f1411,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1264,f1404,f1407]) ).
fof(f1415,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f336]) ).
fof(f1425,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)],[f377]) ).
fof(f1426,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)],[f378]) ).
fof(f1427,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)],[f379]) ).
fof(f1428,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK10_skl(X1,relation_image(X0,X2),X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f387]) ).
fof(f1430,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f389]) ).
fof(f1431,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)],[f397]) ).
fof(f1432,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)],[f398]) ).
fof(f1433,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),X0)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f399]) ).
fof(f1437,plain,
! [X0,X1] :
( in(sK21_skl(X1,set_meet(X0),X0),X0)
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(destructive_equality_resolution,[status(thm)],[f441]) ).
fof(f1441,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f451]) ).
fof(f1442,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f452]) ).
fof(f1443,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f458]) ).
fof(f1444,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f463]) ).
fof(f1445,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f464]) ).
fof(f1447,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f493]) ).
fof(f1448,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f494]) ).
fof(f1450,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f510]) ).
fof(f1451,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f511]) ).
fof(f1456,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f561]) ).
fof(f1457,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)],[f568]) ).
fof(f1458,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f570]) ).
fof(f1460,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK47_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f581]) ).
fof(f1461,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f582]) ).
fof(f1463,plain,
! [X0,X1] :
( in(sK52_skl(X0,union(X1),X1),X1)
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f600]) ).
fof(f1468,plain,
! [X0,X1] :
( in(sK56_skl(X1,relation_rng(X0),X0),relation_dom(X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f618]) ).
fof(f1469,plain,
! [X0,X1] :
( X1 = apply(X0,sK56_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f619]) ).
fof(f1470,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)],[f620]) ).
fof(f1505,plain,
relation_field(sK117_skl) = set_union2(relation_dom(sK117_skl),relation_rng(sK117_skl)),
inference(resolution,[status(thm)],[f640,f1262]) ).
fof(f1510,plain,
relation_field(empty_set) = set_union2(relation_dom(empty_set),relation_rng(empty_set)),
inference(resolution,[status(thm)],[f745,f640]) ).
fof(f1565,plain,
! [X0] : relation_field(identity_relation(X0)) = set_union2(relation_dom(identity_relation(X0)),relation_rng(identity_relation(X0))),
inference(resolution,[status(thm)],[f723,f640]) ).
fof(f1573,plain,
! [X0] : ~ in(singleton(X0),X0),
inference(resolution,[status(thm)],[f1442,f299]) ).
fof(f1574,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK2_skl(relation_field(X2),X1,X0)),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f346,f1113]) ).
fof(f1575,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f346,f1112]) ).
fof(f1591,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,sK117_skl,X0),sK3_skl(X1,sK117_skl,X0)),X0)
| in(ordered_pair(sK2_skl(X1,sK117_skl,X0),sK3_skl(X1,sK117_skl,X0)),sK117_skl)
| sK117_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f348,f1262]) ).
fof(f1596,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X3,ordered_pair(X4,sK2_skl(relation_field(relation_field(X2)),X1,X0))),X2)
| ~ relation(X2)
| ~ relation(relation_field(X2))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(X2)),X1,X0),sK3_skl(relation_field(relation_field(X2)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(X2)),X1,X0),sK3_skl(relation_field(relation_field(X2)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(X2)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1574,f1113]) ).
fof(f1597,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(X3,sK2_skl(relation_field(relation_field(X2)),X1,X0)),X4),X2)
| ~ relation(X2)
| ~ relation(relation_field(X2))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(X2)),X1,X0),sK3_skl(relation_field(relation_field(X2)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(X2)),X1,X0),sK3_skl(relation_field(relation_field(X2)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(X2)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1574,f1112]) ).
fof(f1598,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(relation_field(X1),sK117_skl,X0),sK3_skl(relation_field(X1),sK117_skl,X0)),X0)
| sK117_skl = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),sK117_skl,X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),sK117_skl,X0),sK3_skl(relation_field(X1),sK117_skl,X0)),X0)
| sK117_skl = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(sK117_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1575,f1591]) ).
fof(f1599,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,ordered_pair(sK2_skl(relation_field(X2),relation_field(X1),X0),sK3_skl(relation_field(X2),relation_field(X1),X0))),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(X1),X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(X1),X0),sK3_skl(relation_field(X2),relation_field(X1),X0)),X0)
| relation_field(X1) = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(relation_field(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1575,f1113]) ).
fof(f1600,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),relation_field(X1),X0),sK3_skl(relation_field(X2),relation_field(X1),X0)),X4),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(X1),X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(X1),X0),sK3_skl(relation_field(X2),relation_field(X1),X0)),X0)
| relation_field(X1) = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(relation_field(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1575,f1112]) ).
fof(f1601,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( in(ordered_pair(sK2_skl(relation_field(X1),sK117_skl,X0),sK3_skl(relation_field(X1),sK117_skl,X0)),X0)
| sK117_skl = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),sK117_skl,X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),sK117_skl,X0),sK3_skl(relation_field(X1),sK117_skl,X0)),X0)
| sK117_skl = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1604,definition,
( sQ5_spl
<=> relation(sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1606,plain,
( sQ5_spl
| ~ relation(sK117_skl) ),
inference(component_clause,[status(thm)],[f1604]) ).
fof(f1607,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1598,f1601,f1604]) ).
fof(f1610,plain,
! [X0] : ~ in(succ(X0),X0),
inference(resolution,[status(thm)],[f974,f299]) ).
fof(f1611,plain,
! [X0] : ~ in(sK100_skl(X0),X0),
inference(resolution,[status(thm)],[f1007,f299]) ).
fof(f1613,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f320,f1061]) ).
fof(f1618,plain,
relation_field(empty_set) = set_union2(empty_set,relation_rng(empty_set)),
inference(backward_demodulation,[status(thm)],[f1265,f1510]) ).
fof(f1622,plain,
relation_field(empty_set) = set_union2(empty_set,empty_set),
inference(backward_demodulation,[status(thm)],[f1266,f1618]) ).
fof(f1623,plain,
relation_field(empty_set) = empty_set,
inference(forward_demodulation,[status(thm)],[f1061,f1622]) ).
fof(f1624,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0)),X3),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0)),X0)
| relation_field(empty_set) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1600]) ).
fof(f1625,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0))),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0)),X0)
| relation_field(empty_set) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1599]) ).
fof(f1626,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(X2,sK2_skl(relation_field(relation_field(empty_set)),X1,X0)),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(empty_set)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1597]) ).
fof(f1627,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,ordered_pair(X3,sK2_skl(relation_field(relation_field(empty_set)),X1,X0))),empty_set)
| ~ relation(empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(empty_set)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1596]) ).
fof(f1628,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(empty_set,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1575]) ).
fof(f1629,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(empty_set,X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1575]) ).
fof(f1630,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK2_skl(empty_set,X1,X0)),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1574]) ).
fof(f1631,plain,
! [X0,X1] :
( in(X1,empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1113]) ).
fof(f1632,plain,
! [X0,X1] :
( in(X0,empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1112]) ).
fof(f1633,definition,
! [X0,X1,X2,X3] :
( sQ6_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0)),X3),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0)),X0)
| relation_field(empty_set) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1636,definition,
( sQ7_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1638,plain,
( sQ7_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f1636]) ).
fof(f1639,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1624,f1633,f1636]) ).
fof(f1640,definition,
! [X0,X1,X2,X3] :
( sQ8_spl
<=> ( ~ in(ordered_pair(X3,ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0))),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(empty_set),X0),sK3_skl(relation_field(X1),relation_field(empty_set),X0)),X0)
| relation_field(empty_set) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1643,plain,
( ~ sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f1625,f1640,f1636]) ).
fof(f1644,definition,
! [X0,X1,X2,X3] :
( sQ9_spl
<=> ( ~ in(ordered_pair(ordered_pair(X2,sK2_skl(relation_field(relation_field(empty_set)),X1,X0)),X3),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(empty_set)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1647,plain,
( ~ sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1626,f1644,f1636]) ).
fof(f1648,definition,
! [X0,X1,X2,X3] :
( sQ10_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(X3,sK2_skl(relation_field(relation_field(empty_set)),X1,X0))),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(empty_set)),X1,X0),sK3_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(empty_set)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1651,plain,
( ~ sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1627,f1648,f1636]) ).
fof(f1652,definition,
! [X0,X1,X2] :
( sQ11_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(empty_set,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
( ~ sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1628,f1652,f1636]) ).
fof(f1656,definition,
! [X0,X1,X2] :
( sQ12_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(empty_set,X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1659,plain,
( ~ sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f1629,f1656,f1636]) ).
fof(f1660,definition,
! [X0,X1,X2] :
( sQ13_spl
<=> ( ~ in(ordered_pair(X2,sK2_skl(empty_set,X1,X0)),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1663,plain,
( ~ sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1630,f1660,f1636]) ).
fof(f1664,definition,
! [X0,X1] :
( sQ14_spl
<=> ( in(X1,empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1667,plain,
( sQ14_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1631,f1636,f1664]) ).
fof(f1668,definition,
! [X0,X1] :
( sQ15_spl
<=> ( in(X0,empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1671,plain,
( sQ15_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1632,f1636,f1668]) ).
fof(f1672,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1638,f745]) ).
fof(f1673,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1672]) ).
fof(f1809,plain,
! [X0] : relation_field(identity_relation(X0)) = set_union2(X0,relation_rng(identity_relation(X0))),
inference(backward_demodulation,[status(thm)],[f1302,f1565]) ).
fof(f1810,plain,
! [X0] : ~ in(sK120_skl(X0),X0),
inference(resolution,[status(thm)],[f1364,f299]) ).
fof(f1811,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK8_skl(relation_field(X2),X1,X0)),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK7_skl(relation_field(X2),X1,X0),sK8_skl(relation_field(X2),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(X2),X1,X0),sK8_skl(relation_field(X2),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(X2),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f366,f1113]) ).
fof(f1812,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK8_skl(relation_field(X2),X1,X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK7_skl(relation_field(X2),X1,X0),sK8_skl(relation_field(X2),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(X2),X1,X0),sK8_skl(relation_field(X2),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(X2),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f366,f1112]) ).
fof(f1813,plain,
! [X0] : relation_field(identity_relation(X0)) = set_union2(X0,X0),
inference(forward_demodulation,[status(thm)],[f1303,f1809]) ).
fof(f1816,plain,
! [X0] : relation_field(identity_relation(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f817,f1813]) ).
fof(f1817,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X4),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X0)
| relation_field(identity_relation(X1)) = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1816,f1600]) ).
fof(f1826,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X4),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1816,f1817]) ).
fof(f1827,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X4),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1816,f1826]) ).
fof(f1828,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X4),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1816,f1827]) ).
fof(f1829,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),relation_field(identity_relation(X1)),X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X4),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1816,f1828]) ).
fof(f1830,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),relation_field(identity_relation(X1)),X0)),X4),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1816,f1829]) ).
fof(f1831,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X4),identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1816,f1830]) ).
fof(f1832,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X4),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),X3),X2)
| ~ relation(X2)
| ~ in(ordered_pair(sK2_skl(relation_field(X2),X1,X0),sK3_skl(relation_field(X2),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(X2))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1831,f723]) ).
fof(f1874,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X3,ordered_pair(X4,sK8_skl(relation_field(relation_field(X2)),X1,X0))),X2)
| ~ relation(X2)
| ~ relation(relation_field(X2))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(X2)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1811,f1113]) ).
fof(f1875,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(X3,sK8_skl(relation_field(relation_field(X2)),X1,X0)),X4),X2)
| ~ relation(X2)
| ~ relation(relation_field(X2))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(X2)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1811,f1112]) ).
fof(f1877,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK8_skl(empty_set,X1,X0)),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(empty_set),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1811]) ).
fof(f1884,definition,
! [X0,X1,X2] :
( sQ16_spl
<=> ( ~ in(ordered_pair(X2,sK8_skl(empty_set,X1,X0)),empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(empty_set),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1887,plain,
( ~ sQ7_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f1877,f1884,f1636]) ).
fof(f1893,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X3,ordered_pair(sK8_skl(relation_field(relation_field(X2)),X1,X0),X4)),X2)
| ~ relation(X2)
| ~ relation(relation_field(X2))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(X2)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1812,f1113]) ).
fof(f1894,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(sK8_skl(relation_field(relation_field(X2)),X1,X0),X3),X4),X2)
| ~ relation(X2)
| ~ relation(relation_field(X2))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(X2)),X1,X0),sK8_skl(relation_field(relation_field(X2)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(X2)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1812,f1112]) ).
fof(f1896,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK8_skl(empty_set,X1,X0),X2),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(empty_set),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1812]) ).
fof(f1903,definition,
! [X0,X1,X2] :
( sQ17_spl
<=> ( ~ in(ordered_pair(sK8_skl(empty_set,X1,X0),X2),empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(empty_set),X1,X0),sK8_skl(relation_field(empty_set),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(empty_set),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f1906,plain,
( ~ sQ7_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f1896,f1903,f1636]) ).
fof(f1913,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,ordered_pair(X3,sK8_skl(relation_field(relation_field(empty_set)),X1,X0))),empty_set)
| ~ relation(empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1874]) ).
fof(f1921,definition,
! [X0,X1,X2,X3] :
( sQ18_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(X3,sK8_skl(relation_field(relation_field(empty_set)),X1,X0))),empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f1924,plain,
( ~ sQ7_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f1913,f1921,f1636]) ).
fof(f1937,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,singleton(relation_field(X0))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1573,f1113]) ).
fof(f1938,plain,
! [X0,X1] :
( ~ in(ordered_pair(singleton(relation_field(X0)),X1),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1573,f1112]) ).
fof(f1939,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,succ(relation_field(X0))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1610,f1113]) ).
fof(f1940,plain,
! [X0,X1] :
( ~ in(ordered_pair(succ(relation_field(X0)),X1),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1610,f1112]) ).
fof(f1941,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK100_skl(relation_field(X0))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1611,f1113]) ).
fof(f1942,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK100_skl(relation_field(X0)),X1),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1611,f1112]) ).
fof(f1951,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK120_skl(relation_field(X0))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1810,f1113]) ).
fof(f1952,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK120_skl(relation_field(X0)),X1),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1810,f1112]) ).
fof(f1953,plain,
! [X0,X1] : ~ in(unordered_pair(X0,X1),X0),
inference(resolution,[status(thm)],[f1447,f299]) ).
fof(f1966,plain,
! [X0,X1] :
( in(ordered_pair(sK7_skl(X1,sK117_skl,X0),sK8_skl(X1,sK117_skl,X0)),X0)
| in(ordered_pair(sK7_skl(X1,sK117_skl,X0),sK8_skl(X1,sK117_skl,X0)),sK117_skl)
| sK117_skl = relation_rng_restriction(X1,X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f368,f1262]) ).
fof(f1968,plain,
! [X0] :
( ~ relation(sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),sK117_skl,X0),sK8_skl(relation_field(sK117_skl),sK117_skl,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),sK117_skl,X0),sK8_skl(relation_field(sK117_skl),sK117_skl,X0)),sK117_skl)
| sK117_skl = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(sK117_skl)
| ~ relation(X0)
| in(ordered_pair(sK7_skl(relation_field(sK117_skl),sK117_skl,X0),sK8_skl(relation_field(sK117_skl),sK117_skl,X0)),X0)
| sK117_skl = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1966,f1811]) ).
fof(f1972,definition,
! [X0] :
( sQ19_spl
<=> ( ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),sK117_skl,X0),sK8_skl(relation_field(sK117_skl),sK117_skl,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),sK117_skl,X0),sK8_skl(relation_field(sK117_skl),sK117_skl,X0)),sK117_skl)
| sK117_skl = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(X0)
| in(ordered_pair(sK7_skl(relation_field(sK117_skl),sK117_skl,X0),sK8_skl(relation_field(sK117_skl),sK117_skl,X0)),X0)
| sK117_skl = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f1975,plain,
( ~ sQ5_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f1968,f1972,f1604]) ).
fof(f1976,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1606,f1262]) ).
fof(f1977,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1976]) ).
fof(f1981,plain,
! [X0] :
( ~ in(ordered_pair(X0,singleton(empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1937]) ).
fof(f1983,definition,
! [X0] :
( sQ20_spl
<=> ~ in(ordered_pair(X0,singleton(empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1986,plain,
( sQ20_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1981,f1636,f1983]) ).
fof(f1990,plain,
! [X0] :
( ~ in(ordered_pair(singleton(empty_set),X0),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1938]) ).
fof(f1992,definition,
! [X0] :
( sQ21_spl
<=> ~ in(ordered_pair(singleton(empty_set),X0),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1995,plain,
( sQ21_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1990,f1636,f1992]) ).
fof(f1999,plain,
! [X0] :
( ~ in(ordered_pair(X0,succ(empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1939]) ).
fof(f2001,definition,
! [X0] :
( sQ22_spl
<=> ~ in(ordered_pair(X0,succ(empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f2004,plain,
( sQ22_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1999,f1636,f2001]) ).
fof(f2006,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(X2,sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1875]) ).
fof(f2014,definition,
! [X0,X1,X2,X3] :
( sQ23_spl
<=> ( ~ in(ordered_pair(ordered_pair(X2,sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X3),empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2017,plain,
( ~ sQ7_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f2006,f2014,f1636]) ).
fof(f2031,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,ordered_pair(sK8_skl(relation_field(relation_field(empty_set)),X1,X0),X3)),empty_set)
| ~ relation(empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1893]) ).
fof(f2039,definition,
! [X0,X1,X2,X3] :
( sQ24_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(sK8_skl(relation_field(relation_field(empty_set)),X1,X0),X3)),empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f2042,plain,
( ~ sQ7_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f2031,f2039,f1636]) ).
fof(f2055,plain,
! [X0,X1] : ~ in(unordered_pair(X0,X1),X1),
inference(resolution,[status(thm)],[f1448,f299]) ).
fof(f2086,plain,
! [X0] :
( ~ in(ordered_pair(succ(empty_set),X0),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1940]) ).
fof(f2088,definition,
! [X0] :
( sQ25_spl
<=> ~ in(ordered_pair(succ(empty_set),X0),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f2091,plain,
( sQ25_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2086,f1636,f2088]) ).
fof(f2095,plain,
! [X0] :
( ~ in(ordered_pair(X0,sK100_skl(empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1941]) ).
fof(f2097,definition,
! [X0] :
( sQ26_spl
<=> ~ in(ordered_pair(X0,sK100_skl(empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f2100,plain,
( sQ26_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2095,f1636,f2097]) ).
fof(f2102,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(sK8_skl(relation_field(relation_field(empty_set)),X1,X0),X2),X3),empty_set)
| ~ relation(empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1894]) ).
fof(f2110,definition,
! [X0,X1,X2,X3] :
( sQ27_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK8_skl(relation_field(relation_field(empty_set)),X1,X0),X2),X3),empty_set)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(empty_set)),X1,X0),sK8_skl(relation_field(relation_field(empty_set)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(empty_set)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f2113,plain,
( ~ sQ7_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f2102,f2110,f1636]) ).
fof(f2129,plain,
! [X0] :
( ~ in(ordered_pair(sK100_skl(empty_set),X0),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1942]) ).
fof(f2131,definition,
! [X0] :
( sQ28_spl
<=> ~ in(ordered_pair(sK100_skl(empty_set),X0),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f2134,plain,
( sQ28_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2129,f1636,f2131]) ).
fof(f2138,plain,
! [X0] :
( ~ in(ordered_pair(X0,sK120_skl(empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1951]) ).
fof(f2140,definition,
! [X0] :
( sQ29_spl
<=> ~ in(ordered_pair(X0,sK120_skl(empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f2143,plain,
( sQ29_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2138,f1636,f2140]) ).
fof(f2147,plain,
! [X0] :
( ~ in(ordered_pair(sK120_skl(empty_set),X0),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f1952]) ).
fof(f2149,definition,
! [X0] :
( sQ30_spl
<=> ~ in(ordered_pair(sK120_skl(empty_set),X0),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f2152,plain,
( sQ30_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2147,f1636,f2149]) ).
fof(f2154,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(empty_set,X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1832]) ).
fof(f2156,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(empty_set,X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f1832]) ).
fof(f2163,definition,
! [X0,X1,X2,X3] :
( sQ31_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(empty_set,X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f2166,plain,
( ~ sQ7_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f2154,f2163,f1636]) ).
fof(f2173,definition,
! [X0,X1,X2,X3] :
( sQ32_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(empty_set,X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),X2),empty_set)
| ~ in(ordered_pair(sK2_skl(relation_field(empty_set),X1,X0),sK3_skl(relation_field(empty_set),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(empty_set))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f2176,plain,
( ~ sQ7_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f2156,f2173,f1636]) ).
fof(f2198,plain,
subset(relation_dom(sK117_skl),relation_field(sK117_skl)),
inference(paramodulation,[status(thm)],[f1505,f1321]) ).
fof(f2201,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(paramodulation,[status(thm)],[f320,f1321]) ).
fof(f2203,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,unordered_pair(relation_field(X0),X2)),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1953,f1113]) ).
fof(f2204,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(unordered_pair(relation_field(X0),X1),X2),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1953,f1112]) ).
fof(f2208,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,unordered_pair(X2,relation_field(X0))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f2055,f1113]) ).
fof(f2209,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(unordered_pair(X1,relation_field(X0)),X2),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f2055,f1112]) ).
fof(f2219,plain,
! [X0,X1] :
( ~ in(apply(sK99_skl,X0),X1)
| ~ in(X0,relation_dom(sK99_skl))
| in(X0,relation_inverse_image(sK99_skl,X1))
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f1427,f951]) ).
fof(f2220,plain,
! [X0,X1] :
( ~ in(apply(sK96_skl,X0),X1)
| ~ in(X0,relation_dom(sK96_skl))
| in(X0,relation_inverse_image(sK96_skl,X1))
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f1427,f938]) ).
fof(f2221,plain,
! [X0,X1] :
( ~ in(apply(sK86_skl,X0),X1)
| ~ in(X0,relation_dom(sK86_skl))
| in(X0,relation_inverse_image(sK86_skl,X1))
| ~ relation(sK86_skl) ),
inference(resolution,[status(thm)],[f1427,f902]) ).
fof(f2222,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)],[f1427,f765]) ).
fof(f2226,definition,
( sQ33_spl
<=> relation(sK99_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f2228,plain,
( sQ33_spl
| ~ relation(sK99_skl) ),
inference(component_clause,[status(thm)],[f2226]) ).
fof(f2229,definition,
! [X0,X1] :
( sQ34_spl
<=> ( ~ in(apply(sK99_skl,X0),X1)
| ~ in(X0,relation_dom(sK99_skl))
| in(X0,relation_inverse_image(sK99_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f2232,plain,
( sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2219,f2226,f2229]) ).
fof(f2233,definition,
( sQ35_spl
<=> relation(sK96_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f2235,plain,
( sQ35_spl
| ~ relation(sK96_skl) ),
inference(component_clause,[status(thm)],[f2233]) ).
fof(f2236,definition,
! [X0,X1] :
( sQ36_spl
<=> ( ~ in(apply(sK96_skl,X0),X1)
| ~ in(X0,relation_dom(sK96_skl))
| in(X0,relation_inverse_image(sK96_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f2239,plain,
( sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2220,f2233,f2236]) ).
fof(f2240,definition,
( sQ37_spl
<=> relation(sK86_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f2242,plain,
( sQ37_spl
| ~ relation(sK86_skl) ),
inference(component_clause,[status(thm)],[f2240]) ).
fof(f2243,definition,
! [X0,X1] :
( sQ38_spl
<=> ( ~ in(apply(sK86_skl,X0),X1)
| ~ in(X0,relation_dom(sK86_skl))
| in(X0,relation_inverse_image(sK86_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f2246,plain,
( sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f2221,f2240,f2243]) ).
fof(f2247,definition,
! [X0,X1] :
( sQ39_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,[sQ39_spl])],[split_symbol_definition]) ).
fof(f2250,plain,
( sQ39_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2222,f1636,f2247]) ).
fof(f2253,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2242,f901]) ).
fof(f2254,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f2253]) ).
fof(f2255,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2235,f937]) ).
fof(f2256,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f2255]) ).
fof(f2257,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2228,f949]) ).
fof(f2258,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f2257]) ).
fof(f2260,plain,
! [X0,X1] :
( ~ in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| ~ in(sK9_skl(X0,X1,empty_set),empty_set)
| ~ in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1265,f380]) ).
fof(f2262,definition,
( sQ40_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f2264,plain,
( sQ40_spl
| ~ function(empty_set) ),
inference(component_clause,[status(thm)],[f2262]) ).
fof(f2265,definition,
! [X0,X1] :
( sQ41_spl
<=> ( ~ in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| ~ in(sK9_skl(X0,X1,empty_set),empty_set)
| ~ in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f2268,plain,
( sQ41_spl
| ~ sQ40_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2260,f1636,f2262,f2265]) ).
fof(f2269,plain,
( sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2264,f765]) ).
fof(f2270,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f2269]) ).
fof(f2274,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,empty_set),empty_set)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1265,f381]) ).
fof(f2276,definition,
! [X0,X1] :
( sQ42_spl
<=> ( in(sK9_skl(X0,X1,empty_set),empty_set)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f2279,plain,
( sQ42_spl
| ~ sQ40_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2274,f1636,f2262,f2276]) ).
fof(f2281,plain,
( ~ subset(relation_field(sK117_skl),relation_dom(sK117_skl))
| relation_field(sK117_skl) = relation_dom(sK117_skl) ),
inference(resolution,[status(thm)],[f2198,f338]) ).
fof(f2282,definition,
( sQ43_spl
<=> relation_field(sK117_skl) = relation_dom(sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f2283,plain,
( ~ sQ43_spl
| relation_field(sK117_skl) = relation_dom(sK117_skl) ),
inference(component_clause,[status(thm)],[f2282]) ).
fof(f2284,plain,
( sQ43_spl
| relation_field(sK117_skl) != relation_dom(sK117_skl) ),
inference(component_clause,[status(thm)],[f2282]) ).
fof(f2285,definition,
( sQ44_spl
<=> subset(relation_field(sK117_skl),relation_dom(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f2287,plain,
( sQ44_spl
| ~ subset(relation_field(sK117_skl),relation_dom(sK117_skl)) ),
inference(component_clause,[status(thm)],[f2285]) ).
fof(f2288,plain,
( ~ sQ44_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f2281,f2282,f2285]) ).
fof(f2298,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_dom(sK117_skl),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1832]) ).
fof(f2299,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(ordered_pair(sK2_skl(relation_dom(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1832]) ).
fof(f2300,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(sK120_skl(relation_dom(sK117_skl)),X0),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1952]) ).
fof(f2301,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(X0,sK120_skl(relation_dom(sK117_skl))),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1951]) ).
fof(f2302,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(sK100_skl(relation_dom(sK117_skl)),X0),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1942]) ).
fof(f2303,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(ordered_pair(sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0),X2),X3),sK117_skl)
| ~ relation(sK117_skl)
| ~ relation(relation_dom(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1894]) ).
fof(f2304,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(X0,sK100_skl(relation_dom(sK117_skl))),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1941]) ).
fof(f2305,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(succ(relation_dom(sK117_skl)),X0),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1940]) ).
fof(f2306,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(X2,ordered_pair(sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0),X3)),sK117_skl)
| ~ relation(sK117_skl)
| ~ relation(relation_dom(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1893]) ).
fof(f2307,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(ordered_pair(X2,sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X3),sK117_skl)
| ~ relation(sK117_skl)
| ~ relation(relation_dom(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1875]) ).
fof(f2308,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(X0,succ(relation_dom(sK117_skl))),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1939]) ).
fof(f2309,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(singleton(relation_dom(sK117_skl)),X0),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1938]) ).
fof(f2310,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(ordered_pair(X0,singleton(relation_dom(sK117_skl))),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1937]) ).
fof(f2311,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(X2,ordered_pair(X3,sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0))),sK117_skl)
| ~ relation(sK117_skl)
| ~ relation(relation_dom(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1874]) ).
fof(f2312,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| ~ in(ordered_pair(sK8_skl(relation_dom(sK117_skl),X1,X0),X2),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1812]) ).
fof(f2313,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| ~ in(ordered_pair(X2,sK8_skl(relation_dom(sK117_skl),X1,X0)),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1811]) ).
fof(f2314,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0)),X3),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0)),X0)
| relation_field(sK117_skl) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(relation_dom(sK117_skl))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1600]) ).
fof(f2315,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(X3,ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0))),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0)),X0)
| relation_field(sK117_skl) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(relation_dom(sK117_skl))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1599]) ).
fof(f2316,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(ordered_pair(X2,sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X3),sK117_skl)
| ~ relation(sK117_skl)
| ~ relation(relation_dom(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1597]) ).
fof(f2317,plain,
! [X0,X1,X2,X3] :
( ~ sQ43_spl
| ~ in(ordered_pair(X2,ordered_pair(X3,sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0))),sK117_skl)
| ~ relation(sK117_skl)
| ~ relation(relation_dom(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1596]) ).
fof(f2318,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_dom(sK117_skl),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1575]) ).
fof(f2319,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_dom(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1575]) ).
fof(f2320,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| ~ in(ordered_pair(X2,sK2_skl(relation_dom(sK117_skl),X1,X0)),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f2283,f1574]) ).
fof(f2321,plain,
! [X0,X1] :
( ~ sQ43_spl
| in(X1,relation_dom(sK117_skl))
| ~ in(ordered_pair(X0,X1),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1113]) ).
fof(f2322,plain,
! [X0,X1] :
( ~ sQ43_spl
| in(X0,relation_dom(sK117_skl))
| ~ in(ordered_pair(X0,X1),sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f2283,f1112]) ).
fof(f2323,definition,
! [X0,X1,X2,X3] :
( sQ45_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_dom(sK117_skl),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f2326,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f2298,f2323,f1604,f2282]) ).
fof(f2327,definition,
! [X0,X1,X2,X3] :
( sQ46_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_dom(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f2330,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f2299,f2327,f1604,f2282]) ).
fof(f2331,definition,
! [X0] :
( sQ47_spl
<=> ~ in(ordered_pair(sK120_skl(relation_dom(sK117_skl)),X0),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f2334,plain,
( ~ sQ43_spl
| sQ47_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2300,f1604,f2331,f2282]) ).
fof(f2335,definition,
! [X0] :
( sQ48_spl
<=> ~ in(ordered_pair(X0,sK120_skl(relation_dom(sK117_skl))),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f2338,plain,
( ~ sQ43_spl
| sQ48_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2301,f1604,f2335,f2282]) ).
fof(f2339,definition,
! [X0] :
( sQ49_spl
<=> ~ in(ordered_pair(sK100_skl(relation_dom(sK117_skl)),X0),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f2342,plain,
( ~ sQ43_spl
| sQ49_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2302,f1604,f2339,f2282]) ).
fof(f2343,definition,
! [X0,X1,X2,X3] :
( sQ50_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0),X2),X3),sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f2346,definition,
( sQ51_spl
<=> relation(relation_dom(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f2348,plain,
( sQ51_spl
| ~ relation(relation_dom(sK117_skl)) ),
inference(component_clause,[status(thm)],[f2346]) ).
fof(f2349,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f2303,f2343,f2346,f1604,f2282]) ).
fof(f2350,definition,
! [X0] :
( sQ52_spl
<=> ~ in(ordered_pair(X0,sK100_skl(relation_dom(sK117_skl))),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f2353,plain,
( ~ sQ43_spl
| sQ52_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2304,f1604,f2350,f2282]) ).
fof(f2354,definition,
! [X0] :
( sQ53_spl
<=> ~ in(ordered_pair(succ(relation_dom(sK117_skl)),X0),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f2357,plain,
( ~ sQ43_spl
| sQ53_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2305,f1604,f2354,f2282]) ).
fof(f2358,definition,
! [X0,X1,X2,X3] :
( sQ54_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0),X3)),sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f2361,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f2306,f2358,f2346,f1604,f2282]) ).
fof(f2362,definition,
! [X0,X1,X2,X3] :
( sQ55_spl
<=> ( ~ in(ordered_pair(ordered_pair(X2,sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X3),sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f2365,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f2307,f2362,f2346,f1604,f2282]) ).
fof(f2366,definition,
! [X0] :
( sQ56_spl
<=> ~ in(ordered_pair(X0,succ(relation_dom(sK117_skl))),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f2369,plain,
( ~ sQ43_spl
| sQ56_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2308,f1604,f2366,f2282]) ).
fof(f2370,definition,
! [X0] :
( sQ57_spl
<=> ~ in(ordered_pair(singleton(relation_dom(sK117_skl)),X0),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f2373,plain,
( ~ sQ43_spl
| sQ57_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2309,f1604,f2370,f2282]) ).
fof(f2374,definition,
! [X0] :
( sQ58_spl
<=> ~ in(ordered_pair(X0,singleton(relation_dom(sK117_skl))),sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f2377,plain,
( ~ sQ43_spl
| sQ58_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2310,f1604,f2374,f2282]) ).
fof(f2378,definition,
! [X0,X1,X2,X3] :
( sQ59_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(X3,sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0))),sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f2381,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f2311,f2378,f2346,f1604,f2282]) ).
fof(f2382,definition,
! [X0,X1,X2] :
( sQ60_spl
<=> ( ~ in(ordered_pair(sK8_skl(relation_dom(sK117_skl),X1,X0),X2),sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2385,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f2312,f2382,f1604,f2282]) ).
fof(f2386,definition,
! [X0,X1,X2] :
( sQ61_spl
<=> ( ~ in(ordered_pair(X2,sK8_skl(relation_dom(sK117_skl),X1,X0)),sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X1,X0),sK8_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(sK117_skl),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f2389,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f2313,f2386,f1604,f2282]) ).
fof(f2390,definition,
! [X0,X1,X2,X3] :
( sQ62_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0)),X3),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0)),X0)
| relation_field(sK117_skl) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2393,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f2314,f2390,f2346,f1604,f2282]) ).
fof(f2394,definition,
! [X0,X1,X2,X3] :
( sQ63_spl
<=> ( ~ in(ordered_pair(X3,ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0))),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(sK117_skl),X0),sK3_skl(relation_field(X1),relation_field(sK117_skl),X0)),X0)
| relation_field(sK117_skl) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2397,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f2315,f2394,f2346,f1604,f2282]) ).
fof(f2398,definition,
! [X0,X1,X2,X3] :
( sQ64_spl
<=> ( ~ in(ordered_pair(ordered_pair(X2,sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X3),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2401,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f2316,f2398,f2346,f1604,f2282]) ).
fof(f2402,definition,
! [X0,X1,X2,X3] :
( sQ65_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(X3,sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0))),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_field(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2405,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| ~ sQ51_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f2317,f2402,f2346,f1604,f2282]) ).
fof(f2406,definition,
! [X0,X1,X2] :
( sQ66_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_dom(sK117_skl),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2409,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f2318,f2406,f1604,f2282]) ).
fof(f2410,definition,
! [X0,X1,X2] :
( sQ67_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),X2),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_dom(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2413,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f2319,f2410,f1604,f2282]) ).
fof(f2414,definition,
! [X0,X1,X2] :
( sQ68_spl
<=> ( ~ in(ordered_pair(X2,sK2_skl(relation_dom(sK117_skl),X1,X0)),sK117_skl)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(sK117_skl),X1,X0),sK3_skl(relation_field(sK117_skl),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(sK117_skl))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2417,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f2320,f2414,f1604,f2282]) ).
fof(f2418,definition,
! [X0,X1] :
( sQ69_spl
<=> ( in(X1,relation_dom(sK117_skl))
| ~ in(ordered_pair(X0,X1),sK117_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2421,plain,
( ~ sQ43_spl
| sQ69_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2321,f1604,f2418,f2282]) ).
fof(f2422,definition,
! [X0,X1] :
( sQ70_spl
<=> ( in(X0,relation_dom(sK117_skl))
| ~ in(ordered_pair(X0,X1),sK117_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f2425,plain,
( ~ sQ43_spl
| sQ70_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2322,f1604,f2422,f2282]) ).
fof(f2607,definition,
( sQ102_spl
<=> relation(sK98_skl) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f2609,plain,
( sQ102_spl
| ~ relation(sK98_skl) ),
inference(component_clause,[status(thm)],[f2607]) ).
fof(f2710,plain,
( sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2609,f946]) ).
fof(f2711,plain,
sQ102_spl,
inference(contradiction_clause,[status(thm)],[f2710]) ).
fof(f2728,plain,
subset(relation_rng(sK117_skl),relation_field(sK117_skl)),
inference(paramodulation,[status(thm)],[f1505,f2201]) ).
fof(f2933,definition,
( sQ159_spl
<=> relation(sK93_skl) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2935,plain,
( sQ159_spl
| ~ relation(sK93_skl) ),
inference(component_clause,[status(thm)],[f2933]) ).
fof(f3036,plain,
( sQ159_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2935,f930]) ).
fof(f3037,plain,
sQ159_spl,
inference(contradiction_clause,[status(thm)],[f3036]) ).
fof(f3055,plain,
! [X0] :
( relation_field(relation_inverse(X0)) = set_union2(relation_dom(relation_inverse(X0)),relation_rng(relation_inverse(X0)))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f718,f640]) ).
fof(f3056,plain,
empty(relation_inverse(empty_set)),
inference(resolution,[status(thm)],[f742,f744]) ).
fof(f3059,plain,
relation_inverse(empty_set) = empty_set,
inference(resolution,[status(thm)],[f3056,f1295]) ).
fof(f3074,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X2,X0),sK117_skl)
| in(X0,relation_image(sK117_skl,X1)) ),
inference(resolution,[status(thm)],[f1430,f1262]) ).
fof(f3075,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,sK11_skl(relation_field(X1),X2,X0)),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(ordered_pair(X3,sK11_skl(relation_field(X1),X2,X0)),X0)
| relation_field(X1) = relation_image(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f390,f1113]) ).
fof(f3076,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(sK11_skl(relation_field(X1),X2,X0),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(ordered_pair(X3,sK11_skl(relation_field(X1),X2,X0)),X0)
| relation_field(X1) = relation_image(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f390,f1112]) ).
fof(f3084,plain,
( ~ subset(relation_field(sK117_skl),relation_rng(sK117_skl))
| relation_field(sK117_skl) = relation_rng(sK117_skl) ),
inference(resolution,[status(thm)],[f2728,f338]) ).
fof(f3085,definition,
( sQ185_spl
<=> relation_field(sK117_skl) = relation_rng(sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f3088,definition,
( sQ186_spl
<=> subset(relation_field(sK117_skl),relation_rng(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f3090,plain,
( sQ186_spl
| ~ subset(relation_field(sK117_skl),relation_rng(sK117_skl)) ),
inference(component_clause,[status(thm)],[f3088]) ).
fof(f3091,plain,
( ~ sQ186_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f3084,f3085,f3088]) ).
fof(f3096,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK7_skl(X0,sK117_skl,X1),X2)
| in(sK8_skl(X0,sK117_skl,X1),relation_image(sK117_skl,X2)) ),
inference(resolution,[status(thm)],[f3074,f1966]) ).
fof(f3097,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK2_skl(X0,sK117_skl,X1),X2)
| in(sK3_skl(X0,sK117_skl,X1),relation_image(sK117_skl,X2)) ),
inference(resolution,[status(thm)],[f3074,f1591]) ).
fof(f3248,plain,
relation_field(relation_inverse(sK117_skl)) = set_union2(relation_dom(relation_inverse(sK117_skl)),relation_rng(relation_inverse(sK117_skl))),
inference(resolution,[status(thm)],[f3055,f1262]) ).
fof(f3258,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK11_skl(empty_set,X1,X0)),empty_set)
| ~ relation(empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(relation_field(empty_set),X1,X0)),X0)
| relation_field(empty_set) = relation_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f3075]) ).
fof(f3262,definition,
! [X0,X1,X2,X3] :
( sQ215_spl
<=> ( ~ in(ordered_pair(X3,sK11_skl(empty_set,X1,X0)),empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(relation_field(empty_set),X1,X0)),X0)
| relation_field(empty_set) = relation_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f3265,plain,
( ~ sQ7_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f3258,f3262,f1636]) ).
fof(f3287,plain,
! [X0,X1] :
( in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ),
inference(resolution,[status(thm)],[f1431,f745]) ).
fof(f3288,plain,
! [X0,X1] :
( in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl)),sK117_skl)
| ~ in(X0,relation_inverse_image(sK117_skl,X1)) ),
inference(resolution,[status(thm)],[f1431,f1262]) ).
fof(f3289,plain,
! [X0,X1] : ~ in(X0,relation_inverse_image(empty_set,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f3287,f1443]) ).
fof(f3298,plain,
subset(relation_dom(relation_inverse(sK117_skl)),relation_field(relation_inverse(sK117_skl))),
inference(paramodulation,[status(thm)],[f3248,f1321]) ).
fof(f3307,plain,
! [X0] :
( ~ relation(sK117_skl)
| ~ in(sK120_skl(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
inference(resolution,[status(thm)],[f3288,f1952]) ).
fof(f3308,plain,
! [X0] :
( ~ relation(sK117_skl)
| ~ in(sK100_skl(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
inference(resolution,[status(thm)],[f3288,f1942]) ).
fof(f3309,plain,
! [X0] :
( ~ relation(sK117_skl)
| ~ in(succ(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
inference(resolution,[status(thm)],[f3288,f1940]) ).
fof(f3310,plain,
! [X0] :
( ~ relation(sK117_skl)
| ~ in(singleton(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
inference(resolution,[status(thm)],[f3288,f1938]) ).
fof(f3311,plain,
! [X0,X1,X2] :
( ~ relation(sK117_skl)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X0,X1),sK8_skl(relation_field(sK117_skl),X0,X1)),X1)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X0,X1),sK8_skl(relation_field(sK117_skl),X0,X1)),X0)
| X0 = relation_rng_restriction(relation_field(sK117_skl),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(sK8_skl(relation_field(sK117_skl),X0,X1),relation_inverse_image(sK117_skl,X2)) ),
inference(resolution,[status(thm)],[f3288,f1812]) ).
fof(f3313,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),relation_image(sK117_skl,X2))
| ~ in(X0,relation_inverse_image(sK117_skl,X1)) ),
inference(resolution,[status(thm)],[f3288,f3074]) ).
fof(f3316,definition,
! [X0] :
( sQ218_spl
<=> ~ in(sK120_skl(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f3319,plain,
( ~ sQ5_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f3307,f3316,f1604]) ).
fof(f3320,definition,
! [X0] :
( sQ219_spl
<=> ~ in(sK100_skl(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f3323,plain,
( ~ sQ5_spl
| sQ219_spl ),
inference(split_clause,[status(thm)],[f3308,f3320,f1604]) ).
fof(f3324,definition,
! [X0] :
( sQ220_spl
<=> ~ in(succ(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f3327,plain,
( ~ sQ5_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f3309,f3324,f1604]) ).
fof(f3328,definition,
! [X0] :
( sQ221_spl
<=> ~ in(singleton(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f3331,plain,
( ~ sQ5_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f3310,f3328,f1604]) ).
fof(f3332,definition,
! [X0,X1,X2] :
( sQ222_spl
<=> ( ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X0,X1),sK8_skl(relation_field(sK117_skl),X0,X1)),X1)
| ~ in(ordered_pair(sK7_skl(relation_field(sK117_skl),X0,X1),sK8_skl(relation_field(sK117_skl),X0,X1)),X0)
| X0 = relation_rng_restriction(relation_field(sK117_skl),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(sK8_skl(relation_field(sK117_skl),X0,X1),relation_inverse_image(sK117_skl,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f3335,plain,
( ~ sQ5_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f3311,f3332,f1604]) ).
fof(f3351,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK11_skl(relation_field(empty_set),X1,X0),X3),empty_set)
| ~ relation(empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(empty_set,X1,X0)),X0)
| relation_field(empty_set) = relation_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f3076]) ).
fof(f3355,definition,
! [X0,X1,X2,X3] :
( sQ225_spl
<=> ( ~ in(ordered_pair(sK11_skl(relation_field(empty_set),X1,X0),X3),empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(empty_set,X1,X0)),X0)
| relation_field(empty_set) = relation_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f3358,plain,
( ~ sQ7_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f3351,f3355,f1636]) ).
fof(f3372,plain,
union(singleton(empty_set)) = empty_set,
inference(paramodulation,[status(thm)],[f1067,f1360]) ).
fof(f3382,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sK117_skl)
| in(X0,relation_inverse_image(sK117_skl,X1)) ),
inference(resolution,[status(thm)],[f1433,f1262]) ).
fof(f3383,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,sK14_skl(relation_field(X1),X2,X0)),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(ordered_pair(sK14_skl(relation_field(X1),X2,X0),X3),X0)
| relation_field(X1) = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f400,f1113]) ).
fof(f3384,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(sK14_skl(relation_field(X1),X2,X0),X4),X1)
| ~ relation(X1)
| ~ in(X3,X2)
| ~ in(ordered_pair(sK14_skl(relation_field(X1),X2,X0),X3),X0)
| relation_field(X1) = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f400,f1112]) ).
fof(f3394,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK8_skl(X0,sK117_skl,X1),X2)
| in(sK7_skl(X0,sK117_skl,X1),relation_inverse_image(sK117_skl,X2)) ),
inference(resolution,[status(thm)],[f3382,f1966]) ).
fof(f3395,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK3_skl(X0,sK117_skl,X1),X2)
| in(sK2_skl(X0,sK117_skl,X1),relation_inverse_image(sK117_skl,X2)) ),
inference(resolution,[status(thm)],[f3382,f1591]) ).
fof(f3396,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_inverse_image(sK117_skl,X2))
| ~ in(sK13_skl(X0,relation_inverse_image(sK117_skl,X2),X2,sK117_skl),X1)
| in(X0,relation_inverse_image(sK117_skl,X1)) ),
inference(resolution,[status(thm)],[f3382,f3288]) ).
fof(f3432,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK14_skl(empty_set,X1,X0)),empty_set)
| ~ relation(empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(empty_set),X1,X0),X2),X0)
| relation_field(empty_set) = relation_inverse_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f3383]) ).
fof(f3436,definition,
! [X0,X1,X2,X3] :
( sQ232_spl
<=> ( ~ in(ordered_pair(X3,sK14_skl(empty_set,X1,X0)),empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(empty_set),X1,X0),X2),X0)
| relation_field(empty_set) = relation_inverse_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f3439,plain,
( ~ sQ7_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f3432,f3436,f1636]) ).
fof(f3456,plain,
( ~ subset(relation_field(relation_inverse(sK117_skl)),relation_dom(relation_inverse(sK117_skl)))
| relation_field(relation_inverse(sK117_skl)) = relation_dom(relation_inverse(sK117_skl)) ),
inference(resolution,[status(thm)],[f3298,f338]) ).
fof(f3457,definition,
( sQ233_spl
<=> relation_field(relation_inverse(sK117_skl)) = relation_dom(relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3458,plain,
( ~ sQ233_spl
| relation_field(relation_inverse(sK117_skl)) = relation_dom(relation_inverse(sK117_skl)) ),
inference(component_clause,[status(thm)],[f3457]) ).
fof(f3460,definition,
( sQ234_spl
<=> subset(relation_field(relation_inverse(sK117_skl)),relation_dom(relation_inverse(sK117_skl))) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3462,plain,
( sQ234_spl
| ~ subset(relation_field(relation_inverse(sK117_skl)),relation_dom(relation_inverse(sK117_skl))) ),
inference(component_clause,[status(thm)],[f3460]) ).
fof(f3463,plain,
( ~ sQ234_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f3456,f3457,f3460]) ).
fof(f3464,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),sK8_skl(relation_image(sK117_skl,X0),sK117_skl,X1)),X1)
| ~ in(ordered_pair(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),sK8_skl(relation_image(sK117_skl,X0),sK117_skl,X1)),sK117_skl)
| sK117_skl = relation_rng_restriction(relation_image(sK117_skl,X0),X1)
| ~ relation(sK117_skl)
| ~ relation(X1)
| in(ordered_pair(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),sK8_skl(relation_image(sK117_skl,X0),sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(relation_image(sK117_skl,X0),X1)
| ~ relation(X1)
| ~ in(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),X0) ),
inference(resolution,[status(thm)],[f3096,f366]) ).
fof(f3465,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK10_skl(sK8_skl(X0,sK117_skl,X1),relation_image(sK117_skl,X2),X2,sK117_skl),sK8_skl(X0,sK117_skl,X1)),sK117_skl)
| ~ relation(sK117_skl)
| in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK7_skl(X0,sK117_skl,X1),X2) ),
inference(resolution,[status(thm)],[f3096,f1428]) ).
fof(f3467,definition,
! [X0,X1] :
( sQ235_spl
<=> ( ~ in(ordered_pair(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),sK8_skl(relation_image(sK117_skl,X0),sK117_skl,X1)),X1)
| ~ in(ordered_pair(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),sK8_skl(relation_image(sK117_skl,X0),sK117_skl,X1)),sK117_skl)
| sK117_skl = relation_rng_restriction(relation_image(sK117_skl,X0),X1)
| ~ relation(X1)
| in(ordered_pair(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),sK8_skl(relation_image(sK117_skl,X0),sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(relation_image(sK117_skl,X0),X1)
| ~ relation(X1)
| ~ in(sK7_skl(relation_image(sK117_skl,X0),sK117_skl,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3470,plain,
( ~ sQ5_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f3464,f3467,f1604]) ).
fof(f3471,definition,
! [X0,X1,X2] :
( sQ236_spl
<=> ( in(ordered_pair(sK10_skl(sK8_skl(X0,sK117_skl,X1),relation_image(sK117_skl,X2),X2,sK117_skl),sK8_skl(X0,sK117_skl,X1)),sK117_skl)
| in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK7_skl(X0,sK117_skl,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f3474,plain,
( ~ sQ5_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f3465,f3471,f1604]) ).
fof(f3489,plain,
! [X0,X1,X2,X3] :
( ~ in(sK14_skl(relation_field(sK117_skl),X1,X0),relation_inverse_image(sK117_skl,X3))
| ~ relation(sK117_skl)
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(sK117_skl),X1,X0),X2),X0)
| relation_field(sK117_skl) = relation_inverse_image(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f3384,f3288]) ).
fof(f3493,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK14_skl(empty_set,X1,X0),X3),empty_set)
| ~ relation(empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(empty_set),X1,X0),X2),X0)
| relation_field(empty_set) = relation_inverse_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f3384]) ).
fof(f3494,definition,
! [X0,X1,X2,X3] :
( sQ239_spl
<=> ( ~ in(sK14_skl(relation_field(sK117_skl),X1,X0),relation_inverse_image(sK117_skl,X3))
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(sK117_skl),X1,X0),X2),X0)
| relation_field(sK117_skl) = relation_inverse_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f3497,plain,
( ~ sQ5_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f3489,f3494,f1604]) ).
fof(f3501,definition,
! [X0,X1,X2,X3] :
( sQ240_spl
<=> ( ~ in(ordered_pair(sK14_skl(empty_set,X1,X0),X3),empty_set)
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(empty_set),X1,X0),X2),X0)
| relation_field(empty_set) = relation_inverse_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f3504,plain,
( ~ sQ7_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f3493,f3501,f1636]) ).
fof(f3521,plain,
( ordinal(empty_set)
| ~ ordinal(singleton(empty_set)) ),
inference(paramodulation,[status(thm)],[f3372,f798]) ).
fof(f3524,definition,
( sQ241_spl
<=> ordinal(singleton(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f3525,plain,
( ~ sQ241_spl
| ordinal(singleton(empty_set)) ),
inference(component_clause,[status(thm)],[f3524]) ).
fof(f3526,plain,
( sQ241_spl
| ~ ordinal(singleton(empty_set)) ),
inference(component_clause,[status(thm)],[f3524]) ).
fof(f3527,definition,
( sQ242_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3530,plain,
( sQ242_spl
| ~ sQ241_spl ),
inference(split_clause,[status(thm)],[f3521,f3524,f3527]) ).
fof(f3531,definition,
( sQ243_spl
<=> epsilon_connected(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f3535,definition,
( sQ244_spl
<=> epsilon_transitive(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f3542,definition,
( sQ245_spl
<=> epsilon_transitive(singleton(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3544,plain,
( sQ245_spl
| ~ epsilon_transitive(singleton(empty_set)) ),
inference(component_clause,[status(thm)],[f3542]) ).
fof(f3568,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(sK14_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),X3),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_inverse_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f3384]) ).
fof(f3569,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(X3,sK14_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_inverse_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f3383]) ).
fof(f3570,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(sK11_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X3),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f3076]) ).
fof(f3571,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(X3,sK11_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_image(X0,X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f3075]) ).
fof(f3572,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1832]) ).
fof(f3573,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(ordered_pair(sK2_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1832]) ).
fof(f3574,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(sK120_skl(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1952]) ).
fof(f3575,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(X0,sK120_skl(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1951]) ).
fof(f3576,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(sK100_skl(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1942]) ).
fof(f3577,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(ordered_pair(sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),X2),X3),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1894]) ).
fof(f3578,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(X0,sK100_skl(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1941]) ).
fof(f3579,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(succ(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1940]) ).
fof(f3580,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(X2,ordered_pair(sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),X3)),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1893]) ).
fof(f3581,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(ordered_pair(X2,sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X3),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1875]) ).
fof(f3582,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(X0,succ(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1939]) ).
fof(f3583,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(singleton(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1938]) ).
fof(f3584,plain,
! [X0] :
( ~ sQ233_spl
| ~ in(ordered_pair(X0,singleton(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1937]) ).
fof(f3585,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(X2,ordered_pair(X3,sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0))),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1874]) ).
fof(f3586,plain,
! [X0,X1,X2] :
( ~ sQ233_spl
| ~ in(ordered_pair(sK8_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_inverse(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1812]) ).
fof(f3587,plain,
! [X0,X1,X2] :
( ~ sQ233_spl
| ~ in(ordered_pair(X2,sK8_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_inverse(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1811]) ).
fof(f3588,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0)),X3),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1600]) ).
fof(f3589,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(X3,ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0))),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1599]) ).
fof(f3590,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(ordered_pair(X2,sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X3),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(relation_inverse(sK117_skl))))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1597]) ).
fof(f3591,plain,
! [X0,X1,X2,X3] :
( ~ sQ233_spl
| ~ in(ordered_pair(X2,ordered_pair(X3,sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0))),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ relation(relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(relation_inverse(sK117_skl))))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1596]) ).
fof(f3592,plain,
! [X0,X1,X2] :
( ~ sQ233_spl
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1575]) ).
fof(f3593,plain,
! [X0,X1,X2] :
( ~ sQ233_spl
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1575]) ).
fof(f3594,plain,
! [X0,X1,X2] :
( ~ sQ233_spl
| ~ in(ordered_pair(X2,sK2_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3458,f1574]) ).
fof(f3595,plain,
! [X0,X1] :
( ~ sQ233_spl
| in(X1,relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1113]) ).
fof(f3596,plain,
! [X0,X1] :
( ~ sQ233_spl
| in(X0,relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK117_skl))
| ~ relation(relation_inverse(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f3458,f1112]) ).
fof(f3597,definition,
! [X0,X1,X2,X3] :
( sQ249_spl
<=> ( ~ in(ordered_pair(sK14_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),X3),relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_inverse_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3600,definition,
( sQ250_spl
<=> relation(relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3602,plain,
( sQ250_spl
| ~ relation(relation_inverse(sK117_skl)) ),
inference(component_clause,[status(thm)],[f3600]) ).
fof(f3603,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f3568,f3597,f3600,f3457]) ).
fof(f3604,definition,
! [X0,X1,X2,X3] :
( sQ251_spl
<=> ( ~ in(ordered_pair(X3,sK14_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_inverse_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3607,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f3569,f3604,f3600,f3457]) ).
fof(f3608,definition,
! [X0,X1,X2,X3] :
( sQ252_spl
<=> ( ~ in(ordered_pair(sK11_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X3),relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3611,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f3570,f3608,f3600,f3457]) ).
fof(f3612,definition,
! [X0,X1,X2,X3] :
( sQ253_spl
<=> ( ~ in(ordered_pair(X3,sK11_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_image(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3615,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f3571,f3612,f3600,f3457]) ).
fof(f3616,definition,
! [X0,X1,X2,X3] :
( sQ254_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3619,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f3572,f3616,f3600,f3457]) ).
fof(f3620,definition,
! [X0,X1,X2,X3] :
( sQ255_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X3),identity_relation(X1))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3623,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f3573,f3620,f3600,f3457]) ).
fof(f3624,definition,
! [X0] :
( sQ256_spl
<=> ~ in(ordered_pair(sK120_skl(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3627,plain,
( ~ sQ233_spl
| sQ256_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3574,f3600,f3624,f3457]) ).
fof(f3628,definition,
! [X0] :
( sQ257_spl
<=> ~ in(ordered_pair(X0,sK120_skl(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3631,plain,
( ~ sQ233_spl
| sQ257_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3575,f3600,f3628,f3457]) ).
fof(f3632,definition,
! [X0] :
( sQ258_spl
<=> ~ in(ordered_pair(sK100_skl(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3635,plain,
( ~ sQ233_spl
| sQ258_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3576,f3600,f3632,f3457]) ).
fof(f3636,definition,
! [X0,X1,X2,X3] :
( sQ259_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),X2),X3),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3639,definition,
( sQ260_spl
<=> relation(relation_dom(relation_inverse(sK117_skl))) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3642,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f3577,f3636,f3639,f3600,f3457]) ).
fof(f3643,definition,
! [X0] :
( sQ261_spl
<=> ~ in(ordered_pair(X0,sK100_skl(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3646,plain,
( ~ sQ233_spl
| sQ261_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3578,f3600,f3643,f3457]) ).
fof(f3647,definition,
! [X0] :
( sQ262_spl
<=> ~ in(ordered_pair(succ(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3650,plain,
( ~ sQ233_spl
| sQ262_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3579,f3600,f3647,f3457]) ).
fof(f3651,definition,
! [X0,X1,X2,X3] :
( sQ263_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),X3)),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3654,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f3580,f3651,f3639,f3600,f3457]) ).
fof(f3655,definition,
! [X0,X1,X2,X3] :
( sQ264_spl
<=> ( ~ in(ordered_pair(ordered_pair(X2,sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X3),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3658,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3581,f3655,f3639,f3600,f3457]) ).
fof(f3659,definition,
! [X0] :
( sQ265_spl
<=> ~ in(ordered_pair(X0,succ(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3662,plain,
( ~ sQ233_spl
| sQ265_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3582,f3600,f3659,f3457]) ).
fof(f3663,definition,
! [X0] :
( sQ266_spl
<=> ~ in(ordered_pair(singleton(relation_dom(relation_inverse(sK117_skl))),X0),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3666,plain,
( ~ sQ233_spl
| sQ266_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3583,f3600,f3663,f3457]) ).
fof(f3667,definition,
! [X0] :
( sQ267_spl
<=> ~ in(ordered_pair(X0,singleton(relation_dom(relation_inverse(sK117_skl)))),relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3670,plain,
( ~ sQ233_spl
| sQ267_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3584,f3600,f3667,f3457]) ).
fof(f3671,definition,
! [X0,X1,X2,X3] :
( sQ268_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(X3,sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0))),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK8_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_field(relation_inverse(sK117_skl))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3674,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f3585,f3671,f3639,f3600,f3457]) ).
fof(f3675,definition,
! [X0,X1,X2] :
( sQ269_spl
<=> ( ~ in(ordered_pair(sK8_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_inverse(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3678,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f3586,f3675,f3600,f3457]) ).
fof(f3679,definition,
! [X0,X1,X2] :
( sQ270_spl
<=> ( ~ in(ordered_pair(X2,sK8_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK7_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK8_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_rng_restriction(relation_field(relation_inverse(sK117_skl)),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3682,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f3587,f3679,f3600,f3457]) ).
fof(f3683,definition,
! [X0,X1,X2,X3] :
( sQ271_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0)),X3),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f3686,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f3588,f3683,f3639,f3600,f3457]) ).
fof(f3687,definition,
! [X0,X1,X2,X3] :
( sQ272_spl
<=> ( ~ in(ordered_pair(X3,ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0))),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK2_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0),sK3_skl(relation_field(X1),relation_field(relation_inverse(sK117_skl)),X0)),X0)
| relation_field(relation_inverse(sK117_skl)) = relation_dom_restriction(X0,relation_field(X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3690,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f3589,f3687,f3639,f3600,f3457]) ).
fof(f3691,definition,
! [X0,X1,X2,X3] :
( sQ273_spl
<=> ( ~ in(ordered_pair(ordered_pair(X2,sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X3),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(relation_inverse(sK117_skl))))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3694,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f3590,f3691,f3639,f3600,f3457]) ).
fof(f3695,definition,
! [X0,X1,X2,X3] :
( sQ274_spl
<=> ( ~ in(ordered_pair(X2,ordered_pair(X3,sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0))),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0),sK3_skl(relation_field(relation_field(relation_inverse(sK117_skl))),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_field(relation_inverse(sK117_skl))))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3698,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| ~ sQ260_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f3591,f3695,f3639,f3600,f3457]) ).
fof(f3699,definition,
! [X0,X1,X2] :
( sQ275_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3702,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f3592,f3699,f3600,f3457]) ).
fof(f3703,definition,
! [X0,X1,X2] :
( sQ276_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),X2),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f3706,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f3593,f3703,f3600,f3457]) ).
fof(f3707,definition,
! [X0,X1,X2] :
( sQ277_spl
<=> ( ~ in(ordered_pair(X2,sK2_skl(relation_dom(relation_inverse(sK117_skl)),X1,X0)),relation_inverse(sK117_skl))
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_field(relation_inverse(sK117_skl)),X1,X0),sK3_skl(relation_field(relation_inverse(sK117_skl)),X1,X0)),X1)
| X1 = relation_dom_restriction(X0,relation_field(relation_inverse(sK117_skl)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3710,plain,
( ~ sQ233_spl
| ~ sQ250_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f3594,f3707,f3600,f3457]) ).
fof(f3711,definition,
! [X0,X1] :
( sQ278_spl
<=> ( in(X1,relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3714,plain,
( ~ sQ233_spl
| sQ278_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3595,f3600,f3711,f3457]) ).
fof(f3715,definition,
! [X0,X1] :
( sQ279_spl
<=> ( in(X0,relation_dom(relation_inverse(sK117_skl)))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f3718,plain,
( ~ sQ233_spl
| sQ279_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f3596,f3600,f3715,f3457]) ).
fof(f3719,plain,
( sQ250_spl
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f3602,f718]) ).
fof(f3720,plain,
( sQ250_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3719,f1604,f3600]) ).
fof(f3730,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK10_skl(sK3_skl(X0,sK117_skl,X1),relation_image(sK117_skl,X2),X2,sK117_skl),sK3_skl(X0,sK117_skl,X1)),sK117_skl)
| ~ relation(sK117_skl)
| in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK2_skl(X0,sK117_skl,X1),X2) ),
inference(resolution,[status(thm)],[f3097,f1428]) ).
fof(f3732,definition,
! [X0,X1,X2] :
( sQ280_spl
<=> ( in(ordered_pair(sK10_skl(sK3_skl(X0,sK117_skl,X1),relation_image(sK117_skl,X2),X2,sK117_skl),sK3_skl(X0,sK117_skl,X1)),sK117_skl)
| in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK2_skl(X0,sK117_skl,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3735,plain,
( ~ sQ5_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f3730,f3732,f1604]) ).
fof(f3744,plain,
succ(empty_set) = singleton(empty_set),
inference(paramodulation,[status(thm)],[f1613,f421]) ).
fof(f3755,plain,
( sQ245_spl
| ~ epsilon_transitive(succ(empty_set)) ),
inference(backward_demodulation,[status(thm)],[f3744,f3544]) ).
fof(f3756,plain,
( sQ241_spl
| ~ ordinal(succ(empty_set)) ),
inference(backward_demodulation,[status(thm)],[f3744,f3526]) ).
fof(f3766,plain,
succ(empty_set) != empty_set,
inference(paramodulation,[status(thm)],[f3744,f834]) ).
fof(f3768,plain,
( sQ245_spl
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f3755,f782]) ).
fof(f3772,plain,
( sQ245_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3768,f770]) ).
fof(f3773,plain,
sQ245_spl,
inference(contradiction_clause,[status(thm)],[f3772]) ).
fof(f3776,plain,
( sQ241_spl
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f3756,f784]) ).
fof(f3780,plain,
( sQ241_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3776,f770]) ).
fof(f3781,plain,
sQ241_spl,
inference(contradiction_clause,[status(thm)],[f3780]) ).
fof(f3782,plain,
( ~ sQ241_spl
| ordinal(succ(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f3744,f3525]) ).
fof(f3790,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK10_skl(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),relation_image(sK117_skl,X2),X2,sK117_skl),sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl)),sK117_skl)
| ~ relation(sK117_skl)
| ~ in(X0,X2)
| ~ in(X0,relation_inverse_image(sK117_skl,X1)) ),
inference(resolution,[status(thm)],[f3313,f1428]) ).
fof(f3792,definition,
! [X0,X1,X2] :
( sQ281_spl
<=> ( in(ordered_pair(sK10_skl(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),relation_image(sK117_skl,X2),X2,sK117_skl),sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl)),sK117_skl)
| ~ in(X0,X2)
| ~ in(X0,relation_inverse_image(sK117_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3795,plain,
( ~ sQ5_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f3790,f3792,f1604]) ).
fof(f3807,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,unordered_pair(empty_set,X1)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f2203]) ).
fof(f3809,definition,
! [X0,X1] :
( sQ282_spl
<=> ~ in(ordered_pair(X0,unordered_pair(empty_set,X1)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3812,plain,
( sQ282_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3807,f1636,f3809]) ).
fof(f3813,plain,
! [X0,X1] :
( ~ in(unordered_pair(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f2204,f3288]) ).
fof(f3820,plain,
! [X0,X1] :
( ~ in(ordered_pair(unordered_pair(empty_set,X0),X1),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f2204]) ).
fof(f3821,definition,
! [X0,X1] :
( sQ283_spl
<=> ~ in(unordered_pair(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3824,plain,
( sQ283_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3813,f1604,f3821]) ).
fof(f3826,definition,
! [X0,X1] :
( sQ284_spl
<=> ~ in(ordered_pair(unordered_pair(empty_set,X0),X1),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3829,plain,
( sQ284_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3820,f1636,f3826]) ).
fof(f3836,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,unordered_pair(X1,empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f2208]) ).
fof(f3838,definition,
! [X0,X1] :
( sQ285_spl
<=> ~ in(ordered_pair(X0,unordered_pair(X1,empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3841,plain,
( sQ285_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3836,f1636,f3838]) ).
fof(f3847,definition,
( sQ286_spl
<=> ordinal(succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3849,plain,
( sQ286_spl
| ~ ordinal(succ(empty_set)) ),
inference(component_clause,[status(thm)],[f3847]) ).
fof(f3873,plain,
! [X0] :
( X0 = ordered_pair(sK17_skl(X0,sK117_skl),sK18_skl(X0,sK117_skl))
| ~ in(X0,sK117_skl) ),
inference(resolution,[status(thm)],[f426,f1262]) ).
fof(f3942,plain,
! [X0,X1] :
( ~ in(unordered_pair(X0,relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f2209,f3288]) ).
fof(f3949,plain,
! [X0,X1] :
( ~ in(ordered_pair(unordered_pair(X0,empty_set),X1),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f2209]) ).
fof(f3950,definition,
! [X0,X1] :
( sQ288_spl
<=> ~ in(unordered_pair(X0,relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f3953,plain,
( sQ288_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3942,f1604,f3950]) ).
fof(f3954,definition,
! [X0,X1] :
( sQ289_spl
<=> ~ in(ordered_pair(unordered_pair(X0,empty_set),X1),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f3957,plain,
( sQ289_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3949,f1636,f3954]) ).
fof(f3973,plain,
( sK25_skl(sK117_skl) = ordered_pair(sK17_skl(sK25_skl(sK117_skl),sK117_skl),sK18_skl(sK25_skl(sK117_skl),sK117_skl))
| sK117_skl = empty_set ),
inference(resolution,[status(thm)],[f459,f3873]) ).
fof(f3974,plain,
! [X0] :
( sK25_skl(singleton(X0)) = X0
| singleton(X0) = empty_set ),
inference(resolution,[status(thm)],[f459,f1441]) ).
fof(f3976,plain,
! [X0] : relation_inverse_image(empty_set,X0) = empty_set,
inference(resolution,[status(thm)],[f459,f3289]) ).
fof(f3979,plain,
! [X0] :
( ~ in(X0,sK25_skl(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f459,f299]) ).
fof(f3980,definition,
( sQ290_spl
<=> sK117_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f3981,plain,
( ~ sQ290_spl
| sK117_skl = empty_set ),
inference(component_clause,[status(thm)],[f3980]) ).
fof(f3983,definition,
( sQ291_spl
<=> sK25_skl(sK117_skl) = ordered_pair(sK17_skl(sK25_skl(sK117_skl),sK117_skl),sK18_skl(sK25_skl(sK117_skl),sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3986,plain,
( sQ291_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f3973,f3980,f3983]) ).
fof(f3987,plain,
! [X0] : sK25_skl(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f3974,f834]) ).
fof(f3993,plain,
( sQ234_spl
| ~ sQ290_spl
| ~ subset(relation_field(relation_inverse(sK117_skl)),relation_dom(relation_inverse(empty_set))) ),
inference(backward_demodulation,[status(thm)],[f3981,f3462]) ).
fof(f4034,plain,
( sQ234_spl
| ~ sQ290_spl
| ~ subset(relation_field(relation_inverse(empty_set)),relation_dom(relation_inverse(empty_set))) ),
inference(forward_demodulation,[status(thm)],[f3981,f3993]) ).
fof(f4035,plain,
( sQ234_spl
| ~ sQ290_spl
| ~ subset(relation_field(empty_set),relation_dom(relation_inverse(empty_set))) ),
inference(forward_demodulation,[status(thm)],[f3059,f4034]) ).
fof(f4036,plain,
( sQ234_spl
| ~ sQ290_spl
| ~ subset(empty_set,relation_dom(relation_inverse(empty_set))) ),
inference(forward_demodulation,[status(thm)],[f1623,f4035]) ).
fof(f4037,plain,
( sQ234_spl
| ~ sQ290_spl
| ~ subset(empty_set,relation_dom(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f3059,f4036]) ).
fof(f4038,plain,
( sQ234_spl
| ~ sQ290_spl
| ~ subset(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1265,f4037]) ).
fof(f4039,plain,
( sQ234_spl
| ~ sQ290_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4038,f1109]) ).
fof(f4040,plain,
( sQ234_spl
| ~ sQ290_spl ),
inference(contradiction_clause,[status(thm)],[f4039]) ).
fof(f4050,plain,
relation_field(sK117_skl) = set_union2(relation_dom(sK117_skl),relation_rng(sK117_skl)),
inference(resolution,[status(thm)],[f1262,f640]) ).
fof(f4051,plain,
sK25_skl(succ(empty_set)) = empty_set,
inference(paramodulation,[status(thm)],[f3744,f3987]) ).
fof(f4106,plain,
! [X0,X1] :
( in(sK13_skl(X0,empty_set,X1,empty_set),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3976,f1432]) ).
fof(f4107,plain,
! [X0] :
( in(X0,relation_dom(empty_set))
| ~ in(X0,empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3976,f1425]) ).
fof(f4108,definition,
! [X0,X1] :
( sQ292_spl
<=> ( in(sK13_skl(X0,empty_set,X1,empty_set),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f4111,plain,
( sQ292_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4106,f1636,f4108]) ).
fof(f4112,definition,
! [X0] :
( sQ293_spl
<=> ( in(X0,relation_dom(empty_set))
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f4115,plain,
( sQ293_spl
| ~ sQ40_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4107,f1636,f2262,f4112]) ).
fof(f4117,plain,
( in(empty_set,succ(empty_set))
| succ(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f4051,f459]) ).
fof(f4118,definition,
( sQ294_spl
<=> succ(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f4119,plain,
( ~ sQ294_spl
| succ(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f4118]) ).
fof(f4121,definition,
( sQ295_spl
<=> in(empty_set,succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f4124,plain,
( sQ295_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f4117,f4118,f4121]) ).
fof(f4125,plain,
( ~ sQ294_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4119,f3766]) ).
fof(f4126,plain,
~ sQ294_spl,
inference(contradiction_clause,[status(thm)],[f4125]) ).
fof(f4156,definition,
( sQ296_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f4164,plain,
! [X0] :
( sK21_skl(X0,set_meet(sK117_skl),sK117_skl) = ordered_pair(sK17_skl(sK21_skl(X0,set_meet(sK117_skl),sK117_skl),sK117_skl),sK18_skl(sK21_skl(X0,set_meet(sK117_skl),sK117_skl),sK117_skl))
| in(X0,set_meet(sK117_skl))
| sK117_skl = empty_set ),
inference(resolution,[status(thm)],[f1437,f3873]) ).
fof(f4171,definition,
! [X0] :
( sQ298_spl
<=> ( sK21_skl(X0,set_meet(sK117_skl),sK117_skl) = ordered_pair(sK17_skl(sK21_skl(X0,set_meet(sK117_skl),sK117_skl),sK117_skl),sK18_skl(sK21_skl(X0,set_meet(sK117_skl),sK117_skl),sK117_skl))
| in(X0,set_meet(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f4174,plain,
( sQ298_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f4164,f3980,f4171]) ).
fof(f4367,definition,
( sQ304_spl
<=> empty(relation_dom(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f4368,plain,
( ~ sQ304_spl
| empty(relation_dom(sK117_skl)) ),
inference(component_clause,[status(thm)],[f4367]) ).
fof(f4370,definition,
( sQ305_spl
<=> empty(relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f4409,plain,
( sQ286_spl
| ~ sQ241_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3849,f3782]) ).
fof(f4410,plain,
( sQ286_spl
| ~ sQ241_spl ),
inference(contradiction_clause,[status(thm)],[f4409]) ).
fof(f4411,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK22_skl(relation_field(X1),X0)),X1)
| ~ relation(X1)
| in(sK23_skl(relation_field(X1),X0),X0)
| relation_field(X1) = set_meet(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f443,f1113]) ).
fof(f4412,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK22_skl(relation_field(X1),X0),X2),X1)
| ~ relation(X1)
| in(sK23_skl(relation_field(X1),X0),X0)
| relation_field(X1) = set_meet(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f443,f1112]) ).
fof(f4495,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK24_skl(relation_field(X0),X1)),X0)
| ~ relation(X0)
| sK24_skl(relation_field(X0),X1) != X1
| relation_field(X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f453,f1113]) ).
fof(f4496,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK24_skl(relation_field(X0),X1),X2),X0)
| ~ relation(X0)
| sK24_skl(relation_field(X0),X1) != X1
| relation_field(X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f453,f1112]) ).
fof(f4507,plain,
( sQ44_spl
| ~ in(relation_field(sK117_skl),powerset(relation_dom(sK117_skl))) ),
inference(resolution,[status(thm)],[f1444,f2287]) ).
fof(f4516,plain,
( sQ186_spl
| ~ in(relation_field(sK117_skl),powerset(relation_rng(sK117_skl))) ),
inference(resolution,[status(thm)],[f3090,f1444]) ).
fof(f4630,definition,
( sQ316_spl
<=> relation(relation_inverse(sK99_skl)) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f4632,plain,
( sQ316_spl
| ~ relation(relation_inverse(sK99_skl)) ),
inference(component_clause,[status(thm)],[f4630]) ).
fof(f4634,plain,
( sQ316_spl
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f4632,f718]) ).
fof(f4636,plain,
( sQ316_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f4634,f2226,f4630]) ).
fof(f4653,definition,
( sQ317_spl
<=> relation(relation_inverse(sK98_skl)) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f4655,plain,
( sQ317_spl
| ~ relation(relation_inverse(sK98_skl)) ),
inference(component_clause,[status(thm)],[f4653]) ).
fof(f4657,plain,
( sQ317_spl
| ~ relation(sK98_skl) ),
inference(resolution,[status(thm)],[f4655,f718]) ).
fof(f4659,plain,
( sQ317_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f4657,f2607,f4653]) ).
fof(f4671,plain,
! [X0] : in(empty_set,powerset(X0)),
inference(resolution,[status(thm)],[f1445,f1109]) ).
fof(f4676,plain,
! [X0] : in(X0,powerset(X0)),
inference(resolution,[status(thm)],[f1445,f1415]) ).
fof(f4733,plain,
( ~ empty(relation_field(sK117_skl))
| empty(relation_rng(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f4050,f790]) ).
fof(f4734,plain,
( ~ empty(relation_field(sK117_skl))
| empty(relation_dom(sK117_skl)) ),
inference(paramodulation,[status(thm)],[f4050,f776]) ).
fof(f4737,definition,
( sQ318_spl
<=> empty(relation_rng(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f4738,plain,
( ~ sQ318_spl
| empty(relation_rng(sK117_skl)) ),
inference(component_clause,[status(thm)],[f4737]) ).
fof(f4740,plain,
( ~ sQ305_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f4733,f4737,f4370]) ).
fof(f4741,plain,
( ~ sQ305_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f4734,f4367,f4370]) ).
fof(f4793,plain,
! [X0] : ~ in(powerset(X0),X0),
inference(resolution,[status(thm)],[f4676,f299]) ).
fof(f4804,plain,
( ~ sQ304_spl
| relation(relation_dom(sK117_skl)) ),
inference(resolution,[status(thm)],[f4368,f308]) ).
fof(f4805,plain,
( ~ sQ304_spl
| sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4804,f2348]) ).
fof(f4806,plain,
( ~ sQ304_spl
| sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f4805]) ).
fof(f4815,plain,
( ~ sQ318_spl
| relation_rng(sK117_skl) = empty_set ),
inference(resolution,[status(thm)],[f4738,f1295]) ).
fof(f4817,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,powerset(relation_field(X0))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f4793,f1113]) ).
fof(f4818,plain,
! [X0,X1] :
( ~ in(ordered_pair(powerset(relation_field(X0)),X1),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f4793,f1112]) ).
fof(f4834,plain,
( ~ sQ318_spl
| relation_field(sK117_skl) = set_union2(relation_dom(sK117_skl),empty_set) ),
inference(backward_demodulation,[status(thm)],[f4815,f4050]) ).
fof(f4838,plain,
( ~ sQ318_spl
| relation_field(sK117_skl) = relation_dom(sK117_skl) ),
inference(forward_demodulation,[status(thm)],[f1061,f4834]) ).
fof(f4839,plain,
( ~ sQ318_spl
| sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4838,f2284]) ).
fof(f4840,plain,
( ~ sQ318_spl
| sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f4839]) ).
fof(f4853,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,ordered_pair(sK28_skl(relation_field(X1),X0),sK29_skl(relation_field(X1),X0))),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK28_skl(relation_field(X1),X0),sK29_skl(relation_field(X1),X0)),X0)
| X0 = relation_field(X1)
| ~ relation(relation_field(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f480,f1113]) ).
fof(f4854,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(ordered_pair(sK28_skl(relation_field(X1),X0),sK29_skl(relation_field(X1),X0)),X2),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK28_skl(relation_field(X1),X0),sK29_skl(relation_field(X1),X0)),X0)
| X0 = relation_field(X1)
| ~ relation(relation_field(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f480,f1112]) ).
fof(f4856,plain,
! [X0,X1] :
( ~ in(sK28_skl(sK117_skl,X0),X1)
| in(sK29_skl(sK117_skl,X0),relation_image(sK117_skl,X1))
| in(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),X0)
| X0 = sK117_skl
| ~ relation(sK117_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f481,f3074]) ).
fof(f4857,plain,
! [X0,X1] :
( ~ in(sK29_skl(sK117_skl,X0),X1)
| in(sK28_skl(sK117_skl,X0),relation_inverse_image(sK117_skl,X1))
| in(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),X0)
| X0 = sK117_skl
| ~ relation(sK117_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f481,f3382]) ).
fof(f4863,plain,
! [X0] :
( ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)) = ordered_pair(sK17_skl(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),sK117_skl),sK18_skl(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),sK117_skl))
| in(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),X0)
| X0 = sK117_skl
| ~ relation(sK117_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f481,f3873]) ).
fof(f4867,plain,
! [X0] :
( in(ordered_pair(sK28_skl(empty_set,X0),sK29_skl(empty_set,X0)),X0)
| X0 = empty_set
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f481,f1443]) ).
fof(f4869,definition,
! [X0,X1] :
( sQ319_spl
<=> ( ~ in(sK28_skl(sK117_skl,X0),X1)
| in(sK29_skl(sK117_skl,X0),relation_image(sK117_skl,X1))
| in(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),X0)
| X0 = sK117_skl
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f4872,plain,
( ~ sQ5_spl
| sQ319_spl ),
inference(split_clause,[status(thm)],[f4856,f4869,f1604]) ).
fof(f4873,definition,
! [X0,X1] :
( sQ320_spl
<=> ( ~ in(sK29_skl(sK117_skl,X0),X1)
| in(sK28_skl(sK117_skl,X0),relation_inverse_image(sK117_skl,X1))
| in(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),X0)
| X0 = sK117_skl
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f4876,plain,
( ~ sQ5_spl
| sQ320_spl ),
inference(split_clause,[status(thm)],[f4857,f4873,f1604]) ).
fof(f4881,definition,
! [X0] :
( sQ321_spl
<=> ( ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)) = ordered_pair(sK17_skl(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),sK117_skl),sK18_skl(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),sK117_skl))
| in(ordered_pair(sK28_skl(sK117_skl,X0),sK29_skl(sK117_skl,X0)),X0)
| X0 = sK117_skl
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f4884,plain,
( ~ sQ5_spl
| sQ321_spl ),
inference(split_clause,[status(thm)],[f4863,f4881,f1604]) ).
fof(f4885,definition,
! [X0] :
( sQ322_spl
<=> ( in(ordered_pair(sK28_skl(empty_set,X0),sK29_skl(empty_set,X0)),X0)
| X0 = empty_set
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f4888,plain,
( ~ sQ7_spl
| sQ322_spl ),
inference(split_clause,[status(thm)],[f4867,f4885,f1636]) ).
fof(f4977,definition,
( sQ325_spl
<=> relation(relation_inverse(sK96_skl)) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f4979,plain,
( sQ325_spl
| ~ relation(relation_inverse(sK96_skl)) ),
inference(component_clause,[status(thm)],[f4977]) ).
fof(f4981,plain,
( sQ325_spl
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f4979,f718]) ).
fof(f4983,plain,
( sQ325_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f4981,f2233,f4977]) ).
fof(f5002,plain,
! [X0] :
( in(sK76_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f485,f737]) ).
fof(f5005,definition,
( sQ326_spl
<=> empty(succ(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f5006,plain,
( ~ sQ326_spl
| empty(succ(empty_set)) ),
inference(component_clause,[status(thm)],[f5005]) ).
fof(f5009,plain,
( ~ sQ326_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5006,f754]) ).
fof(f5010,plain,
~ sQ326_spl,
inference(contradiction_clause,[status(thm)],[f5009]) ).
fof(f5078,definition,
( sQ329_spl
<=> relation(relation_inverse(sK93_skl)) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f5080,plain,
( sQ329_spl
| ~ relation(relation_inverse(sK93_skl)) ),
inference(component_clause,[status(thm)],[f5078]) ).
fof(f5082,plain,
( sQ329_spl
| ~ relation(sK93_skl) ),
inference(resolution,[status(thm)],[f5080,f718]) ).
fof(f5084,plain,
( sQ329_spl
| ~ sQ159_spl ),
inference(split_clause,[status(thm)],[f5082,f2933,f5078]) ).
fof(f5126,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK30_skl(relation_field(X0),X2,X1)),X0)
| ~ relation(X0)
| sK30_skl(relation_field(X0),X2,X1) != X1
| relation_field(X0) = unordered_pair(X1,X2) ),
inference(resolution,[status(thm)],[f495,f1113]) ).
fof(f5127,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK30_skl(relation_field(X0),X2,X1),X3),X0)
| ~ relation(X0)
| sK30_skl(relation_field(X0),X2,X1) != X1
| relation_field(X0) = unordered_pair(X1,X2) ),
inference(resolution,[status(thm)],[f495,f1112]) ).
fof(f5170,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK22_skl(empty_set,X0)),empty_set)
| ~ relation(empty_set)
| in(sK23_skl(relation_field(empty_set),X0),X0)
| relation_field(empty_set) = set_meet(X0)
| X0 = empty_set ),
inference(paramodulation,[status(thm)],[f1623,f4411]) ).
fof(f5174,definition,
! [X0,X1] :
( sQ332_spl
<=> ( ~ in(ordered_pair(X1,sK22_skl(empty_set,X0)),empty_set)
| in(sK23_skl(relation_field(empty_set),X0),X0)
| relation_field(empty_set) = set_meet(X0)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f5177,plain,
( ~ sQ7_spl
| sQ332_spl ),
inference(split_clause,[status(thm)],[f5170,f5174,f1636]) ).
fof(f5211,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK30_skl(relation_field(X0),X2,X1)),X0)
| ~ relation(X0)
| sK30_skl(relation_field(X0),X2,X1) != X2
| relation_field(X0) = unordered_pair(X1,X2) ),
inference(resolution,[status(thm)],[f496,f1113]) ).
fof(f5212,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK30_skl(relation_field(X0),X2,X1),X3),X0)
| ~ relation(X0)
| sK30_skl(relation_field(X0),X2,X1) != X2
| relation_field(X0) = unordered_pair(X1,X2) ),
inference(resolution,[status(thm)],[f496,f1112]) ).
fof(f5223,plain,
! [X0] :
( ~ sQ2_spl
| in(sK31_skl(X0,sK117_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f501,f1405]) ).
fof(f5224,definition,
! [X0] :
( sQ335_spl
<=> ( in(sK31_skl(X0,sK117_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f5225,plain,
! [X0] :
( ~ sQ335_spl
| in(sK31_skl(X0,sK117_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f5224]) ).
fof(f5227,plain,
( ~ sQ2_spl
| sQ335_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5223,f1604,f5224,f1404]) ).
fof(f5230,plain,
( ~ sQ335_spl
| sK31_skl(sK117_skl,sK117_skl) = ordered_pair(sK17_skl(sK31_skl(sK117_skl,sK117_skl),sK117_skl),sK18_skl(sK31_skl(sK117_skl,sK117_skl),sK117_skl))
| sK117_skl = empty_set
| ~ subset(sK117_skl,relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f5225,f3873]) ).
fof(f5236,definition,
( sQ336_spl
<=> subset(sK117_skl,relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f5239,definition,
( sQ337_spl
<=> sK31_skl(sK117_skl,sK117_skl) = ordered_pair(sK17_skl(sK31_skl(sK117_skl,sK117_skl),sK117_skl),sK18_skl(sK31_skl(sK117_skl,sK117_skl),sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f5242,plain,
( ~ sQ335_spl
| sQ337_spl
| sQ290_spl
| ~ sQ336_spl ),
inference(split_clause,[status(thm)],[f5230,f5236,f3980,f5239,f5224]) ).
fof(f5250,plain,
! [X0,X1] :
( ~ in(sK22_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| in(sK23_skl(relation_field(sK117_skl),X0),X0)
| relation_field(sK117_skl) = set_meet(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f4412,f3288]) ).
fof(f5254,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK22_skl(empty_set,X0),X1),empty_set)
| ~ relation(empty_set)
| in(sK23_skl(relation_field(empty_set),X0),X0)
| relation_field(empty_set) = set_meet(X0)
| X0 = empty_set ),
inference(paramodulation,[status(thm)],[f1623,f4412]) ).
fof(f5255,definition,
! [X0,X1] :
( sQ339_spl
<=> ( ~ in(sK22_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1))
| in(sK23_skl(relation_field(sK117_skl),X0),X0)
| relation_field(sK117_skl) = set_meet(X0)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f5258,plain,
( ~ sQ5_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f5250,f5255,f1604]) ).
fof(f5262,definition,
! [X0,X1] :
( sQ340_spl
<=> ( ~ in(ordered_pair(sK22_skl(empty_set,X0),X1),empty_set)
| in(sK23_skl(relation_field(empty_set),X0),X0)
| relation_field(empty_set) = set_meet(X0)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f5265,plain,
( ~ sQ7_spl
| sQ340_spl ),
inference(split_clause,[status(thm)],[f5254,f5262,f1636]) ).
fof(f5271,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK24_skl(empty_set,X0)),empty_set)
| ~ relation(empty_set)
| sK24_skl(relation_field(empty_set),X0) != X0
| relation_field(empty_set) = singleton(X0) ),
inference(paramodulation,[status(thm)],[f1623,f4495]) ).
fof(f5275,definition,
! [X0,X1] :
( sQ341_spl
<=> ( ~ in(ordered_pair(X1,sK24_skl(empty_set,X0)),empty_set)
| sK24_skl(relation_field(empty_set),X0) != X0
| relation_field(empty_set) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f5278,plain,
( ~ sQ7_spl
| sQ341_spl ),
inference(split_clause,[status(thm)],[f5271,f5275,f1636]) ).
fof(f5361,plain,
! [X0,X1] :
( ~ in(sK24_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| sK24_skl(relation_field(sK117_skl),X0) != X0
| relation_field(sK117_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4496,f3288]) ).
fof(f5365,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK24_skl(empty_set,X0),X1),empty_set)
| ~ relation(empty_set)
| sK24_skl(relation_field(empty_set),X0) != X0
| relation_field(empty_set) = singleton(X0) ),
inference(paramodulation,[status(thm)],[f1623,f4496]) ).
fof(f5366,definition,
! [X0,X1] :
( sQ345_spl
<=> ( ~ in(sK24_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1))
| sK24_skl(relation_field(sK117_skl),X0) != X0
| relation_field(sK117_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f5369,plain,
( ~ sQ5_spl
| sQ345_spl ),
inference(split_clause,[status(thm)],[f5361,f5366,f1604]) ).
fof(f5373,definition,
! [X0,X1] :
( sQ346_spl
<=> ( ~ in(ordered_pair(sK24_skl(empty_set,X0),X1),empty_set)
| sK24_skl(relation_field(empty_set),X0) != X0
| relation_field(empty_set) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f5376,plain,
( ~ sQ7_spl
| sQ346_spl ),
inference(split_clause,[status(thm)],[f5365,f5373,f1636]) ).
fof(f5384,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0))),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0)),X0)
| X0 = relation_field(empty_set)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f4853]) ).
fof(f5391,definition,
! [X0,X1] :
( sQ347_spl
<=> ( ~ in(ordered_pair(X1,ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0))),empty_set)
| ~ in(ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0)),X0)
| X0 = relation_field(empty_set)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f5394,plain,
( ~ sQ7_spl
| sQ347_spl ),
inference(split_clause,[status(thm)],[f5384,f5391,f1636]) ).
fof(f5544,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X0),X1)
| ~ relation(X1)
| in(X0,set_union2(relation_field(X1),X2)) ),
inference(resolution,[status(thm)],[f1450,f1113]) ).
fof(f5545,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X3),X1)
| ~ relation(X1)
| in(X0,set_union2(relation_field(X1),X2)) ),
inference(resolution,[status(thm)],[f1450,f1112]) ).
fof(f5577,plain,
! [X0,X1] :
( ~ in(ordered_pair(ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0)),X1),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0)),X0)
| X0 = relation_field(empty_set)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f4854]) ).
fof(f5584,definition,
! [X0,X1] :
( sQ352_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0)),X1),empty_set)
| ~ in(ordered_pair(sK28_skl(relation_field(empty_set),X0),sK29_skl(relation_field(empty_set),X0)),X0)
| X0 = relation_field(empty_set)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f5587,plain,
( ~ sQ7_spl
| sQ352_spl ),
inference(split_clause,[status(thm)],[f5577,f5584,f1636]) ).
fof(f5658,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X0),X2)
| ~ relation(X2)
| in(X0,set_union2(X1,relation_field(X2))) ),
inference(resolution,[status(thm)],[f1451,f1113]) ).
fof(f5659,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X3),X2)
| ~ relation(X2)
| in(X0,set_union2(X1,relation_field(X2))) ),
inference(resolution,[status(thm)],[f1451,f1112]) ).
fof(f5660,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK33_skl(X0,X2,relation_field(X1))),X1)
| ~ relation(X1)
| ~ in(sK33_skl(X0,X2,relation_field(X1)),X0)
| X0 = set_union2(relation_field(X1),X2) ),
inference(resolution,[status(thm)],[f512,f1113]) ).
fof(f5661,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK33_skl(X0,X2,relation_field(X1)),X3),X1)
| ~ relation(X1)
| ~ in(sK33_skl(X0,X2,relation_field(X1)),X0)
| X0 = set_union2(relation_field(X1),X2) ),
inference(resolution,[status(thm)],[f512,f1112]) ).
fof(f5662,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK33_skl(X0,relation_field(X2),X1)),X2)
| ~ relation(X2)
| ~ in(sK33_skl(X0,relation_field(X2),X1),X0)
| X0 = set_union2(X1,relation_field(X2)) ),
inference(resolution,[status(thm)],[f513,f1113]) ).
fof(f5663,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK33_skl(X0,relation_field(X2),X1),X3),X2)
| ~ relation(X2)
| ~ in(sK33_skl(X0,relation_field(X2),X1),X0)
| X0 = set_union2(X1,relation_field(X2)) ),
inference(resolution,[status(thm)],[f513,f1112]) ).
fof(f5665,plain,
! [X0,X1,X2] :
( in(sK7_skl(X0,sK117_skl,X1),relation_dom(sK117_skl))
| ~ function(sK117_skl)
| ~ relation(sK117_skl)
| in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK8_skl(X0,sK117_skl,X1),X2) ),
inference(resolution,[status(thm)],[f3394,f1425]) ).
fof(f5669,definition,
! [X0,X1,X2] :
( sQ353_spl
<=> ( in(sK7_skl(X0,sK117_skl,X1),relation_dom(sK117_skl))
| in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK8_skl(X0,sK117_skl,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f5672,definition,
( sQ354_spl
<=> function(sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f5673,plain,
( ~ sQ354_spl
| function(sK117_skl) ),
inference(component_clause,[status(thm)],[f5672]) ).
fof(f5674,plain,
( sQ354_spl
| ~ function(sK117_skl) ),
inference(component_clause,[status(thm)],[f5672]) ).
fof(f5675,plain,
( ~ sQ354_spl
| ~ sQ5_spl
| sQ353_spl ),
inference(split_clause,[status(thm)],[f5665,f5669,f1604,f5672]) ).
fof(f5676,plain,
( sQ354_spl
| ~ empty(sK117_skl) ),
inference(resolution,[status(thm)],[f5674,f303]) ).
fof(f5897,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1)),X1)
| ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1)),sK117_skl)
| sK117_skl = relation_dom_restriction(X1,relation_inverse_image(sK117_skl,X0))
| ~ relation(sK117_skl)
| ~ relation(X1)
| in(ordered_pair(sK2_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,relation_inverse_image(sK117_skl,X0))
| ~ relation(X1)
| ~ in(sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),X0) ),
inference(resolution,[status(thm)],[f3395,f346]) ).
fof(f5898,plain,
! [X0,X1,X2] :
( in(sK2_skl(X0,sK117_skl,X1),relation_dom(sK117_skl))
| ~ function(sK117_skl)
| ~ relation(sK117_skl)
| in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK3_skl(X0,sK117_skl,X1),X2) ),
inference(resolution,[status(thm)],[f3395,f1425]) ).
fof(f5902,definition,
! [X0,X1] :
( sQ355_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1)),X1)
| ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1)),sK117_skl)
| sK117_skl = relation_dom_restriction(X1,relation_inverse_image(sK117_skl,X0))
| ~ relation(X1)
| in(ordered_pair(sK2_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,relation_inverse_image(sK117_skl,X0))
| ~ relation(X1)
| ~ in(sK3_skl(relation_inverse_image(sK117_skl,X0),sK117_skl,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f5905,plain,
( ~ sQ5_spl
| sQ355_spl ),
inference(split_clause,[status(thm)],[f5897,f5902,f1604]) ).
fof(f5906,definition,
! [X0,X1,X2] :
( sQ356_spl
<=> ( in(sK2_skl(X0,sK117_skl,X1),relation_dom(sK117_skl))
| in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK3_skl(X0,sK117_skl,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f5909,plain,
( ~ sQ354_spl
| ~ sQ5_spl
| sQ356_spl ),
inference(split_clause,[status(thm)],[f5898,f5906,f1604,f5672]) ).
fof(f5961,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK30_skl(empty_set,X1,X0)),empty_set)
| ~ relation(empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X0
| relation_field(empty_set) = unordered_pair(X0,X1) ),
inference(paramodulation,[status(thm)],[f1623,f5126]) ).
fof(f5965,definition,
! [X0,X1,X2] :
( sQ357_spl
<=> ( ~ in(ordered_pair(X2,sK30_skl(empty_set,X1,X0)),empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X0
| relation_field(empty_set) = unordered_pair(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f5968,plain,
( ~ sQ7_spl
| sQ357_spl ),
inference(split_clause,[status(thm)],[f5961,f5965,f1636]) ).
fof(f6071,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| ~ in(X0,relation_inverse_image(sK117_skl,X1))
| in(X0,relation_inverse_image(sK117_skl,X1)) ),
inference(resolution,[status(thm)],[f3396,f1432]) ).
fof(f6085,definition,
! [X0,X1] :
( sQ358_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| ~ in(X0,relation_inverse_image(sK117_skl,X1))
| in(X0,relation_inverse_image(sK117_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f6088,plain,
( ~ sQ5_spl
| sQ358_spl ),
inference(split_clause,[status(thm)],[f6071,f6085,f1604]) ).
fof(f6101,plain,
! [X0,X1,X2] :
( ~ in(sK30_skl(relation_field(sK117_skl),X1,X0),relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| sK30_skl(relation_field(sK117_skl),X1,X0) != X0
| relation_field(sK117_skl) = unordered_pair(X0,X1) ),
inference(resolution,[status(thm)],[f5127,f3288]) ).
fof(f6105,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK30_skl(empty_set,X1,X0),X2),empty_set)
| ~ relation(empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X0
| relation_field(empty_set) = unordered_pair(X0,X1) ),
inference(paramodulation,[status(thm)],[f1623,f5127]) ).
fof(f6106,definition,
! [X0,X1,X2] :
( sQ359_spl
<=> ( ~ in(sK30_skl(relation_field(sK117_skl),X1,X0),relation_inverse_image(sK117_skl,X2))
| sK30_skl(relation_field(sK117_skl),X1,X0) != X0
| relation_field(sK117_skl) = unordered_pair(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f6109,plain,
( ~ sQ5_spl
| sQ359_spl ),
inference(split_clause,[status(thm)],[f6101,f6106,f1604]) ).
fof(f6113,definition,
! [X0,X1,X2] :
( sQ360_spl
<=> ( ~ in(ordered_pair(sK30_skl(empty_set,X1,X0),X2),empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X0
| relation_field(empty_set) = unordered_pair(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f6116,plain,
( ~ sQ7_spl
| sQ360_spl ),
inference(split_clause,[status(thm)],[f6105,f6113,f1636]) ).
fof(f6122,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK30_skl(empty_set,X1,X0)),empty_set)
| ~ relation(empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X1
| relation_field(empty_set) = unordered_pair(X0,X1) ),
inference(paramodulation,[status(thm)],[f1623,f5211]) ).
fof(f6126,definition,
! [X0,X1,X2] :
( sQ361_spl
<=> ( ~ in(ordered_pair(X2,sK30_skl(empty_set,X1,X0)),empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X1
| relation_field(empty_set) = unordered_pair(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f6129,plain,
( ~ sQ7_spl
| sQ361_spl ),
inference(split_clause,[status(thm)],[f6122,f6126,f1636]) ).
fof(f6147,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X1,sK117_skl,X2),sK3_skl(X1,sK117_skl,X2)),X2)
| sK117_skl = relation_dom_restriction(X2,X1)
| ~ relation(X2)
| in(ordered_pair(sK2_skl(X1,sK117_skl,X2),sK3_skl(X1,sK117_skl,X2)),X0)
| ~ subset(sK117_skl,X0)
| ~ relation(X0)
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f537,f1591]) ).
fof(f6148,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X1,sK117_skl,X2),sK8_skl(X1,sK117_skl,X2)),X2)
| sK117_skl = relation_rng_restriction(X1,X2)
| ~ relation(X2)
| in(ordered_pair(sK7_skl(X1,sK117_skl,X2),sK8_skl(X1,sK117_skl,X2)),X0)
| ~ subset(sK117_skl,X0)
| ~ relation(X0)
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f537,f1966]) ).
fof(f6149,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_inverse_image(sK117_skl,X2))
| in(ordered_pair(X1,sK13_skl(X1,relation_inverse_image(sK117_skl,X2),X2,sK117_skl)),X0)
| ~ subset(sK117_skl,X0)
| ~ relation(X0)
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f537,f3288]) ).
fof(f6161,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,ordered_pair(X2,X3)),X0)
| ~ relation(X0)
| in(ordered_pair(X2,X3),X1)
| ~ subset(relation_field(X0),X1)
| ~ relation(X1)
| ~ relation(relation_field(X0)) ),
inference(resolution,[status(thm)],[f537,f1113]) ).
fof(f6162,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(ordered_pair(X2,X3),X4),X0)
| ~ relation(X0)
| in(ordered_pair(X2,X3),X1)
| ~ subset(relation_field(X0),X1)
| ~ relation(X1)
| ~ relation(relation_field(X0)) ),
inference(resolution,[status(thm)],[f537,f1112]) ).
fof(f6164,definition,
! [X0,X1,X2] :
( sQ362_spl
<=> ( in(ordered_pair(sK2_skl(X1,sK117_skl,X2),sK3_skl(X1,sK117_skl,X2)),X2)
| sK117_skl = relation_dom_restriction(X2,X1)
| ~ relation(X2)
| in(ordered_pair(sK2_skl(X1,sK117_skl,X2),sK3_skl(X1,sK117_skl,X2)),X0)
| ~ subset(sK117_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f6167,plain,
( sQ362_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6147,f1604,f6164]) ).
fof(f6168,definition,
! [X0,X1,X2] :
( sQ363_spl
<=> ( in(ordered_pair(sK7_skl(X1,sK117_skl,X2),sK8_skl(X1,sK117_skl,X2)),X2)
| sK117_skl = relation_rng_restriction(X1,X2)
| ~ relation(X2)
| in(ordered_pair(sK7_skl(X1,sK117_skl,X2),sK8_skl(X1,sK117_skl,X2)),X0)
| ~ subset(sK117_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f6171,plain,
( sQ363_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6148,f1604,f6168]) ).
fof(f6172,definition,
! [X0,X1,X2] :
( sQ364_spl
<=> ( ~ in(X1,relation_inverse_image(sK117_skl,X2))
| in(ordered_pair(X1,sK13_skl(X1,relation_inverse_image(sK117_skl,X2),X2,sK117_skl)),X0)
| ~ subset(sK117_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f6175,plain,
( sQ364_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6149,f1604,f6172]) ).
fof(f6190,plain,
! [X0,X1,X2] :
( ~ in(sK30_skl(relation_field(sK117_skl),X1,X0),relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| sK30_skl(relation_field(sK117_skl),X1,X0) != X1
| relation_field(sK117_skl) = unordered_pair(X0,X1) ),
inference(resolution,[status(thm)],[f5212,f3288]) ).
fof(f6194,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK30_skl(empty_set,X1,X0),X2),empty_set)
| ~ relation(empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X1
| relation_field(empty_set) = unordered_pair(X0,X1) ),
inference(paramodulation,[status(thm)],[f1623,f5212]) ).
fof(f6195,definition,
! [X0,X1,X2] :
( sQ365_spl
<=> ( ~ in(sK30_skl(relation_field(sK117_skl),X1,X0),relation_inverse_image(sK117_skl,X2))
| sK30_skl(relation_field(sK117_skl),X1,X0) != X1
| relation_field(sK117_skl) = unordered_pair(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f6198,plain,
( ~ sQ5_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f6190,f6195,f1604]) ).
fof(f6202,definition,
! [X0,X1,X2] :
( sQ366_spl
<=> ( ~ in(ordered_pair(sK30_skl(empty_set,X1,X0),X2),empty_set)
| sK30_skl(relation_field(empty_set),X1,X0) != X1
| relation_field(empty_set) = unordered_pair(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f6205,plain,
( ~ sQ7_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f6194,f6202,f1636]) ).
fof(f6209,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK3_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ),
inference(resolution,[status(thm)],[f5544,f1591]) ).
fof(f6210,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK8_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ),
inference(resolution,[status(thm)],[f5544,f1966]) ).
fof(f6211,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),set_union2(relation_field(sK117_skl),X2)) ),
inference(resolution,[status(thm)],[f5544,f3288]) ).
fof(f6226,definition,
! [X0,X1,X2] :
( sQ367_spl
<=> ( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(sK3_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f6229,plain,
( ~ sQ5_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f6209,f6226,f1604]) ).
fof(f6230,definition,
! [X0,X1,X2] :
( sQ368_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(sK8_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f6233,plain,
( ~ sQ5_spl
| sQ368_spl ),
inference(split_clause,[status(thm)],[f6210,f6230,f1604]) ).
fof(f6234,definition,
! [X0,X1,X2] :
( sQ369_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),set_union2(relation_field(sK117_skl),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f6237,plain,
( ~ sQ5_spl
| sQ369_spl ),
inference(split_clause,[status(thm)],[f6211,f6234,f1604]) ).
fof(f6256,plain,
( ~ in(succ(empty_set),empty_set)
| succ(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f4051,f3979]) ).
fof(f6258,definition,
( sQ370_spl
<=> in(succ(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f6261,plain,
( ~ sQ370_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f6256,f4118,f6258]) ).
fof(f6275,plain,
! [X0,X1] :
( ~ in(sK41_skl(X0,sK117_skl),X1)
| in(sK42_skl(X0,sK117_skl),relation_image(sK117_skl,X1))
| subset(sK117_skl,X0)
| ~ relation(X0)
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f538,f3074]) ).
fof(f6276,plain,
! [X0,X1] :
( ~ in(sK42_skl(X0,sK117_skl),X1)
| in(sK41_skl(X0,sK117_skl),relation_inverse_image(sK117_skl,X1))
| subset(sK117_skl,X0)
| ~ relation(X0)
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f538,f3382]) ).
fof(f6286,plain,
! [X0] :
( ordered_pair(sK41_skl(X0,sK117_skl),sK42_skl(X0,sK117_skl)) = ordered_pair(sK17_skl(ordered_pair(sK41_skl(X0,sK117_skl),sK42_skl(X0,sK117_skl)),sK117_skl),sK18_skl(ordered_pair(sK41_skl(X0,sK117_skl),sK42_skl(X0,sK117_skl)),sK117_skl))
| subset(sK117_skl,X0)
| ~ relation(X0)
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f538,f3873]) ).
fof(f6290,plain,
! [X0] :
( subset(empty_set,X0)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f538,f1443]) ).
fof(f6294,definition,
! [X0,X1] :
( sQ371_spl
<=> ( ~ in(sK41_skl(X0,sK117_skl),X1)
| in(sK42_skl(X0,sK117_skl),relation_image(sK117_skl,X1))
| subset(sK117_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f6297,plain,
( sQ371_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6275,f1604,f6294]) ).
fof(f6298,definition,
! [X0,X1] :
( sQ372_spl
<=> ( ~ in(sK42_skl(X0,sK117_skl),X1)
| in(sK41_skl(X0,sK117_skl),relation_inverse_image(sK117_skl,X1))
| subset(sK117_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f6301,plain,
( sQ372_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6276,f1604,f6298]) ).
fof(f6308,definition,
! [X0] :
( sQ373_spl
<=> ( ordered_pair(sK41_skl(X0,sK117_skl),sK42_skl(X0,sK117_skl)) = ordered_pair(sK17_skl(ordered_pair(sK41_skl(X0,sK117_skl),sK42_skl(X0,sK117_skl)),sK117_skl),sK18_skl(ordered_pair(sK41_skl(X0,sK117_skl),sK42_skl(X0,sK117_skl)),sK117_skl))
| subset(sK117_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f6311,plain,
( sQ373_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6286,f1604,f6308]) ).
fof(f6312,definition,
! [X0] :
( sQ374_spl
<=> ( subset(empty_set,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f6315,plain,
( sQ374_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6290,f1636,f6312]) ).
fof(f6317,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,ordered_pair(sK41_skl(relation_field(X1),X0),sK42_skl(relation_field(X1),X0))),X1)
| ~ relation(X1)
| subset(X0,relation_field(X1))
| ~ relation(relation_field(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f539,f1113]) ).
fof(f6318,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(ordered_pair(sK41_skl(relation_field(X1),X0),sK42_skl(relation_field(X1),X0)),X2),X1)
| ~ relation(X1)
| subset(X0,relation_field(X1))
| ~ relation(relation_field(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f539,f1112]) ).
fof(f6330,plain,
! [X0] :
( in(X0,relation_field(sK117_skl))
| ~ in(X0,relation_dom(sK117_skl)) ),
inference(resolution,[status(thm)],[f544,f2198]) ).
fof(f6347,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK2_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ),
inference(resolution,[status(thm)],[f5545,f1591]) ).
fof(f6348,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK7_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ),
inference(resolution,[status(thm)],[f5545,f1966]) ).
fof(f6349,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| in(X0,set_union2(relation_field(sK117_skl),X1)) ),
inference(resolution,[status(thm)],[f5545,f3288]) ).
fof(f6365,definition,
! [X0,X1,X2] :
( sQ375_spl
<=> ( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(sK2_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f6368,plain,
( ~ sQ5_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f6347,f6365,f1604]) ).
fof(f6369,definition,
! [X0,X1,X2] :
( sQ376_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(sK7_skl(X0,sK117_skl,X1),set_union2(relation_field(sK117_skl),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f6372,plain,
( ~ sQ5_spl
| sQ376_spl ),
inference(split_clause,[status(thm)],[f6348,f6369,f1604]) ).
fof(f6373,definition,
! [X0,X1,X2] :
( sQ377_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X2))
| in(X0,set_union2(relation_field(sK117_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f6376,plain,
( ~ sQ5_spl
| sQ377_spl ),
inference(split_clause,[status(thm)],[f6349,f6373,f1604]) ).
fof(f6379,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK3_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f5658,f1591]) ).
fof(f6380,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK8_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f5658,f1966]) ).
fof(f6381,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),set_union2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f5658,f3288]) ).
fof(f6397,definition,
! [X0,X1,X2] :
( sQ378_spl
<=> ( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(sK3_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f6400,plain,
( ~ sQ5_spl
| sQ378_spl ),
inference(split_clause,[status(thm)],[f6379,f6397,f1604]) ).
fof(f6401,definition,
! [X0,X1,X2] :
( sQ379_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(sK8_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f6404,plain,
( ~ sQ5_spl
| sQ379_spl ),
inference(split_clause,[status(thm)],[f6380,f6401,f1604]) ).
fof(f6405,definition,
! [X0,X1,X2] :
( sQ380_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),set_union2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f6408,plain,
( ~ sQ5_spl
| sQ380_spl ),
inference(split_clause,[status(thm)],[f6381,f6405,f1604]) ).
fof(f6542,plain,
( sK76_skl(sK117_skl) = ordered_pair(sK17_skl(sK76_skl(sK117_skl),sK117_skl),sK18_skl(sK76_skl(sK117_skl),sK117_skl))
| empty(sK117_skl) ),
inference(resolution,[status(thm)],[f5002,f3873]) ).
fof(f6552,definition,
( sQ381_spl
<=> empty(sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f6553,plain,
( ~ sQ381_spl
| empty(sK117_skl) ),
inference(component_clause,[status(thm)],[f6552]) ).
fof(f6555,definition,
( sQ382_spl
<=> sK76_skl(sK117_skl) = ordered_pair(sK17_skl(sK76_skl(sK117_skl),sK117_skl),sK18_skl(sK76_skl(sK117_skl),sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f6558,plain,
( sQ382_spl
| sQ381_spl ),
inference(split_clause,[status(thm)],[f6542,f6552,f6555]) ).
fof(f6561,plain,
( ~ sQ381_spl
| sQ354_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6553,f5676]) ).
fof(f6562,plain,
( ~ sQ381_spl
| sQ354_spl ),
inference(contradiction_clause,[status(thm)],[f6561]) ).
fof(f6563,plain,
! [X0,X1] :
( ~ sQ354_spl
| ~ in(apply(sK117_skl,X0),X1)
| ~ in(X0,relation_dom(sK117_skl))
| in(X0,relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f5673,f1427]) ).
fof(f6564,definition,
! [X0,X1] :
( sQ383_spl
<=> ( ~ in(apply(sK117_skl,X0),X1)
| ~ in(X0,relation_dom(sK117_skl))
| in(X0,relation_inverse_image(sK117_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f6567,plain,
( ~ sQ354_spl
| sQ383_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6563,f1604,f6564,f5672]) ).
fof(f6580,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK43_skl(relation_field(X1),X0)),X1)
| ~ relation(X1)
| subset(X0,relation_field(X1)) ),
inference(resolution,[status(thm)],[f546,f1113]) ).
fof(f6581,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK43_skl(relation_field(X1),X0),X2),X1)
| ~ relation(X1)
| subset(X0,relation_field(X1)) ),
inference(resolution,[status(thm)],[f546,f1112]) ).
fof(f6586,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK2_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f5659,f1591]) ).
fof(f6587,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ relation(sK117_skl)
| in(sK7_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f5659,f1966]) ).
fof(f6588,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| in(X0,set_union2(X1,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f5659,f3288]) ).
fof(f6606,definition,
! [X0,X1,X2] :
( sQ384_spl
<=> ( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(sK2_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f6609,plain,
( ~ sQ5_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f6586,f6606,f1604]) ).
fof(f6610,definition,
! [X0,X1,X2] :
( sQ385_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(sK7_skl(X0,sK117_skl,X1),set_union2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f6613,plain,
( ~ sQ5_spl
| sQ385_spl ),
inference(split_clause,[status(thm)],[f6587,f6610,f1604]) ).
fof(f6614,definition,
! [X0,X1,X2] :
( sQ386_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X2))
| in(X0,set_union2(X1,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f6617,plain,
( ~ sQ5_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f6588,f6614,f1604]) ).
fof(f6621,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK33_skl(X0,X1,empty_set)),empty_set)
| ~ relation(empty_set)
| ~ in(sK33_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_union2(relation_field(empty_set),X1) ),
inference(paramodulation,[status(thm)],[f1623,f5660]) ).
fof(f6625,definition,
! [X0,X1,X2] :
( sQ387_spl
<=> ( ~ in(ordered_pair(X2,sK33_skl(X0,X1,empty_set)),empty_set)
| ~ in(sK33_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_union2(relation_field(empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f6628,plain,
( ~ sQ7_spl
| sQ387_spl ),
inference(split_clause,[status(thm)],[f6621,f6625,f1636]) ).
fof(f6676,plain,
( sQ3_spl
| subset(sK45_skl(relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f553,f1409]) ).
fof(f6679,definition,
( sQ388_spl
<=> subset(sK45_skl(relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f6680,plain,
( ~ sQ388_spl
| subset(sK45_skl(relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f6679]) ).
fof(f6682,plain,
( sQ3_spl
| sQ388_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6676,f1604,f6679,f1407]) ).
fof(f6685,plain,
( sQ3_spl
| sK45_skl(relation_field(sK117_skl),sK117_skl) != empty_set
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f554,f1409]) ).
fof(f6688,definition,
( sQ389_spl
<=> sK45_skl(relation_field(sK117_skl),sK117_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f6691,plain,
( sQ3_spl
| ~ sQ389_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6685,f1604,f6688,f1407]) ).
fof(f6694,plain,
! [X0] :
( sQ2_spl
| ~ disjoint(fiber(sK117_skl,X0),sK32_skl(sK117_skl))
| ~ in(X0,sK32_skl(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1406,f505]) ).
fof(f6695,plain,
( sQ2_spl
| sK32_skl(sK117_skl) != empty_set
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1406,f504]) ).
fof(f6696,plain,
( sQ2_spl
| subset(sK32_skl(sK117_skl),relation_field(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1406,f503]) ).
fof(f6697,definition,
! [X0] :
( sQ390_spl
<=> ( ~ disjoint(fiber(sK117_skl,X0),sK32_skl(sK117_skl))
| ~ in(X0,sK32_skl(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f6698,plain,
! [X0] :
( ~ sQ390_spl
| ~ disjoint(fiber(sK117_skl,X0),sK32_skl(sK117_skl))
| ~ in(X0,sK32_skl(sK117_skl)) ),
inference(component_clause,[status(thm)],[f6697]) ).
fof(f6700,plain,
( sQ2_spl
| sQ390_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6694,f1604,f6697,f1404]) ).
fof(f6701,definition,
( sQ391_spl
<=> sK32_skl(sK117_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f6704,plain,
( sQ2_spl
| ~ sQ391_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6695,f1604,f6701,f1404]) ).
fof(f6705,definition,
( sQ392_spl
<=> subset(sK32_skl(sK117_skl),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f6706,plain,
( ~ sQ392_spl
| subset(sK32_skl(sK117_skl),relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f6705]) ).
fof(f6708,plain,
( sQ2_spl
| sQ392_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6696,f1604,f6705,f1404]) ).
fof(f6709,plain,
! [X0] :
( ~ sQ3_spl
| disjoint(fiber(sK117_skl,sK44_skl(X0,relation_field(sK117_skl),sK117_skl)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1408,f552]) ).
fof(f6710,plain,
! [X0] :
( ~ sQ3_spl
| in(sK44_skl(X0,relation_field(sK117_skl),sK117_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1408,f551]) ).
fof(f6711,definition,
! [X0] :
( sQ393_spl
<=> ( disjoint(fiber(sK117_skl,sK44_skl(X0,relation_field(sK117_skl),sK117_skl)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f6712,plain,
! [X0] :
( ~ sQ393_spl
| disjoint(fiber(sK117_skl,sK44_skl(X0,relation_field(sK117_skl),sK117_skl)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f6711]) ).
fof(f6714,plain,
( ~ sQ3_spl
| sQ393_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6709,f1604,f6711,f1407]) ).
fof(f6715,definition,
! [X0] :
( sQ394_spl
<=> ( in(sK44_skl(X0,relation_field(sK117_skl),sK117_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f6716,plain,
! [X0] :
( ~ sQ394_spl
| in(sK44_skl(X0,relation_field(sK117_skl),sK117_skl),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f6715]) ).
fof(f6718,plain,
( ~ sQ3_spl
| sQ394_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6710,f1604,f6715,f1407]) ).
fof(f6749,plain,
! [X0,X1,X2] :
( ~ in(sK33_skl(X0,X1,relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| ~ in(sK33_skl(X0,X1,relation_field(sK117_skl)),X0)
| X0 = set_union2(relation_field(sK117_skl),X1) ),
inference(resolution,[status(thm)],[f5661,f3288]) ).
fof(f6753,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK33_skl(X0,X1,empty_set),X2),empty_set)
| ~ relation(empty_set)
| ~ in(sK33_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_union2(relation_field(empty_set),X1) ),
inference(paramodulation,[status(thm)],[f1623,f5661]) ).
fof(f6754,definition,
! [X0,X1,X2] :
( sQ399_spl
<=> ( ~ in(sK33_skl(X0,X1,relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X2))
| ~ in(sK33_skl(X0,X1,relation_field(sK117_skl)),X0)
| X0 = set_union2(relation_field(sK117_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f6757,plain,
( ~ sQ5_spl
| sQ399_spl ),
inference(split_clause,[status(thm)],[f6749,f6754,f1604]) ).
fof(f6761,definition,
! [X0,X1,X2] :
( sQ400_spl
<=> ( ~ in(ordered_pair(sK33_skl(X0,X1,empty_set),X2),empty_set)
| ~ in(sK33_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_union2(relation_field(empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f6764,plain,
( ~ sQ7_spl
| sQ400_spl ),
inference(split_clause,[status(thm)],[f6753,f6761,f1636]) ).
fof(f6771,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK33_skl(X0,empty_set,X1)),empty_set)
| ~ relation(empty_set)
| ~ in(sK33_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_union2(X1,relation_field(empty_set)) ),
inference(paramodulation,[status(thm)],[f1623,f5662]) ).
fof(f6775,definition,
! [X0,X1,X2] :
( sQ401_spl
<=> ( ~ in(ordered_pair(X2,sK33_skl(X0,empty_set,X1)),empty_set)
| ~ in(sK33_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_union2(X1,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f6778,plain,
( ~ sQ7_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f6771,f6775,f1636]) ).
fof(f6934,definition,
( sQ402_spl
<=> in(sK31_skl(relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f6937,definition,
( sQ403_spl
<=> subset(relation_field(sK117_skl),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f6939,plain,
( sQ403_spl
| ~ subset(relation_field(sK117_skl),relation_field(sK117_skl)) ),
inference(component_clause,[status(thm)],[f6937]) ).
fof(f6940,definition,
( sQ404_spl
<=> relation_field(sK117_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f6941,plain,
( ~ sQ404_spl
| relation_field(sK117_skl) = empty_set ),
inference(component_clause,[status(thm)],[f6940]) ).
fof(f6944,plain,
( sQ403_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6939,f1415]) ).
fof(f6945,plain,
sQ403_spl,
inference(contradiction_clause,[status(thm)],[f6944]) ).
fof(f6966,plain,
( sQ186_spl
| ~ sQ404_spl
| ~ in(empty_set,powerset(relation_rng(sK117_skl))) ),
inference(backward_demodulation,[status(thm)],[f6941,f4516]) ).
fof(f6972,plain,
( sQ44_spl
| ~ sQ404_spl
| ~ in(empty_set,powerset(relation_dom(sK117_skl))) ),
inference(backward_demodulation,[status(thm)],[f6941,f4507]) ).
fof(f7047,plain,
( sQ186_spl
| ~ sQ404_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6966,f4671]) ).
fof(f7048,plain,
( sQ186_spl
| ~ sQ404_spl ),
inference(contradiction_clause,[status(thm)],[f7047]) ).
fof(f7049,plain,
! [X0] :
( sQ3_spl
| ~ disjoint(fiber(sK117_skl,X0),sK45_skl(relation_field(sK117_skl),sK117_skl))
| ~ in(X0,sK45_skl(relation_field(sK117_skl),sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1409,f555]) ).
fof(f7052,definition,
! [X0] :
( sQ405_spl
<=> ( ~ disjoint(fiber(sK117_skl,X0),sK45_skl(relation_field(sK117_skl),sK117_skl))
| ~ in(X0,sK45_skl(relation_field(sK117_skl),sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f7053,plain,
! [X0] :
( ~ sQ405_spl
| ~ disjoint(fiber(sK117_skl,X0),sK45_skl(relation_field(sK117_skl),sK117_skl))
| ~ in(X0,sK45_skl(relation_field(sK117_skl),sK117_skl)) ),
inference(component_clause,[status(thm)],[f7052]) ).
fof(f7055,plain,
( sQ3_spl
| sQ405_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7049,f1604,f7052,f1407]) ).
fof(f7164,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X0),X2)
| ~ relation(X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,relation_field(X2))) ),
inference(resolution,[status(thm)],[f1456,f1113]) ).
fof(f7165,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X3),X2)
| ~ relation(X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,relation_field(X2))) ),
inference(resolution,[status(thm)],[f1456,f1112]) ).
fof(f7168,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK46_skl(X0,relation_field(X1),relation_field(X1))),X1)
| ~ relation(X1)
| ~ in(sK46_skl(X0,relation_field(X1),relation_field(X1)),X0)
| X0 = set_intersection2(relation_field(X1),relation_field(X1)) ),
inference(resolution,[status(thm)],[f562,f1113]) ).
fof(f7169,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK46_skl(X0,X2,relation_field(X1))),X1)
| ~ relation(X1)
| ~ in(sK46_skl(X0,X2,relation_field(X1)),X2)
| ~ in(sK46_skl(X0,X2,relation_field(X1)),X0)
| X0 = set_intersection2(relation_field(X1),X2) ),
inference(resolution,[status(thm)],[f562,f1113]) ).
fof(f7170,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK46_skl(X0,relation_field(X1),relation_field(X1)),X2),X1)
| ~ relation(X1)
| ~ in(sK46_skl(X0,relation_field(X1),relation_field(X1)),X0)
| X0 = set_intersection2(relation_field(X1),relation_field(X1)) ),
inference(resolution,[status(thm)],[f562,f1112]) ).
fof(f7171,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK46_skl(X0,X2,relation_field(X1)),X3),X1)
| ~ relation(X1)
| ~ in(sK46_skl(X0,X2,relation_field(X1)),X2)
| ~ in(sK46_skl(X0,X2,relation_field(X1)),X0)
| X0 = set_intersection2(relation_field(X1),X2) ),
inference(resolution,[status(thm)],[f562,f1112]) ).
fof(f7172,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK46_skl(X0,relation_field(X2),X1)),X2)
| ~ relation(X2)
| ~ in(sK46_skl(X0,relation_field(X2),X1),X1)
| ~ in(sK46_skl(X0,relation_field(X2),X1),X0)
| X0 = set_intersection2(X1,relation_field(X2)) ),
inference(resolution,[status(thm)],[f562,f1113]) ).
fof(f7173,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK46_skl(X0,relation_field(X2),X1),X3),X2)
| ~ relation(X2)
| ~ in(sK46_skl(X0,relation_field(X2),X1),X1)
| ~ in(sK46_skl(X0,relation_field(X2),X1),X0)
| X0 = set_intersection2(X1,relation_field(X2)) ),
inference(resolution,[status(thm)],[f562,f1112]) ).
fof(f7174,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK46_skl(X0,relation_field(X1),relation_field(X1))),X1)
| ~ relation(X1)
| ~ in(sK46_skl(X0,relation_field(X1),relation_field(X1)),X0)
| X0 = relation_field(X1) ),
inference(forward_demodulation,[status(thm)],[f819,f7168]) ).
fof(f7175,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK46_skl(X0,relation_field(X1),relation_field(X1)),X2),X1)
| ~ relation(X1)
| ~ in(sK46_skl(X0,relation_field(X1),relation_field(X1)),X0)
| X0 = relation_field(X1) ),
inference(forward_demodulation,[status(thm)],[f819,f7170]) ).
fof(f7206,plain,
! [X0,X1,X2] :
( ~ in(sK33_skl(X0,relation_field(sK117_skl),X1),relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| ~ in(sK33_skl(X0,relation_field(sK117_skl),X1),X0)
| X0 = set_union2(X1,relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f5663,f3288]) ).
fof(f7210,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK33_skl(X0,empty_set,X1),X2),empty_set)
| ~ relation(empty_set)
| ~ in(sK33_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_union2(X1,relation_field(empty_set)) ),
inference(paramodulation,[status(thm)],[f1623,f5663]) ).
fof(f7211,definition,
! [X0,X1,X2] :
( sQ406_spl
<=> ( ~ in(sK33_skl(X0,relation_field(sK117_skl),X1),relation_inverse_image(sK117_skl,X2))
| ~ in(sK33_skl(X0,relation_field(sK117_skl),X1),X0)
| X0 = set_union2(X1,relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f7214,plain,
( ~ sQ5_spl
| sQ406_spl ),
inference(split_clause,[status(thm)],[f7206,f7211,f1604]) ).
fof(f7218,definition,
! [X0,X1,X2] :
( sQ407_spl
<=> ( ~ in(ordered_pair(sK33_skl(X0,empty_set,X1),X2),empty_set)
| ~ in(sK33_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_union2(X1,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f7221,plain,
( ~ sQ7_spl
| sQ407_spl ),
inference(split_clause,[status(thm)],[f7210,f7218,f1636]) ).
fof(f7227,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,ordered_pair(X1,X2)),empty_set)
| ~ relation(empty_set)
| in(ordered_pair(X1,X2),X0)
| ~ subset(relation_field(empty_set),X0)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f6161]) ).
fof(f7230,definition,
! [X0,X1,X2,X3] :
( sQ408_spl
<=> ( ~ in(ordered_pair(X3,ordered_pair(X1,X2)),empty_set)
| in(ordered_pair(X1,X2),X0)
| ~ subset(relation_field(empty_set),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f7233,plain,
( sQ408_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7227,f1636,f7230]) ).
fof(f7319,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK99_skl,X0)),sK99_skl)
| ~ in(X0,relation_dom(sK99_skl))
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f1457,f951]) ).
fof(f7320,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK96_skl,X0)),sK96_skl)
| ~ in(X0,relation_dom(sK96_skl))
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f1457,f938]) ).
fof(f7321,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK86_skl,X0)),sK86_skl)
| ~ in(X0,relation_dom(sK86_skl))
| ~ relation(sK86_skl) ),
inference(resolution,[status(thm)],[f1457,f902]) ).
fof(f7322,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)],[f1457,f765]) ).
fof(f7326,definition,
! [X0] :
( sQ409_spl
<=> ( in(ordered_pair(X0,apply(sK99_skl,X0)),sK99_skl)
| ~ in(X0,relation_dom(sK99_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f7329,plain,
( sQ409_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f7319,f2226,f7326]) ).
fof(f7330,definition,
! [X0] :
( sQ410_spl
<=> ( in(ordered_pair(X0,apply(sK96_skl,X0)),sK96_skl)
| ~ in(X0,relation_dom(sK96_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f7333,plain,
( sQ410_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f7320,f2233,f7330]) ).
fof(f7334,definition,
! [X0] :
( sQ411_spl
<=> ( in(ordered_pair(X0,apply(sK86_skl,X0)),sK86_skl)
| ~ in(X0,relation_dom(sK86_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f7337,plain,
( sQ411_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f7321,f2240,f7334]) ).
fof(f7338,definition,
! [X0] :
( sQ412_spl
<=> ( in(ordered_pair(X0,apply(empty_set,X0)),empty_set)
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f7341,plain,
( sQ412_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7322,f1636,f7338]) ).
fof(f7345,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK99_skl)
| X1 = apply(sK99_skl,X0)
| ~ in(X0,relation_dom(sK99_skl))
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f569,f951]) ).
fof(f7346,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK96_skl)
| X1 = apply(sK96_skl,X0)
| ~ in(X0,relation_dom(sK96_skl))
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f569,f938]) ).
fof(f7347,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK86_skl)
| X1 = apply(sK86_skl,X0)
| ~ in(X0,relation_dom(sK86_skl))
| ~ relation(sK86_skl) ),
inference(resolution,[status(thm)],[f569,f902]) ).
fof(f7348,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)],[f569,f765]) ).
fof(f7352,definition,
! [X0,X1] :
( sQ413_spl
<=> ( ~ in(ordered_pair(X0,X1),sK99_skl)
| X1 = apply(sK99_skl,X0)
| ~ in(X0,relation_dom(sK99_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f7355,plain,
( sQ413_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f7345,f2226,f7352]) ).
fof(f7356,definition,
! [X0,X1] :
( sQ414_spl
<=> ( ~ in(ordered_pair(X0,X1),sK96_skl)
| X1 = apply(sK96_skl,X0)
| ~ in(X0,relation_dom(sK96_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f7359,plain,
( sQ414_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f7346,f2233,f7356]) ).
fof(f7360,definition,
! [X0,X1] :
( sQ415_spl
<=> ( ~ in(ordered_pair(X0,X1),sK86_skl)
| X1 = apply(sK86_skl,X0)
| ~ in(X0,relation_dom(sK86_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f7363,plain,
( sQ415_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f7347,f2240,f7360]) ).
fof(f7364,definition,
! [X0,X1] :
( sQ416_spl
<=> ( ~ in(ordered_pair(X0,X1),empty_set)
| X1 = apply(empty_set,X0)
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f7367,plain,
( sQ416_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7348,f1636,f7364]) ).
fof(f7375,plain,
( ~ sQ394_spl
| in(sK44_skl(relation_dom(sK117_skl),relation_field(sK117_skl),sK117_skl),relation_dom(sK117_skl))
| relation_dom(sK117_skl) = empty_set ),
inference(resolution,[status(thm)],[f6716,f2198]) ).
fof(f7379,plain,
( ~ sQ394_spl
| in(sK44_skl(empty_set,relation_field(sK117_skl),sK117_skl),empty_set)
| empty_set = empty_set ),
inference(resolution,[status(thm)],[f6716,f1109]) ).
fof(f7381,plain,
( ~ sQ394_spl
| in(sK44_skl(relation_field(sK117_skl),relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl))
| relation_field(sK117_skl) = empty_set ),
inference(resolution,[status(thm)],[f6716,f1415]) ).
fof(f7382,definition,
( sQ417_spl
<=> relation_dom(sK117_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f7383,plain,
( ~ sQ417_spl
| relation_dom(sK117_skl) = empty_set ),
inference(component_clause,[status(thm)],[f7382]) ).
fof(f7385,definition,
( sQ418_spl
<=> in(sK44_skl(relation_dom(sK117_skl),relation_field(sK117_skl),sK117_skl),relation_dom(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f7388,plain,
( ~ sQ394_spl
| sQ418_spl
| sQ417_spl ),
inference(split_clause,[status(thm)],[f7375,f7382,f7385,f6715]) ).
fof(f7389,definition,
( sQ419_spl
<=> in(sK44_skl(empty_set,relation_field(sK117_skl),sK117_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f7390,plain,
( ~ sQ419_spl
| in(sK44_skl(empty_set,relation_field(sK117_skl),sK117_skl),empty_set) ),
inference(component_clause,[status(thm)],[f7389]) ).
fof(f7392,plain,
( ~ sQ394_spl
| sQ419_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f7379,f4156,f7389,f6715]) ).
fof(f7393,definition,
( sQ420_spl
<=> in(sK44_skl(relation_field(sK117_skl),relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f7396,plain,
( ~ sQ394_spl
| sQ420_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f7381,f6940,f7393,f6715]) ).
fof(f7397,plain,
( ~ sQ419_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7390,f1443]) ).
fof(f7398,plain,
~ sQ419_spl,
inference(contradiction_clause,[status(thm)],[f7397]) ).
fof(f7404,plain,
( sQ44_spl
| ~ sQ404_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6972,f4671]) ).
fof(f7405,plain,
( sQ44_spl
| ~ sQ404_spl ),
inference(contradiction_clause,[status(thm)],[f7404]) ).
fof(f7417,plain,
! [X0,X1] :
( ~ sQ417_spl
| in(sK9_skl(X0,X1,sK117_skl),empty_set)
| in(sK9_skl(X0,X1,sK117_skl),X0)
| X0 = relation_inverse_image(sK117_skl,X1)
| ~ function(sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f7383,f381]) ).
fof(f7418,plain,
! [X0,X1] :
( ~ sQ417_spl
| ~ in(apply(sK117_skl,sK9_skl(X0,X1,sK117_skl)),X1)
| ~ in(sK9_skl(X0,X1,sK117_skl),empty_set)
| ~ in(sK9_skl(X0,X1,sK117_skl),X0)
| X0 = relation_inverse_image(sK117_skl,X1)
| ~ function(sK117_skl)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f7383,f380]) ).
fof(f7421,definition,
! [X0,X1] :
( sQ421_spl
<=> ( in(sK9_skl(X0,X1,sK117_skl),empty_set)
| in(sK9_skl(X0,X1,sK117_skl),X0)
| X0 = relation_inverse_image(sK117_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f7424,plain,
( ~ sQ417_spl
| sQ421_spl
| ~ sQ354_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7417,f1604,f5672,f7421,f7382]) ).
fof(f7425,definition,
! [X0,X1] :
( sQ422_spl
<=> ( ~ in(apply(sK117_skl,sK9_skl(X0,X1,sK117_skl)),X1)
| ~ in(sK9_skl(X0,X1,sK117_skl),empty_set)
| ~ in(sK9_skl(X0,X1,sK117_skl),X0)
| X0 = relation_inverse_image(sK117_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f7428,plain,
( ~ sQ417_spl
| sQ422_spl
| ~ sQ354_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7418,f1604,f5672,f7425,f7382]) ).
fof(f7451,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(X1,X2),X3),empty_set)
| ~ relation(empty_set)
| in(ordered_pair(X1,X2),X0)
| ~ subset(relation_field(empty_set),X0)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f6162]) ).
fof(f7454,definition,
! [X0,X1,X2,X3] :
( sQ423_spl
<=> ( ~ in(ordered_pair(ordered_pair(X1,X2),X3),empty_set)
| in(ordered_pair(X1,X2),X0)
| ~ subset(relation_field(empty_set),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f7457,plain,
( sQ423_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7451,f1636,f7454]) ).
fof(f7461,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,ordered_pair(sK41_skl(relation_field(empty_set),X0),sK42_skl(relation_field(empty_set),X0))),empty_set)
| ~ relation(empty_set)
| subset(X0,relation_field(empty_set))
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f6317]) ).
fof(f7466,definition,
! [X0,X1] :
( sQ424_spl
<=> ( ~ in(ordered_pair(X1,ordered_pair(sK41_skl(relation_field(empty_set),X0),sK42_skl(relation_field(empty_set),X0))),empty_set)
| subset(X0,relation_field(empty_set))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f7469,plain,
( ~ sQ7_spl
| sQ424_spl ),
inference(split_clause,[status(thm)],[f7461,f7466,f1636]) ).
fof(f7591,plain,
! [X0] :
( apply(sK99_skl,X0) = empty_set
| in(X0,relation_dom(sK99_skl))
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f1458,f951]) ).
fof(f7592,plain,
! [X0] :
( apply(sK96_skl,X0) = empty_set
| in(X0,relation_dom(sK96_skl))
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f1458,f938]) ).
fof(f7593,plain,
! [X0] :
( apply(sK86_skl,X0) = empty_set
| in(X0,relation_dom(sK86_skl))
| ~ relation(sK86_skl) ),
inference(resolution,[status(thm)],[f1458,f902]) ).
fof(f7594,plain,
! [X0] :
( apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1458,f765]) ).
fof(f7598,definition,
! [X0] :
( sQ425_spl
<=> ( apply(sK99_skl,X0) = empty_set
| in(X0,relation_dom(sK99_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f7601,plain,
( sQ425_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f7591,f2226,f7598]) ).
fof(f7602,definition,
! [X0] :
( sQ426_spl
<=> ( apply(sK96_skl,X0) = empty_set
| in(X0,relation_dom(sK96_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f7605,plain,
( sQ426_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f7592,f2233,f7602]) ).
fof(f7606,definition,
! [X0] :
( sQ427_spl
<=> ( apply(sK86_skl,X0) = empty_set
| in(X0,relation_dom(sK86_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f7609,plain,
( sQ427_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f7593,f2240,f7606]) ).
fof(f7610,definition,
! [X0] :
( sQ428_spl
<=> ( apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f7611,plain,
! [X0] :
( ~ sQ428_spl
| apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f7610]) ).
fof(f7613,plain,
( sQ428_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7594,f1636,f7610]) ).
fof(f7615,plain,
! [X0] :
( ~ sQ428_spl
| apply(empty_set,X0) = empty_set
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1265,f7611]) ).
fof(f7616,plain,
! [X0] :
( ~ sQ428_spl
| apply(empty_set,X0) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f7615,f1443]) ).
fof(f7647,plain,
! [X0] :
( in(ordered_pair(X0,sK47_skl(X0,relation_dom(empty_set),empty_set)),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1265,f1460]) ).
fof(f7653,definition,
! [X0] :
( sQ429_spl
<=> ( in(ordered_pair(X0,sK47_skl(X0,relation_dom(empty_set),empty_set)),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f7656,plain,
( sQ429_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7647,f1636,f7653]) ).
fof(f7678,plain,
( ~ sQ335_spl
| in(sK31_skl(relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl))
| relation_field(sK117_skl) = empty_set ),
inference(resolution,[status(thm)],[f5225,f1415]) ).
fof(f7679,definition,
( sQ430_spl
<=> in(sK31_skl(empty_set,sK117_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f7680,plain,
( ~ sQ430_spl
| in(sK31_skl(empty_set,sK117_skl),empty_set) ),
inference(component_clause,[status(thm)],[f7679]) ).
fof(f7683,plain,
( ~ sQ335_spl
| sQ402_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f7678,f6940,f6934,f5224]) ).
fof(f7684,plain,
( ~ sQ430_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7680,f1443]) ).
fof(f7685,plain,
~ sQ430_spl,
inference(contradiction_clause,[status(thm)],[f7684]) ).
fof(f7686,plain,
( ~ sQ335_spl
| in(sK31_skl(relation_dom(sK117_skl),sK117_skl),relation_dom(sK117_skl))
| relation_dom(sK117_skl) = empty_set ),
inference(resolution,[status(thm)],[f2198,f5225]) ).
fof(f7692,definition,
( sQ431_spl
<=> in(sK31_skl(relation_dom(sK117_skl),sK117_skl),relation_dom(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f7695,plain,
( ~ sQ335_spl
| sQ431_spl
| sQ417_spl ),
inference(split_clause,[status(thm)],[f7686,f7382,f7692,f5224]) ).
fof(f7705,plain,
! [X0,X1] :
( ~ in(ordered_pair(ordered_pair(sK41_skl(relation_field(empty_set),X0),sK42_skl(relation_field(empty_set),X0)),X1),empty_set)
| ~ relation(empty_set)
| subset(X0,relation_field(empty_set))
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f6318]) ).
fof(f7710,definition,
! [X0,X1] :
( sQ432_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK41_skl(relation_field(empty_set),X0),sK42_skl(relation_field(empty_set),X0)),X1),empty_set)
| subset(X0,relation_field(empty_set))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f7713,plain,
( ~ sQ7_spl
| sQ432_spl ),
inference(split_clause,[status(thm)],[f7705,f7710,f1636]) ).
fof(f7720,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK43_skl(empty_set,X0)),empty_set)
| ~ relation(empty_set)
| subset(X0,relation_field(empty_set)) ),
inference(paramodulation,[status(thm)],[f1623,f6580]) ).
fof(f7723,definition,
! [X0,X1] :
( sQ433_spl
<=> ( ~ in(ordered_pair(X1,sK43_skl(empty_set,X0)),empty_set)
| subset(X0,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f7726,plain,
( ~ sQ7_spl
| sQ433_spl ),
inference(split_clause,[status(thm)],[f7720,f7723,f1636]) ).
fof(f7728,plain,
! [X0,X1] :
( ~ sQ428_spl
| in(empty_set,X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f7616,f382]) ).
fof(f7729,plain,
! [X0,X1] :
( ~ sQ428_spl
| in(empty_set,X1)
| ~ in(X0,relation_inverse_image(empty_set,X1))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f7616,f1426]) ).
fof(f7730,definition,
! [X0,X1] :
( sQ434_spl
<=> ( in(empty_set,X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f7733,plain,
( ~ sQ428_spl
| sQ434_spl
| ~ sQ40_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7728,f1636,f2262,f7730,f7610]) ).
fof(f7734,definition,
! [X0,X1] :
( sQ435_spl
<=> ( in(empty_set,X1)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f7737,plain,
( ~ sQ428_spl
| sQ435_spl
| ~ sQ40_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f7729,f1636,f2262,f7734,f7610]) ).
fof(f7770,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(sK2_skl(X0,sK117_skl,X1),relation_dom(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1461,f1591]) ).
fof(f7771,plain,
! [X0,X1] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(sK7_skl(X0,sK117_skl,X1),relation_dom(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1461,f1966]) ).
fof(f7772,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| in(X0,relation_dom(sK117_skl))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f1461,f3288]) ).
fof(f7801,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,ordered_pair(X1,X3)),X0)
| ~ relation(X0)
| in(X1,relation_dom(relation_field(X0)))
| ~ relation(relation_field(X0)) ),
inference(resolution,[status(thm)],[f1461,f1113]) ).
fof(f7802,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(ordered_pair(X1,X2),X3),X0)
| ~ relation(X0)
| in(X1,relation_dom(relation_field(X0)))
| ~ relation(relation_field(X0)) ),
inference(resolution,[status(thm)],[f1461,f1112]) ).
fof(f7805,definition,
! [X0,X1] :
( sQ436_spl
<=> ( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(sK2_skl(X0,sK117_skl,X1),relation_dom(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f7808,plain,
( sQ436_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7770,f1604,f7805]) ).
fof(f7809,definition,
! [X0,X1] :
( sQ437_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(sK7_skl(X0,sK117_skl,X1),relation_dom(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f7812,plain,
( sQ437_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7771,f1604,f7809]) ).
fof(f7813,definition,
! [X0,X1] :
( sQ438_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| in(X0,relation_dom(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f7816,plain,
( sQ438_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7772,f1604,f7813]) ).
fof(f7817,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,sK48_skl(relation_field(X1),X0)),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK48_skl(relation_field(X1),X0),X2),X0)
| relation_field(X1) = relation_dom(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f583,f1113]) ).
fof(f7818,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(sK48_skl(relation_field(X1),X0),X3),X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK48_skl(relation_field(X1),X0),X2),X0)
| relation_field(X1) = relation_dom(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f583,f1112]) ).
fof(f7865,plain,
! [X0,X1] :
( ~ in(sK43_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| subset(X0,relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6581,f3288]) ).
fof(f7869,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK43_skl(empty_set,X0),X1),empty_set)
| ~ relation(empty_set)
| subset(X0,relation_field(empty_set)) ),
inference(paramodulation,[status(thm)],[f1623,f6581]) ).
fof(f7870,definition,
! [X0,X1] :
( sQ439_spl
<=> ( ~ in(sK43_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X1))
| subset(X0,relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f7873,plain,
( ~ sQ5_spl
| sQ439_spl ),
inference(split_clause,[status(thm)],[f7865,f7870,f1604]) ).
fof(f7876,definition,
! [X0,X1] :
( sQ440_spl
<=> ( ~ in(ordered_pair(sK43_skl(empty_set,X0),X1),empty_set)
| subset(X0,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ440_spl])],[split_symbol_definition]) ).
fof(f7879,plain,
( ~ sQ7_spl
| sQ440_spl ),
inference(split_clause,[status(thm)],[f7869,f7876,f1636]) ).
fof(f7955,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ relation(sK117_skl)
| ~ in(sK3_skl(X0,sK117_skl,X1),X2)
| in(sK3_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f7164,f1591]) ).
fof(f7956,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ relation(sK117_skl)
| ~ in(sK8_skl(X0,sK117_skl,X1),X2)
| in(sK8_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f7164,f1966]) ).
fof(f7957,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| ~ in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),X2)
| in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),set_intersection2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f7164,f3288]) ).
fof(f7990,definition,
! [X0,X1,X2] :
( sQ441_spl
<=> ( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK3_skl(X0,sK117_skl,X1),X2)
| in(sK3_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f7993,plain,
( ~ sQ5_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f7955,f7990,f1604]) ).
fof(f7994,definition,
! [X0,X1,X2] :
( sQ442_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK8_skl(X0,sK117_skl,X1),X2)
| in(sK8_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f7997,plain,
( ~ sQ5_spl
| sQ442_spl ),
inference(split_clause,[status(thm)],[f7956,f7994,f1604]) ).
fof(f7998,definition,
! [X0,X1,X2] :
( sQ443_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X1))
| ~ in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),X2)
| in(sK13_skl(X0,relation_inverse_image(sK117_skl,X1),X1,sK117_skl),set_intersection2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f8001,plain,
( ~ sQ5_spl
| sQ443_spl ),
inference(split_clause,[status(thm)],[f7957,f7998,f1604]) ).
fof(f8004,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ relation(sK117_skl)
| ~ in(sK2_skl(X0,sK117_skl,X1),X2)
| in(sK2_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f7165,f1591]) ).
fof(f8005,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ relation(sK117_skl)
| ~ in(sK7_skl(X0,sK117_skl,X1),X2)
| in(sK7_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f7165,f1966]) ).
fof(f8006,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,relation_field(sK117_skl))) ),
inference(resolution,[status(thm)],[f7165,f3288]) ).
fof(f8039,definition,
! [X0,X1,X2] :
( sQ444_spl
<=> ( in(ordered_pair(sK2_skl(X0,sK117_skl,X1),sK3_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK2_skl(X0,sK117_skl,X1),X2)
| in(sK2_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f8042,plain,
( ~ sQ5_spl
| sQ444_spl ),
inference(split_clause,[status(thm)],[f8004,f8039,f1604]) ).
fof(f8043,definition,
! [X0,X1,X2] :
( sQ445_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK117_skl,X1),sK8_skl(X0,sK117_skl,X1)),X1)
| sK117_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| ~ in(sK7_skl(X0,sK117_skl,X1),X2)
| in(sK7_skl(X0,sK117_skl,X1),set_intersection2(X2,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f8046,plain,
( ~ sQ5_spl
| sQ445_spl ),
inference(split_clause,[status(thm)],[f8005,f8043,f1604]) ).
fof(f8047,definition,
! [X0,X1,X2] :
( sQ446_spl
<=> ( ~ in(X0,relation_inverse_image(sK117_skl,X2))
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,relation_field(sK117_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f8050,plain,
( ~ sQ5_spl
| sQ446_spl ),
inference(split_clause,[status(thm)],[f8006,f8047,f1604]) ).
fof(f8100,plain,
( ~ sQ405_spl
| sK45_skl(relation_field(sK117_skl),sK117_skl) = empty_set
| ~ subset(sK45_skl(relation_field(sK117_skl),sK117_skl),relation_field(sK117_skl))
| ~ well_founded_relation(sK117_skl)
| ~ relation(sK117_skl)
| ~ in(sK31_skl(sK45_skl(relation_field(sK117_skl),sK117_skl),sK117_skl),sK45_skl(relation_field(sK117_skl),sK117_skl)) ),
inference(resolution,[status(thm)],[f7053,f502]) ).
fof(f8103,definition,
( sQ447_spl
<=> in(sK31_skl(sK45_skl(relation_field(sK117_skl),sK117_skl),sK117_skl),sK45_skl(relation_field(sK117_skl),sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f8106,plain,
( ~ sQ405_spl
| sQ389_spl
| ~ sQ388_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ447_spl ),
inference(split_clause,[status(thm)],[f8100,f8103,f1604,f1404,f6679,f6688,f7052]) ).
fof(f8110,plain,
! [X0] :
( ~ in(ordered_pair(X0,powerset(empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f4817]) ).
fof(f8112,definition,
! [X0] :
( sQ448_spl
<=> ~ in(ordered_pair(X0,powerset(empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f8115,plain,
( sQ448_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f8110,f1636,f8112]) ).
fof(f8118,plain,
! [X0] :
( ~ in(powerset(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0))
| ~ relation(sK117_skl) ),
inference(resolution,[status(thm)],[f4818,f3288]) ).
fof(f8122,plain,
! [X0] :
( ~ in(ordered_pair(powerset(empty_set),X0),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f4818]) ).
fof(f8123,definition,
! [X0] :
( sQ449_spl
<=> ~ in(powerset(relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f8126,plain,
( sQ449_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f8118,f1604,f8123]) ).
fof(f8128,definition,
! [X0] :
( sQ450_spl
<=> ~ in(ordered_pair(powerset(empty_set),X0),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f8131,plain,
( sQ450_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f8122,f1636,f8128]) ).
fof(f8137,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK46_skl(X0,empty_set,relation_field(empty_set))),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f7174]) ).
fof(f8139,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK46_skl(X0,relation_field(empty_set),empty_set)),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f7174]) ).
fof(f8145,definition,
! [X0,X1] :
( sQ451_spl
<=> ( ~ in(ordered_pair(X1,sK46_skl(X0,empty_set,relation_field(empty_set))),empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f8148,plain,
( ~ sQ7_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f8137,f8145,f1636]) ).
fof(f8154,definition,
! [X0,X1] :
( sQ452_spl
<=> ( ~ in(ordered_pair(X1,sK46_skl(X0,relation_field(empty_set),empty_set)),empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f8157,plain,
( ~ sQ7_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f8139,f8154,f1636]) ).
fof(f8169,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK46_skl(X0,X1,empty_set)),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X1)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_intersection2(relation_field(empty_set),X1) ),
inference(paramodulation,[status(thm)],[f1623,f7169]) ).
fof(f8174,definition,
! [X0,X1,X2] :
( sQ453_spl
<=> ( ~ in(ordered_pair(X2,sK46_skl(X0,X1,empty_set)),empty_set)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X1)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_intersection2(relation_field(empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f8177,plain,
( ~ sQ7_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f8169,f8174,f1636]) ).
fof(f8244,plain,
! [X0] : ~ in(X0,union(empty_set)),
inference(resolution,[status(thm)],[f1463,f1443]) ).
fof(f8373,plain,
( ~ sQ335_spl
| ~ sQ388_spl
| in(sK31_skl(sK45_skl(relation_field(sK117_skl),sK117_skl),sK117_skl),sK45_skl(relation_field(sK117_skl),sK117_skl))
| sK45_skl(relation_field(sK117_skl),sK117_skl) = empty_set ),
inference(resolution,[status(thm)],[f6680,f5225]) ).
fof(f8379,plain,
( ~ sQ335_spl
| ~ sQ388_spl
| sQ447_spl
| sQ389_spl ),
inference(split_clause,[status(thm)],[f8373,f6688,f8103,f6679,f5224]) ).
fof(f8395,plain,
! [X0,X1] :
( ~ in(sK46_skl(X0,relation_field(sK117_skl),relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X1))
| ~ relation(sK117_skl)
| ~ in(sK46_skl(X0,relation_field(sK117_skl),relation_field(sK117_skl)),X0)
| X0 = relation_field(sK117_skl) ),
inference(resolution,[status(thm)],[f7175,f3288]) ).
fof(f8399,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK46_skl(X0,empty_set,relation_field(empty_set)),X1),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f7175]) ).
fof(f8401,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK46_skl(X0,relation_field(empty_set),empty_set),X1),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f7175]) ).
fof(f8402,definition,
! [X0,X1] :
( sQ454_spl
<=> ( ~ in(sK46_skl(X0,relation_field(sK117_skl),relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X1))
| ~ in(sK46_skl(X0,relation_field(sK117_skl),relation_field(sK117_skl)),X0)
| X0 = relation_field(sK117_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f8405,plain,
( ~ sQ5_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f8395,f8402,f1604]) ).
fof(f8411,definition,
! [X0,X1] :
( sQ455_spl
<=> ( ~ in(ordered_pair(sK46_skl(X0,empty_set,relation_field(empty_set)),X1),empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f8414,plain,
( ~ sQ7_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f8399,f8411,f1636]) ).
fof(f8420,definition,
! [X0,X1] :
( sQ456_spl
<=> ( ~ in(ordered_pair(sK46_skl(X0,relation_field(empty_set),empty_set),X1),empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),relation_field(empty_set)),X0)
| X0 = relation_field(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f8423,plain,
( ~ sQ7_spl
| sQ456_spl ),
inference(split_clause,[status(thm)],[f8401,f8420,f1636]) ).
fof(f8432,plain,
! [X0,X1,X2] :
( ~ in(sK46_skl(X0,X1,relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| ~ in(sK46_skl(X0,X1,relation_field(sK117_skl)),X1)
| ~ in(sK46_skl(X0,X1,relation_field(sK117_skl)),X0)
| X0 = set_intersection2(relation_field(sK117_skl),X1) ),
inference(resolution,[status(thm)],[f7171,f3288]) ).
fof(f8436,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK46_skl(X0,X1,empty_set),X2),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X1)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_intersection2(relation_field(empty_set),X1) ),
inference(paramodulation,[status(thm)],[f1623,f7171]) ).
fof(f8437,definition,
! [X0,X1,X2] :
( sQ457_spl
<=> ( ~ in(sK46_skl(X0,X1,relation_field(sK117_skl)),relation_inverse_image(sK117_skl,X2))
| ~ in(sK46_skl(X0,X1,relation_field(sK117_skl)),X1)
| ~ in(sK46_skl(X0,X1,relation_field(sK117_skl)),X0)
| X0 = set_intersection2(relation_field(sK117_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f8440,plain,
( ~ sQ5_spl
| sQ457_spl ),
inference(split_clause,[status(thm)],[f8432,f8437,f1604]) ).
fof(f8445,definition,
! [X0,X1,X2] :
( sQ458_spl
<=> ( ~ in(ordered_pair(sK46_skl(X0,X1,empty_set),X2),empty_set)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X1)
| ~ in(sK46_skl(X0,X1,relation_field(empty_set)),X0)
| X0 = set_intersection2(relation_field(empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f8448,plain,
( ~ sQ7_spl
| sQ458_spl ),
inference(split_clause,[status(thm)],[f8436,f8445,f1636]) ).
fof(f8467,plain,
! [X0] :
( subset(union(empty_set),X0)
| ~ relation(X0)
| ~ relation(union(empty_set)) ),
inference(resolution,[status(thm)],[f8244,f538]) ).
fof(f8468,plain,
! [X0] :
( in(ordered_pair(sK28_skl(union(empty_set),X0),sK29_skl(union(empty_set),X0)),X0)
| X0 = union(empty_set)
| ~ relation(union(empty_set))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f8244,f481]) ).
fof(f8469,plain,
union(empty_set) = empty_set,
inference(resolution,[status(thm)],[f8244,f459]) ).
fof(f8492,definition,
( sQ461_spl
<=> relation(union(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f8494,plain,
( sQ461_spl
| ~ relation(union(empty_set)) ),
inference(component_clause,[status(thm)],[f8492]) ).
fof(f8495,definition,
! [X0] :
( sQ462_spl
<=> ( subset(union(empty_set),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f8498,plain,
( sQ462_spl
| ~ sQ461_spl ),
inference(split_clause,[status(thm)],[f8467,f8492,f8495]) ).
fof(f8499,definition,
! [X0] :
( sQ463_spl
<=> ( in(ordered_pair(sK28_skl(union(empty_set),X0),sK29_skl(union(empty_set),X0)),X0)
| X0 = union(empty_set)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f8502,plain,
( ~ sQ461_spl
| sQ463_spl ),
inference(split_clause,[status(thm)],[f8468,f8499,f8492]) ).
fof(f8524,plain,
( epsilon_connected(empty_set)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f8469,f797]) ).
fof(f8525,plain,
( epsilon_transitive(empty_set)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f8469,f796]) ).
fof(f8529,plain,
( sQ243_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f8524,f3527,f3531]) ).
fof(f8530,plain,
( sQ244_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f8525,f3527,f3535]) ).
fof(f8532,plain,
( sQ461_spl
| ~ relation(empty_set) ),
inference(forward_demodulation,[status(thm)],[f8469,f8494]) ).
fof(f8533,plain,
( sQ461_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8532,f745]) ).
fof(f8534,plain,
sQ461_spl,
inference(contradiction_clause,[status(thm)],[f8533]) ).
fof(f8657,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK46_skl(X0,empty_set,X1)),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X1)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_intersection2(X1,relation_field(empty_set)) ),
inference(paramodulation,[status(thm)],[f1623,f7172]) ).
fof(f8662,definition,
! [X0,X1,X2] :
( sQ464_spl
<=> ( ~ in(ordered_pair(X2,sK46_skl(X0,empty_set,X1)),empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X1)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_intersection2(X1,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f8665,plain,
( ~ sQ7_spl
| sQ464_spl ),
inference(split_clause,[status(thm)],[f8657,f8662,f1636]) ).
fof(f8670,plain,
! [X0,X1,X2] :
( ~ in(sK46_skl(X0,relation_field(sK117_skl),X1),relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| ~ in(sK46_skl(X0,relation_field(sK117_skl),X1),X1)
| ~ in(sK46_skl(X0,relation_field(sK117_skl),X1),X0)
| X0 = set_intersection2(X1,relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f7173,f3288]) ).
fof(f8674,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK46_skl(X0,empty_set,X1),X2),empty_set)
| ~ relation(empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X1)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_intersection2(X1,relation_field(empty_set)) ),
inference(paramodulation,[status(thm)],[f1623,f7173]) ).
fof(f8675,definition,
! [X0,X1,X2] :
( sQ465_spl
<=> ( ~ in(sK46_skl(X0,relation_field(sK117_skl),X1),relation_inverse_image(sK117_skl,X2))
| ~ in(sK46_skl(X0,relation_field(sK117_skl),X1),X1)
| ~ in(sK46_skl(X0,relation_field(sK117_skl),X1),X0)
| X0 = set_intersection2(X1,relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f8678,plain,
( ~ sQ5_spl
| sQ465_spl ),
inference(split_clause,[status(thm)],[f8670,f8675,f1604]) ).
fof(f8683,definition,
! [X0,X1,X2] :
( sQ466_spl
<=> ( ~ in(ordered_pair(sK46_skl(X0,empty_set,X1),X2),empty_set)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X1)
| ~ in(sK46_skl(X0,relation_field(empty_set),X1),X0)
| X0 = set_intersection2(X1,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f8686,plain,
( ~ sQ7_spl
| sQ466_spl ),
inference(split_clause,[status(thm)],[f8674,f8683,f1636]) ).
fof(f8984,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,ordered_pair(X0,X2)),empty_set)
| ~ relation(empty_set)
| in(X0,relation_dom(relation_field(empty_set)))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f7801]) ).
fof(f8987,definition,
! [X0,X1,X2] :
( sQ467_spl
<=> ( ~ in(ordered_pair(X1,ordered_pair(X0,X2)),empty_set)
| in(X0,relation_dom(relation_field(empty_set))) ) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f8990,plain,
( sQ467_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f8984,f1636,f8987]) ).
fof(f8995,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(ordered_pair(X0,X1),X2),empty_set)
| ~ relation(empty_set)
| in(X0,relation_dom(relation_field(empty_set)))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1623,f7802]) ).
fof(f8998,definition,
! [X0,X1,X2] :
( sQ468_spl
<=> ( ~ in(ordered_pair(ordered_pair(X0,X1),X2),empty_set)
| in(X0,relation_dom(relation_field(empty_set))) ) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f9001,plain,
( sQ468_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f8995,f1636,f8998]) ).
fof(f9097,plain,
( empty(relation_dom(sK117_skl))
| in(sK76_skl(relation_dom(sK117_skl)),relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6330,f5002]) ).
fof(f9105,plain,
! [X0] :
( in(X0,set_meet(relation_dom(sK117_skl)))
| relation_dom(sK117_skl) = empty_set
| in(sK21_skl(X0,set_meet(relation_dom(sK117_skl)),relation_dom(sK117_skl)),relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6330,f1437]) ).
fof(f9106,plain,
! [X0] :
( subset(relation_dom(sK117_skl),X0)
| ~ relation(X0)
| ~ relation(relation_dom(sK117_skl))
| in(ordered_pair(sK41_skl(X0,relation_dom(sK117_skl)),sK42_skl(X0,relation_dom(sK117_skl))),relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6330,f538]) ).
fof(f9107,plain,
! [X0] :
( in(ordered_pair(sK28_skl(relation_dom(sK117_skl),X0),sK29_skl(relation_dom(sK117_skl),X0)),X0)
| X0 = relation_dom(sK117_skl)
| ~ relation(relation_dom(sK117_skl))
| ~ relation(X0)
| in(ordered_pair(sK28_skl(relation_dom(sK117_skl),X0),sK29_skl(relation_dom(sK117_skl),X0)),relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6330,f481]) ).
fof(f9108,plain,
( relation_dom(sK117_skl) = empty_set
| in(sK25_skl(relation_dom(sK117_skl)),relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6330,f459]) ).
fof(f9109,plain,
( relation(relation_dom(sK117_skl))
| in(sK19_skl(relation_dom(sK117_skl)),relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6330,f427]) ).
fof(f9116,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK117_skl),X0)
| X0 = relation_inverse_image(sK117_skl,X1)
| ~ function(sK117_skl)
| ~ relation(sK117_skl)
| in(sK9_skl(X0,X1,sK117_skl),relation_field(sK117_skl)) ),
inference(resolution,[status(thm)],[f6330,f381]) ).
fof(f9123,definition,
( sQ469_spl
<=> in(sK76_skl(relation_dom(sK117_skl)),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ469_spl])],[split_symbol_definition]) ).
fof(f9126,plain,
( sQ304_spl
| sQ469_spl ),
inference(split_clause,[status(thm)],[f9097,f9123,f4367]) ).
fof(f9129,definition,
! [X0] :
( sQ470_spl
<=> ( in(X0,set_meet(relation_dom(sK117_skl)))
| in(sK21_skl(X0,set_meet(relation_dom(sK117_skl)),relation_dom(sK117_skl)),relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ470_spl])],[split_symbol_definition]) ).
fof(f9132,plain,
( sQ417_spl
| sQ470_spl ),
inference(split_clause,[status(thm)],[f9105,f9129,f7382]) ).
fof(f9133,definition,
! [X0] :
( sQ471_spl
<=> ( subset(relation_dom(sK117_skl),X0)
| ~ relation(X0)
| in(ordered_pair(sK41_skl(X0,relation_dom(sK117_skl)),sK42_skl(X0,relation_dom(sK117_skl))),relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ471_spl])],[split_symbol_definition]) ).
fof(f9136,plain,
( ~ sQ51_spl
| sQ471_spl ),
inference(split_clause,[status(thm)],[f9106,f9133,f2346]) ).
fof(f9137,definition,
! [X0] :
( sQ472_spl
<=> ( in(ordered_pair(sK28_skl(relation_dom(sK117_skl),X0),sK29_skl(relation_dom(sK117_skl),X0)),X0)
| X0 = relation_dom(sK117_skl)
| ~ relation(X0)
| in(ordered_pair(sK28_skl(relation_dom(sK117_skl),X0),sK29_skl(relation_dom(sK117_skl),X0)),relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f9140,plain,
( ~ sQ51_spl
| sQ472_spl ),
inference(split_clause,[status(thm)],[f9107,f9137,f2346]) ).
fof(f9141,definition,
( sQ473_spl
<=> in(sK25_skl(relation_dom(sK117_skl)),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f9144,plain,
( sQ417_spl
| sQ473_spl ),
inference(split_clause,[status(thm)],[f9108,f9141,f7382]) ).
fof(f9145,definition,
( sQ474_spl
<=> in(sK19_skl(relation_dom(sK117_skl)),relation_field(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ474_spl])],[split_symbol_definition]) ).
fof(f9148,plain,
( sQ51_spl
| sQ474_spl ),
inference(split_clause,[status(thm)],[f9109,f9145,f2346]) ).
fof(f9149,definition,
! [X0,X1] :
( sQ475_spl
<=> ( in(sK9_skl(X0,X1,sK117_skl),X0)
| X0 = relation_inverse_image(sK117_skl,X1)
| in(sK9_skl(X0,X1,sK117_skl),relation_field(sK117_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f9152,plain,
( ~ sQ354_spl
| ~ sQ5_spl
| sQ475_spl ),
inference(split_clause,[status(thm)],[f9116,f9149,f1604,f5672]) ).
fof(f9168,plain,
! [X0] :
( ~ sQ417_spl
| in(ordered_pair(X0,sK47_skl(X0,relation_dom(sK117_skl),sK117_skl)),sK117_skl)
| ~ in(X0,empty_set)
| ~ relation(sK117_skl) ),
inference(paramodulation,[status(thm)],[f7383,f1460]) ).
fof(f9176,definition,
! [X0] :
( sQ476_spl
<=> ( in(ordered_pair(X0,sK47_skl(X0,relation_dom(sK117_skl),sK117_skl)),sK117_skl)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f9179,plain,
( ~ sQ417_spl
| sQ476_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f9168,f1604,f9176,f7382]) ).
fof(f9195,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK48_skl(empty_set,X0)),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK48_skl(relation_field(empty_set),X0),X1),X0)
| relation_field(empty_set) = relation_dom(X0)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f7817]) ).
fof(f9199,definition,
! [X0,X1,X2] :
( sQ477_spl
<=> ( ~ in(ordered_pair(X2,sK48_skl(empty_set,X0)),empty_set)
| ~ in(ordered_pair(sK48_skl(relation_field(empty_set),X0),X1),X0)
| relation_field(empty_set) = relation_dom(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f9202,plain,
( ~ sQ7_spl
| sQ477_spl ),
inference(split_clause,[status(thm)],[f9195,f9199,f1636]) ).
fof(f9205,plain,
! [X0,X1,X2] :
( ~ in(sK48_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X2))
| ~ relation(sK117_skl)
| ~ in(ordered_pair(sK48_skl(relation_field(sK117_skl),X0),X1),X0)
| relation_field(sK117_skl) = relation_dom(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f7818,f3288]) ).
fof(f9209,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK48_skl(empty_set,X0),X2),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(sK48_skl(relation_field(empty_set),X0),X1),X0)
| relation_field(empty_set) = relation_dom(X0)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1623,f7818]) ).
fof(f9210,definition,
! [X0,X1,X2] :
( sQ478_spl
<=> ( ~ in(sK48_skl(relation_field(sK117_skl),X0),relation_inverse_image(sK117_skl,X2))
| ~ in(ordered_pair(sK48_skl(relation_field(sK117_skl),X0),X1),X0)
| relation_field(sK117_skl) = relation_dom(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f9213,plain,
( ~ sQ5_spl
| sQ478_spl ),
inference(split_clause,[status(thm)],[f9205,f9210,f1604]) ).
fof(f9217,definition,
! [X0,X1,X2] :
( sQ479_spl
<=> ( ~ in(ordered_pair(sK48_skl(empty_set,X0),X2),empty_set)
| ~ in(ordered_pair(sK48_skl(relation_field(empty_set),X0),X1),X0)
| relation_field(empty_set) = relation_dom(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ479_spl])],[split_symbol_definition]) ).
fof(f9220,plain,
( ~ sQ7_spl
| sQ479_spl ),
inference(split_clause,[status(thm)],[f9209,f9217,f1636]) ).
fof(f9236,plain,
! [X0] :
( in(sK56_skl(X0,relation_rng(sK99_skl),sK99_skl),relation_dom(sK99_skl))
| ~ in(X0,relation_rng(sK99_skl))
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f1468,f951]) ).
fof(f9237,plain,
! [X0] :
( in(sK56_skl(X0,relation_rng(sK96_skl),sK96_skl),relation_dom(sK96_skl))
| ~ in(X0,relation_rng(sK96_skl))
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f1468,f938]) ).
fof(f9238,plain,
! [X0] :
( in(sK56_skl(X0,relation_rng(sK86_skl),sK86_skl),relation_dom(sK86_skl))
| ~ in(X0,relation_rng(sK86_skl))
| ~ relation(sK86_skl) ),
inference(resolution,[status(thm)],[f1468,f902]) ).
fof(f9239,plain,
! [X0] :
( in(sK56_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)],[f1468,f765]) ).
fof(f9245,definition,
! [X0] :
( sQ480_spl
<=> ( in(sK56_skl(X0,relation_rng(sK99_skl),sK99_skl),relation_dom(sK99_skl))
| ~ in(X0,relation_rng(sK99_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f9248,plain,
( sQ480_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f9236,f2226,f9245]) ).
fof(f9249,definition,
! [X0] :
( sQ481_spl
<=> ( in(sK56_skl(X0,relation_rng(sK96_skl),sK96_skl),relation_dom(sK96_skl))
| ~ in(X0,relation_rng(sK96_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f9252,plain,
( sQ481_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f9237,f2233,f9249]) ).
fof(f9253,definition,
! [X0] :
( sQ482_spl
<=> ( in(sK56_skl(X0,relation_rng(sK86_skl),sK86_skl),relation_dom(sK86_skl))
| ~ in(X0,relation_rng(sK86_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f9256,plain,
( sQ482_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f9238,f2240,f9253]) ).
fof(f9257,definition,
! [X0] :
( sQ483_spl
<=> ( in(sK56_skl(X0,relation_rng(empty_set),empty_set),relation_dom(empty_set))
| ~ in(X0,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f9260,plain,
( sQ483_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f9239,f1636,f9257]) ).
fof(f9266,plain,
! [X0] :
( X0 = apply(sK99_skl,sK56_skl(X0,relation_rng(sK99_skl),sK99_skl))
| ~ in(X0,relation_rng(sK99_skl))
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f1469,f951]) ).
fof(f9267,plain,
! [X0] :
( X0 = apply(sK96_skl,sK56_skl(X0,relation_rng(sK96_skl),sK96_skl))
| ~ in(X0,relation_rng(sK96_skl))
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f1469,f938]) ).
fof(f9268,plain,
! [X0] :
( X0 = apply(sK86_skl,sK56_skl(X0,relation_rng(sK86_skl),sK86_skl))
| ~ in(X0,relation_rng(sK86_skl))
| ~ relation(sK86_skl) ),
inference(resolution,[status(thm)],[f1469,f902]) ).
fof(f9269,plain,
! [X0] :
( X0 = apply(empty_set,sK56_skl(X0,relation_rng(empty_set),empty_set))
| ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1469,f765]) ).
fof(f9274,definition,
! [X0] :
( sQ484_spl
<=> ( X0 = apply(sK99_skl,sK56_skl(X0,relation_rng(sK99_skl),sK99_skl))
| ~ in(X0,relation_rng(sK99_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f9277,plain,
( sQ484_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f9266,f2226,f9274]) ).
fof(f9278,definition,
! [X0] :
( sQ485_spl
<=> ( X0 = apply(sK96_skl,sK56_skl(X0,relation_rng(sK96_skl),sK96_skl))
| ~ in(X0,relation_rng(sK96_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f9281,plain,
( sQ485_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f9267,f2233,f9278]) ).
fof(f9282,definition,
! [X0] :
( sQ486_spl
<=> ( X0 = apply(sK86_skl,sK56_skl(X0,relation_rng(sK86_skl),sK86_skl))
| ~ in(X0,relation_rng(sK86_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f9285,plain,
( sQ486_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f9268,f2240,f9282]) ).
fof(f9286,definition,
! [X0] :
( sQ487_spl
<=> ( X0 = apply(empty_set,sK56_skl(X0,relation_rng(empty_set),empty_set))
| ~ in(X0,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f9289,plain,
( sQ487_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f9269,f1636,f9286]) ).
fof(f9294,plain,
! [X0] :
( ~ in(X0,relation_dom(sK99_skl))
| in(apply(sK99_skl,X0),relation_rng(sK99_skl))
| ~ relation(sK99_skl) ),
inference(resolution,[status(thm)],[f1470,f951]) ).
fof(f9295,plain,
! [X0] :
( ~ in(X0,relation_dom(sK96_skl))
| in(apply(sK96_skl,X0),relation_rng(sK96_skl))
| ~ relation(sK96_skl) ),
inference(resolution,[status(thm)],[f1470,f938]) ).
fof(f9296,plain,
! [X0] :
( ~ in(X0,relation_dom(sK86_skl))
| in(apply(sK86_skl,X0),relation_rng(sK86_skl))
| ~ relation(sK86_skl) ),
inference(resolution,[status(thm)],[f1470,f902]) ).
fof(f9297,plain,
! [X0] :
( ~ in(X0,relation_dom(empty_set))
| in(apply(empty_set,X0),relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1470,f765]) ).
fof(f9302,definition,
! [X0] :
( sQ488_spl
<=> ( ~ in(X0,relation_dom(sK99_skl))
| in(apply(sK99_skl,X0),relation_rng(sK99_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f9305,plain,
( sQ488_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f9294,f2226,f9302]) ).
fof(f9306,definition,
! [X0] :
( sQ489_spl
<=> ( ~ in(X0,relation_dom(sK96_skl))
| in(apply(sK96_skl,X0),relation_rng(sK96_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f9309,plain,
( sQ489_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f9295,f2233,f9306]) ).
fof(f9310,definition,
! [X0] :
( sQ490_spl
<=> ( ~ in(X0,relation_dom(sK86_skl))
| in(apply(sK86_skl,X0),relation_rng(sK86_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f9313,plain,
( sQ490_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f9296,f2240,f9310]) ).
fof(f9314,definition,
! [X0] :
( sQ491_spl
<=> ( ~ in(X0,relation_dom(empty_set))
| in(apply(empty_set,X0),relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f9317,plain,
( sQ491_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f9297,f1636,f9314]) ).
fof(f9335,plain,
( ~ sQ393_spl
| ~ sQ390_spl
| sK32_skl(sK117_skl) = empty_set
| ~ subset(sK32_skl(sK117_skl),relation_field(sK117_skl))
| ~ in(sK44_skl(sK32_skl(sK117_skl),relation_field(sK117_skl),sK117_skl),sK32_skl(sK117_skl)) ),
inference(resolution,[status(thm)],[f6698,f6712]) ).
fof(f9339,definition,
( sQ492_spl
<=> in(sK44_skl(sK32_skl(sK117_skl),relation_field(sK117_skl),sK117_skl),sK32_skl(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f9342,plain,
( ~ sQ393_spl
| ~ sQ390_spl
| sQ391_spl
| ~ sQ392_spl
| ~ sQ492_spl ),
inference(split_clause,[status(thm)],[f9335,f9339,f6705,f6701,f6697,f6711]) ).
fof(f9347,plain,
( ~ sQ394_spl
| ~ sQ392_spl
| in(sK44_skl(sK32_skl(sK117_skl),relation_field(sK117_skl),sK117_skl),sK32_skl(sK117_skl))
| sK32_skl(sK117_skl) = empty_set ),
inference(resolution,[status(thm)],[f6706,f6716]) ).
fof(f9353,plain,
( ~ sQ394_spl
| ~ sQ392_spl
| sQ492_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f9347,f6701,f9339,f6705,f6715]) ).
fof(f9355,plain,
$false,
inference(sat_refutation,[status(thm)],[f1410,f1411,f1607,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1673,f1887,f1906,f1924,f1975,f1977,f1986,f1995,f2004,f2017,f2042,f2091,f2100,f2113,f2134,f2143,f2152,f2166,f2176,f2232,f2239,f2246,f2250,f2254,f2256,f2258,f2268,f2270,f2279,f2288,f2326,f2330,f2334,f2338,f2342,f2349,f2353,f2357,f2361,f2365,f2369,f2373,f2377,f2381,f2385,f2389,f2393,f2397,f2401,f2405,f2409,f2413,f2417,f2421,f2425,f2711,f3037,f3091,f3265,f3319,f3323,f3327,f3331,f3335,f3358,f3439,f3463,f3470,f3474,f3497,f3504,f3530,f3603,f3607,f3611,f3615,f3619,f3623,f3627,f3631,f3635,f3642,f3646,f3650,f3654,f3658,f3662,f3666,f3670,f3674,f3678,f3682,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3714,f3718,f3720,f3735,f3773,f3781,f3795,f3812,f3824,f3829,f3841,f3953,f3957,f3986,f4040,f4111,f4115,f4124,f4126,f4174,f4410,f4636,f4659,f4740,f4741,f4806,f4840,f4872,f4876,f4884,f4888,f4983,f5010,f5084,f5177,f5227,f5242,f5258,f5265,f5278,f5369,f5376,f5394,f5587,f5675,f5905,f5909,f5968,f6088,f6109,f6116,f6129,f6167,f6171,f6175,f6198,f6205,f6229,f6233,f6237,f6261,f6297,f6301,f6311,f6315,f6368,f6372,f6376,f6400,f6404,f6408,f6558,f6562,f6567,f6609,f6613,f6617,f6628,f6682,f6691,f6700,f6704,f6708,f6714,f6718,f6757,f6764,f6778,f6945,f7048,f7055,f7214,f7221,f7233,f7329,f7333,f7337,f7341,f7355,f7359,f7363,f7367,f7388,f7392,f7396,f7398,f7405,f7424,f7428,f7457,f7469,f7601,f7605,f7609,f7613,f7656,f7683,f7685,f7695,f7713,f7726,f7733,f7737,f7808,f7812,f7816,f7873,f7879,f7993,f7997,f8001,f8042,f8046,f8050,f8106,f8115,f8126,f8131,f8148,f8157,f8177,f8379,f8405,f8414,f8423,f8440,f8448,f8498,f8502,f8529,f8530,f8534,f8665,f8678,f8686,f8990,f9001,f9126,f9132,f9136,f9140,f9144,f9148,f9152,f9179,f9202,f9213,f9220,f9248,f9252,f9256,f9260,f9277,f9281,f9285,f9289,f9305,f9309,f9313,f9317,f9342,f9353]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU243+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n005.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 06:02:33 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 12.57/2.25 % Refutation found
% 12.57/2.25 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.57/2.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.74/2.31 % Elapsed time: 1.816622 seconds
% 7.74/2.31 % CPU time: 13.793111 seconds
% 7.74/2.31 % Total memory used: 212.098 MB
% 7.74/2.31 % Net memory used: 199.465 MB
%------------------------------------------------------------------------------