%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:19:43 PM UTC 2026
% Result : Theorem 284.61s 36.39s
% Output : CNFRefutation 284.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 314
% Syntax : Number of formulae : 1470 ( 87 unt; 288 def)
% Number of atoms : 4446 ( 828 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 5166 (2190 ~;2579 |; 78 &)
% ( 300 <=>; 18 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 296 ( 294 usr; 289 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 800 ( 782 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,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(f15,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f47,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f49,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [A,B] :
( ( ( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ( ! [C,D] :
( ( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [B] :
( ( ! [A] :
( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
! [B] :
( ( ! [A] :
( ( ( ( sK0_skl(A,B) = sK1_skl(A,B)
& in(sK0_skl(A,B),A) )
| in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) )
& ( sK0_skl(A,B) != sK1_skl(A,B)
| ~ in(sK0_skl(A,B),A)
| ~ in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f53]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| ~ in(X2,X1)
| in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( sK0_skl(X1,X0) != sK1_skl(X1,X0)
| ~ in(sK0_skl(X1,X0),X1)
| ~ in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f59,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f60,plain,
! [X0,X1] :
( sK0_skl(X1,X0) = sK1_skl(X1,X0)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f61,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)],[f6]) ).
fof(f62,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)],[f61]) ).
fof(f63,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)],[f62]) ).
fof(f64,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)],[f63]) ).
fof(f66,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)],[f63]) ).
fof(f69,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
! [A] : element(sK2_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B,sK2_skl(A))],[f17]) ).
fof(f71,plain,
! [X0] : element(sK2_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f76,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f77,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f79,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f84,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f85,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f87,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f89,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f91,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f92,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
( function(sK3_skl)
& relation(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f29]) ).
fof(f95,plain,
relation(sK3_skl),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
function(sK3_skl),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
( relation(sK4_skl)
& empty(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f30]) ).
fof(f98,plain,
empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
relation(sK4_skl),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f100,plain,
empty(sK5_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f31]) ).
fof(f101,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
( relation(sK6_skl)
& ~ empty(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f32]) ).
fof(f103,plain,
~ empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
relation(sK6_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f107,plain,
( relation_empty_yielding(sK8_skl)
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f34]) ).
fof(f108,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f113,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
? [A,B] :
( ( B = identity_relation(A)
<~> ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A ) )
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f115,plain,
? [A,B] :
( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B != identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B = identity_relation(A) )
& function(B)
& relation(B) ),
inference(NNF_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
? [B] :
( ? [A] :
( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B != identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B = identity_relation(A) ) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
( ( ( apply(sK9_skl,sK11_skl) != sK11_skl
& in(sK11_skl,sK10_skl) )
| relation_dom(sK9_skl) != sK10_skl
| sK9_skl != identity_relation(sK10_skl) )
& ( ( ! [C] :
( apply(sK9_skl,C) = C
| ~ in(C,sK10_skl) )
& relation_dom(sK9_skl) = sK10_skl )
| sK9_skl = identity_relation(sK10_skl) )
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(B,sK9_skl),skolemize(A,sK10_skl),skolemize(C,sK11_skl)],[f116]) ).
fof(f118,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f120,plain,
( relation_dom(sK9_skl) = sK10_skl
| sK9_skl = identity_relation(sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f121,plain,
! [X0] :
( apply(sK9_skl,X0) = X0
| ~ in(X0,sK10_skl)
| sK9_skl = identity_relation(sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f122,plain,
( in(sK11_skl,sK10_skl)
| relation_dom(sK9_skl) != sK10_skl
| sK9_skl != identity_relation(sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f123,plain,
( apply(sK9_skl,sK11_skl) != sK11_skl
| relation_dom(sK9_skl) != sK10_skl
| sK9_skl != identity_relation(sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f124,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f125,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f127,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f130,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f133,plain,
! [B] :
( ~ empty(B)
| ! [A] :
( A = B
| ~ empty(A) ) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [A,B,C] :
( ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f136,plain,
! [A,B,C] :
( ( ( B != apply(C,A)
| ~ in(A,relation_dom(C))
| in(ordered_pair(A,B),C) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [C] :
( ( ! [A,B] :
( B != apply(C,A)
| ~ in(A,relation_dom(C))
| in(ordered_pair(A,B),C) )
& ! [A,B] :
( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f136]) ).
fof(f138,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
! [X0,X1,X2] :
( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f141,definition,
( sQ0_spl
<=> sK9_skl = identity_relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ0_spl
| sK9_skl = identity_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f143,plain,
( sQ0_spl
| sK9_skl != identity_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ1_spl
<=> relation_dom(sK9_skl) = sK10_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ1_spl
| relation_dom(sK9_skl) = sK10_skl ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f120,f141,f144]) ).
fof(f148,definition,
! [X0] :
( sQ2_spl
<=> ( apply(sK9_skl,X0) = X0
| ~ in(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f149,plain,
! [X0] :
( ~ sQ2_spl
| apply(sK9_skl,X0) = X0
| ~ in(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f121,f141,f148]) ).
fof(f152,definition,
( sQ3_spl
<=> in(sK11_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ3_spl
| in(sK11_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f154,plain,
( sQ3_spl
| ~ in(sK11_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f122,f141,f144,f152]) ).
fof(f156,definition,
( sQ4_spl
<=> apply(sK9_skl,sK11_skl) = sK11_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ4_spl
| apply(sK9_skl,sK11_skl) = sK11_skl ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f123,f141,f144,f156]) ).
fof(f160,plain,
! [X0,X1,X2] :
( in(X1,X0)
| ~ in(ordered_pair(X1,X2),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f55]) ).
fof(f161,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f162,plain,
! [X0,X1] :
( ~ in(X1,X0)
| in(ordered_pair(X1,X1),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f163,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)],[f64]) ).
fof(f164,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f171,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),identity_relation(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f160,f69]) ).
fof(f172,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ in(ordered_pair(X0,X1),identity_relation(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f69]) ).
fof(f173,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(ordered_pair(X0,X0),identity_relation(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f69]) ).
fof(f174,plain,
! [X0] :
( in(sK0_skl(X0,empty_set),X0)
| in(ordered_pair(sK0_skl(X0,empty_set),sK1_skl(X0,empty_set)),empty_set)
| empty_set = identity_relation(X0) ),
inference(resolution,[status(thm)],[f59,f73]) ).
fof(f175,plain,
! [X0,X1] :
( in(sK0_skl(X1,identity_relation(X0)),X1)
| in(ordered_pair(sK0_skl(X1,identity_relation(X0)),sK1_skl(X1,identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(X1) ),
inference(resolution,[status(thm)],[f59,f69]) ).
fof(f176,plain,
! [X0] :
( in(sK0_skl(X0,sK9_skl),X0)
| in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0) ),
inference(resolution,[status(thm)],[f59,f118]) ).
fof(f177,plain,
! [X0,X1] :
( ~ empty(X0)
| in(sK0_skl(X1,X0),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1) ),
inference(resolution,[status(thm)],[f59,f49]) ).
fof(f178,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| apply(sK9_skl,sK11_skl) = sK11_skl ),
inference(resolution,[status(thm)],[f153,f149]) ).
fof(f179,plain,
( ~ sQ3_spl
| in(ordered_pair(sK11_skl,sK11_skl),identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f153,f173]) ).
fof(f181,plain,
! [X0] :
( ~ sQ1_spl
| in(ordered_pair(X0,apply(sK9_skl,X0)),sK9_skl)
| ~ in(X0,sK10_skl)
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f145,f163]) ).
fof(f182,definition,
( sQ5_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ5_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ6_spl
<=> function(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ6_spl
| ~ function(sK9_skl) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
! [X0] :
( sQ7_spl
<=> ( in(ordered_pair(X0,apply(sK9_skl,X0)),sK9_skl)
| ~ in(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f189,plain,
! [X0] :
( ~ sQ7_spl
| in(ordered_pair(X0,apply(sK9_skl,X0)),sK9_skl)
| ~ in(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f181,f182,f185,f188,f144]) ).
fof(f192,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(identity_relation(X0),X1)),identity_relation(X0))
| ~ in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f127,f163]) ).
fof(f193,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(identity_relation(X0),X1)),identity_relation(X0))
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f69]) ).
fof(f194,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = empty_set
| in(X1,relation_dom(identity_relation(X0)))
| ~ relation(identity_relation(X0)) ),
inference(resolution,[status(thm)],[f164,f79]) ).
fof(f195,plain,
! [X0] :
( apply(sK9_skl,X0) = empty_set
| in(X0,relation_dom(sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f164,f119]) ).
fof(f196,plain,
! [X0,X1] :
( ~ empty(X0)
| apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f164,f47]) ).
fof(f197,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = empty_set
| in(X1,X0)
| ~ relation(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f127,f194]) ).
fof(f198,plain,
! [X0,X1] :
( apply(identity_relation(X1),X0) = empty_set
| in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f69]) ).
fof(f199,definition,
! [X0] :
( sQ8_spl
<=> ( apply(sK9_skl,X0) = empty_set
| in(X0,relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ8_spl
| apply(sK9_skl,X0) = empty_set
| in(X0,relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f195,f182,f199]) ).
fof(f203,plain,
! [X0,X1] :
( ~ empty(X1)
| apply(X1,X0) = empty_set
| in(X0,relation_dom(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f49]) ).
fof(f204,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f118]) ).
fof(f205,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ1_spl
| apply(sK9_skl,X0) = empty_set
| in(X0,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f200]) ).
fof(f207,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f119]) ).
fof(f208,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f223,plain,
( ~ sQ0_spl
| relation_dom(sK9_skl) = sK10_skl ),
inference(paramodulation,[status(thm)],[f142,f127]) ).
fof(f225,plain,
! [X0,X1] :
( ~ sQ0_spl
| X0 = X1
| ~ in(ordered_pair(X0,X1),sK9_skl) ),
inference(paramodulation,[status(thm)],[f142,f172]) ).
fof(f228,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f223,f144,f141]) ).
fof(f233,plain,
( ~ sQ1_spl
| empty(sK10_skl)
| ~ empty(sK9_skl) ),
inference(paramodulation,[status(thm)],[f145,f89]) ).
fof(f234,plain,
! [X0] :
( empty(X0)
| ~ empty(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f127,f89]) ).
fof(f235,definition,
( sQ9_spl
<=> empty(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( sQ9_spl
| ~ empty(sK9_skl) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
( sQ10_spl
<=> empty(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ10_spl
| empty(sK10_skl) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ sQ1_spl
| sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f233,f235,f238,f144]) ).
fof(f244,plain,
! [X0] :
( relation(X0)
| ~ empty(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f127,f90]) ).
fof(f245,definition,
( sQ11_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f251,plain,
! [X0] :
( apply(sK3_skl,X0) = empty_set
| in(X0,relation_dom(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f96,f164]) ).
fof(f252,definition,
( sQ12_spl
<=> relation(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ12_spl
| ~ relation(sK3_skl) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
! [X0] :
( sQ13_spl
<=> ( apply(sK3_skl,X0) = empty_set
| in(X0,relation_dom(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f256,plain,
! [X0] :
( ~ sQ13_spl
| apply(sK3_skl,X0) = empty_set
| in(X0,relation_dom(sK3_skl)) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f251,f252,f255]) ).
fof(f259,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f95]) ).
fof(f260,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f261,plain,
! [X0] :
( ~ empty(relation_dom(relation_rng(X0)))
| ~ relation(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f87,f85]) ).
fof(f263,plain,
! [X0,X1] :
( in(sK0_skl(X1,relation_rng(X0)),X1)
| in(ordered_pair(sK0_skl(X1,relation_rng(X0)),sK1_skl(X1,relation_rng(X0))),relation_rng(X0))
| relation_rng(X0) = identity_relation(X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f93,f59]) ).
fof(f264,plain,
! [X0] :
( in(sK0_skl(X0,sK4_skl),X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(resolution,[status(thm)],[f99,f59]) ).
fof(f265,plain,
( ~ empty(relation_dom(sK6_skl))
| ~ relation(sK6_skl) ),
inference(resolution,[status(thm)],[f103,f85]) ).
fof(f266,definition,
( sQ14_spl
<=> relation(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ14_spl
| relation(sK6_skl) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( sQ14_spl
| ~ relation(sK6_skl) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,definition,
( sQ15_spl
<=> empty(relation_dom(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ15_spl
| ~ empty(relation_dom(sK6_skl)) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f265,f266,f269]) ).
fof(f273,plain,
( sQ9_spl
| ~ empty(relation_dom(sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f237,f85]) ).
fof(f274,definition,
( sQ16_spl
<=> empty(relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ9_spl
| ~ sQ16_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f273,f182,f274,f235]) ).
fof(f281,definition,
( sQ17_spl
<=> empty(relation_dom(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ17_spl
| ~ empty(relation_dom(sK10_skl)) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f285,plain,
! [X0] :
( ~ sQ2_spl
| apply(sK9_skl,sK0_skl(sK10_skl,identity_relation(X0))) = sK0_skl(sK10_skl,identity_relation(X0))
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(X0)),sK1_skl(sK10_skl,identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f175,f149]) ).
fof(f286,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(relation_dom(X1),identity_relation(X0)),apply(X1,sK0_skl(relation_dom(X1),identity_relation(X0)))),X1)
| ~ function(X1)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(relation_dom(X1),identity_relation(X0)),sK1_skl(relation_dom(X1),identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(relation_dom(X1)) ),
inference(resolution,[status(thm)],[f175,f163]) ).
fof(f290,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),sK9_skl),apply(X0,sK0_skl(relation_dom(X0),sK9_skl))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),sK9_skl),sK1_skl(relation_dom(X0),sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f176,f163]) ).
fof(f291,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK9_skl),sK0_skl(X0,sK9_skl)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0) ),
inference(resolution,[status(thm)],[f176,f173]) ).
fof(f293,definition,
( sQ18_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( ~ sQ18_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f295,plain,
( sQ18_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ19_spl
<=> apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) = sK0_skl(sK10_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ19_spl
| apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) = sK0_skl(sK10_skl,sK9_skl) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f300,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f268]) ).
fof(f301,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f311,plain,
! [X0] :
( in(sK2_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f113,f71]) ).
fof(f313,plain,
sK5_skl = empty_set,
inference(resolution,[status(thm)],[f125,f101]) ).
fof(f314,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set ),
inference(resolution,[status(thm)],[f125,f92]) ).
fof(f315,plain,
sK4_skl = empty_set,
inference(resolution,[status(thm)],[f125,f98]) ).
fof(f316,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f125,f89]) ).
fof(f318,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f125,f85]) ).
fof(f321,plain,
! [X0] :
( ~ empty(X0)
| ~ relation(identity_relation(X0))
| empty(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f128,f87]) ).
fof(f322,plain,
! [X0] :
( ~ empty(X0)
| empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f69]) ).
fof(f323,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f131,f176]) ).
fof(f325,plain,
( sQ17_spl
| ~ empty(sK10_skl) ),
inference(resolution,[status(thm)],[f283,f89]) ).
fof(f350,plain,
! [X0,X1] :
( ~ empty(X0)
| in(sK0_skl(X1,X0),X1)
| X0 = identity_relation(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f131]) ).
fof(f355,plain,
! [X0,X1] :
( in(ordered_pair(X0,apply(identity_relation(X1),X0)),identity_relation(X1))
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f79]) ).
fof(f357,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0)
| in(ordered_pair(sK0_skl(X0,sK9_skl),apply(identity_relation(X0),sK0_skl(X0,sK9_skl))),identity_relation(X0)) ),
inference(resolution,[status(thm)],[f355,f176]) ).
fof(f363,plain,
! [X0,X1] :
( apply(identity_relation(X1),X0) = sK5_skl
| in(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f313,f198]) ).
fof(f364,plain,
! [X0] :
( X0 = sK5_skl
| ~ empty(X0) ),
inference(backward_demodulation,[status(thm)],[f313,f125]) ).
fof(f365,plain,
! [X0,X1] :
( apply(X0,X1) = sK5_skl
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(backward_demodulation,[status(thm)],[f313,f164]) ).
fof(f369,plain,
sK4_skl = empty_set,
inference(backward_demodulation,[status(thm)],[f371,f313]) ).
fof(f371,plain,
sK4_skl = sK5_skl,
inference(forward_demodulation,[status(thm)],[f313,f315]) ).
fof(f375,plain,
! [X0,X1] :
( ~ empty(relation_dom(X1))
| ~ relation(X1)
| X0 = X1
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f134,f85]) ).
fof(f376,plain,
! [X0] :
( X0 = sK4_skl
| ~ empty(X0) ),
inference(forward_demodulation,[status(thm)],[f371,f364]) ).
fof(f379,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK4_skl ),
inference(resolution,[status(thm)],[f376,f89]) ).
fof(f380,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| X0 = sK4_skl ),
inference(resolution,[status(thm)],[f376,f85]) ).
fof(f381,plain,
! [X0,X1] :
( apply(X0,X1) = sK4_skl
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f371,f365]) ).
fof(f384,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),empty_set),apply(X0,sK0_skl(relation_dom(X0),empty_set))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),empty_set),sK1_skl(relation_dom(X0),empty_set)),empty_set)
| empty_set = identity_relation(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f174,f163]) ).
fof(f385,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),apply(identity_relation(X0),sK0_skl(X0,empty_set))),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,empty_set),sK1_skl(X0,empty_set)),empty_set)
| empty_set = identity_relation(X0) ),
inference(resolution,[status(thm)],[f174,f355]) ).
fof(f387,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),sK0_skl(X0,empty_set)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,empty_set),sK1_skl(X0,empty_set)),empty_set)
| empty_set = identity_relation(X0) ),
inference(resolution,[status(thm)],[f174,f173]) ).
fof(f390,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ1_spl
| apply(sK9_skl,X0) = empty_set
| in(X0,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f200]) ).
fof(f392,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ1_spl
| in(X0,sK10_skl)
| empty_set = sK4_skl
| in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f390,f381]) ).
fof(f393,definition,
( sQ24_spl
<=> empty_set = sK11_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ24_spl
| empty_set = sK11_skl ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f395,plain,
( sQ24_spl
| empty_set != sK11_skl ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f397,definition,
! [X0] :
( sQ25_spl
<=> ( in(X0,sK10_skl)
| in(X0,relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f398,plain,
! [X0] :
( ~ sQ25_spl
| in(X0,sK10_skl)
| in(X0,relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
( sQ26_spl
<=> empty_set = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ26_spl
| empty_set = sK4_skl ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| sQ26_spl
| sQ25_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f392,f182,f185,f397,f400,f144,f199]) ).
fof(f404,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ1_spl
| in(X0,sK10_skl)
| in(X0,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f398]) ).
fof(f405,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ1_spl
| in(X0,sK10_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f404]) ).
fof(f418,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ empty(X1)
| apply(X1,X0) = sK4_skl
| in(X0,relation_dom(X1)) ),
inference(forward_demodulation,[status(thm)],[f401,f203]) ).
fof(f420,plain,
! [X0] :
( ~ sQ26_spl
| apply(sK4_skl,X0) = sK4_skl
| in(X0,relation_dom(sK4_skl)) ),
inference(resolution,[status(thm)],[f418,f98]) ).
fof(f432,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ1_spl
| ~ in(sK10_skl,X0) ),
inference(resolution,[status(thm)],[f405,f45]) ).
fof(f433,definition,
( sQ27_spl
<=> function(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( sQ27_spl
| ~ function(sK10_skl) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f444,plain,
( sQ27_spl
| ~ empty(sK10_skl) ),
inference(resolution,[status(thm)],[f435,f47]) ).
fof(f482,plain,
( ~ sQ7_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))),sK9_skl) ),
inference(resolution,[status(thm)],[f189,f176]) ).
fof(f483,plain,
! [X0] :
( ~ sQ7_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(X0)),sK1_skl(sK10_skl,identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(X0)),apply(sK9_skl,sK0_skl(sK10_skl,identity_relation(X0)))),sK9_skl) ),
inference(resolution,[status(thm)],[f189,f175]) ).
fof(f484,plain,
! [X0] :
( ~ sQ7_spl
| ~ empty(X0)
| X0 = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,X0),apply(sK9_skl,sK0_skl(sK10_skl,X0))),sK9_skl) ),
inference(resolution,[status(thm)],[f189,f350]) ).
fof(f485,definition,
( sQ31_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( ~ sQ31_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))),sK9_skl) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f488,plain,
( ~ sQ7_spl
| sQ18_spl
| sQ0_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f482,f485,f141,f293,f188]) ).
fof(f491,definition,
( sQ32_spl
<=> sK4_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ24_spl
| sK4_skl != sK11_skl ),
inference(backward_demodulation,[status(thm)],[f369,f395]) ).
fof(f518,plain,
( ~ sQ25_spl
| ~ sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f432,f405]) ).
fof(f519,plain,
( ~ sQ25_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f550,plain,
( ~ sQ3_spl
| sK11_skl = apply(identity_relation(sK10_skl),sK11_skl)
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f179,f139]) ).
fof(f551,plain,
( ~ sQ3_spl
| in(sK11_skl,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f179,f138]) ).
fof(f553,plain,
( ~ sQ3_spl
| ~ empty(identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f179,f131]) ).
fof(f556,definition,
( sQ33_spl
<=> relation(identity_relation(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( sQ33_spl
| ~ relation(identity_relation(sK10_skl)) ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f559,definition,
( sQ34_spl
<=> function(identity_relation(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( sQ34_spl
| ~ function(identity_relation(sK10_skl)) ),
inference(component_clause,[status(thm)],[f559]) ).
fof(f562,definition,
( sQ35_spl
<=> sK11_skl = apply(identity_relation(sK10_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( ~ sQ35_spl
| sK11_skl = apply(identity_relation(sK10_skl),sK11_skl) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f565,plain,
( ~ sQ3_spl
| sQ35_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f550,f556,f559,f562,f152]) ).
fof(f566,definition,
( sQ36_spl
<=> in(sK11_skl,relation_dom(identity_relation(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ36_spl
| in(sK11_skl,relation_dom(identity_relation(sK10_skl))) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,plain,
( ~ sQ3_spl
| sQ36_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f551,f556,f559,f566,f152]) ).
fof(f570,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f79]) ).
fof(f571,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f572,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f69]) ).
fof(f573,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f572]) ).
fof(f574,plain,
( ~ sQ36_spl
| in(sK11_skl,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f127,f567]) ).
fof(f590,definition,
! [X0] :
( sQ39_spl
<=> X0 = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f591,plain,
! [X0] :
( ~ sQ39_spl
| X0 = sK4_skl ),
inference(component_clause,[status(thm)],[f590]) ).
fof(f594,plain,
( sQ24_spl
| ~ sQ39_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f517,f591]) ).
fof(f599,plain,
( sQ24_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f594]) ).
fof(f611,plain,
( ~ sQ3_spl
| ~ sQ24_spl
| in(sK4_skl,sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f613,f153]) ).
fof(f613,plain,
( ~ sQ24_spl
| sK4_skl = sK11_skl ),
inference(forward_demodulation,[status(thm)],[f394,f369]) ).
fof(f641,definition,
( sQ43_spl
<=> function(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f643,plain,
( sQ43_spl
| ~ function(sK3_skl) ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f649,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f643,f96]) ).
fof(f650,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f649]) ).
fof(f653,plain,
! [X0] :
( ~ empty(relation_dom(relation_rng(identity_relation(X0))))
| ~ relation(X0)
| ~ relation(identity_relation(X0))
| empty(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f128,f261]) ).
fof(f654,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| ~ relation(identity_relation(X0))
| empty(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f128,f653]) ).
fof(f655,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f654,f69]) ).
fof(f659,plain,
! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| in(sK0_skl(X1,relation_rng(X0)),X1)
| in(ordered_pair(sK0_skl(X1,relation_rng(X0)),sK1_skl(X1,relation_rng(X0))),relation_rng(X0))
| relation_rng(X0) = identity_relation(X1) ),
inference(resolution,[status(thm)],[f263,f85]) ).
fof(f675,plain,
relation_dom(sK4_skl) = empty_set,
inference(resolution,[status(thm)],[f316,f98]) ).
fof(f680,plain,
( ~ sQ1_spl
| ~ empty(sK10_skl)
| ~ relation(sK9_skl)
| sK9_skl = empty_set ),
inference(paramodulation,[status(thm)],[f145,f318]) ).
fof(f683,definition,
( sQ47_spl
<=> sK9_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f684,plain,
( ~ sQ47_spl
| sK9_skl = empty_set ),
inference(component_clause,[status(thm)],[f683]) ).
fof(f685,plain,
( sQ47_spl
| sK9_skl != empty_set ),
inference(component_clause,[status(thm)],[f683]) ).
fof(f686,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ5_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f680,f683,f182,f238,f144]) ).
fof(f689,plain,
empty(identity_relation(sK4_skl)),
inference(resolution,[status(thm)],[f322,f98]) ).
fof(f692,plain,
! [X0,X1] :
( apply(identity_relation(X1),X0) = sK4_skl
| in(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f371,f363]) ).
fof(f694,definition,
! [X0,X1] :
( sQ48_spl
<=> ( in(X1,X0)
| in(X1,relation_dom(identity_relation(X0)))
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f695,plain,
! [X0,X1] :
( ~ sQ48_spl
| in(X1,X0)
| in(X1,relation_dom(identity_relation(X0)))
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(component_clause,[status(thm)],[f694]) ).
fof(f698,plain,
! [X0,X1] :
( ~ sQ48_spl
| in(X1,X0)
| in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f127,f695]) ).
fof(f699,plain,
! [X0,X1] :
( ~ sQ48_spl
| in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f698]) ).
fof(f700,plain,
! [X0,X1] :
( ~ sQ48_spl
| in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f69]) ).
fof(f703,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ1_spl
| apply(sK9_skl,X0) = sK4_skl
| in(X0,sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f369,f206]) ).
fof(f704,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ47_spl
| apply(sK4_skl,X0) = X0
| ~ in(X0,sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f711,f149]) ).
fof(f705,plain,
( sQ0_spl
| ~ sQ47_spl
| sK4_skl != identity_relation(sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f711,f143]) ).
fof(f707,plain,
( sQ9_spl
| ~ sQ47_spl
| ~ empty(sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f711,f237]) ).
fof(f711,plain,
( ~ sQ47_spl
| sK9_skl = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f369,f684]) ).
fof(f716,plain,
( sQ9_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f98]) ).
fof(f717,plain,
( sQ9_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f716]) ).
fof(f719,plain,
( sQ27_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f444,f238,f433]) ).
fof(f720,plain,
( sQ17_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f325,f238,f281]) ).
fof(f732,definition,
( sQ50_spl
<=> empty(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f734,plain,
( sQ50_spl
| ~ empty(sK4_skl) ),
inference(component_clause,[status(thm)],[f732]) ).
fof(f737,definition,
( sQ51_spl
<=> relation(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( sQ51_spl
| ~ relation(sK4_skl) ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f740,definition,
( sQ52_spl
<=> function(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( ~ sQ52_spl
| function(sK4_skl) ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f742,plain,
( sQ52_spl
| ~ function(sK4_skl) ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f747,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f734,f98]) ).
fof(f748,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f747]) ).
fof(f751,plain,
( sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f99]) ).
fof(f752,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f751]) ).
fof(f753,plain,
( ~ sQ2_spl
| ~ sQ47_spl
| apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl)) = sK0_skl(sK10_skl,sK4_skl)
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f264,f704]) ).
fof(f759,definition,
( sQ54_spl
<=> sK4_skl = identity_relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f760,plain,
( ~ sQ54_spl
| sK4_skl = identity_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f761,plain,
( sQ54_spl
| sK4_skl != identity_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f762,definition,
( sQ55_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( ~ sQ55_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f762]) ).
fof(f765,definition,
( sQ56_spl
<=> apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl)) = sK0_skl(sK10_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f766,plain,
( ~ sQ56_spl
| apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl)) = sK0_skl(sK10_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f765]) ).
fof(f767,plain,
( sQ56_spl
| apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl)) != sK0_skl(sK10_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f765]) ).
fof(f768,plain,
( ~ sQ2_spl
| ~ sQ47_spl
| sQ56_spl
| sQ55_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f753,f759,f762,f765,f683,f148]) ).
fof(f769,plain,
( ~ sQ54_spl
| sQ0_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f760,f705]) ).
fof(f770,plain,
( ~ sQ54_spl
| sQ0_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f769]) ).
fof(f771,plain,
( sQ47_spl
| sK9_skl != sK4_skl ),
inference(forward_demodulation,[status(thm)],[f369,f685]) ).
fof(f776,definition,
( sQ57_spl
<=> apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl)) = sK0_skl(sK10_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f777,plain,
( ~ sQ57_spl
| apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl)) = sK0_skl(sK10_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f789,plain,
! [X0] :
( in(sK0_skl(X0,sK9_skl),X0)
| in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0) ),
inference(resolution,[status(thm)],[f118,f59]) ).
fof(f796,plain,
! [X0] :
( ~ sQ1_spl
| ~ empty(sK10_skl)
| ~ relation(sK9_skl)
| X0 = sK9_skl
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f145,f375]) ).
fof(f798,definition,
! [X0] :
( sQ58_spl
<=> ( X0 = sK9_skl
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f799,plain,
! [X0] :
( ~ sQ58_spl
| X0 = sK9_skl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f798]) ).
fof(f801,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ5_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f796,f798,f182,f238,f144]) ).
fof(f804,plain,
relation_dom(sK4_skl) = sK4_skl,
inference(resolution,[status(thm)],[f379,f98]) ).
fof(f809,plain,
( ~ sQ1_spl
| ~ empty(sK10_skl)
| ~ relation(sK9_skl)
| sK9_skl = sK4_skl ),
inference(paramodulation,[status(thm)],[f145,f380]) ).
fof(f811,definition,
( sQ59_spl
<=> sK9_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f812,plain,
( ~ sQ59_spl
| sK9_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f811]) ).
fof(f814,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ5_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f809,f811,f182,f238,f144]) ).
fof(f816,plain,
( ~ sQ59_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f812,f771]) ).
fof(f817,plain,
( ~ sQ59_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f816]) ).
fof(f838,plain,
( ~ sQ2_spl
| apply(sK9_skl,sK2_skl(sK10_skl)) = sK2_skl(sK10_skl)
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f311,f149]) ).
fof(f839,plain,
! [X0] :
( in(ordered_pair(sK2_skl(relation_dom(X0)),apply(X0,sK2_skl(relation_dom(X0)))),X0)
| ~ function(X0)
| ~ relation(X0)
| empty(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f311,f163]) ).
fof(f844,definition,
( sQ63_spl
<=> apply(sK9_skl,sK2_skl(sK10_skl)) = sK2_skl(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f845,plain,
( ~ sQ63_spl
| apply(sK9_skl,sK2_skl(sK10_skl)) = sK2_skl(sK10_skl) ),
inference(component_clause,[status(thm)],[f844]) ).
fof(f847,plain,
( ~ sQ2_spl
| sQ63_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f838,f238,f844,f148]) ).
fof(f855,definition,
( sQ64_spl
<=> apply(sK4_skl,sK2_skl(sK10_skl)) = sK2_skl(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( ~ sQ64_spl
| apply(sK4_skl,sK2_skl(sK10_skl)) = sK2_skl(sK10_skl) ),
inference(component_clause,[status(thm)],[f855]) ).
fof(f857,plain,
( sQ64_spl
| apply(sK4_skl,sK2_skl(sK10_skl)) != sK2_skl(sK10_skl) ),
inference(component_clause,[status(thm)],[f855]) ).
fof(f871,definition,
! [X0] :
( sQ66_spl
<=> ( X0 = sK4_skl
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f883,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ59_spl
| in(ordered_pair(X0,apply(sK4_skl,X0)),sK9_skl)
| ~ in(X0,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f812,f189]) ).
fof(f884,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ59_spl
| in(ordered_pair(X0,apply(sK4_skl,X0)),sK4_skl)
| ~ in(X0,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f812,f883]) ).
fof(f887,plain,
( ~ sQ7_spl
| ~ sQ59_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl))),sK4_skl) ),
inference(resolution,[status(thm)],[f884,f264]) ).
fof(f891,definition,
( sQ67_spl
<=> in(ordered_pair(sK2_skl(sK10_skl),apply(sK4_skl,sK2_skl(sK10_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f892,plain,
( ~ sQ67_spl
| in(ordered_pair(sK2_skl(sK10_skl),apply(sK4_skl,sK2_skl(sK10_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f891]) ).
fof(f895,definition,
( sQ68_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK8_skl),apply(sK4_skl,sK0_skl(sK10_skl,sK8_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f896,plain,
( ~ sQ68_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK8_skl),apply(sK4_skl,sK0_skl(sK10_skl,sK8_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f899,definition,
( sQ69_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f900,plain,
( ~ sQ69_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f899]) ).
fof(f902,plain,
( ~ sQ7_spl
| ~ sQ59_spl
| sQ55_spl
| sQ54_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f887,f899,f759,f762,f811,f188]) ).
fof(f903,definition,
( sQ70_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK3_skl),apply(sK4_skl,sK0_skl(sK10_skl,sK3_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f904,plain,
( ~ sQ70_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK3_skl),apply(sK4_skl,sK0_skl(sK10_skl,sK3_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f903]) ).
fof(f924,definition,
! [X0] :
( sQ73_spl
<=> apply(sK4_skl,X0) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f925,plain,
! [X0] :
( ~ sQ73_spl
| apply(sK4_skl,X0) = sK4_skl ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f929,plain,
! [X0,X1] :
( ~ empty(X1)
| apply(X1,X0) = sK4_skl
| in(X0,relation_dom(X1)) ),
inference(forward_demodulation,[status(thm)],[f369,f203]) ).
fof(f942,plain,
( ~ sQ10_spl
| sK10_skl = sK4_skl ),
inference(resolution,[status(thm)],[f239,f376]) ).
fof(f946,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f369,f314]) ).
fof(f949,plain,
relation_rng(sK4_skl) = sK4_skl,
inference(resolution,[status(thm)],[f946,f98]) ).
fof(f951,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| relation_rng(X0) = sK4_skl ),
inference(resolution,[status(thm)],[f946,f85]) ).
fof(f964,plain,
( sQ0_spl
| ~ sQ47_spl
| ~ sQ10_spl
| sK4_skl != identity_relation(sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f942,f705]) ).
fof(f1002,definition,
( sQ80_spl
<=> sK4_skl = identity_relation(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1030,plain,
( ~ sQ36_spl
| ~ sQ10_spl
| in(sK11_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f942,f574]) ).
fof(f1033,plain,
( ~ sQ36_spl
| ~ sQ10_spl
| ~ empty(sK4_skl) ),
inference(resolution,[status(thm)],[f1030,f131]) ).
fof(f1036,plain,
( ~ sQ36_spl
| ~ sQ10_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1033,f732,f238,f566]) ).
fof(f1086,plain,
! [X0] :
( ~ sQ13_spl
| apply(sK3_skl,X0) = sK4_skl
| in(X0,relation_dom(sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f369,f256]) ).
fof(f1089,plain,
! [X0] :
( ~ sQ13_spl
| in(ordered_pair(X0,apply(sK3_skl,X0)),sK3_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| apply(sK3_skl,X0) = sK4_skl ),
inference(resolution,[status(thm)],[f1086,f163]) ).
fof(f1093,plain,
! [X0] :
( ~ sQ13_spl
| ~ in(relation_dom(sK3_skl),X0)
| apply(sK3_skl,X0) = sK4_skl ),
inference(resolution,[status(thm)],[f1086,f45]) ).
fof(f1108,definition,
! [X0] :
( sQ93_spl
<=> ( in(ordered_pair(X0,apply(sK3_skl,X0)),sK3_skl)
| apply(sK3_skl,X0) = sK4_skl ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1111,plain,
( ~ sQ13_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1089,f1108,f252,f641,f255]) ).
fof(f1144,plain,
identity_relation(sK4_skl) = sK4_skl,
inference(resolution,[status(thm)],[f689,f376]) ).
fof(f1155,plain,
( sQ0_spl
| ~ sQ47_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1144,f964]) ).
fof(f1156,plain,
( sQ0_spl
| ~ sQ47_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1155]) ).
fof(f1162,plain,
! [X0,X1] :
( ~ sQ48_spl
| in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f700,f79]) ).
fof(f1163,plain,
relation_dom(sK4_skl) = sK4_skl,
inference(forward_demodulation,[status(thm)],[f369,f675]) ).
fof(f1166,plain,
! [X0,X1] :
( ~ sQ48_spl
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f45,f1162]) ).
fof(f1171,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1166,f1162]) ).
fof(f1172,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f1171]) ).
fof(f1194,plain,
! [X0] :
( ~ sQ1_spl
| apply(sK9_skl,X0) = sK4_skl
| in(X0,sK10_skl)
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f145,f381]) ).
fof(f1196,definition,
! [X0] :
( sQ99_spl
<=> ( apply(sK9_skl,X0) = sK4_skl
| in(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1197,plain,
! [X0] :
( ~ sQ99_spl
| apply(sK9_skl,X0) = sK4_skl
| in(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f1196]) ).
fof(f1199,plain,
( ~ sQ1_spl
| sQ99_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1194,f182,f185,f1196,f144]) ).
fof(f1201,plain,
! [X0,X1] :
( ~ sQ1_spl
| in(X0,sK10_skl)
| ~ in(ordered_pair(X0,X1),sK9_skl)
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f145,f138]) ).
fof(f1203,definition,
! [X0,X1] :
( sQ100_spl
<=> ( in(X0,sK10_skl)
| ~ in(ordered_pair(X0,X1),sK9_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1204,plain,
! [X0,X1] :
( ~ sQ100_spl
| in(X0,sK10_skl)
| ~ in(ordered_pair(X0,X1),sK9_skl) ),
inference(component_clause,[status(thm)],[f1203]) ).
fof(f1206,plain,
( ~ sQ1_spl
| sQ100_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1201,f182,f185,f1203,f144]) ).
fof(f1215,plain,
! [X0,X1] :
( ~ sQ2_spl
| apply(sK9_skl,X0) = X0
| ~ in(ordered_pair(X0,X1),identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f171,f149]) ).
fof(f1216,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK0_skl(relation_dom(X1),X0),X2),X1)
| ~ function(X1)
| ~ relation(X1)
| sK0_skl(relation_dom(X1),X0) != sK1_skl(relation_dom(X1),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(X1),X0),sK1_skl(relation_dom(X1),X0)),X0)
| X0 = identity_relation(relation_dom(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f58,f138]) ).
fof(f1217,plain,
! [X0,X1] :
( apply(X1,sK0_skl(relation_dom(X1),X0)) = sK4_skl
| ~ function(X1)
| ~ relation(X1)
| sK0_skl(relation_dom(X1),X0) != sK1_skl(relation_dom(X1),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(X1),X0),sK1_skl(relation_dom(X1),X0)),X0)
| X0 = identity_relation(relation_dom(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f58,f381]) ).
fof(f1218,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK0_skl(X1,X0),X2),identity_relation(X1))
| sK0_skl(X1,X0) != sK1_skl(X1,X0)
| ~ in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f58,f171]) ).
fof(f1220,plain,
! [X0,X1] :
( sK0_skl(X1,X0) = sK1_skl(X1,X0)
| X0 = identity_relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0))) ),
inference(resolution,[status(thm)],[f45,f60]) ).
fof(f1221,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| X0 = identity_relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0))) ),
inference(resolution,[status(thm)],[f45,f59]) ).
fof(f1223,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ in(X0,ordered_pair(X1,apply(X0,X1))) ),
inference(resolution,[status(thm)],[f45,f163]) ).
fof(f1225,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(resolution,[status(thm)],[f45,f138]) ).
fof(f1226,plain,
! [X0,X1] :
( apply(X0,X1) = sK4_skl
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(resolution,[status(thm)],[f45,f381]) ).
fof(f1229,plain,
( sQ52_spl
| ~ empty(sK4_skl) ),
inference(resolution,[status(thm)],[f742,f47]) ).
fof(f1230,plain,
( sQ52_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1229,f732,f740]) ).
fof(f1235,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(identity_relation(X1)))
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| X0 = apply(identity_relation(X1),X0) ),
inference(resolution,[status(thm)],[f172,f163]) ).
fof(f1241,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| X0 = apply(identity_relation(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f127,f1235]) ).
fof(f1242,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ function(identity_relation(X1))
| X0 = apply(identity_relation(X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1241,f69]) ).
fof(f1243,plain,
! [X0,X1] :
( X1 = apply(sK9_skl,X0)
| ~ in(ordered_pair(X0,X1),sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f139,f119]) ).
fof(f1244,plain,
! [X0,X1] :
( X1 = apply(sK3_skl,X0)
| ~ in(ordered_pair(X0,X1),sK3_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f139,f96]) ).
fof(f1247,definition,
! [X0,X1] :
( sQ102_spl
<=> ( X1 = apply(sK9_skl,X0)
| ~ in(ordered_pair(X0,X1),sK9_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1248,plain,
! [X0,X1] :
( ~ sQ102_spl
| X1 = apply(sK9_skl,X0)
| ~ in(ordered_pair(X0,X1),sK9_skl) ),
inference(component_clause,[status(thm)],[f1247]) ).
fof(f1250,plain,
( sQ102_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1243,f182,f1247]) ).
fof(f1251,definition,
! [X0,X1] :
( sQ103_spl
<=> ( X1 = apply(sK3_skl,X0)
| ~ in(ordered_pair(X0,X1),sK3_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1252,plain,
! [X0,X1] :
( ~ sQ103_spl
| X1 = apply(sK3_skl,X0)
| ~ in(ordered_pair(X0,X1),sK3_skl) ),
inference(component_clause,[status(thm)],[f1251]) ).
fof(f1254,plain,
( sQ103_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1244,f252,f1251]) ).
fof(f1258,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ1_spl
| sK0_skl(sK10_skl,X0) != sK1_skl(sK10_skl,X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0)
| apply(sK9_skl,sK0_skl(sK10_skl,X0)) = sK4_skl ),
inference(resolution,[status(thm)],[f703,f58]) ).
fof(f1260,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ1_spl
| ~ in(sK10_skl,X0)
| apply(sK9_skl,X0) = sK4_skl ),
inference(resolution,[status(thm)],[f703,f45]) ).
fof(f1261,plain,
! [X0,X1] :
( ~ sQ52_spl
| X1 = apply(sK4_skl,X0)
| ~ in(ordered_pair(X0,X1),sK4_skl)
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f741,f139]) ).
fof(f1262,definition,
! [X0,X1] :
( sQ104_spl
<=> ( X1 = apply(sK4_skl,X0)
| ~ in(ordered_pair(X0,X1),sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1265,plain,
( ~ sQ52_spl
| sQ104_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1261,f737,f1262,f740]) ).
fof(f1268,plain,
( ~ sQ58_spl
| sK4_skl = sK9_skl ),
inference(resolution,[status(thm)],[f799,f98]) ).
fof(f1271,plain,
( ~ sQ58_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f1268,f811,f798]) ).
fof(f1273,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(resolution,[status(thm)],[f131,f92]) ).
fof(f1274,plain,
! [X0] : ~ in(X0,sK4_skl),
inference(resolution,[status(thm)],[f131,f98]) ).
fof(f1275,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(resolution,[status(thm)],[f131,f89]) ).
fof(f1276,plain,
! [X0,X1] :
( ~ empty(relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f131,f85]) ).
fof(f1277,plain,
! [X0] :
( ~ sQ7_spl
| ~ in(sK9_skl,ordered_pair(X0,apply(sK9_skl,X0)))
| ~ in(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f189,f45]) ).
fof(f1279,plain,
! [X0,X1] :
( in(sK0_skl(X1,relation_rng(identity_relation(X0))),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,relation_rng(identity_relation(X0)))),relation_rng(identity_relation(X0)))
| relation_rng(identity_relation(X0)) = identity_relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f128,f263]) ).
fof(f1282,plain,
! [X0,X1] :
( in(sK0_skl(X1,relation_rng(identity_relation(X0))),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,relation_rng(identity_relation(X0)))),relation_rng(identity_relation(X0)))
| X0 = identity_relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f128,f1279]) ).
fof(f1283,plain,
! [X0,X1] :
( in(sK0_skl(X1,relation_rng(identity_relation(X0))),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),relation_rng(identity_relation(X0)))
| X0 = identity_relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f128,f1282]) ).
fof(f1284,plain,
! [X0,X1] :
( in(sK0_skl(X1,relation_rng(identity_relation(X0))),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f128,f1283]) ).
fof(f1285,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ empty(identity_relation(X0)) ),
inference(forward_demodulation,[status(thm)],[f128,f1284]) ).
fof(f1339,definition,
( sQ110_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1341,plain,
( sQ110_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f1339]) ).
fof(f1346,plain,
( sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1341,f108]) ).
fof(f1347,plain,
sQ110_spl,
inference(contradiction_clause,[status(thm)],[f1346]) ).
fof(f1363,plain,
! [X0] :
( sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f1274,f60]) ).
fof(f1364,plain,
! [X0] :
( in(sK0_skl(X0,sK4_skl),X0)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f1274,f59]) ).
fof(f1365,plain,
! [X0] :
( ~ in(X0,relation_dom(sK4_skl))
| ~ function(sK4_skl)
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f1274,f163]) ).
fof(f1367,definition,
! [X0] :
( sQ113_spl
<=> ( sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1368,plain,
! [X0] :
( ~ sQ113_spl
| sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(component_clause,[status(thm)],[f1367]) ).
fof(f1370,plain,
( sQ113_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1363,f737,f1367]) ).
fof(f1371,definition,
! [X0] :
( sQ114_spl
<=> ( in(sK0_skl(X0,sK4_skl),X0)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1374,plain,
( sQ114_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1364,f737,f1371]) ).
fof(f1375,definition,
! [X0] :
( sQ115_spl
<=> ~ in(X0,relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1378,plain,
( sQ115_spl
| ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1365,f737,f740,f1375]) ).
fof(f1388,definition,
! [X0] :
( sQ117_spl
<=> ( in(sK0_skl(X0,sK10_skl),X0)
| sK10_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
! [X0] :
( ~ sQ117_spl
| in(sK0_skl(X0,sK10_skl),X0)
| sK10_skl = identity_relation(X0) ),
inference(component_clause,[status(thm)],[f1388]) ).
fof(f1397,plain,
! [X0,X1] :
( in(X0,sK4_skl)
| ~ in(ordered_pair(X0,X1),sK4_skl)
| ~ function(sK4_skl)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f804,f138]) ).
fof(f1398,plain,
! [X0] :
( apply(sK4_skl,X0) = sK4_skl
| in(X0,sK4_skl)
| ~ function(sK4_skl)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f804,f381]) ).
fof(f1399,plain,
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| sK4_skl = sK4_skl ),
inference(paramodulation,[status(thm)],[f804,f380]) ).
fof(f1400,plain,
! [X0] :
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| X0 = sK4_skl
| ~ empty(X0) ),
inference(paramodulation,[status(thm)],[f804,f375]) ).
fof(f1403,definition,
! [X0] :
( sQ119_spl
<=> ( apply(sK4_skl,X0) = sK4_skl
| in(X0,sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1407,definition,
! [X0,X1] :
( sQ120_spl
<=> ( in(X0,sK4_skl)
| ~ in(ordered_pair(X0,X1),sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1410,plain,
( sQ120_spl
| ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1397,f737,f740,f1407]) ).
fof(f1411,plain,
( sQ119_spl
| ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1398,f737,f740,f1403]) ).
fof(f1412,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1399,f491,f737,f732]) ).
fof(f1413,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1400,f871,f737,f732]) ).
fof(f1425,plain,
! [X0] :
( in(sK0_skl(X0,sK4_skl),X0)
| sK4_skl = identity_relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f1274]) ).
fof(f1426,plain,
! [X0] :
( sK0_skl(X0,sK4_skl) != sK1_skl(X0,sK4_skl)
| ~ in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(resolution,[status(thm)],[f1425,f58]) ).
fof(f1427,plain,
( ~ sQ2_spl
| apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl)) = sK0_skl(sK10_skl,sK4_skl)
| sK4_skl = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f1425,f149]) ).
fof(f1430,definition,
! [X0] :
( sQ121_spl
<=> ( sK0_skl(X0,sK4_skl) != sK1_skl(X0,sK4_skl)
| ~ in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1433,plain,
( ~ sQ51_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1426,f1430,f737]) ).
fof(f1434,plain,
( ~ sQ2_spl
| sQ57_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f1427,f759,f776,f148]) ).
fof(f1439,plain,
! [X0] :
( ~ sQ2_spl
| apply(sK9_skl,X0) = X0
| apply(identity_relation(sK10_skl),X0) = sK4_skl ),
inference(resolution,[status(thm)],[f692,f149]) ).
fof(f1489,plain,
! [X0] :
( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,relation_rng(sK4_skl)),sK1_skl(X0,relation_rng(sK4_skl))),sK4_skl)
| relation_rng(sK4_skl) = identity_relation(X0)
| ~ empty(sK4_skl) ),
inference(paramodulation,[status(thm)],[f949,f263]) ).
fof(f1490,plain,
! [X0] :
( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,relation_rng(sK4_skl)),sK1_skl(X0,sK4_skl)),relation_rng(sK4_skl))
| relation_rng(sK4_skl) = identity_relation(X0)
| ~ empty(sK4_skl) ),
inference(paramodulation,[status(thm)],[f949,f263]) ).
fof(f1491,plain,
! [X0] :
( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,relation_rng(sK4_skl))),relation_rng(sK4_skl))
| relation_rng(sK4_skl) = identity_relation(X0)
| ~ empty(sK4_skl) ),
inference(paramodulation,[status(thm)],[f949,f263]) ).
fof(f1496,definition,
! [X0] :
( sQ122_spl
<=> ( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,relation_rng(sK4_skl)),sK1_skl(X0,relation_rng(sK4_skl))),sK4_skl)
| relation_rng(sK4_skl) = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1499,plain,
( sQ122_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1489,f732,f1496]) ).
fof(f1500,definition,
! [X0] :
( sQ123_spl
<=> ( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,relation_rng(sK4_skl)),sK1_skl(X0,sK4_skl)),relation_rng(sK4_skl))
| relation_rng(sK4_skl) = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1503,plain,
( sQ123_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1490,f732,f1500]) ).
fof(f1504,definition,
! [X0] :
( sQ124_spl
<=> ( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,relation_rng(sK4_skl))),relation_rng(sK4_skl))
| relation_rng(sK4_skl) = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1507,plain,
( sQ124_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1491,f732,f1504]) ).
fof(f1544,plain,
! [X0,X1] :
( ~ sQ100_spl
| sK0_skl(sK10_skl,X0) != sK1_skl(sK10_skl,X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),X1),sK9_skl) ),
inference(resolution,[status(thm)],[f1204,f58]) ).
fof(f1545,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ100_spl
| apply(sK9_skl,X0) = X0
| ~ in(ordered_pair(X0,X1),sK9_skl) ),
inference(resolution,[status(thm)],[f1204,f149]) ).
fof(f1546,plain,
! [X0,X1] :
( ~ sQ100_spl
| ~ in(sK10_skl,X0)
| ~ in(ordered_pair(X0,X1),sK9_skl) ),
inference(resolution,[status(thm)],[f1204,f45]) ).
fof(f1560,plain,
! [X0] :
( ~ sQ2_spl
| sK0_skl(X0,identity_relation(sK10_skl)) = sK1_skl(X0,identity_relation(sK10_skl))
| identity_relation(sK10_skl) = identity_relation(X0)
| ~ relation(identity_relation(sK10_skl))
| apply(sK9_skl,sK0_skl(X0,identity_relation(sK10_skl))) = sK0_skl(X0,identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f1215,f60]) ).
fof(f1561,plain,
! [X0] :
( ~ sQ2_spl
| in(sK0_skl(X0,identity_relation(sK10_skl)),X0)
| identity_relation(sK10_skl) = identity_relation(X0)
| ~ relation(identity_relation(sK10_skl))
| apply(sK9_skl,sK0_skl(X0,identity_relation(sK10_skl))) = sK0_skl(X0,identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f1215,f59]) ).
fof(f1563,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(X0,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl))
| apply(sK9_skl,X0) = X0 ),
inference(resolution,[status(thm)],[f1215,f163]) ).
fof(f1565,plain,
! [X0,X1] :
( ~ sQ2_spl
| apply(identity_relation(identity_relation(sK10_skl)),ordered_pair(X0,X1)) = sK4_skl
| apply(sK9_skl,X0) = X0 ),
inference(resolution,[status(thm)],[f1215,f692]) ).
fof(f1566,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ in(ordered_pair(ordered_pair(X0,X1),X2),identity_relation(identity_relation(sK10_skl)))
| apply(sK9_skl,X0) = X0 ),
inference(resolution,[status(thm)],[f1215,f171]) ).
fof(f1567,definition,
! [X0] :
( sQ129_spl
<=> ( sK0_skl(X0,identity_relation(sK10_skl)) = sK1_skl(X0,identity_relation(sK10_skl))
| identity_relation(sK10_skl) = identity_relation(X0)
| apply(sK9_skl,sK0_skl(X0,identity_relation(sK10_skl))) = sK0_skl(X0,identity_relation(sK10_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1570,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1560,f1567,f556,f148]) ).
fof(f1571,definition,
! [X0] :
( sQ130_spl
<=> ( in(sK0_skl(X0,identity_relation(sK10_skl)),X0)
| identity_relation(sK10_skl) = identity_relation(X0)
| apply(sK9_skl,sK0_skl(X0,identity_relation(sK10_skl))) = sK0_skl(X0,identity_relation(sK10_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1572,plain,
! [X0] :
( ~ sQ130_spl
| in(sK0_skl(X0,identity_relation(sK10_skl)),X0)
| identity_relation(sK10_skl) = identity_relation(X0)
| apply(sK9_skl,sK0_skl(X0,identity_relation(sK10_skl))) = sK0_skl(X0,identity_relation(sK10_skl)) ),
inference(component_clause,[status(thm)],[f1571]) ).
fof(f1574,plain,
( ~ sQ2_spl
| ~ sQ33_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f1561,f1571,f556,f148]) ).
fof(f1575,definition,
! [X0] :
( sQ131_spl
<=> ( ~ in(X0,relation_dom(identity_relation(sK10_skl)))
| apply(sK9_skl,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1578,plain,
( ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ33_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1563,f1575,f556,f559,f148]) ).
fof(f1580,plain,
! [X0,X1] :
( ~ sQ52_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK4_skl),X0),X1),sK4_skl)
| ~ relation(sK4_skl)
| sK0_skl(relation_dom(sK4_skl),X0) != sK1_skl(relation_dom(sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK4_skl),X0),sK1_skl(relation_dom(sK4_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK4_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1216,f741]) ).
fof(f1581,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| ~ relation(sK9_skl)
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),sK1_skl(relation_dom(sK9_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK9_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1216,f119]) ).
fof(f1582,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),X1),sK3_skl)
| ~ relation(sK3_skl)
| sK0_skl(relation_dom(sK3_skl),X0) != sK1_skl(relation_dom(sK3_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),sK1_skl(relation_dom(sK3_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK3_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1216,f96]) ).
fof(f1585,definition,
! [X0,X1] :
( sQ132_spl
<=> ( ~ in(ordered_pair(sK0_skl(relation_dom(sK4_skl),X0),X1),sK4_skl)
| sK0_skl(relation_dom(sK4_skl),X0) != sK1_skl(relation_dom(sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK4_skl),X0),sK1_skl(relation_dom(sK4_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK4_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1588,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f1580,f1585,f737,f740]) ).
fof(f1589,definition,
! [X0,X1] :
( sQ133_spl
<=> ( ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),sK1_skl(relation_dom(sK9_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK9_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1590,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),sK1_skl(relation_dom(sK9_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK9_skl))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f1589]) ).
fof(f1592,plain,
( ~ sQ5_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f1581,f1589,f182]) ).
fof(f1593,definition,
! [X0,X1] :
( sQ134_spl
<=> ( ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),X1),sK3_skl)
| sK0_skl(relation_dom(sK3_skl),X0) != sK1_skl(relation_dom(sK3_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),sK1_skl(relation_dom(sK3_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK3_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1594,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),X1),sK3_skl)
| sK0_skl(relation_dom(sK3_skl),X0) != sK1_skl(relation_dom(sK3_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),sK1_skl(relation_dom(sK3_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK3_skl))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f1593]) ).
fof(f1596,plain,
( ~ sQ12_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1582,f1593,f252]) ).
fof(f1604,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),sK1_skl(relation_dom(sK9_skl),X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f145,f1590]) ).
fof(f1605,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(relation_dom(sK9_skl),X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f145,f1604]) ).
fof(f1606,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f145,f1605]) ).
fof(f1607,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| sK0_skl(sK10_skl,X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f145,f1606]) ).
fof(f1608,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1_spl
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),X1),sK9_skl)
| sK0_skl(sK10_skl,X0) != sK1_skl(sK10_skl,X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f145,f1607]) ).
fof(f1609,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),X1),sK9_skl)
| sK0_skl(sK10_skl,X0) != sK1_skl(sK10_skl,X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f145,f1608]) ).
fof(f1616,plain,
! [X0] :
( ~ sQ52_spl
| apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),X0)) = sK4_skl
| ~ relation(sK4_skl)
| sK0_skl(relation_dom(sK4_skl),X0) != sK1_skl(relation_dom(sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK4_skl),X0),sK1_skl(relation_dom(sK4_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK4_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1217,f741]) ).
fof(f1617,plain,
! [X0] :
( apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),X0)) = sK4_skl
| ~ relation(sK9_skl)
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),sK1_skl(relation_dom(sK9_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK9_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1217,f119]) ).
fof(f1618,plain,
! [X0] :
( apply(sK3_skl,sK0_skl(relation_dom(sK3_skl),X0)) = sK4_skl
| ~ relation(sK3_skl)
| sK0_skl(relation_dom(sK3_skl),X0) != sK1_skl(relation_dom(sK3_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),sK1_skl(relation_dom(sK3_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK3_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1217,f96]) ).
fof(f1621,definition,
! [X0] :
( sQ135_spl
<=> ( apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),X0)) = sK4_skl
| sK0_skl(relation_dom(sK4_skl),X0) != sK1_skl(relation_dom(sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK4_skl),X0),sK1_skl(relation_dom(sK4_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK4_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1624,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ135_spl ),
inference(split_clause,[status(thm)],[f1616,f1621,f737,f740]) ).
fof(f1625,definition,
! [X0] :
( sQ136_spl
<=> ( apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),X0)) = sK4_skl
| sK0_skl(relation_dom(sK9_skl),X0) != sK1_skl(relation_dom(sK9_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK9_skl),X0),sK1_skl(relation_dom(sK9_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK9_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1628,plain,
( ~ sQ5_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1617,f1625,f182]) ).
fof(f1629,definition,
! [X0] :
( sQ137_spl
<=> ( apply(sK3_skl,sK0_skl(relation_dom(sK3_skl),X0)) = sK4_skl
| sK0_skl(relation_dom(sK3_skl),X0) != sK1_skl(relation_dom(sK3_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),sK1_skl(relation_dom(sK3_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK3_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1632,plain,
( ~ sQ12_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1618,f1629,f252]) ).
fof(f1694,plain,
! [X0] :
( ~ sQ102_spl
| in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| sK1_skl(X0,sK9_skl) = apply(sK9_skl,sK0_skl(X0,sK9_skl)) ),
inference(resolution,[status(thm)],[f1248,f789]) ).
fof(f1695,plain,
! [X0] :
( ~ sQ102_spl
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| ~ relation(sK9_skl)
| sK1_skl(X0,sK9_skl) = apply(sK9_skl,sK0_skl(X0,sK9_skl)) ),
inference(resolution,[status(thm)],[f1248,f60]) ).
fof(f1696,plain,
! [X0] :
( ~ sQ102_spl
| in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| ~ relation(sK9_skl)
| sK1_skl(X0,sK9_skl) = apply(sK9_skl,sK0_skl(X0,sK9_skl)) ),
inference(resolution,[status(thm)],[f1248,f59]) ).
fof(f1697,plain,
! [X0] :
( ~ sQ102_spl
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| apply(sK9_skl,X0) = apply(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f1248,f163]) ).
fof(f1698,plain,
! [X0,X1,X2] :
( ~ sQ102_spl
| ~ in(ordered_pair(ordered_pair(X1,X0),X2),identity_relation(sK9_skl))
| X0 = apply(sK9_skl,X1) ),
inference(resolution,[status(thm)],[f1248,f171]) ).
fof(f1699,definition,
! [X0] :
( sQ140_spl
<=> ( sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| sK1_skl(X0,sK9_skl) = apply(sK9_skl,sK0_skl(X0,sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1700,plain,
! [X0] :
( ~ sQ140_spl
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| sK1_skl(X0,sK9_skl) = apply(sK9_skl,sK0_skl(X0,sK9_skl)) ),
inference(component_clause,[status(thm)],[f1699]) ).
fof(f1702,plain,
( ~ sQ102_spl
| ~ sQ5_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1695,f1699,f182,f1247]) ).
fof(f1703,definition,
! [X0] :
( sQ141_spl
<=> ( in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| sK1_skl(X0,sK9_skl) = apply(sK9_skl,sK0_skl(X0,sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1706,plain,
( ~ sQ102_spl
| ~ sQ5_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f1696,f1703,f182,f1247]) ).
fof(f1707,definition,
! [X0] :
( sQ142_spl
<=> ( ~ in(X0,relation_dom(sK9_skl))
| apply(sK9_skl,X0) = apply(sK9_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1710,plain,
( ~ sQ102_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1697,f1707,f182,f185,f1247]) ).
fof(f1729,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X0,X2),identity_relation(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0))))
| sK0_skl(X1,X0) = sK1_skl(X1,X0)
| X0 = identity_relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1220,f171]) ).
fof(f1742,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X0,X2),identity_relation(ordered_pair(X1,apply(X0,X1))))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1223,f171]) ).
fof(f1747,plain,
! [X0] :
( ~ sQ7_spl
| ~ in(sK9_skl,ordered_pair(X0,apply(sK9_skl,X0)))
| ~ in(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f189,f45]) ).
fof(f1754,plain,
! [X0,X1] :
( ~ sQ52_spl
| ~ in(ordered_pair(X0,X1),sK4_skl)
| ~ relation(sK4_skl)
| ~ in(relation_dom(sK4_skl),X0) ),
inference(resolution,[status(thm)],[f1225,f741]) ).
fof(f1755,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK9_skl)
| ~ relation(sK9_skl)
| ~ in(relation_dom(sK9_skl),X0) ),
inference(resolution,[status(thm)],[f1225,f119]) ).
fof(f1756,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK3_skl)
| ~ relation(sK3_skl)
| ~ in(relation_dom(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f1225,f96]) ).
fof(f1759,definition,
! [X0,X1] :
( sQ143_spl
<=> ( ~ in(ordered_pair(X0,X1),sK4_skl)
| ~ in(relation_dom(sK4_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1762,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f1754,f1759,f737,f740]) ).
fof(f1763,definition,
! [X0,X1] :
( sQ144_spl
<=> ( ~ in(ordered_pair(X0,X1),sK9_skl)
| ~ in(relation_dom(sK9_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1766,plain,
( ~ sQ5_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f1755,f1763,f182]) ).
fof(f1767,definition,
! [X0,X1] :
( sQ145_spl
<=> ( ~ in(ordered_pair(X0,X1),sK3_skl)
| ~ in(relation_dom(sK3_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1768,plain,
! [X0,X1] :
( ~ sQ145_spl
| ~ in(ordered_pair(X0,X1),sK3_skl)
| ~ in(relation_dom(sK3_skl),X0) ),
inference(component_clause,[status(thm)],[f1767]) ).
fof(f1770,plain,
( ~ sQ12_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1756,f1767,f252]) ).
fof(f1774,plain,
! [X0] :
( ~ sQ52_spl
| apply(sK4_skl,X0) = sK4_skl
| ~ relation(sK4_skl)
| ~ in(relation_dom(sK4_skl),X0) ),
inference(resolution,[status(thm)],[f1226,f741]) ).
fof(f1775,plain,
! [X0] :
( apply(sK9_skl,X0) = sK4_skl
| ~ relation(sK9_skl)
| ~ in(relation_dom(sK9_skl),X0) ),
inference(resolution,[status(thm)],[f1226,f119]) ).
fof(f1776,plain,
! [X0] :
( apply(sK3_skl,X0) = sK4_skl
| ~ relation(sK3_skl)
| ~ in(relation_dom(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f1226,f96]) ).
fof(f1779,definition,
! [X0] :
( sQ146_spl
<=> ( apply(sK4_skl,X0) = sK4_skl
| ~ in(relation_dom(sK4_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1782,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ146_spl ),
inference(split_clause,[status(thm)],[f1774,f1779,f737,f740]) ).
fof(f1783,definition,
! [X0] :
( sQ147_spl
<=> ( apply(sK9_skl,X0) = sK4_skl
| ~ in(relation_dom(sK9_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1786,plain,
( ~ sQ5_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1775,f1783,f182]) ).
fof(f1787,definition,
! [X0] :
( sQ148_spl
<=> ( apply(sK3_skl,X0) = sK4_skl
| ~ in(relation_dom(sK3_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1790,plain,
( ~ sQ12_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1776,f1787,f252]) ).
fof(f1861,plain,
! [X0,X1] :
( ~ in(X0,X1)
| X0 = apply(identity_relation(X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1242,f79]) ).
fof(f1867,plain,
! [X0] :
( in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)) = apply(identity_relation(sK9_skl),ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl))) ),
inference(resolution,[status(thm)],[f1861,f789]) ).
fof(f1870,plain,
! [X0] :
( ~ sQ7_spl
| ~ in(X0,sK10_skl)
| ordered_pair(X0,apply(sK9_skl,X0)) = apply(identity_relation(sK9_skl),ordered_pair(X0,apply(sK9_skl,X0))) ),
inference(resolution,[status(thm)],[f1861,f189]) ).
fof(f1872,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ordered_pair(X0,apply(X1,X0)) = apply(identity_relation(X1),ordered_pair(X0,apply(X1,X0))) ),
inference(resolution,[status(thm)],[f1861,f163]) ).
fof(f1875,plain,
! [X0,X1] :
( ~ sQ100_spl
| ~ in(ordered_pair(X0,X1),sK9_skl)
| X0 = apply(identity_relation(sK10_skl),X0) ),
inference(resolution,[status(thm)],[f1861,f1204]) ).
fof(f1876,plain,
! [X0,X1] :
( apply(X1,X0) = sK4_skl
| ~ function(X1)
| ~ relation(X1)
| X0 = apply(identity_relation(relation_dom(X1)),X0) ),
inference(resolution,[status(thm)],[f1861,f381]) ).
fof(f1877,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X0,X2),X1)
| ~ function(X1)
| ~ relation(X1)
| X0 = apply(identity_relation(relation_dom(X1)),X0) ),
inference(resolution,[status(thm)],[f1861,f138]) ).
fof(f1893,plain,
! [X0] :
( ~ sQ103_spl
| sK0_skl(X0,sK3_skl) = sK1_skl(X0,sK3_skl)
| sK3_skl = identity_relation(X0)
| ~ relation(sK3_skl)
| sK1_skl(X0,sK3_skl) = apply(sK3_skl,sK0_skl(X0,sK3_skl)) ),
inference(resolution,[status(thm)],[f1252,f60]) ).
fof(f1894,plain,
! [X0] :
( ~ sQ103_spl
| in(sK0_skl(X0,sK3_skl),X0)
| sK3_skl = identity_relation(X0)
| ~ relation(sK3_skl)
| sK1_skl(X0,sK3_skl) = apply(sK3_skl,sK0_skl(X0,sK3_skl)) ),
inference(resolution,[status(thm)],[f1252,f59]) ).
fof(f1895,plain,
! [X0] :
( ~ sQ103_spl
| ~ in(X0,relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| apply(sK3_skl,X0) = apply(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f1252,f163]) ).
fof(f1896,plain,
! [X0,X1,X2] :
( ~ sQ103_spl
| ~ in(ordered_pair(ordered_pair(X1,X0),X2),identity_relation(sK3_skl))
| X0 = apply(sK3_skl,X1) ),
inference(resolution,[status(thm)],[f1252,f171]) ).
fof(f1897,definition,
! [X0] :
( sQ149_spl
<=> ( sK0_skl(X0,sK3_skl) = sK1_skl(X0,sK3_skl)
| sK3_skl = identity_relation(X0)
| sK1_skl(X0,sK3_skl) = apply(sK3_skl,sK0_skl(X0,sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1898,plain,
! [X0] :
( ~ sQ149_spl
| sK0_skl(X0,sK3_skl) = sK1_skl(X0,sK3_skl)
| sK3_skl = identity_relation(X0)
| sK1_skl(X0,sK3_skl) = apply(sK3_skl,sK0_skl(X0,sK3_skl)) ),
inference(component_clause,[status(thm)],[f1897]) ).
fof(f1900,plain,
( ~ sQ103_spl
| ~ sQ12_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f1893,f1897,f252,f1251]) ).
fof(f1901,definition,
! [X0] :
( sQ150_spl
<=> ( in(sK0_skl(X0,sK3_skl),X0)
| sK3_skl = identity_relation(X0)
| sK1_skl(X0,sK3_skl) = apply(sK3_skl,sK0_skl(X0,sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1904,plain,
( ~ sQ103_spl
| ~ sQ12_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f1894,f1901,f252,f1251]) ).
fof(f1905,definition,
! [X0] :
( sQ151_spl
<=> ( ~ in(X0,relation_dom(sK3_skl))
| apply(sK3_skl,X0) = apply(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1908,plain,
( ~ sQ103_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f1895,f1905,f252,f641,f1251]) ).
fof(f1975,plain,
! [X0] :
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| ~ in(X0,sK4_skl) ),
inference(paramodulation,[status(thm)],[f1163,f1276]) ).
fof(f1978,definition,
! [X0] :
( sQ152_spl
<=> ~ in(X0,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1981,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f1975,f1978,f737,f732]) ).
fof(f1982,definition,
! [X0] :
( sQ153_spl
<=> ~ in(X0,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1983,plain,
! [X0] :
( ~ sQ153_spl
| ~ in(X0,sK9_skl) ),
inference(component_clause,[status(thm)],[f1982]) ).
fof(f2009,plain,
( ~ sQ153_spl
| empty(sK9_skl) ),
inference(resolution,[status(thm)],[f1983,f311]) ).
fof(f2014,plain,
( ~ sQ153_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f2009,f235,f1982]) ).
fof(f2023,definition,
! [X0] :
( sQ156_spl
<=> ~ in(X0,relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2024,plain,
! [X0] :
( ~ sQ156_spl
| ~ in(X0,relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f2023]) ).
fof(f2027,plain,
! [X0] :
( ~ sQ156_spl
| ~ sQ1_spl
| ~ in(X0,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f2024]) ).
fof(f2030,plain,
( ~ sQ156_spl
| ~ sQ1_spl
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f2027,f311]) ).
fof(f2035,plain,
( ~ sQ156_spl
| ~ sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f2030,f238,f144,f2023]) ).
fof(f2041,plain,
( ~ sQ36_spl
| ~ sQ2_spl
| apply(sK9_skl,sK11_skl) = sK11_skl ),
inference(resolution,[status(thm)],[f149,f574]) ).
fof(f2051,plain,
! [X0,X1] :
( in(sK0_skl(X1,relation_rng(X0)),X1)
| relation_rng(X0) = identity_relation(X1)
| ~ empty(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f263,f1273]) ).
fof(f2055,plain,
! [X0,X1] :
( ~ empty(relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(resolution,[status(thm)],[f1273,f85]) ).
fof(f2057,plain,
! [X0] :
( ~ sQ13_spl
| X0 = apply(identity_relation(relation_dom(sK3_skl)),X0)
| apply(sK3_skl,X0) = sK4_skl ),
inference(resolution,[status(thm)],[f1086,f1861]) ).
fof(f2091,plain,
( ~ sQ54_spl
| relation(sK10_skl)
| ~ empty(sK4_skl) ),
inference(paramodulation,[status(thm)],[f760,f244]) ).
fof(f2092,plain,
( ~ sQ54_spl
| empty(sK10_skl)
| ~ empty(sK4_skl) ),
inference(paramodulation,[status(thm)],[f760,f234]) ).
fof(f2119,plain,
( ~ sQ54_spl
| sQ11_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2091,f732,f245,f759]) ).
fof(f2120,plain,
( ~ sQ54_spl
| sQ10_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2092,f732,f238,f759]) ).
fof(f2122,plain,
! [X0] :
( ~ sQ100_spl
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| ~ relation(sK9_skl)
| in(sK0_skl(X0,sK9_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f1204,f60]) ).
fof(f2123,plain,
! [X0] :
( ~ sQ100_spl
| in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| ~ relation(sK9_skl)
| in(sK0_skl(X0,sK9_skl),sK10_skl) ),
inference(resolution,[status(thm)],[f1204,f59]) ).
fof(f2124,plain,
! [X0] :
( ~ sQ100_spl
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| in(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1204,f163]) ).
fof(f2125,plain,
! [X0,X1,X2] :
( ~ sQ100_spl
| ~ in(ordered_pair(ordered_pair(X0,X1),X2),identity_relation(sK9_skl))
| in(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1204,f171]) ).
fof(f2126,definition,
! [X0] :
( sQ157_spl
<=> ( sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| in(sK0_skl(X0,sK9_skl),sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2129,plain,
( ~ sQ100_spl
| ~ sQ5_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f2122,f2126,f182,f1203]) ).
fof(f2130,definition,
! [X0] :
( sQ158_spl
<=> ( in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| in(sK0_skl(X0,sK9_skl),sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2133,plain,
( ~ sQ100_spl
| ~ sQ5_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f2123,f2130,f182,f1203]) ).
fof(f2134,definition,
! [X0] :
( sQ159_spl
<=> ( ~ in(X0,relation_dom(sK9_skl))
| in(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( ~ sQ100_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f2124,f2134,f182,f185,f1203]) ).
fof(f2191,plain,
! [X0,X1] :
( ~ empty(X0)
| apply(X0,X1) = sK4_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f929,f1275]) ).
fof(f2195,plain,
! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| apply(X0,X1) = sK4_skl ),
inference(resolution,[status(thm)],[f2191,f85]) ).
fof(f2257,plain,
! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| in(sK0_skl(X1,relation_rng(X0)),X1)
| relation_rng(X0) = identity_relation(X1) ),
inference(resolution,[status(thm)],[f2051,f85]) ).
fof(f2270,plain,
! [X0] :
( ~ sQ52_spl
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),identity_relation(X0)),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),identity_relation(X0)))),sK4_skl)
| ~ relation(sK4_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),identity_relation(X0)),sK1_skl(relation_dom(sK4_skl),identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(relation_dom(sK4_skl)) ),
inference(resolution,[status(thm)],[f286,f741]) ).
fof(f2271,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(sK9_skl),identity_relation(X0)),apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),identity_relation(X0)))),sK9_skl)
| ~ relation(sK9_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK9_skl),identity_relation(X0)),sK1_skl(relation_dom(sK9_skl),identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(relation_dom(sK9_skl)) ),
inference(resolution,[status(thm)],[f286,f119]) ).
fof(f2272,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(sK3_skl),identity_relation(X0)),apply(sK3_skl,sK0_skl(relation_dom(sK3_skl),identity_relation(X0)))),sK3_skl)
| ~ relation(sK3_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK3_skl),identity_relation(X0)),sK1_skl(relation_dom(sK3_skl),identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(relation_dom(sK3_skl)) ),
inference(resolution,[status(thm)],[f286,f96]) ).
fof(f2275,definition,
! [X0] :
( sQ162_spl
<=> ( in(ordered_pair(sK0_skl(relation_dom(sK4_skl),identity_relation(X0)),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),identity_relation(X0)))),sK4_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),identity_relation(X0)),sK1_skl(relation_dom(sK4_skl),identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(relation_dom(sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f2278,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f2270,f2275,f737,f740]) ).
fof(f2279,definition,
! [X0] :
( sQ163_spl
<=> ( in(ordered_pair(sK0_skl(relation_dom(sK9_skl),identity_relation(X0)),apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),identity_relation(X0)))),sK9_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK9_skl),identity_relation(X0)),sK1_skl(relation_dom(sK9_skl),identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2282,plain,
( ~ sQ5_spl
| sQ163_spl ),
inference(split_clause,[status(thm)],[f2271,f2279,f182]) ).
fof(f2283,definition,
! [X0] :
( sQ164_spl
<=> ( in(ordered_pair(sK0_skl(relation_dom(sK3_skl),identity_relation(X0)),apply(sK3_skl,sK0_skl(relation_dom(sK3_skl),identity_relation(X0)))),sK3_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK3_skl),identity_relation(X0)),sK1_skl(relation_dom(sK3_skl),identity_relation(X0))),identity_relation(X0))
| identity_relation(X0) = identity_relation(relation_dom(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2286,plain,
( ~ sQ12_spl
| sQ164_spl ),
inference(split_clause,[status(thm)],[f2272,f2283,f252]) ).
fof(f2338,plain,
( ~ sQ52_spl
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK9_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK9_skl))),sK4_skl)
| ~ relation(sK4_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK9_skl),sK1_skl(relation_dom(sK4_skl),sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(relation_dom(sK4_skl)) ),
inference(resolution,[status(thm)],[f290,f741]) ).
fof(f2339,plain,
( in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),sK9_skl))),sK9_skl)
| ~ relation(sK9_skl)
| in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(relation_dom(sK9_skl)) ),
inference(resolution,[status(thm)],[f290,f119]) ).
fof(f2343,definition,
( sQ165_spl
<=> sK9_skl = identity_relation(relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2344,plain,
( ~ sQ165_spl
| sK9_skl = identity_relation(relation_dom(sK4_skl)) ),
inference(component_clause,[status(thm)],[f2343]) ).
fof(f2346,definition,
( sQ166_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK9_skl),sK1_skl(relation_dom(sK4_skl),sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f2349,definition,
( sQ167_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK9_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK9_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2350,plain,
( ~ sQ167_spl
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK9_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK9_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f2349]) ).
fof(f2352,plain,
( ~ sQ52_spl
| sQ167_spl
| ~ sQ51_spl
| sQ166_spl
| sQ165_spl ),
inference(split_clause,[status(thm)],[f2338,f2343,f2346,f737,f2349,f740]) ).
fof(f2353,definition,
( sQ168_spl
<=> sK9_skl = identity_relation(relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2354,plain,
( ~ sQ168_spl
| sK9_skl = identity_relation(relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f2353]) ).
fof(f2356,definition,
( sQ169_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f2359,definition,
( sQ170_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),sK9_skl))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f2362,plain,
( sQ170_spl
| ~ sQ5_spl
| sQ169_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f2339,f2353,f2356,f182,f2359]) ).
fof(f2384,plain,
( ~ sQ168_spl
| ~ sQ1_spl
| sK9_skl = identity_relation(sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f2354]) ).
fof(f2385,plain,
( ~ sQ168_spl
| ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2384,f143]) ).
fof(f2386,plain,
( ~ sQ168_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f2385]) ).
fof(f2387,plain,
( ~ sQ167_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK9_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK9_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f2350]) ).
fof(f2388,plain,
( ~ sQ167_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK9_skl),apply(sK4_skl,sK0_skl(sK4_skl,sK9_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f2387]) ).
fof(f2389,plain,
( ~ sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2388,f1274]) ).
fof(f2390,plain,
~ sQ167_spl,
inference(contradiction_clause,[status(thm)],[f2389]) ).
fof(f2393,plain,
( ~ sQ165_spl
| sK9_skl = identity_relation(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f2344]) ).
fof(f2394,plain,
( ~ sQ165_spl
| sK9_skl = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f1144,f2393]) ).
fof(f2395,plain,
( ~ sQ165_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2394,f771]) ).
fof(f2396,plain,
( ~ sQ165_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f2395]) ).
fof(f2470,plain,
( ~ sQ102_spl
| ~ sQ18_spl
| sK1_skl(sK10_skl,sK9_skl) = apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f294,f1248]) ).
fof(f2481,plain,
( ~ sQ2_spl
| apply(sK9_skl,sK0_skl(sK10_skl,identity_relation(sK4_skl))) = sK0_skl(sK10_skl,identity_relation(sK4_skl))
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl))
| identity_relation(sK4_skl) = identity_relation(sK10_skl) ),
inference(paramodulation,[status(thm)],[f1144,f285]) ).
fof(f2499,definition,
( sQ178_spl
<=> identity_relation(sK4_skl) = identity_relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2500,plain,
( ~ sQ178_spl
| identity_relation(sK4_skl) = identity_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f2499]) ).
fof(f2502,definition,
( sQ179_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2503,plain,
( ~ sQ179_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f2502]) ).
fof(f2505,definition,
( sQ180_spl
<=> apply(sK9_skl,sK0_skl(sK10_skl,identity_relation(sK4_skl))) = sK0_skl(sK10_skl,identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2508,plain,
( ~ sQ2_spl
| sQ180_spl
| sQ179_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f2481,f2499,f2502,f2505,f148]) ).
fof(f2510,definition,
( sQ181_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2511,plain,
( ~ sQ181_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f2510]) ).
fof(f2514,definition,
( sQ182_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,identity_relation(sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2515,plain,
( ~ sQ182_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,identity_relation(sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f2514]) ).
fof(f2520,plain,
( ~ sQ178_spl
| sK4_skl = identity_relation(sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2500]) ).
fof(f2521,plain,
( ~ sQ178_spl
| sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2520,f761]) ).
fof(f2522,plain,
( ~ sQ178_spl
| sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f2521]) ).
fof(f2523,plain,
( ~ sQ182_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,identity_relation(sK4_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2515]) ).
fof(f2524,plain,
( ~ sQ182_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2523]) ).
fof(f2525,plain,
( ~ sQ182_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2524,f1274]) ).
fof(f2526,plain,
~ sQ182_spl,
inference(contradiction_clause,[status(thm)],[f2525]) ).
fof(f2527,plain,
( ~ sQ181_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f2511]) ).
fof(f2528,plain,
( ~ sQ181_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2527]) ).
fof(f2529,plain,
( ~ sQ181_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2528,f1274]) ).
fof(f2530,plain,
~ sQ181_spl,
inference(contradiction_clause,[status(thm)],[f2529]) ).
fof(f2531,plain,
( ~ sQ179_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f2503]) ).
fof(f2532,plain,
( ~ sQ179_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2531]) ).
fof(f2533,plain,
( ~ sQ179_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2532,f1274]) ).
fof(f2534,plain,
~ sQ179_spl,
inference(contradiction_clause,[status(thm)],[f2533]) ).
fof(f2548,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),empty_set),apply(X0,sK0_skl(relation_dom(X0),empty_set))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),empty_set),sK1_skl(relation_dom(X0),empty_set)),empty_set)
| sK4_skl = identity_relation(relation_dom(X0)) ),
inference(forward_demodulation,[status(thm)],[f369,f384]) ).
fof(f2549,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),empty_set),apply(X0,sK0_skl(relation_dom(X0),empty_set))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),sK1_skl(relation_dom(X0),empty_set)),empty_set)
| sK4_skl = identity_relation(relation_dom(X0)) ),
inference(forward_demodulation,[status(thm)],[f369,f2548]) ).
fof(f2550,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),empty_set),apply(X0,sK0_skl(relation_dom(X0),empty_set))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),sK1_skl(relation_dom(X0),sK4_skl)),empty_set)
| sK4_skl = identity_relation(relation_dom(X0)) ),
inference(forward_demodulation,[status(thm)],[f369,f2549]) ).
fof(f2551,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),empty_set),apply(X0,sK0_skl(relation_dom(X0),empty_set))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),sK1_skl(relation_dom(X0),sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(relation_dom(X0)) ),
inference(forward_demodulation,[status(thm)],[f369,f2550]) ).
fof(f2552,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),apply(X0,sK0_skl(relation_dom(X0),empty_set))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),sK1_skl(relation_dom(X0),sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(relation_dom(X0)) ),
inference(forward_demodulation,[status(thm)],[f369,f2551]) ).
fof(f2553,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),apply(X0,sK0_skl(relation_dom(X0),sK4_skl))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),sK1_skl(relation_dom(X0),sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(relation_dom(X0)) ),
inference(forward_demodulation,[status(thm)],[f369,f2552]) ).
fof(f2554,plain,
! [X0] :
( in(ordered_pair(sK0_skl(relation_dom(X0),sK4_skl),apply(X0,sK0_skl(relation_dom(X0),sK4_skl))),X0)
| ~ function(X0)
| ~ relation(X0)
| sK4_skl = identity_relation(relation_dom(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2553,f1274]) ).
fof(f2555,plain,
( ~ sQ52_spl
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK4_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK4_skl))),sK4_skl)
| ~ relation(sK4_skl)
| sK4_skl = identity_relation(relation_dom(sK4_skl)) ),
inference(resolution,[status(thm)],[f2554,f741]) ).
fof(f2556,plain,
( in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK4_skl),apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),sK4_skl))),sK9_skl)
| ~ relation(sK9_skl)
| sK4_skl = identity_relation(relation_dom(sK9_skl)) ),
inference(resolution,[status(thm)],[f2554,f119]) ).
fof(f2560,definition,
( sQ183_spl
<=> sK4_skl = identity_relation(relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2563,definition,
( sQ184_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK4_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2564,plain,
( ~ sQ184_spl
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK4_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f2563]) ).
fof(f2566,plain,
( ~ sQ52_spl
| sQ184_spl
| ~ sQ51_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f2555,f2560,f737,f2563,f740]) ).
fof(f2567,definition,
( sQ185_spl
<=> sK4_skl = identity_relation(relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2568,plain,
( ~ sQ185_spl
| sK4_skl = identity_relation(relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f2567]) ).
fof(f2570,definition,
( sQ186_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK4_skl),apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),sK4_skl))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f2573,plain,
( sQ186_spl
| ~ sQ5_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f2556,f2567,f182,f2570]) ).
fof(f2587,plain,
( ~ sQ185_spl
| ~ sQ1_spl
| sK4_skl = identity_relation(sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f2568]) ).
fof(f2588,plain,
( ~ sQ185_spl
| ~ sQ1_spl
| sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2587,f761]) ).
fof(f2589,plain,
( ~ sQ185_spl
| ~ sQ1_spl
| sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f2588]) ).
fof(f2592,plain,
( ~ sQ184_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK4_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f2564]) ).
fof(f2593,plain,
( ~ sQ184_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK4_skl,sK4_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f2592]) ).
fof(f2594,plain,
( ~ sQ184_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2593,f1274]) ).
fof(f2595,plain,
~ sQ184_spl,
inference(contradiction_clause,[status(thm)],[f2594]) ).
fof(f2599,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),apply(identity_relation(X0),sK0_skl(X0,empty_set))),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,empty_set),sK1_skl(X0,empty_set)),empty_set)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f385]) ).
fof(f2600,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),apply(identity_relation(X0),sK0_skl(X0,empty_set))),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,empty_set)),empty_set)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2599]) ).
fof(f2601,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),apply(identity_relation(X0),sK0_skl(X0,empty_set))),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),empty_set)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2600]) ).
fof(f2602,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),apply(identity_relation(X0),sK0_skl(X0,empty_set))),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2601]) ).
fof(f2603,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK4_skl),apply(identity_relation(X0),sK0_skl(X0,empty_set))),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2602]) ).
fof(f2604,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK4_skl),apply(identity_relation(X0),sK0_skl(X0,sK4_skl))),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2603]) ).
fof(f2605,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK4_skl),apply(identity_relation(X0),sK0_skl(X0,sK4_skl))),identity_relation(X0))
| sK4_skl = identity_relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2604,f1274]) ).
fof(f2615,plain,
( in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(identity_relation(sK4_skl),sK0_skl(sK4_skl,sK4_skl))),sK4_skl)
| sK4_skl = identity_relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f1144,f2605]) ).
fof(f2618,definition,
( sQ189_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK4_skl,sK4_skl))),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2619,plain,
( ~ sQ189_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK4_skl,sK4_skl))),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f2618]) ).
fof(f2622,definition,
( sQ190_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(identity_relation(sK4_skl),sK0_skl(sK4_skl,sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f2623,plain,
( ~ sQ190_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(identity_relation(sK4_skl),sK0_skl(sK4_skl,sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f2622]) ).
fof(f2625,plain,
( sQ190_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f2615,f1002,f2622]) ).
fof(f2626,plain,
( ~ sQ190_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK4_skl,sK4_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2623]) ).
fof(f2627,plain,
( ~ sQ190_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2626,f1274]) ).
fof(f2628,plain,
~ sQ190_spl,
inference(contradiction_clause,[status(thm)],[f2627]) ).
fof(f2629,plain,
( ~ sQ189_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(sK4_skl,sK0_skl(sK4_skl,sK4_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2619]) ).
fof(f2630,plain,
( ~ sQ189_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2629,f1274]) ).
fof(f2631,plain,
~ sQ189_spl,
inference(contradiction_clause,[status(thm)],[f2630]) ).
fof(f2634,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),sK0_skl(X0,empty_set)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,empty_set),sK1_skl(X0,empty_set)),empty_set)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f387]) ).
fof(f2635,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),sK0_skl(X0,empty_set)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,empty_set)),empty_set)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2634]) ).
fof(f2636,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),sK0_skl(X0,empty_set)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),empty_set)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2635]) ).
fof(f2637,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,empty_set),sK0_skl(X0,empty_set)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2636]) ).
fof(f2638,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,empty_set)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2637]) ).
fof(f2639,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl)),identity_relation(X0))
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(forward_demodulation,[status(thm)],[f369,f2638]) ).
fof(f2640,plain,
! [X0] :
( in(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl)),identity_relation(X0))
| sK4_skl = identity_relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2639,f1274]) ).
fof(f2651,definition,
( sQ191_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK0_skl(sK4_skl,sK4_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2652,plain,
( ~ sQ191_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK0_skl(sK4_skl,sK4_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f2651]) ).
fof(f2655,plain,
( ~ sQ191_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2652,f1274]) ).
fof(f2656,plain,
~ sQ191_spl,
inference(contradiction_clause,[status(thm)],[f2655]) ).
fof(f2661,plain,
! [X0] :
( ~ sQ73_spl
| ~ in(X0,relation_dom(sK4_skl))
| ~ function(sK4_skl)
| ~ relation(sK4_skl)
| ~ in(sK4_skl,ordered_pair(X0,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f925,f1223]) ).
fof(f2662,plain,
! [X0] :
( ~ sQ73_spl
| in(ordered_pair(X0,sK4_skl),sK4_skl)
| ~ in(X0,relation_dom(sK4_skl))
| ~ function(sK4_skl)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f925,f163]) ).
fof(f2663,definition,
! [X0] :
( sQ192_spl
<=> ( ~ in(X0,relation_dom(sK4_skl))
| ~ in(sK4_skl,ordered_pair(X0,sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2666,plain,
( ~ sQ73_spl
| ~ sQ52_spl
| ~ sQ51_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f2661,f2663,f737,f740,f924]) ).
fof(f2667,definition,
! [X0] :
( sQ193_spl
<=> ( in(ordered_pair(X0,sK4_skl),sK4_skl)
| ~ in(X0,relation_dom(sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2670,plain,
( ~ sQ73_spl
| sQ193_spl
| ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f2662,f737,f740,f2667,f924]) ).
fof(f2714,plain,
( ~ sQ7_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl))
| identity_relation(sK4_skl) = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,identity_relation(sK4_skl)))),sK9_skl) ),
inference(paramodulation,[status(thm)],[f1144,f483]) ).
fof(f2715,plain,
( ~ sQ7_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl))
| identity_relation(sK4_skl) = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl))),sK9_skl) ),
inference(paramodulation,[status(thm)],[f1144,f483]) ).
fof(f2716,definition,
( sQ196_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,identity_relation(sK4_skl)))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2719,definition,
( sQ197_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2720,plain,
( ~ sQ197_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f2719]) ).
fof(f2722,plain,
( ~ sQ7_spl
| sQ197_spl
| sQ178_spl
| sQ196_spl ),
inference(split_clause,[status(thm)],[f2714,f2716,f2499,f2719,f188]) ).
fof(f2723,definition,
( sQ198_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2726,plain,
( ~ sQ7_spl
| sQ197_spl
| sQ178_spl
| sQ198_spl ),
inference(split_clause,[status(thm)],[f2715,f2723,f2499,f2719,f188]) ).
fof(f2727,plain,
( ~ sQ197_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f2720]) ).
fof(f2728,plain,
( ~ sQ197_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f2727]) ).
fof(f2729,plain,
( ~ sQ197_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK1_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f2728]) ).
fof(f2730,plain,
( ~ sQ197_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2729,f1274]) ).
fof(f2731,plain,
~ sQ197_spl,
inference(contradiction_clause,[status(thm)],[f2730]) ).
fof(f2742,plain,
( ~ sQ0_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),sK9_skl)
| sK4_skl = identity_relation(sK10_skl) ),
inference(paramodulation,[status(thm)],[f142,f2640]) ).
fof(f2772,definition,
( sQ199_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2775,plain,
( ~ sQ0_spl
| sQ199_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f2742,f759,f2772,f141]) ).
fof(f2848,plain,
! [X0] :
( ~ sQ0_spl
| in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| ~ relation(sK9_skl)
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl) ),
inference(resolution,[status(thm)],[f225,f59]) ).
fof(f2849,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ in(X0,sK10_skl)
| X0 = apply(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f225,f189]) ).
fof(f2856,definition,
! [X0] :
( sQ203_spl
<=> ( in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2857,plain,
! [X0] :
( ~ sQ203_spl
| in(sK0_skl(X0,sK9_skl),X0)
| sK9_skl = identity_relation(X0)
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl) ),
inference(component_clause,[status(thm)],[f2856]) ).
fof(f2859,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f2848,f2856,f182,f141]) ).
fof(f2860,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2849,f148,f141,f188]) ).
fof(f2861,definition,
! [X0] :
( sQ204_spl
<=> ( ~ in(X0,relation_dom(sK9_skl))
| X0 = apply(sK9_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2955,plain,
! [X0] :
( ~ sQ26_spl
| apply(sK4_skl,X0) = sK4_skl
| in(X0,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f420]) ).
fof(f2956,plain,
! [X0] :
( ~ sQ26_spl
| apply(sK4_skl,X0) = sK4_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f2955,f1274]) ).
fof(f3068,plain,
( ~ sQ35_spl
| in(sK11_skl,sK10_skl)
| sK11_skl = sK4_skl ),
inference(paramodulation,[status(thm)],[f692,f563]) ).
fof(f3070,plain,
( ~ sQ35_spl
| in(ordered_pair(sK11_skl,sK11_skl),identity_relation(sK10_skl))
| ~ in(sK11_skl,sK10_skl) ),
inference(paramodulation,[status(thm)],[f563,f355]) ).
fof(f3071,plain,
( ~ sQ35_spl
| ~ in(sK11_skl,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl))
| ~ in(identity_relation(sK10_skl),ordered_pair(sK11_skl,sK11_skl)) ),
inference(paramodulation,[status(thm)],[f563,f1223]) ).
fof(f3072,plain,
( ~ sQ35_spl
| in(ordered_pair(sK11_skl,sK11_skl),identity_relation(sK10_skl))
| ~ in(sK11_skl,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl)) ),
inference(paramodulation,[status(thm)],[f563,f163]) ).
fof(f3073,definition,
( sQ213_spl
<=> sK11_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f3074,plain,
( ~ sQ213_spl
| sK11_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f3073]) ).
fof(f3076,plain,
( ~ sQ35_spl
| sQ3_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f3068,f3073,f152,f562]) ).
fof(f3078,definition,
( sQ214_spl
<=> in(ordered_pair(sK11_skl,sK11_skl),identity_relation(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f3081,plain,
( ~ sQ35_spl
| sQ214_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3070,f152,f3078,f562]) ).
fof(f3082,definition,
( sQ215_spl
<=> in(identity_relation(sK10_skl),ordered_pair(sK11_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f3085,plain,
( ~ sQ35_spl
| ~ sQ36_spl
| ~ sQ34_spl
| ~ sQ33_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f3071,f3082,f556,f559,f566,f562]) ).
fof(f3086,plain,
( ~ sQ35_spl
| sQ214_spl
| ~ sQ36_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f3072,f556,f559,f566,f3078,f562]) ).
fof(f3087,plain,
( ~ sQ213_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3074,f517]) ).
fof(f3088,plain,
( ~ sQ213_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f3087]) ).
fof(f3102,definition,
( sQ216_spl
<=> in(sK4_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f3103,plain,
( ~ sQ216_spl
| in(sK4_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f3102]) ).
fof(f3105,definition,
( sQ217_spl
<=> in(ordered_pair(sK4_skl,sK4_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f3106,plain,
( ~ sQ217_spl
| in(ordered_pair(sK4_skl,sK4_skl),sK9_skl) ),
inference(component_clause,[status(thm)],[f3105]) ).
fof(f3109,definition,
( sQ218_spl
<=> in(sK9_skl,ordered_pair(sK4_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f3112,definition,
( sQ219_spl
<=> in(sK4_skl,relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f3114,plain,
( sQ219_spl
| ~ in(sK4_skl,relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f3112]) ).
fof(f3117,plain,
( sQ219_spl
| ~ sQ1_spl
| ~ in(sK4_skl,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f3114]) ).
fof(f3118,plain,
( sQ219_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3117,f611]) ).
fof(f3119,plain,
( sQ219_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f3118]) ).
fof(f3121,plain,
( ~ sQ99_spl
| sQ3_spl
| apply(sK9_skl,sK11_skl) = sK4_skl ),
inference(resolution,[status(thm)],[f154,f1197]) ).
fof(f3122,plain,
! [X0] :
( sQ3_spl
| ~ in(ordered_pair(sK11_skl,X0),identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f154,f171]) ).
fof(f3127,plain,
( sQ3_spl
| ~ in(sK11_skl,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f3122,f163]) ).
fof(f3129,plain,
! [X0,X1] :
( sQ3_spl
| ~ in(ordered_pair(ordered_pair(sK11_skl,X0),X1),identity_relation(identity_relation(sK10_skl))) ),
inference(resolution,[status(thm)],[f3122,f171]) ).
fof(f3130,plain,
( sQ3_spl
| ~ sQ36_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f3127,f556,f559,f566,f152]) ).
fof(f3140,plain,
( ~ sQ3_spl
| ~ empty(relation_dom(identity_relation(sK10_skl)))
| ~ relation(identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f553,f85]) ).
fof(f3141,definition,
( sQ220_spl
<=> empty(relation_dom(identity_relation(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f3144,plain,
( ~ sQ3_spl
| ~ sQ220_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f3140,f556,f3141,f152]) ).
fof(f3324,plain,
( ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f763,f1274]) ).
fof(f3325,plain,
~ sQ55_spl,
inference(contradiction_clause,[status(thm)],[f3324]) ).
fof(f3337,definition,
( sQ223_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK3_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK3_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f3338,plain,
( ~ sQ223_spl
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK3_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK3_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f3337]) ).
fof(f3373,plain,
( ~ sQ223_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK3_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK3_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f3338]) ).
fof(f3374,plain,
( ~ sQ223_spl
| ~ sQ26_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK3_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f3373]) ).
fof(f3375,plain,
( ~ sQ223_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3374,f1274]) ).
fof(f3376,plain,
( ~ sQ223_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f3375]) ).
fof(f3627,plain,
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| empty(identity_relation(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f1163,f655]) ).
fof(f3630,definition,
( sQ233_spl
<=> empty(identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3633,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f3627,f3630,f737,f732]) ).
fof(f3634,definition,
( sQ234_spl
<=> empty(identity_relation(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3635,plain,
( ~ sQ234_spl
| empty(identity_relation(sK9_skl)) ),
inference(component_clause,[status(thm)],[f3634]) ).
fof(f3636,plain,
( sQ234_spl
| ~ empty(identity_relation(sK9_skl)) ),
inference(component_clause,[status(thm)],[f3634]) ).
fof(f3656,plain,
! [X0] :
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,relation_rng(sK4_skl)),sK1_skl(X0,relation_rng(sK4_skl))),relation_rng(sK4_skl))
| relation_rng(sK4_skl) = identity_relation(X0) ),
inference(paramodulation,[status(thm)],[f1163,f659]) ).
fof(f3659,definition,
! [X0] :
( sQ235_spl
<=> ( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| in(ordered_pair(sK0_skl(X0,relation_rng(sK4_skl)),sK1_skl(X0,relation_rng(sK4_skl))),relation_rng(sK4_skl))
| relation_rng(sK4_skl) = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3662,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f3656,f3659,f737,f732]) ).
fof(f3692,plain,
( ~ sQ234_spl
| relation_rng(identity_relation(sK9_skl)) = sK4_skl ),
inference(resolution,[status(thm)],[f3635,f946]) ).
fof(f3740,plain,
( ~ sQ234_spl
| sK9_skl = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f128,f3692]) ).
fof(f3741,plain,
( ~ sQ234_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3740,f771]) ).
fof(f3742,plain,
( ~ sQ234_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f3741]) ).
fof(f3743,plain,
( sQ234_spl
| ~ empty(relation_dom(identity_relation(sK9_skl)))
| ~ relation(identity_relation(sK9_skl)) ),
inference(resolution,[status(thm)],[f3636,f85]) ).
fof(f3744,definition,
( sQ237_spl
<=> relation(identity_relation(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f3746,plain,
( sQ237_spl
| ~ relation(identity_relation(sK9_skl)) ),
inference(component_clause,[status(thm)],[f3744]) ).
fof(f3747,definition,
( sQ238_spl
<=> empty(relation_dom(identity_relation(sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f3750,plain,
( sQ234_spl
| ~ sQ238_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f3743,f3744,f3747,f3634]) ).
fof(f3751,plain,
( sQ237_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3746,f69]) ).
fof(f3752,plain,
sQ237_spl,
inference(contradiction_clause,[status(thm)],[f3751]) ).
fof(f3762,definition,
! [X0] :
( sQ239_spl
<=> in(X0,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f3763,plain,
! [X0] :
( ~ sQ239_spl
| in(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f3762]) ).
fof(f3793,plain,
! [X0] :
( ~ sQ239_spl
| ~ in(sK10_skl,X0) ),
inference(resolution,[status(thm)],[f3763,f45]) ).
fof(f3842,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ99_spl
| apply(sK9_skl,X0) = X0
| apply(sK9_skl,X0) = sK4_skl ),
inference(resolution,[status(thm)],[f1197,f149]) ).
fof(f3843,plain,
! [X0] :
( ~ sQ99_spl
| X0 = apply(identity_relation(sK10_skl),X0)
| apply(sK9_skl,X0) = sK4_skl ),
inference(resolution,[status(thm)],[f1197,f1861]) ).
fof(f3844,plain,
! [X0] :
( ~ sQ99_spl
| ~ in(sK10_skl,X0)
| apply(sK9_skl,X0) = sK4_skl ),
inference(resolution,[status(thm)],[f1197,f45]) ).
fof(f3851,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ7_spl
| in(ordered_pair(sK11_skl,sK11_skl),sK9_skl)
| ~ in(sK11_skl,sK10_skl) ),
inference(paramodulation,[status(thm)],[f178,f189]) ).
fof(f3854,definition,
( sQ242_spl
<=> in(ordered_pair(sK11_skl,sK11_skl),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3855,plain,
( ~ sQ242_spl
| in(ordered_pair(sK11_skl,sK11_skl),sK9_skl) ),
inference(component_clause,[status(thm)],[f3854]) ).
fof(f3857,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| sQ242_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3851,f152,f3854,f188,f148]) ).
fof(f3858,definition,
( sQ243_spl
<=> in(sK9_skl,ordered_pair(sK11_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f3861,definition,
( sQ244_spl
<=> in(sK11_skl,relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f3863,plain,
( sQ244_spl
| ~ in(sK11_skl,relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f3861]) ).
fof(f3866,plain,
( sQ244_spl
| ~ sQ1_spl
| ~ in(sK11_skl,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f3863]) ).
fof(f3869,plain,
! [X0] :
( sQ3_spl
| ~ sQ100_spl
| ~ in(ordered_pair(sK11_skl,X0),sK9_skl) ),
inference(resolution,[status(thm)],[f1204,f154]) ).
fof(f3904,definition,
( sQ245_spl
<=> empty(relation_dom(relation_dom(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3906,plain,
( sQ245_spl
| ~ empty(relation_dom(relation_dom(sK4_skl))) ),
inference(component_clause,[status(thm)],[f3904]) ).
fof(f3915,plain,
( sQ245_spl
| ~ empty(relation_dom(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1163,f3906]) ).
fof(f3916,plain,
( sQ245_spl
| ~ empty(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f3915]) ).
fof(f3917,plain,
( sQ245_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3916,f98]) ).
fof(f3918,plain,
sQ245_spl,
inference(contradiction_clause,[status(thm)],[f3917]) ).
fof(f3925,definition,
( sQ247_spl
<=> sK10_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f3926,plain,
( ~ sQ247_spl
| sK10_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f3925]) ).
fof(f3927,plain,
( sQ247_spl
| sK10_skl != sK4_skl ),
inference(component_clause,[status(thm)],[f3925]) ).
fof(f3942,plain,
( sQ54_spl
| ~ sQ247_spl
| sK4_skl != identity_relation(sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f3926,f761]) ).
fof(f4109,definition,
( sQ249_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK4_skl),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f4110,plain,
( ~ sQ249_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK4_skl),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f4109]) ).
fof(f4113,definition,
( sQ250_spl
<=> in(ordered_pair(sK4_skl,sK0_skl(sK4_skl,sK4_skl)),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f4114,plain,
( ~ sQ250_spl
| in(ordered_pair(sK4_skl,sK0_skl(sK4_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f4113]) ).
fof(f4117,definition,
( sQ251_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(identity_relation(sK4_skl),sK4_skl)),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f4118,plain,
( ~ sQ251_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(identity_relation(sK4_skl),sK4_skl)),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f4117]) ).
fof(f4121,definition,
( sQ252_spl
<=> in(ordered_pair(sK4_skl,apply(identity_relation(sK4_skl),sK0_skl(sK4_skl,sK4_skl))),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f4122,plain,
( ~ sQ252_spl
| in(ordered_pair(sK4_skl,apply(identity_relation(sK4_skl),sK0_skl(sK4_skl,sK4_skl))),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f4121]) ).
fof(f4130,definition,
( sQ254_spl
<=> in(sK0_skl(sK4_skl,sK4_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f4131,plain,
( ~ sQ254_spl
| in(sK0_skl(sK4_skl,sK4_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f4130]) ).
fof(f4143,definition,
( sQ257_spl
<=> in(ordered_pair(sK4_skl,sK1_skl(sK4_skl,sK4_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f4144,plain,
( ~ sQ257_spl
| in(ordered_pair(sK4_skl,sK1_skl(sK4_skl,sK4_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f4143]) ).
fof(f4148,plain,
( ~ sQ254_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4131,f1274]) ).
fof(f4149,plain,
~ sQ254_spl,
inference(contradiction_clause,[status(thm)],[f4148]) ).
fof(f4150,plain,
( ~ sQ257_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4144,f1274]) ).
fof(f4151,plain,
~ sQ257_spl,
inference(contradiction_clause,[status(thm)],[f4150]) ).
fof(f4153,plain,
( ~ sQ252_spl
| in(ordered_pair(sK4_skl,apply(sK4_skl,sK0_skl(sK4_skl,sK4_skl))),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f4122]) ).
fof(f4154,plain,
( ~ sQ252_spl
| ~ sQ26_spl
| in(ordered_pair(sK4_skl,sK4_skl),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f2956,f4153]) ).
fof(f4155,plain,
( ~ sQ252_spl
| ~ sQ26_spl
| in(ordered_pair(sK4_skl,sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f4154]) ).
fof(f4156,plain,
( ~ sQ252_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4155,f1274]) ).
fof(f4157,plain,
( ~ sQ252_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4156]) ).
fof(f4158,plain,
( ~ sQ251_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),apply(sK4_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f4118]) ).
fof(f4159,plain,
( ~ sQ251_spl
| ~ sQ26_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK4_skl),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f2956,f4158]) ).
fof(f4160,plain,
( ~ sQ251_spl
| ~ sQ26_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f4159]) ).
fof(f4161,plain,
( ~ sQ251_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4160,f1274]) ).
fof(f4162,plain,
( ~ sQ251_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4161]) ).
fof(f4163,plain,
( ~ sQ250_spl
| in(ordered_pair(sK4_skl,sK0_skl(sK4_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f4114]) ).
fof(f4164,plain,
( ~ sQ250_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4163,f1274]) ).
fof(f4165,plain,
~ sQ250_spl,
inference(contradiction_clause,[status(thm)],[f4164]) ).
fof(f4166,plain,
( ~ sQ249_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f4110]) ).
fof(f4167,plain,
( ~ sQ249_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4166,f1274]) ).
fof(f4168,plain,
~ sQ249_spl,
inference(contradiction_clause,[status(thm)],[f4167]) ).
fof(f4562,plain,
( ~ sQ63_spl
| ~ sQ7_spl
| in(ordered_pair(sK2_skl(sK10_skl),sK2_skl(sK10_skl)),sK9_skl)
| ~ in(sK2_skl(sK10_skl),sK10_skl) ),
inference(paramodulation,[status(thm)],[f845,f189]) ).
fof(f4563,plain,
( ~ sQ63_spl
| ~ in(sK2_skl(sK10_skl),relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ in(sK9_skl,ordered_pair(sK2_skl(sK10_skl),sK2_skl(sK10_skl))) ),
inference(paramodulation,[status(thm)],[f845,f1223]) ).
fof(f4564,plain,
( ~ sQ63_spl
| in(ordered_pair(sK2_skl(sK10_skl),sK2_skl(sK10_skl)),sK9_skl)
| ~ in(sK2_skl(sK10_skl),relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f845,f163]) ).
fof(f4565,definition,
( sQ260_spl
<=> in(sK2_skl(sK10_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f4567,plain,
( sQ260_spl
| ~ in(sK2_skl(sK10_skl),sK10_skl) ),
inference(component_clause,[status(thm)],[f4565]) ).
fof(f4568,definition,
( sQ261_spl
<=> in(ordered_pair(sK2_skl(sK10_skl),sK2_skl(sK10_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f4571,plain,
( ~ sQ63_spl
| ~ sQ7_spl
| sQ261_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f4562,f4565,f4568,f188,f844]) ).
fof(f4572,definition,
( sQ262_spl
<=> in(sK9_skl,ordered_pair(sK2_skl(sK10_skl),sK2_skl(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f4575,definition,
( sQ263_spl
<=> in(sK2_skl(sK10_skl),relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f4577,plain,
( sQ263_spl
| ~ in(sK2_skl(sK10_skl),relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f4575]) ).
fof(f4578,plain,
( ~ sQ63_spl
| ~ sQ263_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ262_spl ),
inference(split_clause,[status(thm)],[f4563,f4572,f182,f185,f4575,f844]) ).
fof(f4579,plain,
( ~ sQ63_spl
| sQ261_spl
| ~ sQ263_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4564,f182,f185,f4575,f4568,f844]) ).
fof(f4580,plain,
( sQ263_spl
| ~ sQ1_spl
| ~ in(sK2_skl(sK10_skl),sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f4577]) ).
fof(f4581,plain,
( ~ sQ57_spl
| ~ sQ7_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),sK9_skl)
| ~ in(sK0_skl(sK10_skl,sK4_skl),sK10_skl) ),
inference(paramodulation,[status(thm)],[f777,f189]) ).
fof(f4582,plain,
( ~ sQ57_spl
| ~ in(sK0_skl(sK10_skl,sK4_skl),relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ in(sK9_skl,ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl))) ),
inference(paramodulation,[status(thm)],[f777,f1223]) ).
fof(f4583,plain,
( ~ sQ57_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),sK9_skl)
| ~ in(sK0_skl(sK10_skl,sK4_skl),relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f777,f163]) ).
fof(f4584,definition,
( sQ264_spl
<=> in(sK0_skl(sK10_skl,sK4_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f4587,plain,
( ~ sQ57_spl
| ~ sQ7_spl
| sQ199_spl
| ~ sQ264_spl ),
inference(split_clause,[status(thm)],[f4581,f4584,f2772,f188,f776]) ).
fof(f4588,definition,
( sQ265_spl
<=> in(sK9_skl,ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f4591,definition,
( sQ266_spl
<=> in(sK0_skl(sK10_skl,sK4_skl),relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f4594,plain,
( ~ sQ57_spl
| ~ sQ266_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ265_spl ),
inference(split_clause,[status(thm)],[f4582,f4588,f182,f185,f4591,f776]) ).
fof(f4595,plain,
( ~ sQ57_spl
| sQ199_spl
| ~ sQ266_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4583,f182,f185,f4591,f2772,f776]) ).
fof(f4768,definition,
( sQ276_spl
<=> in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK8_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK8_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f4769,plain,
( ~ sQ276_spl
| in(ordered_pair(sK0_skl(relation_dom(sK4_skl),sK8_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK8_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f4768]) ).
fof(f4804,plain,
( ~ sQ276_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK8_skl),apply(sK4_skl,sK0_skl(relation_dom(sK4_skl),sK8_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f4769]) ).
fof(f4805,plain,
( ~ sQ276_spl
| ~ sQ26_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK8_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f4804]) ).
fof(f4806,plain,
( ~ sQ276_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4805,f1274]) ).
fof(f4807,plain,
( ~ sQ276_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4806]) ).
fof(f4855,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| sK0_skl(sK10_skl,sK9_skl) != sK1_skl(sK10_skl,sK9_skl)
| ~ in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) = sK4_skl ),
inference(resolution,[status(thm)],[f1258,f118]) ).
fof(f4863,definition,
( sQ283_spl
<=> apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl)) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f4864,plain,
( ~ sQ283_spl
| apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl)) = sK4_skl ),
inference(component_clause,[status(thm)],[f4863]) ).
fof(f4870,definition,
( sQ285_spl
<=> apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f4873,definition,
( sQ286_spl
<=> sK0_skl(sK10_skl,sK9_skl) = sK1_skl(sK10_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f4876,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ286_spl
| ~ sQ18_spl
| sQ0_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f4855,f4870,f141,f293,f4873,f144,f199]) ).
fof(f4911,plain,
( ~ sQ283_spl
| ~ sQ57_spl
| sK0_skl(sK10_skl,sK4_skl) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f777,f4864]) ).
fof(f4915,plain,
( ~ sQ70_spl
| ~ sQ26_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK3_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f904]) ).
fof(f4916,plain,
( ~ sQ70_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4915,f1274]) ).
fof(f4917,plain,
( ~ sQ70_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4916]) ).
fof(f4918,plain,
( ~ sQ69_spl
| ~ sQ26_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f900]) ).
fof(f4919,plain,
( ~ sQ69_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4918,f1274]) ).
fof(f4920,plain,
( ~ sQ69_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4919]) ).
fof(f4921,plain,
( ~ sQ68_spl
| ~ sQ26_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK8_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f896]) ).
fof(f4922,plain,
( ~ sQ68_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4921,f1274]) ).
fof(f4923,plain,
( ~ sQ68_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4922]) ).
fof(f4924,plain,
( ~ sQ67_spl
| ~ sQ26_spl
| in(ordered_pair(sK2_skl(sK10_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f892]) ).
fof(f4925,plain,
( ~ sQ67_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4924,f1274]) ).
fof(f4926,plain,
( ~ sQ67_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4925]) ).
fof(f4928,plain,
( ~ sQ64_spl
| ~ sQ26_spl
| sK4_skl = sK2_skl(sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f856]) ).
fof(f4929,plain,
( ~ sQ56_spl
| ~ sQ26_spl
| sK4_skl = sK0_skl(sK10_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f766]) ).
fof(f4938,plain,
( ~ sQ52_spl
| in(ordered_pair(sK2_skl(relation_dom(sK4_skl)),apply(sK4_skl,sK2_skl(relation_dom(sK4_skl)))),sK4_skl)
| ~ relation(sK4_skl)
| empty(relation_dom(sK4_skl)) ),
inference(resolution,[status(thm)],[f839,f741]) ).
fof(f4939,plain,
( in(ordered_pair(sK2_skl(relation_dom(sK9_skl)),apply(sK9_skl,sK2_skl(relation_dom(sK9_skl)))),sK9_skl)
| ~ relation(sK9_skl)
| empty(relation_dom(sK9_skl)) ),
inference(resolution,[status(thm)],[f839,f119]) ).
fof(f4943,definition,
( sQ297_spl
<=> empty(relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f4946,definition,
( sQ298_spl
<=> in(ordered_pair(sK2_skl(relation_dom(sK4_skl)),apply(sK4_skl,sK2_skl(relation_dom(sK4_skl)))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f4947,plain,
( ~ sQ298_spl
| in(ordered_pair(sK2_skl(relation_dom(sK4_skl)),apply(sK4_skl,sK2_skl(relation_dom(sK4_skl)))),sK4_skl) ),
inference(component_clause,[status(thm)],[f4946]) ).
fof(f4949,plain,
( ~ sQ52_spl
| sQ298_spl
| ~ sQ51_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f4938,f4943,f737,f4946,f740]) ).
fof(f4950,definition,
( sQ299_spl
<=> in(ordered_pair(sK2_skl(relation_dom(sK9_skl)),apply(sK9_skl,sK2_skl(relation_dom(sK9_skl)))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f4953,plain,
( sQ299_spl
| ~ sQ5_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f4939,f274,f182,f4950]) ).
fof(f4966,plain,
( ~ sQ298_spl
| in(ordered_pair(sK2_skl(sK4_skl),apply(sK4_skl,sK2_skl(relation_dom(sK4_skl)))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f4947]) ).
fof(f4967,plain,
( ~ sQ298_spl
| ~ sQ26_spl
| in(ordered_pair(sK2_skl(sK4_skl),sK4_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f4966]) ).
fof(f4968,plain,
( ~ sQ298_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4967,f1274]) ).
fof(f4969,plain,
( ~ sQ298_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f4968]) ).
fof(f5161,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ1_spl
| apply(sK3_skl,sK10_skl) = sK4_skl
| apply(sK9_skl,relation_dom(sK3_skl)) = sK4_skl ),
inference(resolution,[status(thm)],[f1260,f1086]) ).
fof(f5165,definition,
( sQ312_spl
<=> apply(sK9_skl,sK10_skl) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f5166,plain,
( ~ sQ312_spl
| apply(sK9_skl,sK10_skl) = sK4_skl ),
inference(component_clause,[status(thm)],[f5165]) ).
fof(f5173,definition,
( sQ314_spl
<=> apply(sK9_skl,relation_dom(sK3_skl)) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f5176,definition,
( sQ315_spl
<=> apply(sK3_skl,sK10_skl) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f5177,plain,
( ~ sQ315_spl
| apply(sK3_skl,sK10_skl) = sK4_skl ),
inference(component_clause,[status(thm)],[f5176]) ).
fof(f5179,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ1_spl
| sQ315_spl
| sQ314_spl ),
inference(split_clause,[status(thm)],[f5161,f5173,f5176,f144,f199,f255]) ).
fof(f5357,plain,
( ~ sQ64_spl
| ~ sQ26_spl
| in(sK4_skl,sK10_skl)
| empty(sK10_skl) ),
inference(paramodulation,[status(thm)],[f4928,f311]) ).
fof(f5380,plain,
( ~ sQ64_spl
| ~ sQ26_spl
| sQ216_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f5357,f238,f3102,f400,f855]) ).
fof(f5381,plain,
( sQ64_spl
| ~ sQ26_spl
| sK4_skl != sK2_skl(sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f857]) ).
fof(f5395,plain,
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| relation_rng(sK4_skl) = sK4_skl ),
inference(paramodulation,[status(thm)],[f1163,f951]) ).
fof(f5397,definition,
( sQ332_spl
<=> relation_rng(sK9_skl) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f5398,plain,
( ~ sQ332_spl
| relation_rng(sK9_skl) = sK4_skl ),
inference(component_clause,[status(thm)],[f5397]) ).
fof(f5399,plain,
( sQ332_spl
| relation_rng(sK9_skl) != sK4_skl ),
inference(component_clause,[status(thm)],[f5397]) ).
fof(f5401,definition,
( sQ333_spl
<=> relation_rng(sK4_skl) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f5404,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f5395,f5401,f737,f732]) ).
fof(f5419,plain,
( ~ sQ57_spl
| ~ sQ7_spl
| ~ in(sK9_skl,ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)))
| ~ in(sK0_skl(sK10_skl,sK4_skl),sK10_skl) ),
inference(paramodulation,[status(thm)],[f777,f1277]) ).
fof(f5420,plain,
( ~ sQ57_spl
| ~ sQ7_spl
| ~ sQ265_spl
| ~ sQ264_spl ),
inference(split_clause,[status(thm)],[f5419,f4584,f4588,f188,f776]) ).
fof(f5460,plain,
! [X0] :
( ~ sQ100_spl
| ~ sQ13_spl
| ~ in(ordered_pair(relation_dom(sK3_skl),X0),sK9_skl)
| apply(sK3_skl,sK10_skl) = sK4_skl ),
inference(resolution,[status(thm)],[f1093,f1204]) ).
fof(f5461,plain,
( ~ sQ13_spl
| apply(sK3_skl,relation_dom(sK3_skl)) = sK4_skl
| apply(sK3_skl,relation_dom(sK3_skl)) = sK4_skl ),
inference(resolution,[status(thm)],[f1093,f1086]) ).
fof(f5466,definition,
! [X0] :
( sQ338_spl
<=> ~ in(ordered_pair(relation_dom(sK3_skl),X0),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f5469,plain,
( ~ sQ100_spl
| ~ sQ13_spl
| sQ338_spl
| sQ315_spl ),
inference(split_clause,[status(thm)],[f5460,f5176,f5466,f255,f1203]) ).
fof(f5470,definition,
( sQ339_spl
<=> apply(sK3_skl,relation_dom(sK3_skl)) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f5473,plain,
( ~ sQ13_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f5461,f5470,f255]) ).
fof(f5515,plain,
! [X0] :
( in(sK0_skl(X0,sK4_skl),X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ empty(sK4_skl) ),
inference(paramodulation,[status(thm)],[f1144,f1285]) ).
fof(f5517,definition,
! [X0] :
( sQ346_spl
<=> ( in(sK0_skl(X0,sK4_skl),X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f5520,plain,
( sQ346_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f5515,f732,f5517]) ).
fof(f5545,plain,
( ~ sQ117_spl
| sK10_skl = identity_relation(sK4_skl) ),
inference(resolution,[status(thm)],[f1389,f1274]) ).
fof(f5553,plain,
( ~ sQ117_spl
| sK10_skl = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f1144,f5545]) ).
fof(f5554,plain,
( ~ sQ117_spl
| sQ247_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5553,f3927]) ).
fof(f5555,plain,
( ~ sQ117_spl
| sQ247_spl ),
inference(contradiction_clause,[status(thm)],[f5554]) ).
fof(f5561,plain,
( ~ sQ332_spl
| ~ empty(sK4_skl)
| ~ relation(sK9_skl)
| empty(sK9_skl) ),
inference(paramodulation,[status(thm)],[f5398,f87]) ).
fof(f5568,plain,
( ~ sQ332_spl
| ~ sQ50_spl
| ~ sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f5561,f235,f182,f732,f5397]) ).
fof(f5618,definition,
( sQ354_spl
<=> in(ordered_pair(sK2_skl(relation_dom(sK3_skl)),sK2_skl(relation_dom(sK3_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f5619,plain,
( ~ sQ354_spl
| in(ordered_pair(sK2_skl(relation_dom(sK3_skl)),sK2_skl(relation_dom(sK3_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f5618]) ).
fof(f5622,definition,
( sQ355_spl
<=> in(ordered_pair(sK2_skl(relation_dom(sK3_skl)),apply(identity_relation(relation_dom(sK3_skl)),sK2_skl(relation_dom(sK3_skl)))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f5623,plain,
( ~ sQ355_spl
| in(ordered_pair(sK2_skl(relation_dom(sK3_skl)),apply(identity_relation(relation_dom(sK3_skl)),sK2_skl(relation_dom(sK3_skl)))),sK4_skl) ),
inference(component_clause,[status(thm)],[f5622]) ).
fof(f5703,plain,
( ~ sQ355_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5623,f1274]) ).
fof(f5704,plain,
~ sQ355_spl,
inference(contradiction_clause,[status(thm)],[f5703]) ).
fof(f5705,plain,
( ~ sQ354_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5619,f1274]) ).
fof(f5706,plain,
~ sQ354_spl,
inference(contradiction_clause,[status(thm)],[f5705]) ).
fof(f5931,plain,
! [X0] :
( ~ sQ113_spl
| sK4_skl = identity_relation(X0)
| in(sK0_skl(X0,sK4_skl),X0)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl)
| ~ in(sK4_skl,ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl))) ),
inference(paramodulation,[status(thm)],[f1368,f1221]) ).
fof(f5932,plain,
! [X0] :
( ~ sQ113_spl
| sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl)
| ~ in(sK4_skl,ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl))) ),
inference(paramodulation,[status(thm)],[f1368,f1220]) ).
fof(f5933,plain,
! [X0] :
( ~ sQ113_spl
| sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f1368,f60]) ).
fof(f5934,plain,
! [X0] :
( ~ sQ113_spl
| sK4_skl = identity_relation(X0)
| in(sK0_skl(X0,sK4_skl),X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f1368,f59]) ).
fof(f5935,definition,
! [X0] :
( sQ374_spl
<=> ( sK4_skl = identity_relation(X0)
| in(sK0_skl(X0,sK4_skl),X0)
| sK4_skl = identity_relation(X0)
| ~ in(sK4_skl,ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f5938,plain,
( ~ sQ113_spl
| ~ sQ51_spl
| sQ374_spl ),
inference(split_clause,[status(thm)],[f5931,f5935,f737,f1367]) ).
fof(f5939,definition,
! [X0] :
( sQ375_spl
<=> ( sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ in(sK4_skl,ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f5942,plain,
( ~ sQ113_spl
| ~ sQ51_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f5932,f5939,f737,f1367]) ).
fof(f5943,definition,
! [X0] :
( sQ376_spl
<=> ( sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f5946,plain,
( ~ sQ113_spl
| sQ376_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f5933,f737,f5943,f1367]) ).
fof(f5947,definition,
! [X0] :
( sQ377_spl
<=> ( sK4_skl = identity_relation(X0)
| in(sK0_skl(X0,sK4_skl),X0)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f5950,plain,
( ~ sQ113_spl
| sQ377_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f5934,f737,f5947,f1367]) ).
fof(f5968,definition,
! [X0,X1,X2] :
( sQ378_spl
<=> ( in(ordered_pair(X0,X1),identity_relation(X2))
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f5969,plain,
! [X0,X1,X2] :
( ~ sQ378_spl
| in(ordered_pair(X0,X1),identity_relation(X2))
| X0 = X1 ),
inference(component_clause,[status(thm)],[f5968]) ).
fof(f5976,plain,
! [X0,X1] :
( ~ sQ378_spl
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f5969,f172]) ).
fof(f5979,plain,
( ~ sQ100_spl
| sK9_skl = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),apply(identity_relation(sK10_skl),sK0_skl(sK10_skl,sK9_skl))),identity_relation(sK10_skl))
| sK0_skl(sK10_skl,sK9_skl) != sK1_skl(sK10_skl,sK9_skl)
| ~ in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f1544,f357]) ).
fof(f5986,plain,
! [X0] :
( ~ sQ100_spl
| ~ in(sK0_skl(sK10_skl,X0),relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| sK0_skl(sK10_skl,X0) != sK1_skl(sK10_skl,X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1544,f163]) ).
fof(f5988,definition,
( sQ379_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),apply(identity_relation(sK10_skl),sK0_skl(sK10_skl,sK9_skl))),identity_relation(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f5991,plain,
( ~ sQ100_spl
| sQ379_spl
| ~ sQ286_spl
| ~ sQ18_spl
| sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f5979,f182,f141,f293,f4873,f5988,f1203]) ).
fof(f5997,definition,
( sQ381_spl
<=> in(sK0_skl(sK10_skl,sK9_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f6003,definition,
! [X0] :
( sQ382_spl
<=> ( ~ in(sK0_skl(sK10_skl,X0),relation_dom(sK9_skl))
| sK0_skl(sK10_skl,X0) != sK1_skl(sK10_skl,X0)
| ~ in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f6006,plain,
( ~ sQ100_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f5986,f6003,f182,f185,f1203]) ).
fof(f6008,plain,
( sQ332_spl
| ~ sQ378_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5399,f5976]) ).
fof(f6021,plain,
( sQ332_spl
| ~ sQ378_spl ),
inference(contradiction_clause,[status(thm)],[f6008]) ).
fof(f6050,plain,
! [X0] :
( ~ sQ2_spl
| apply(sK9_skl,sK0_skl(sK10_skl,X0)) = sK0_skl(sK10_skl,X0)
| in(ordered_pair(sK0_skl(sK10_skl,X0),sK1_skl(sK10_skl,X0)),X0)
| X0 = identity_relation(sK10_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f59,f149]) ).
fof(f6051,plain,
! [X0] :
( in(ordered_pair(sK0_skl(sK4_skl,X0),sK1_skl(sK4_skl,X0)),X0)
| X0 = identity_relation(sK4_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f59,f1274]) ).
fof(f6275,definition,
( sQ383_spl
<=> sK1_skl(sK10_skl,sK9_skl) = apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f6276,plain,
( ~ sQ383_spl
| sK1_skl(sK10_skl,sK9_skl) = apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) ),
inference(component_clause,[status(thm)],[f6275]) ).
fof(f6277,plain,
( sQ383_spl
| sK1_skl(sK10_skl,sK9_skl) != apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) ),
inference(component_clause,[status(thm)],[f6275]) ).
fof(f6377,plain,
( sQ263_spl
| ~ sQ1_spl
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f4580,f311]) ).
fof(f6381,plain,
( sQ263_spl
| ~ sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f6377,f238,f144,f4575]) ).
fof(f6386,plain,
! [X0] :
( ~ sQ100_spl
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ in(sK10_skl,X0) ),
inference(resolution,[status(thm)],[f1546,f163]) ).
fof(f6392,definition,
! [X0] :
( sQ386_spl
<=> ( ~ in(X0,relation_dom(sK9_skl))
| ~ in(sK10_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f6395,plain,
( ~ sQ100_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f6386,f6392,f182,f185,f1203]) ).
fof(f6400,plain,
( sQ260_spl
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f4567,f311]) ).
fof(f6404,plain,
( sQ260_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f6400,f238,f4565]) ).
fof(f6408,plain,
! [X0,X1] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| ~ empty(relation_dom(X1))
| ~ relation(X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f375,f85]) ).
fof(f6488,definition,
! [X0] :
( sQ389_spl
<=> ~ in(X0,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f6489,plain,
! [X0] :
( ~ sQ389_spl
| ~ in(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f6488]) ).
fof(f6506,plain,
( ~ sQ389_spl
| sK4_skl = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f6489,f1425]) ).
fof(f6513,plain,
( ~ sQ389_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f6506,f759,f6488]) ).
fof(f6568,plain,
( ~ sQ283_spl
| ~ sQ57_spl
| in(sK4_skl,sK10_skl)
| sK4_skl = identity_relation(sK10_skl) ),
inference(paramodulation,[status(thm)],[f4911,f1425]) ).
fof(f6571,plain,
( ~ sQ283_spl
| ~ sQ57_spl
| in(sK0_skl(sK10_skl,sK4_skl),sK10_skl)
| sK4_skl = identity_relation(sK10_skl)
| ~ relation(sK4_skl)
| ~ in(sK4_skl,ordered_pair(sK4_skl,sK1_skl(sK10_skl,sK4_skl))) ),
inference(paramodulation,[status(thm)],[f4911,f1221]) ).
fof(f6578,plain,
( ~ sQ283_spl
| ~ sQ57_spl
| sQ216_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f6568,f759,f3102,f776,f4863]) ).
fof(f6584,definition,
( sQ401_spl
<=> in(sK4_skl,ordered_pair(sK4_skl,sK1_skl(sK10_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f6587,plain,
( ~ sQ283_spl
| ~ sQ57_spl
| sQ264_spl
| sQ54_spl
| ~ sQ51_spl
| ~ sQ401_spl ),
inference(split_clause,[status(thm)],[f6571,f6584,f737,f759,f4584,f776,f4863]) ).
fof(f6598,plain,
( ~ sQ2_spl
| ~ sQ216_spl
| apply(sK9_skl,sK4_skl) = sK4_skl ),
inference(resolution,[status(thm)],[f3103,f149]) ).
fof(f6698,definition,
( sQ406_spl
<=> in(sK0_skl(sK4_skl,sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f6699,plain,
( ~ sQ406_spl
| in(sK0_skl(sK4_skl,sK3_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f6698]) ).
fof(f6713,plain,
( ~ sQ406_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6699,f1274]) ).
fof(f6714,plain,
~ sQ406_spl,
inference(contradiction_clause,[status(thm)],[f6713]) ).
fof(f6725,definition,
( sQ410_spl
<=> in(sK0_skl(sK4_skl,sK8_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f6726,plain,
( ~ sQ410_spl
| in(sK0_skl(sK4_skl,sK8_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f6725]) ).
fof(f6740,plain,
( ~ sQ410_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6726,f1274]) ).
fof(f6741,plain,
~ sQ410_spl,
inference(contradiction_clause,[status(thm)],[f6740]) ).
fof(f6771,plain,
( ~ sQ56_spl
| ~ sQ26_spl
| in(sK4_skl,sK10_skl)
| sK4_skl = identity_relation(sK10_skl) ),
inference(paramodulation,[status(thm)],[f4929,f1425]) ).
fof(f6774,plain,
( ~ sQ56_spl
| ~ sQ26_spl
| in(sK0_skl(sK10_skl,sK4_skl),sK10_skl)
| sK4_skl = identity_relation(sK10_skl)
| ~ relation(sK4_skl)
| ~ in(sK4_skl,ordered_pair(sK4_skl,sK1_skl(sK10_skl,sK4_skl))) ),
inference(paramodulation,[status(thm)],[f4929,f1221]) ).
fof(f6778,plain,
( ~ sQ56_spl
| ~ sQ26_spl
| sQ216_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f6771,f759,f3102,f400,f765]) ).
fof(f6781,plain,
( ~ sQ56_spl
| ~ sQ26_spl
| sQ264_spl
| sQ54_spl
| ~ sQ51_spl
| ~ sQ401_spl ),
inference(split_clause,[status(thm)],[f6774,f6584,f737,f759,f4584,f400,f765]) ).
fof(f6784,plain,
( sQ56_spl
| ~ sQ26_spl
| sK4_skl != sK0_skl(sK10_skl,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f2956,f767]) ).
fof(f6786,plain,
( ~ sQ130_spl
| identity_relation(sK10_skl) = identity_relation(sK4_skl)
| apply(sK9_skl,sK0_skl(sK4_skl,identity_relation(sK10_skl))) = sK0_skl(sK4_skl,identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f1572,f1274]) ).
fof(f6791,definition,
( sQ416_spl
<=> apply(sK9_skl,sK0_skl(sK4_skl,identity_relation(sK10_skl))) = sK0_skl(sK4_skl,identity_relation(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f6794,plain,
( ~ sQ130_spl
| sQ178_spl
| sQ416_spl ),
inference(split_clause,[status(thm)],[f6786,f6791,f2499,f1571]) ).
fof(f6796,plain,
( ~ sQ133_spl
| ~ sQ1_spl
| in(sK0_skl(sK10_skl,sK9_skl),sK10_skl)
| sK9_skl = identity_relation(sK10_skl)
| sK0_skl(sK10_skl,sK9_skl) != sK1_skl(sK10_skl,sK9_skl)
| ~ in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f1609,f789]) ).
fof(f6801,plain,
( ~ sQ133_spl
| ~ sQ1_spl
| sQ381_spl
| ~ sQ286_spl
| ~ sQ18_spl
| sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f6796,f182,f141,f293,f4873,f5997,f144,f1589]) ).
fof(f6811,definition,
! [X0] :
( sQ417_spl
<=> ~ in(ordered_pair(sK4_skl,X0),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f6812,plain,
! [X0] :
( ~ sQ417_spl
| ~ in(ordered_pair(sK4_skl,X0),sK9_skl) ),
inference(component_clause,[status(thm)],[f6811]) ).
fof(f6949,plain,
! [X0] :
( ~ sQ134_spl
| ~ in(sK0_skl(relation_dom(sK3_skl),X0),relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| sK0_skl(relation_dom(sK3_skl),X0) != sK1_skl(relation_dom(sK3_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),sK1_skl(relation_dom(sK3_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK3_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1594,f163]) ).
fof(f6955,definition,
! [X0] :
( sQ445_spl
<=> ( ~ in(sK0_skl(relation_dom(sK3_skl),X0),relation_dom(sK3_skl))
| sK0_skl(relation_dom(sK3_skl),X0) != sK1_skl(relation_dom(sK3_skl),X0)
| ~ in(ordered_pair(sK0_skl(relation_dom(sK3_skl),X0),sK1_skl(relation_dom(sK3_skl),X0)),X0)
| X0 = identity_relation(relation_dom(sK3_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f6958,plain,
( ~ sQ134_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sQ445_spl ),
inference(split_clause,[status(thm)],[f6949,f6955,f252,f641,f1593]) ).
fof(f6959,plain,
( ~ sQ315_spl
| ~ in(sK10_skl,relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ in(sK3_skl,ordered_pair(sK10_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f5177,f1223]) ).
fof(f6960,plain,
( ~ sQ315_spl
| in(ordered_pair(sK10_skl,sK4_skl),sK3_skl)
| ~ in(sK10_skl,relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(paramodulation,[status(thm)],[f5177,f163]) ).
fof(f6961,definition,
( sQ446_spl
<=> in(sK3_skl,ordered_pair(sK10_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f6964,definition,
( sQ447_spl
<=> in(sK10_skl,relation_dom(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f6966,plain,
( sQ447_spl
| ~ in(sK10_skl,relation_dom(sK3_skl)) ),
inference(component_clause,[status(thm)],[f6964]) ).
fof(f6967,plain,
( ~ sQ315_spl
| ~ sQ447_spl
| ~ sQ43_spl
| ~ sQ12_spl
| ~ sQ446_spl ),
inference(split_clause,[status(thm)],[f6959,f6961,f252,f641,f6964,f5176]) ).
fof(f6968,definition,
( sQ448_spl
<=> in(ordered_pair(sK10_skl,sK4_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f6971,plain,
( ~ sQ315_spl
| sQ448_spl
| ~ sQ447_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f6960,f252,f641,f6964,f6968,f5176]) ).
fof(f7000,plain,
( ~ sQ102_spl
| sK9_skl = identity_relation(sK4_skl)
| sK1_skl(sK4_skl,sK9_skl) = apply(sK9_skl,sK0_skl(sK4_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f1694,f1274]) ).
fof(f7005,definition,
( sQ451_spl
<=> sK1_skl(sK4_skl,sK9_skl) = apply(sK9_skl,sK0_skl(sK4_skl,sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f7008,definition,
( sQ452_spl
<=> sK9_skl = identity_relation(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f7009,plain,
( ~ sQ452_spl
| sK9_skl = identity_relation(sK4_skl) ),
inference(component_clause,[status(thm)],[f7008]) ).
fof(f7011,plain,
( ~ sQ102_spl
| sQ452_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f7000,f7005,f7008,f1247]) ).
fof(f7012,plain,
( ~ sQ452_spl
| sK9_skl = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f1144,f7009]) ).
fof(f7013,plain,
( ~ sQ452_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7012,f771]) ).
fof(f7014,plain,
( ~ sQ452_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f7013]) ).
fof(f7017,plain,
! [X0,X1] :
( ~ sQ102_spl
| ~ in(ordered_pair(X1,X0),relation_dom(identity_relation(sK9_skl)))
| ~ function(identity_relation(sK9_skl))
| ~ relation(identity_relation(sK9_skl))
| X0 = apply(sK9_skl,X1) ),
inference(resolution,[status(thm)],[f1698,f163]) ).
fof(f7020,definition,
! [X0,X1] :
( sQ453_spl
<=> ( ~ in(ordered_pair(X1,X0),relation_dom(identity_relation(sK9_skl)))
| X0 = apply(sK9_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f7023,definition,
( sQ454_spl
<=> function(identity_relation(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f7025,plain,
( sQ454_spl
| ~ function(identity_relation(sK9_skl)) ),
inference(component_clause,[status(thm)],[f7023]) ).
fof(f7026,plain,
( ~ sQ102_spl
| ~ sQ454_spl
| ~ sQ237_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f7017,f7020,f3744,f7023,f1247]) ).
fof(f7028,plain,
( sQ454_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7025,f79]) ).
fof(f7029,plain,
sQ454_spl,
inference(contradiction_clause,[status(thm)],[f7028]) ).
fof(f7031,plain,
! [X0] :
( ~ sQ140_spl
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| ~ in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ in(sK9_skl,ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl))) ),
inference(paramodulation,[status(thm)],[f1700,f1223]) ).
fof(f7032,plain,
! [X0] :
( ~ sQ140_spl
| sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| ~ in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f1700,f163]) ).
fof(f7033,definition,
! [X0] :
( sQ455_spl
<=> ( sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| ~ in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl))
| ~ in(sK9_skl,ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f7036,plain,
( ~ sQ140_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f7031,f7033,f182,f185,f1699]) ).
fof(f7037,definition,
! [X0] :
( sQ456_spl
<=> ( sK0_skl(X0,sK9_skl) = sK1_skl(X0,sK9_skl)
| sK9_skl = identity_relation(X0)
| in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| ~ in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f7040,plain,
( ~ sQ140_spl
| sQ456_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7032,f182,f185,f7037,f1699]) ).
fof(f7086,plain,
! [X0,X1] :
( ~ sQ52_spl
| ~ in(ordered_pair(sK4_skl,X1),identity_relation(ordered_pair(X0,apply(sK4_skl,X0))))
| ~ in(X0,relation_dom(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f1742,f741]) ).
fof(f7087,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK9_skl,X1),identity_relation(ordered_pair(X0,apply(sK9_skl,X0))))
| ~ in(X0,relation_dom(sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f1742,f119]) ).
fof(f7088,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK3_skl,X1),identity_relation(ordered_pair(X0,apply(sK3_skl,X0))))
| ~ in(X0,relation_dom(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f1742,f96]) ).
fof(f7091,definition,
! [X0,X1] :
( sQ457_spl
<=> ( ~ in(ordered_pair(sK4_skl,X1),identity_relation(ordered_pair(X0,apply(sK4_skl,X0))))
| ~ in(X0,relation_dom(sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f7094,plain,
( ~ sQ52_spl
| sQ457_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f7086,f737,f7091,f740]) ).
fof(f7095,definition,
! [X0,X1] :
( sQ458_spl
<=> ( ~ in(ordered_pair(sK9_skl,X1),identity_relation(ordered_pair(X0,apply(sK9_skl,X0))))
| ~ in(X0,relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f7098,plain,
( sQ458_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f7087,f182,f7095]) ).
fof(f7099,definition,
! [X0,X1] :
( sQ459_spl
<=> ( ~ in(ordered_pair(sK3_skl,X1),identity_relation(ordered_pair(X0,apply(sK3_skl,X0))))
| ~ in(X0,relation_dom(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ459_spl])],[split_symbol_definition]) ).
fof(f7102,plain,
( sQ459_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7088,f252,f7099]) ).
fof(f7133,plain,
! [X0] :
( ~ sQ145_spl
| ~ in(X0,relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ in(relation_dom(sK3_skl),X0) ),
inference(resolution,[status(thm)],[f1768,f163]) ).
fof(f7139,definition,
! [X0] :
( sQ461_spl
<=> ( ~ in(X0,relation_dom(sK3_skl))
| ~ in(relation_dom(sK3_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f7142,plain,
( ~ sQ145_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f7133,f7139,f252,f641,f1767]) ).
fof(f7146,plain,
( sK9_skl = identity_relation(sK4_skl)
| ordered_pair(sK0_skl(sK4_skl,sK9_skl),sK1_skl(sK4_skl,sK9_skl)) = apply(identity_relation(sK9_skl),ordered_pair(sK0_skl(sK4_skl,sK9_skl),sK1_skl(sK4_skl,sK9_skl))) ),
inference(resolution,[status(thm)],[f1867,f1274]) ).
fof(f7154,definition,
( sQ463_spl
<=> ordered_pair(sK0_skl(sK4_skl,sK9_skl),sK1_skl(sK4_skl,sK9_skl)) = apply(identity_relation(sK9_skl),ordered_pair(sK0_skl(sK4_skl,sK9_skl),sK1_skl(sK4_skl,sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f7157,plain,
( sQ452_spl
| sQ463_spl ),
inference(split_clause,[status(thm)],[f7146,f7154,f7008]) ).
fof(f7253,plain,
( ~ sQ7_spl
| sK4_skl = identity_relation(sK10_skl)
| ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl))) = apply(identity_relation(sK9_skl),ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl)))) ),
inference(resolution,[status(thm)],[f1870,f1425]) ).
fof(f7257,plain,
( ~ sQ7_spl
| empty(sK10_skl)
| ordered_pair(sK2_skl(sK10_skl),apply(sK9_skl,sK2_skl(sK10_skl))) = apply(identity_relation(sK9_skl),ordered_pair(sK2_skl(sK10_skl),apply(sK9_skl,sK2_skl(sK10_skl)))) ),
inference(resolution,[status(thm)],[f1870,f311]) ).
fof(f7272,definition,
( sQ467_spl
<=> ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl))) = apply(identity_relation(sK9_skl),ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f7275,plain,
( ~ sQ7_spl
| sQ54_spl
| sQ467_spl ),
inference(split_clause,[status(thm)],[f7253,f7272,f759,f188]) ).
fof(f7276,definition,
( sQ468_spl
<=> ordered_pair(sK2_skl(sK10_skl),apply(sK9_skl,sK2_skl(sK10_skl))) = apply(identity_relation(sK9_skl),ordered_pair(sK2_skl(sK10_skl),apply(sK9_skl,sK2_skl(sK10_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f7279,plain,
( ~ sQ7_spl
| sQ10_spl
| sQ468_spl ),
inference(split_clause,[status(thm)],[f7257,f7276,f238,f188]) ).
fof(f7305,definition,
! [X0] :
( sQ472_spl
<=> ( X0 = apply(identity_relation(sK10_skl),X0)
| ~ in(X0,relation_dom(sK9_skl))
| ~ in(sK9_skl,ordered_pair(X0,sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f7309,definition,
! [X0] :
( sQ473_spl
<=> ( X0 = apply(identity_relation(sK10_skl),X0)
| in(ordered_pair(X0,sK4_skl),sK9_skl)
| ~ in(X0,relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f7369,plain,
( ~ sQ2_spl
| ~ sQ216_spl
| ~ sQ7_spl
| ~ in(sK9_skl,ordered_pair(sK4_skl,sK4_skl))
| ~ in(sK4_skl,sK10_skl) ),
inference(paramodulation,[status(thm)],[f6598,f1747]) ).
fof(f7370,plain,
( ~ sQ2_spl
| ~ sQ216_spl
| ~ sQ7_spl
| in(ordered_pair(sK4_skl,sK4_skl),sK9_skl)
| ~ in(sK4_skl,sK10_skl) ),
inference(paramodulation,[status(thm)],[f6598,f189]) ).
fof(f7378,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ218_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f7369,f3102,f3109,f188,f148]) ).
fof(f7379,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| sQ217_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f7370,f3102,f3105,f188,f148]) ).
fof(f7434,plain,
! [X0] :
( ~ sQ52_spl
| ~ in(X0,relation_dom(sK4_skl))
| ~ relation(sK4_skl)
| ordered_pair(X0,apply(sK4_skl,X0)) = apply(identity_relation(sK4_skl),ordered_pair(X0,apply(sK4_skl,X0))) ),
inference(resolution,[status(thm)],[f1872,f741]) ).
fof(f7435,plain,
! [X0] :
( ~ in(X0,relation_dom(sK9_skl))
| ~ relation(sK9_skl)
| ordered_pair(X0,apply(sK9_skl,X0)) = apply(identity_relation(sK9_skl),ordered_pair(X0,apply(sK9_skl,X0))) ),
inference(resolution,[status(thm)],[f1872,f119]) ).
fof(f7436,plain,
! [X0] :
( ~ in(X0,relation_dom(sK3_skl))
| ~ relation(sK3_skl)
| ordered_pair(X0,apply(sK3_skl,X0)) = apply(identity_relation(sK3_skl),ordered_pair(X0,apply(sK3_skl,X0))) ),
inference(resolution,[status(thm)],[f1872,f96]) ).
fof(f7439,definition,
! [X0] :
( sQ481_spl
<=> ( ~ in(X0,relation_dom(sK4_skl))
| ordered_pair(X0,apply(sK4_skl,X0)) = apply(identity_relation(sK4_skl),ordered_pair(X0,apply(sK4_skl,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f7442,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ481_spl ),
inference(split_clause,[status(thm)],[f7434,f7439,f737,f740]) ).
fof(f7443,definition,
! [X0] :
( sQ482_spl
<=> ( ~ in(X0,relation_dom(sK9_skl))
| ordered_pair(X0,apply(sK9_skl,X0)) = apply(identity_relation(sK9_skl),ordered_pair(X0,apply(sK9_skl,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f7446,plain,
( ~ sQ5_spl
| sQ482_spl ),
inference(split_clause,[status(thm)],[f7435,f7443,f182]) ).
fof(f7447,definition,
! [X0] :
( sQ483_spl
<=> ( ~ in(X0,relation_dom(sK3_skl))
| ordered_pair(X0,apply(sK3_skl,X0)) = apply(identity_relation(sK3_skl),ordered_pair(X0,apply(sK3_skl,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f7450,plain,
( ~ sQ12_spl
| sQ483_spl ),
inference(split_clause,[status(thm)],[f7436,f7447,f252]) ).
fof(f7490,plain,
! [X0] :
( ~ sQ100_spl
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| X0 = apply(identity_relation(sK10_skl),X0) ),
inference(resolution,[status(thm)],[f1875,f163]) ).
fof(f7496,definition,
! [X0] :
( sQ485_spl
<=> ( ~ in(X0,relation_dom(sK9_skl))
| X0 = apply(identity_relation(sK10_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f7499,plain,
( ~ sQ100_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ485_spl ),
inference(split_clause,[status(thm)],[f7490,f7496,f182,f185,f1203]) ).
fof(f7501,plain,
! [X0] :
( ~ sQ52_spl
| apply(sK4_skl,X0) = sK4_skl
| ~ relation(sK4_skl)
| X0 = apply(identity_relation(relation_dom(sK4_skl)),X0) ),
inference(resolution,[status(thm)],[f1876,f741]) ).
fof(f7502,plain,
! [X0] :
( apply(sK9_skl,X0) = sK4_skl
| ~ relation(sK9_skl)
| X0 = apply(identity_relation(relation_dom(sK9_skl)),X0) ),
inference(resolution,[status(thm)],[f1876,f119]) ).
fof(f7503,plain,
! [X0] :
( apply(sK3_skl,X0) = sK4_skl
| ~ relation(sK3_skl)
| X0 = apply(identity_relation(relation_dom(sK3_skl)),X0) ),
inference(resolution,[status(thm)],[f1876,f96]) ).
fof(f7506,definition,
! [X0] :
( sQ486_spl
<=> ( apply(sK4_skl,X0) = sK4_skl
| X0 = apply(identity_relation(relation_dom(sK4_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f7509,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ486_spl ),
inference(split_clause,[status(thm)],[f7501,f7506,f737,f740]) ).
fof(f7510,definition,
! [X0] :
( sQ487_spl
<=> ( apply(sK9_skl,X0) = sK4_skl
| X0 = apply(identity_relation(relation_dom(sK9_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f7513,plain,
( ~ sQ5_spl
| sQ487_spl ),
inference(split_clause,[status(thm)],[f7502,f7510,f182]) ).
fof(f7514,definition,
! [X0] :
( sQ488_spl
<=> ( apply(sK3_skl,X0) = sK4_skl
| X0 = apply(identity_relation(relation_dom(sK3_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f7517,plain,
( ~ sQ12_spl
| sQ488_spl ),
inference(split_clause,[status(thm)],[f7503,f7514,f252]) ).
fof(f7524,plain,
! [X0,X1] :
( ~ sQ52_spl
| ~ in(ordered_pair(X0,X1),sK4_skl)
| ~ relation(sK4_skl)
| X0 = apply(identity_relation(relation_dom(sK4_skl)),X0) ),
inference(resolution,[status(thm)],[f1877,f741]) ).
fof(f7525,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK9_skl)
| ~ relation(sK9_skl)
| X0 = apply(identity_relation(relation_dom(sK9_skl)),X0) ),
inference(resolution,[status(thm)],[f1877,f119]) ).
fof(f7526,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK3_skl)
| ~ relation(sK3_skl)
| X0 = apply(identity_relation(relation_dom(sK3_skl)),X0) ),
inference(resolution,[status(thm)],[f1877,f96]) ).
fof(f7529,definition,
! [X0,X1] :
( sQ489_spl
<=> ( ~ in(ordered_pair(X0,X1),sK4_skl)
| X0 = apply(identity_relation(relation_dom(sK4_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f7532,plain,
( ~ sQ52_spl
| ~ sQ51_spl
| sQ489_spl ),
inference(split_clause,[status(thm)],[f7524,f7529,f737,f740]) ).
fof(f7533,definition,
! [X0,X1] :
( sQ490_spl
<=> ( ~ in(ordered_pair(X0,X1),sK9_skl)
| X0 = apply(identity_relation(relation_dom(sK9_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f7536,plain,
( ~ sQ5_spl
| sQ490_spl ),
inference(split_clause,[status(thm)],[f7525,f7533,f182]) ).
fof(f7537,definition,
! [X0,X1] :
( sQ491_spl
<=> ( ~ in(ordered_pair(X0,X1),sK3_skl)
| X0 = apply(identity_relation(relation_dom(sK3_skl)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f7540,plain,
( ~ sQ12_spl
| sQ491_spl ),
inference(split_clause,[status(thm)],[f7526,f7537,f252]) ).
fof(f7605,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ in(ordered_pair(X1,X0),relation_dom(identity_relation(sK3_skl)))
| ~ function(identity_relation(sK3_skl))
| ~ relation(identity_relation(sK3_skl))
| X0 = apply(sK3_skl,X1) ),
inference(resolution,[status(thm)],[f1896,f163]) ).
fof(f7608,definition,
! [X0,X1] :
( sQ493_spl
<=> ( ~ in(ordered_pair(X1,X0),relation_dom(identity_relation(sK3_skl)))
| X0 = apply(sK3_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f7611,definition,
( sQ494_spl
<=> relation(identity_relation(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ494_spl])],[split_symbol_definition]) ).
fof(f7613,plain,
( sQ494_spl
| ~ relation(identity_relation(sK3_skl)) ),
inference(component_clause,[status(thm)],[f7611]) ).
fof(f7614,definition,
( sQ495_spl
<=> function(identity_relation(sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f7616,plain,
( sQ495_spl
| ~ function(identity_relation(sK3_skl)) ),
inference(component_clause,[status(thm)],[f7614]) ).
fof(f7617,plain,
( ~ sQ103_spl
| ~ sQ495_spl
| ~ sQ494_spl
| sQ493_spl ),
inference(split_clause,[status(thm)],[f7605,f7608,f7611,f7614,f1251]) ).
fof(f7618,plain,
( sQ495_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7616,f79]) ).
fof(f7619,plain,
sQ495_spl,
inference(contradiction_clause,[status(thm)],[f7618]) ).
fof(f7620,plain,
( sQ494_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7613,f69]) ).
fof(f7621,plain,
sQ494_spl,
inference(contradiction_clause,[status(thm)],[f7620]) ).
fof(f7623,plain,
! [X0] :
( ~ sQ149_spl
| sK0_skl(X0,sK3_skl) = sK1_skl(X0,sK3_skl)
| sK3_skl = identity_relation(X0)
| ~ in(sK0_skl(X0,sK3_skl),relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ in(sK3_skl,ordered_pair(sK0_skl(X0,sK3_skl),sK1_skl(X0,sK3_skl))) ),
inference(paramodulation,[status(thm)],[f1898,f1223]) ).
fof(f7624,plain,
! [X0] :
( ~ sQ149_spl
| sK0_skl(X0,sK3_skl) = sK1_skl(X0,sK3_skl)
| sK3_skl = identity_relation(X0)
| in(ordered_pair(sK0_skl(X0,sK3_skl),sK1_skl(X0,sK3_skl)),sK3_skl)
| ~ in(sK0_skl(X0,sK3_skl),relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(paramodulation,[status(thm)],[f1898,f163]) ).
fof(f7625,definition,
! [X0] :
( sQ496_spl
<=> ( sK0_skl(X0,sK3_skl) = sK1_skl(X0,sK3_skl)
| sK3_skl = identity_relation(X0)
| ~ in(sK0_skl(X0,sK3_skl),relation_dom(sK3_skl))
| ~ in(sK3_skl,ordered_pair(sK0_skl(X0,sK3_skl),sK1_skl(X0,sK3_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f7628,plain,
( ~ sQ149_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sQ496_spl ),
inference(split_clause,[status(thm)],[f7623,f7625,f252,f641,f1897]) ).
fof(f7629,definition,
! [X0] :
( sQ497_spl
<=> ( sK0_skl(X0,sK3_skl) = sK1_skl(X0,sK3_skl)
| sK3_skl = identity_relation(X0)
| in(ordered_pair(sK0_skl(X0,sK3_skl),sK1_skl(X0,sK3_skl)),sK3_skl)
| ~ in(sK0_skl(X0,sK3_skl),relation_dom(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition]) ).
fof(f7632,plain,
( ~ sQ149_spl
| sQ497_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7624,f252,f641,f7629,f1897]) ).
fof(f7634,plain,
( sQ447_spl
| apply(sK3_skl,sK10_skl) = sK4_skl
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f6966,f381]) ).
fof(f7635,plain,
! [X0] :
( sQ447_spl
| ~ in(ordered_pair(sK10_skl,X0),sK3_skl)
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f6966,f138]) ).
fof(f7637,plain,
( sQ447_spl
| sQ315_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7634,f252,f641,f5176,f6964]) ).
fof(f7638,definition,
! [X0] :
( sQ498_spl
<=> ~ in(ordered_pair(sK10_skl,X0),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f7639,plain,
! [X0] :
( ~ sQ498_spl
| ~ in(ordered_pair(sK10_skl,X0),sK3_skl) ),
inference(component_clause,[status(thm)],[f7638]) ).
fof(f7641,plain,
( sQ447_spl
| sQ498_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7635,f252,f641,f7638,f6964]) ).
fof(f7643,plain,
! [X0,X1] :
( ~ sQ100_spl
| ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(sK9_skl)))
| ~ function(identity_relation(sK9_skl))
| ~ relation(identity_relation(sK9_skl))
| in(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2125,f163]) ).
fof(f7646,definition,
! [X0,X1] :
( sQ499_spl
<=> ( ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(sK9_skl)))
| in(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f7649,plain,
( ~ sQ100_spl
| ~ sQ454_spl
| ~ sQ237_spl
| sQ499_spl ),
inference(split_clause,[status(thm)],[f7643,f7646,f3744,f7023,f1203]) ).
fof(f7774,definition,
( sQ504_spl
<=> relation(relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f7776,plain,
( sQ504_spl
| ~ relation(relation_dom(sK4_skl)) ),
inference(component_clause,[status(thm)],[f7774]) ).
fof(f7785,plain,
( sQ504_spl
| ~ relation(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f7776]) ).
fof(f7786,plain,
( sQ504_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7785,f99]) ).
fof(f7787,plain,
sQ504_spl,
inference(contradiction_clause,[status(thm)],[f7786]) ).
fof(f7818,plain,
! [X0] :
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| ~ in(X0,relation_rng(sK4_skl)) ),
inference(paramodulation,[status(thm)],[f1163,f2055]) ).
fof(f7821,definition,
! [X0] :
( sQ507_spl
<=> ~ in(X0,relation_rng(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f7824,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ507_spl ),
inference(split_clause,[status(thm)],[f7818,f7821,f737,f732]) ).
fof(f7928,plain,
! [X0] :
( ~ sQ13_spl
| X0 = apply(identity_relation(relation_dom(sK3_skl)),X0)
| ~ in(X0,relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl)
| ~ in(sK3_skl,ordered_pair(X0,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f2057,f1223]) ).
fof(f7929,plain,
! [X0] :
( ~ sQ13_spl
| X0 = apply(identity_relation(relation_dom(sK3_skl)),X0)
| in(ordered_pair(X0,sK4_skl),sK3_skl)
| ~ in(X0,relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(paramodulation,[status(thm)],[f2057,f163]) ).
fof(f7935,definition,
! [X0] :
( sQ520_spl
<=> ( X0 = apply(identity_relation(relation_dom(sK3_skl)),X0)
| ~ in(X0,relation_dom(sK3_skl))
| ~ in(sK3_skl,ordered_pair(X0,sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f7938,plain,
( ~ sQ13_spl
| ~ sQ43_spl
| ~ sQ12_spl
| sQ520_spl ),
inference(split_clause,[status(thm)],[f7928,f7935,f252,f641,f255]) ).
fof(f7939,definition,
! [X0] :
( sQ521_spl
<=> ( X0 = apply(identity_relation(relation_dom(sK3_skl)),X0)
| in(ordered_pair(X0,sK4_skl),sK3_skl)
| ~ in(X0,relation_dom(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f7942,plain,
( ~ sQ13_spl
| sQ521_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7929,f252,f641,f7939,f255]) ).
fof(f7979,plain,
! [X0] :
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| apply(sK4_skl,X0) = sK4_skl ),
inference(paramodulation,[status(thm)],[f1163,f2195]) ).
fof(f7982,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f7979,f924,f737,f732]) ).
fof(f8083,definition,
( sQ522_spl
<=> sK4_skl = identity_relation(relation_rng(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f8084,plain,
( ~ sQ522_spl
| sK4_skl = identity_relation(relation_rng(sK9_skl)) ),
inference(component_clause,[status(thm)],[f8083]) ).
fof(f8210,plain,
! [X0] :
( ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| relation_rng(sK4_skl) = identity_relation(X0) ),
inference(paramodulation,[status(thm)],[f1163,f2257]) ).
fof(f8213,definition,
! [X0] :
( sQ538_spl
<=> ( in(sK0_skl(X0,relation_rng(sK4_skl)),X0)
| relation_rng(sK4_skl) = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f8216,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ538_spl ),
inference(split_clause,[status(thm)],[f8210,f8213,f737,f732]) ).
fof(f8240,plain,
( ~ sQ203_spl
| sK9_skl = identity_relation(sK4_skl)
| sK0_skl(sK4_skl,sK9_skl) = sK1_skl(sK4_skl,sK9_skl) ),
inference(resolution,[status(thm)],[f2857,f1274]) ).
fof(f8248,definition,
( sQ540_spl
<=> sK0_skl(sK4_skl,sK9_skl) = sK1_skl(sK4_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f8251,plain,
( ~ sQ203_spl
| sQ452_spl
| sQ540_spl ),
inference(split_clause,[status(thm)],[f8240,f8248,f7008,f2856]) ).
fof(f8562,definition,
( sQ562_spl
<=> apply(sK9_skl,sK10_skl) = sK10_skl ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f8563,plain,
( ~ sQ562_spl
| apply(sK9_skl,sK10_skl) = sK10_skl ),
inference(component_clause,[status(thm)],[f8562]) ).
fof(f8573,definition,
! [X0] :
( sQ564_spl
<=> ( apply(sK9_skl,X0) = X0
| ~ in(X0,relation_dom(sK9_skl))
| ~ in(sK9_skl,ordered_pair(X0,sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f8577,definition,
! [X0] :
( sQ565_spl
<=> ( apply(sK9_skl,X0) = X0
| in(ordered_pair(X0,sK4_skl),sK9_skl)
| ~ in(X0,relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f8584,plain,
( ~ sQ562_spl
| ~ sQ312_spl
| sK4_skl = sK10_skl ),
inference(forward_demodulation,[status(thm)],[f5166,f8563]) ).
fof(f8585,plain,
( ~ sQ562_spl
| ~ sQ312_spl
| sQ247_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8584,f3927]) ).
fof(f8586,plain,
( ~ sQ562_spl
| ~ sQ312_spl
| sQ247_spl ),
inference(contradiction_clause,[status(thm)],[f8585]) ).
fof(f8589,plain,
( sQ54_spl
| ~ sQ247_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f3942,f1002,f3925,f759]) ).
fof(f8608,plain,
! [X0] :
( ~ sQ2_spl
| apply(sK9_skl,X0) = X0
| ~ in(X0,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl))
| ~ in(identity_relation(sK10_skl),ordered_pair(X0,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f1439,f1223]) ).
fof(f8609,plain,
! [X0] :
( ~ sQ2_spl
| apply(sK9_skl,X0) = X0
| in(ordered_pair(X0,sK4_skl),identity_relation(sK10_skl))
| ~ in(X0,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl)) ),
inference(paramodulation,[status(thm)],[f1439,f163]) ).
fof(f8610,definition,
( sQ566_spl
<=> sK0_skl(sK10_skl,sK4_skl) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f8611,plain,
( ~ sQ566_spl
| sK0_skl(sK10_skl,sK4_skl) = sK4_skl ),
inference(component_clause,[status(thm)],[f8610]) ).
fof(f8614,definition,
( sQ567_spl
<=> sK2_skl(sK10_skl) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ567_spl])],[split_symbol_definition]) ).
fof(f8615,plain,
( ~ sQ567_spl
| sK2_skl(sK10_skl) = sK4_skl ),
inference(component_clause,[status(thm)],[f8614]) ).
fof(f8618,definition,
! [X0] :
( sQ568_spl
<=> ( in(X0,sK10_skl)
| apply(sK9_skl,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f8619,plain,
! [X0] :
( ~ sQ568_spl
| in(X0,sK10_skl)
| apply(sK9_skl,X0) = X0 ),
inference(component_clause,[status(thm)],[f8618]) ).
fof(f8626,definition,
! [X0] :
( sQ569_spl
<=> ( apply(sK9_skl,X0) = X0
| ~ in(X0,relation_dom(identity_relation(sK10_skl)))
| ~ in(identity_relation(sK10_skl),ordered_pair(X0,sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f8629,plain,
( ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ33_spl
| sQ569_spl ),
inference(split_clause,[status(thm)],[f8608,f8626,f556,f559,f148]) ).
fof(f8630,definition,
! [X0] :
( sQ570_spl
<=> ( apply(sK9_skl,X0) = X0
| in(ordered_pair(X0,sK4_skl),identity_relation(sK10_skl))
| ~ in(X0,relation_dom(identity_relation(sK10_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f8633,plain,
( ~ sQ2_spl
| sQ570_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f8609,f556,f559,f8630,f148]) ).
fof(f8636,plain,
! [X0] :
( ~ sQ568_spl
| ~ sQ2_spl
| apply(sK9_skl,X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f8619,f149]) ).
fof(f8637,plain,
( ~ sQ567_spl
| sQ64_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8615,f5381]) ).
fof(f8638,plain,
( ~ sQ567_spl
| sQ64_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f8637]) ).
fof(f8639,plain,
( ~ sQ566_spl
| sQ56_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8611,f6784]) ).
fof(f8640,plain,
( ~ sQ566_spl
| sQ56_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f8639]) ).
fof(f8641,plain,
( ~ sQ2_spl
| ~ sQ100_spl
| apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) = sK0_skl(sK10_skl,sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| ~ relation(sK9_skl)
| apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl)) = sK0_skl(sK10_skl,sK9_skl) ),
inference(resolution,[status(thm)],[f1545,f6050]) ).
fof(f8644,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ100_spl
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| apply(sK9_skl,X0) = X0 ),
inference(resolution,[status(thm)],[f1545,f163]) ).
fof(f8646,plain,
( ~ sQ2_spl
| ~ sQ100_spl
| sQ0_spl
| ~ sQ5_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f8641,f296,f182,f141,f1203,f148]) ).
fof(f8647,plain,
( ~ sQ2_spl
| ~ sQ100_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f8644,f2861,f182,f185,f1203,f148]) ).
fof(f8652,plain,
! [X0,X1] :
( ~ sQ2_spl
| apply(sK9_skl,X0) = X0
| ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(identity_relation(sK10_skl))))
| ~ function(identity_relation(identity_relation(sK10_skl)))
| ~ relation(identity_relation(identity_relation(sK10_skl)))
| ~ in(identity_relation(identity_relation(sK10_skl)),ordered_pair(ordered_pair(X0,X1),sK4_skl)) ),
inference(paramodulation,[status(thm)],[f1565,f1223]) ).
fof(f8653,plain,
! [X0,X1] :
( ~ sQ2_spl
| apply(sK9_skl,X0) = X0
| in(ordered_pair(ordered_pair(X0,X1),sK4_skl),identity_relation(identity_relation(sK10_skl)))
| ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(identity_relation(sK10_skl))))
| ~ function(identity_relation(identity_relation(sK10_skl)))
| ~ relation(identity_relation(identity_relation(sK10_skl))) ),
inference(paramodulation,[status(thm)],[f1565,f163]) ).
fof(f8659,definition,
! [X0,X1] :
( sQ572_spl
<=> ( apply(sK9_skl,X0) = X0
| ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(identity_relation(sK10_skl))))
| ~ in(identity_relation(identity_relation(sK10_skl)),ordered_pair(ordered_pair(X0,X1),sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ572_spl])],[split_symbol_definition]) ).
fof(f8662,definition,
( sQ573_spl
<=> relation(identity_relation(identity_relation(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ573_spl])],[split_symbol_definition]) ).
fof(f8664,plain,
( sQ573_spl
| ~ relation(identity_relation(identity_relation(sK10_skl))) ),
inference(component_clause,[status(thm)],[f8662]) ).
fof(f8665,definition,
( sQ574_spl
<=> function(identity_relation(identity_relation(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f8667,plain,
( sQ574_spl
| ~ function(identity_relation(identity_relation(sK10_skl))) ),
inference(component_clause,[status(thm)],[f8665]) ).
fof(f8668,plain,
( ~ sQ2_spl
| ~ sQ574_spl
| ~ sQ573_spl
| sQ572_spl ),
inference(split_clause,[status(thm)],[f8652,f8659,f8662,f8665,f148]) ).
fof(f8669,definition,
! [X0,X1] :
( sQ575_spl
<=> ( apply(sK9_skl,X0) = X0
| in(ordered_pair(ordered_pair(X0,X1),sK4_skl),identity_relation(identity_relation(sK10_skl)))
| ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(identity_relation(sK10_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f8672,plain,
( ~ sQ2_spl
| sQ575_spl
| ~ sQ574_spl
| ~ sQ573_spl ),
inference(split_clause,[status(thm)],[f8653,f8662,f8665,f8669,f148]) ).
fof(f8673,plain,
( sQ574_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8667,f79]) ).
fof(f8674,plain,
sQ574_spl,
inference(contradiction_clause,[status(thm)],[f8673]) ).
fof(f8675,plain,
( sQ573_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8664,f69]) ).
fof(f8676,plain,
sQ573_spl,
inference(contradiction_clause,[status(thm)],[f8675]) ).
fof(f8681,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(identity_relation(sK10_skl))))
| ~ function(identity_relation(identity_relation(sK10_skl)))
| ~ relation(identity_relation(identity_relation(sK10_skl)))
| apply(sK9_skl,X0) = X0 ),
inference(resolution,[status(thm)],[f1566,f163]) ).
fof(f8684,definition,
! [X0,X1] :
( sQ576_spl
<=> ( ~ in(ordered_pair(X0,X1),relation_dom(identity_relation(identity_relation(sK10_skl))))
| apply(sK9_skl,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ576_spl])],[split_symbol_definition]) ).
fof(f8687,plain,
( ~ sQ2_spl
| ~ sQ574_spl
| ~ sQ573_spl
| sQ576_spl ),
inference(split_clause,[status(thm)],[f8681,f8684,f8662,f8665,f148]) ).
fof(f8835,plain,
( ~ sQ99_spl
| sQ3_spl
| ~ sQ568_spl
| ~ sQ2_spl
| sK11_skl = sK4_skl ),
inference(backward_demodulation,[status(thm)],[f8636,f3121]) ).
fof(f8836,plain,
( ~ sQ312_spl
| ~ sQ568_spl
| ~ sQ2_spl
| sK10_skl = sK4_skl ),
inference(backward_demodulation,[status(thm)],[f8636,f5166]) ).
fof(f8861,plain,
( ~ sQ99_spl
| sQ3_spl
| ~ sQ568_spl
| ~ sQ2_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f8835,f3073,f148,f8618,f152,f1196]) ).
fof(f8862,plain,
( ~ sQ312_spl
| ~ sQ568_spl
| ~ sQ2_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f8836,f3925,f148,f8618,f5165]) ).
fof(f8875,plain,
( ~ sQ36_spl
| ~ sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f2041,f156,f148,f566]) ).
fof(f8877,plain,
( sQ244_spl
| ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3866,f152,f144,f3861]) ).
fof(f8922,plain,
! [X0] :
( ~ sQ2_spl
| ~ empty(X0)
| apply(sK9_skl,sK0_skl(sK10_skl,relation_rng(X0))) = sK0_skl(sK10_skl,relation_rng(X0))
| in(ordered_pair(sK0_skl(sK10_skl,relation_rng(X0)),sK1_skl(sK10_skl,relation_rng(X0))),relation_rng(X0))
| relation_rng(X0) = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f6050,f93]) ).
fof(f8924,plain,
! [X0] :
( ~ sQ2_spl
| ~ empty(X0)
| apply(sK9_skl,sK0_skl(sK10_skl,relation_dom(X0))) = sK0_skl(sK10_skl,relation_dom(X0))
| in(ordered_pair(sK0_skl(sK10_skl,relation_dom(X0)),sK1_skl(sK10_skl,relation_dom(X0))),relation_dom(X0))
| relation_dom(X0) = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f6050,f90]) ).
fof(f8934,plain,
! [X0] :
( ~ sQ2_spl
| ~ empty(X0)
| apply(sK9_skl,sK0_skl(sK10_skl,relation_rng(X0))) = sK0_skl(sK10_skl,relation_rng(X0))
| relation_rng(X0) = identity_relation(sK10_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f8922,f1273]) ).
fof(f8936,plain,
! [X0] :
( ~ sQ2_spl
| ~ empty(X0)
| apply(sK9_skl,sK0_skl(sK10_skl,relation_dom(X0))) = sK0_skl(sK10_skl,relation_dom(X0))
| relation_dom(X0) = identity_relation(sK10_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f8924,f1275]) ).
fof(f8938,plain,
( sQ3_spl
| ~ sQ99_spl
| apply(sK9_skl,sK11_skl) = sK4_skl ),
inference(resolution,[status(thm)],[f1197,f154]) ).
fof(f9049,plain,
( ~ sQ522_spl
| relation_dom(sK4_skl) = relation_rng(sK9_skl) ),
inference(paramodulation,[status(thm)],[f8084,f127]) ).
fof(f9122,plain,
( ~ sQ522_spl
| sK4_skl = relation_rng(sK9_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f9049]) ).
fof(f9123,plain,
( ~ sQ522_spl
| sQ332_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9122,f5399]) ).
fof(f9124,plain,
( ~ sQ522_spl
| sQ332_spl ),
inference(contradiction_clause,[status(thm)],[f9123]) ).
fof(f9135,plain,
( ~ sQ7_spl
| sK4_skl = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl))),sK9_skl) ),
inference(resolution,[status(thm)],[f484,f98]) ).
fof(f9139,definition,
( sQ594_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),apply(sK9_skl,sK0_skl(sK10_skl,sK4_skl))),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ594_spl])],[split_symbol_definition]) ).
fof(f9142,plain,
( ~ sQ7_spl
| sQ54_spl
| sQ594_spl ),
inference(split_clause,[status(thm)],[f9135,f9139,f759,f188]) ).
fof(f9275,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ99_spl
| apply(sK9_skl,X0) = X0
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ in(sK9_skl,ordered_pair(X0,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f3842,f1223]) ).
fof(f9276,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ99_spl
| apply(sK9_skl,X0) = X0
| in(ordered_pair(X0,sK4_skl),sK9_skl)
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f3842,f163]) ).
fof(f9283,plain,
( ~ sQ2_spl
| ~ sQ99_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ564_spl ),
inference(split_clause,[status(thm)],[f9275,f8573,f182,f185,f1196,f148]) ).
fof(f9284,plain,
( ~ sQ2_spl
| ~ sQ99_spl
| sQ565_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f9276,f182,f185,f8577,f1196,f148]) ).
fof(f9292,plain,
! [X0] :
( ~ sQ99_spl
| X0 = apply(identity_relation(sK10_skl),X0)
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ in(sK9_skl,ordered_pair(X0,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f3843,f1223]) ).
fof(f9293,plain,
! [X0] :
( ~ sQ99_spl
| X0 = apply(identity_relation(sK10_skl),X0)
| in(ordered_pair(X0,sK4_skl),sK9_skl)
| ~ in(X0,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f3843,f163]) ).
fof(f9298,plain,
( ~ sQ99_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ472_spl ),
inference(split_clause,[status(thm)],[f9292,f7305,f182,f185,f1196]) ).
fof(f9299,plain,
( ~ sQ99_spl
| sQ473_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f9293,f182,f185,f7309,f1196]) ).
fof(f9300,plain,
( ~ sQ99_spl
| apply(sK9_skl,sK10_skl) = sK4_skl
| apply(sK9_skl,sK10_skl) = sK4_skl ),
inference(resolution,[status(thm)],[f3844,f1197]) ).
fof(f9306,plain,
( ~ sQ99_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f9300,f5165,f1196]) ).
fof(f9310,plain,
( ~ sQ100_spl
| ~ sQ242_spl
| sK11_skl = apply(identity_relation(sK10_skl),sK11_skl) ),
inference(resolution,[status(thm)],[f3855,f1875]) ).
fof(f9317,plain,
( ~ sQ100_spl
| ~ sQ242_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f9310,f562,f3854,f1203]) ).
fof(f9420,plain,
! [X0] :
( sQ3_spl
| ~ sQ24_spl
| ~ in(ordered_pair(sK4_skl,X0),identity_relation(sK10_skl)) ),
inference(backward_demodulation,[status(thm)],[f613,f3122]) ).
fof(f9424,plain,
( sQ3_spl
| ~ sQ24_spl
| ~ in(sK4_skl,relation_dom(identity_relation(sK10_skl)))
| ~ function(identity_relation(sK10_skl))
| ~ relation(identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f9420,f163]) ).
fof(f9427,definition,
( sQ604_spl
<=> in(sK4_skl,relation_dom(identity_relation(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ604_spl])],[split_symbol_definition]) ).
fof(f9429,plain,
( sQ604_spl
| ~ in(sK4_skl,relation_dom(identity_relation(sK10_skl))) ),
inference(component_clause,[status(thm)],[f9427]) ).
fof(f9430,plain,
( sQ3_spl
| ~ sQ24_spl
| ~ sQ604_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f9424,f556,f559,f9427,f393,f152]) ).
fof(f9431,plain,
( sQ604_spl
| ~ in(sK4_skl,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f127,f9429]) ).
fof(f9522,plain,
( ~ sQ216_spl
| sQ219_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3103,f3117]) ).
fof(f9523,plain,
( ~ sQ216_spl
| sQ219_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f9522]) ).
fof(f9526,plain,
( sQ604_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f9431,f3102,f9427]) ).
fof(f9548,plain,
( ~ sQ99_spl
| ~ sQ4_spl
| sK11_skl = apply(identity_relation(sK10_skl),sK11_skl)
| sK4_skl = sK11_skl ),
inference(paramodulation,[status(thm)],[f3843,f157]) ).
fof(f9554,plain,
( ~ sQ99_spl
| ~ sQ4_spl
| sQ35_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f9548,f3073,f562,f156,f1196]) ).
fof(f9702,plain,
( ~ sQ99_spl
| ~ sQ63_spl
| sK2_skl(sK10_skl) = apply(identity_relation(sK10_skl),sK2_skl(sK10_skl))
| sK4_skl = sK2_skl(sK10_skl) ),
inference(paramodulation,[status(thm)],[f3843,f845]) ).
fof(f9709,definition,
( sQ621_spl
<=> sK2_skl(sK10_skl) = apply(identity_relation(sK10_skl),sK2_skl(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f9712,plain,
( ~ sQ99_spl
| ~ sQ63_spl
| sQ621_spl
| sQ567_spl ),
inference(split_clause,[status(thm)],[f9702,f8614,f9709,f844,f1196]) ).
fof(f9725,definition,
! [X0] :
( sQ622_spl
<=> ordered_pair(sK10_skl,X0) = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ622_spl])],[split_symbol_definition]) ).
fof(f9726,plain,
! [X0] :
( ~ sQ622_spl
| ordered_pair(sK10_skl,X0) = sK4_skl ),
inference(component_clause,[status(thm)],[f9725]) ).
fof(f9970,plain,
( ~ sQ133_spl
| ~ sQ1_spl
| ~ sQ31_spl
| sK0_skl(sK10_skl,sK9_skl) != sK1_skl(sK10_skl,sK9_skl)
| ~ in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f486,f1609]) ).
fof(f9983,plain,
( ~ sQ133_spl
| ~ sQ1_spl
| ~ sQ31_spl
| ~ sQ286_spl
| ~ sQ18_spl
| sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f9970,f182,f141,f293,f4873,f485,f144,f1589]) ).
fof(f10087,plain,
( in(ordered_pair(sK0_skl(sK4_skl,sK9_skl),sK1_skl(sK4_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK4_skl) ),
inference(resolution,[status(thm)],[f323,f98]) ).
fof(f10091,definition,
( sQ672_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK9_skl),sK1_skl(sK4_skl,sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f10094,plain,
( sQ672_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f10087,f7008,f10091]) ).
fof(f10126,plain,
( ~ sQ622_spl
| ~ empty(sK4_skl) ),
inference(paramodulation,[status(thm)],[f9726,f76]) ).
fof(f10135,definition,
! [X0] :
( sQ674_spl
<=> X0 = apply(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f10136,plain,
! [X0] :
( ~ sQ674_spl
| X0 = apply(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f10135]) ).
fof(f10140,definition,
! [X0] :
( sQ675_spl
<=> X0 = apply(sK3_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f10141,plain,
! [X0] :
( ~ sQ675_spl
| X0 = apply(sK3_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f10140]) ).
fof(f10164,plain,
( ~ sQ622_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f10126,f732,f9725]) ).
fof(f10165,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ315_spl
| X0 = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f5177,f10141]) ).
fof(f10166,plain,
! [X0] :
( ~ sQ674_spl
| ~ sQ312_spl
| X0 = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f5166,f10136]) ).
fof(f10204,plain,
( sQ332_spl
| ~ sQ675_spl
| ~ sQ315_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5399,f10165]) ).
fof(f10231,plain,
( sQ332_spl
| ~ sQ675_spl
| ~ sQ315_spl ),
inference(contradiction_clause,[status(thm)],[f10204]) ).
fof(f10250,plain,
! [X0] :
( ~ sQ52_spl
| apply(sK4_skl,X0) = sK4_skl
| in(X0,relation_dom(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f381,f741]) ).
fof(f10251,plain,
! [X0] :
( apply(sK9_skl,X0) = sK4_skl
| in(X0,relation_dom(sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f381,f119]) ).
fof(f10252,plain,
! [X0] :
( apply(sK3_skl,X0) = sK4_skl
| in(X0,relation_dom(sK3_skl))
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f381,f96]) ).
fof(f10255,definition,
! [X0] :
( sQ679_spl
<=> ( apply(sK4_skl,X0) = sK4_skl
| in(X0,relation_dom(sK4_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f10258,plain,
( ~ sQ52_spl
| sQ679_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f10250,f737,f10255,f740]) ).
fof(f10259,definition,
! [X0] :
( sQ680_spl
<=> ( apply(sK9_skl,X0) = sK4_skl
| in(X0,relation_dom(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f10260,plain,
! [X0] :
( ~ sQ680_spl
| apply(sK9_skl,X0) = sK4_skl
| in(X0,relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f10259]) ).
fof(f10262,plain,
( sQ680_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f10251,f182,f10259]) ).
fof(f10263,definition,
! [X0] :
( sQ681_spl
<=> ( apply(sK3_skl,X0) = sK4_skl
| in(X0,relation_dom(sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ681_spl])],[split_symbol_definition]) ).
fof(f10266,plain,
( sQ681_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f10252,f252,f10263]) ).
fof(f10270,plain,
! [X0] :
( ~ sQ680_spl
| ~ sQ1_spl
| apply(sK9_skl,X0) = sK4_skl
| in(X0,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f145,f10260]) ).
fof(f10294,plain,
! [X0] :
( ~ sQ674_spl
| ~ sQ312_spl
| ~ sQ216_spl
| in(X0,sK10_skl) ),
inference(paramodulation,[status(thm)],[f10166,f3103]) ).
fof(f10307,plain,
( ~ sQ674_spl
| ~ sQ312_spl
| ~ sQ216_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f10294,f3762,f3102,f5165,f10135]) ).
fof(f10386,plain,
! [X0] :
( sK0_skl(X0,sK9_skl) != sK1_skl(X0,sK9_skl)
| ~ in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0)
| ~ relation(sK9_skl)
| in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0) ),
inference(resolution,[status(thm)],[f291,f1218]) ).
fof(f10396,definition,
! [X0] :
( sQ682_spl
<=> ( sK0_skl(X0,sK9_skl) != sK1_skl(X0,sK9_skl)
| ~ in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0)
| in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ682_spl])],[split_symbol_definition]) ).
fof(f10399,plain,
( ~ sQ5_spl
| sQ682_spl ),
inference(split_clause,[status(thm)],[f10386,f10396,f182]) ).
fof(f10643,plain,
! [X0] :
( ~ sQ113_spl
| ~ in(sK0_skl(X0,sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl)
| sK4_skl = identity_relation(X0) ),
inference(resolution,[status(thm)],[f1368,f58]) ).
fof(f10644,plain,
! [X0,X1] :
( ~ sQ113_spl
| sK4_skl = identity_relation(X0)
| ~ in(ordered_pair(sK4_skl,X1),identity_relation(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl))))
| sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f1368,f1729]) ).
fof(f10647,plain,
! [X0] :
( ~ sQ113_spl
| sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) != sK0_skl(X0,sK4_skl)
| ~ in(sK0_skl(X0,sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f1368,f58]) ).
fof(f10648,plain,
! [X0] :
( ~ sQ113_spl
| sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) = sK0_skl(X0,sK4_skl)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| ~ relation(sK4_skl) ),
inference(paramodulation,[status(thm)],[f1368,f60]) ).
fof(f10649,definition,
! [X0] :
( sQ684_spl
<=> ( ~ in(sK0_skl(X0,sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ684_spl])],[split_symbol_definition]) ).
fof(f10652,plain,
( ~ sQ113_spl
| ~ sQ51_spl
| sQ684_spl ),
inference(split_clause,[status(thm)],[f10643,f10649,f737,f1367]) ).
fof(f10653,definition,
! [X0,X1] :
( sQ685_spl
<=> ( sK4_skl = identity_relation(X0)
| ~ in(ordered_pair(sK4_skl,X1),identity_relation(ordered_pair(sK0_skl(X0,sK4_skl),sK0_skl(X0,sK4_skl))))
| sK0_skl(X0,sK4_skl) = sK1_skl(X0,sK4_skl)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ685_spl])],[split_symbol_definition]) ).
fof(f10656,plain,
( ~ sQ113_spl
| sQ685_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f10644,f737,f10653,f1367]) ).
fof(f10659,definition,
! [X0] :
( sQ686_spl
<=> ( sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) != sK0_skl(X0,sK4_skl)
| ~ in(sK0_skl(X0,sK4_skl),X0)
| ~ in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ686_spl])],[split_symbol_definition]) ).
fof(f10662,plain,
( ~ sQ113_spl
| sQ686_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f10647,f737,f10659,f1367]) ).
fof(f10663,definition,
! [X0] :
( sQ687_spl
<=> ( sK4_skl = identity_relation(X0)
| sK0_skl(X0,sK4_skl) = sK0_skl(X0,sK4_skl)
| in(ordered_pair(sK0_skl(X0,sK4_skl),sK1_skl(X0,sK4_skl)),sK4_skl)
| sK4_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ687_spl])],[split_symbol_definition]) ).
fof(f10666,plain,
( ~ sQ113_spl
| sQ687_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f10648,f737,f10663,f1367]) ).
fof(f11094,plain,
( ~ sQ239_spl
| $false ),
inference(resolution,[status(thm)],[f3763,f3793]) ).
fof(f11099,plain,
~ sQ239_spl,
inference(contradiction_clause,[status(thm)],[f11094]) ).
fof(f12571,plain,
! [X0] :
( in(ordered_pair(sK0_skl(sK4_skl,X0),sK1_skl(sK4_skl,X0)),X0)
| X0 = sK4_skl
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1144,f6051]) ).
fof(f12574,plain,
( in(ordered_pair(sK0_skl(sK4_skl,sK9_skl),sK1_skl(sK4_skl,sK9_skl)),sK9_skl)
| sK9_skl = sK4_skl ),
inference(resolution,[status(thm)],[f12571,f118]) ).
fof(f12575,plain,
( ~ sQ14_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK6_skl),sK1_skl(sK4_skl,sK6_skl)),sK6_skl)
| sK6_skl = sK4_skl ),
inference(resolution,[status(thm)],[f12571,f267]) ).
fof(f12586,plain,
( sQ672_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f12574,f811,f10091]) ).
fof(f12587,definition,
( sQ737_spl
<=> sK6_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ737_spl])],[split_symbol_definition]) ).
fof(f12588,plain,
( ~ sQ737_spl
| sK6_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f12587]) ).
fof(f12590,definition,
( sQ738_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK6_skl),sK1_skl(sK4_skl,sK6_skl)),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ738_spl])],[split_symbol_definition]) ).
fof(f12593,plain,
( ~ sQ14_spl
| sQ738_spl
| sQ737_spl ),
inference(split_clause,[status(thm)],[f12575,f12587,f12590,f266]) ).
fof(f12632,definition,
( sQ740_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ740_spl])],[split_symbol_definition]) ).
fof(f12633,plain,
( ~ sQ740_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f12632]) ).
fof(f12636,definition,
( sQ741_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK0_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ741_spl])],[split_symbol_definition]) ).
fof(f12637,plain,
( ~ sQ741_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK0_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f12636]) ).
fof(f12640,definition,
( sQ742_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK0_skl(sK10_skl,identity_relation(sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ742_spl])],[split_symbol_definition]) ).
fof(f12641,plain,
( ~ sQ742_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(sK4_skl)),sK0_skl(sK10_skl,identity_relation(sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f12640]) ).
fof(f12644,plain,
( ~ sQ742_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,identity_relation(sK4_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12641]) ).
fof(f12645,plain,
( ~ sQ742_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12644]) ).
fof(f12646,plain,
( ~ sQ742_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12645,f1274]) ).
fof(f12647,plain,
~ sQ742_spl,
inference(contradiction_clause,[status(thm)],[f12646]) ).
fof(f12648,plain,
( ~ sQ741_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f12637]) ).
fof(f12649,plain,
( ~ sQ741_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12648]) ).
fof(f12650,plain,
( ~ sQ741_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12649,f1274]) ).
fof(f12651,plain,
~ sQ741_spl,
inference(contradiction_clause,[status(thm)],[f12650]) ).
fof(f12652,plain,
( ~ sQ740_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f12633]) ).
fof(f12653,plain,
( ~ sQ740_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK4_skl),sK0_skl(sK10_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12652]) ).
fof(f12654,plain,
( ~ sQ740_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12653,f1274]) ).
fof(f12655,plain,
~ sQ740_spl,
inference(contradiction_clause,[status(thm)],[f12654]) ).
fof(f12667,plain,
( sQ15_spl
| ~ sQ737_spl
| ~ empty(relation_dom(sK4_skl)) ),
inference(backward_demodulation,[status(thm)],[f12588,f271]) ).
fof(f12680,plain,
( sQ15_spl
| ~ sQ737_spl
| ~ empty(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f12667]) ).
fof(f12681,plain,
( sQ15_spl
| ~ sQ737_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12680,f98]) ).
fof(f12682,plain,
( sQ15_spl
| ~ sQ737_spl ),
inference(contradiction_clause,[status(thm)],[f12681]) ).
fof(f12728,definition,
( sQ743_spl
<=> relation(identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ743_spl])],[split_symbol_definition]) ).
fof(f12730,plain,
( sQ743_spl
| ~ relation(identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f12728]) ).
fof(f12742,definition,
( sQ747_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ747_spl])],[split_symbol_definition]) ).
fof(f12743,plain,
( ~ sQ747_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,identity_relation(sK4_skl))),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f12742]) ).
fof(f12748,definition,
( sQ748_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,identity_relation(sK4_skl)),sK1_skl(sK4_skl,sK4_skl)),identity_relation(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ748_spl])],[split_symbol_definition]) ).
fof(f12749,plain,
( ~ sQ748_spl
| in(ordered_pair(sK0_skl(sK4_skl,identity_relation(sK4_skl)),sK1_skl(sK4_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(component_clause,[status(thm)],[f12748]) ).
fof(f12752,definition,
( sQ749_spl
<=> in(ordered_pair(sK0_skl(sK4_skl,identity_relation(sK4_skl)),sK1_skl(sK4_skl,identity_relation(sK4_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ749_spl])],[split_symbol_definition]) ).
fof(f12753,plain,
( ~ sQ749_spl
| in(ordered_pair(sK0_skl(sK4_skl,identity_relation(sK4_skl)),sK1_skl(sK4_skl,identity_relation(sK4_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f12752]) ).
fof(f12756,plain,
( ~ sQ749_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,identity_relation(sK4_skl))),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12753]) ).
fof(f12757,plain,
( ~ sQ749_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12756]) ).
fof(f12758,plain,
( ~ sQ749_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12757,f1274]) ).
fof(f12759,plain,
~ sQ749_spl,
inference(contradiction_clause,[status(thm)],[f12758]) ).
fof(f12760,plain,
( ~ sQ748_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f12749]) ).
fof(f12761,plain,
( ~ sQ748_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12760]) ).
fof(f12762,plain,
( ~ sQ748_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12761,f1274]) ).
fof(f12763,plain,
~ sQ748_spl,
inference(contradiction_clause,[status(thm)],[f12762]) ).
fof(f12764,plain,
( ~ sQ747_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,sK4_skl)),identity_relation(sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f12743]) ).
fof(f12765,plain,
( ~ sQ747_spl
| in(ordered_pair(sK0_skl(sK4_skl,sK4_skl),sK1_skl(sK4_skl,sK4_skl)),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12764]) ).
fof(f12766,plain,
( ~ sQ747_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12765,f1274]) ).
fof(f12767,plain,
~ sQ747_spl,
inference(contradiction_clause,[status(thm)],[f12766]) ).
fof(f12773,plain,
( sQ743_spl
| ~ relation(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f1144,f12730]) ).
fof(f12774,plain,
( sQ743_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12773,f99]) ).
fof(f12775,plain,
sQ743_spl,
inference(contradiction_clause,[status(thm)],[f12774]) ).
fof(f12801,plain,
( ~ sQ383_spl
| ~ sQ19_spl
| sK1_skl(sK10_skl,sK9_skl) = sK0_skl(sK10_skl,sK9_skl) ),
inference(forward_demodulation,[status(thm)],[f297,f6276]) ).
fof(f12802,plain,
( ~ sQ383_spl
| ~ sQ19_spl
| ~ in(sK0_skl(sK10_skl,sK9_skl),sK10_skl)
| ~ in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f12801,f58]) ).
fof(f12812,plain,
( ~ sQ383_spl
| ~ sQ19_spl
| ~ sQ381_spl
| ~ sQ18_spl
| sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f12802,f182,f141,f293,f5997,f296,f6275]) ).
fof(f12828,plain,
( sQ383_spl
| ~ sQ19_spl
| sK1_skl(sK10_skl,sK9_skl) != sK0_skl(sK10_skl,sK9_skl) ),
inference(forward_demodulation,[status(thm)],[f297,f6277]) ).
fof(f12920,definition,
( sQ759_spl
<=> sK1_skl(sK10_skl,identity_relation(sK4_skl)) = apply(sK4_skl,sK0_skl(sK10_skl,identity_relation(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ759_spl])],[split_symbol_definition]) ).
fof(f12921,plain,
( ~ sQ759_spl
| sK1_skl(sK10_skl,identity_relation(sK4_skl)) = apply(sK4_skl,sK0_skl(sK10_skl,identity_relation(sK4_skl))) ),
inference(component_clause,[status(thm)],[f12920]) ).
fof(f12924,definition,
( sQ760_spl
<=> sK1_skl(sK10_skl,identity_relation(sK4_skl)) = apply(identity_relation(sK4_skl),sK0_skl(sK10_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ760_spl])],[split_symbol_definition]) ).
fof(f12925,plain,
( ~ sQ760_spl
| sK1_skl(sK10_skl,identity_relation(sK4_skl)) = apply(identity_relation(sK4_skl),sK0_skl(sK10_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f12924]) ).
fof(f12931,plain,
( ~ sQ760_spl
| sK1_skl(sK10_skl,sK4_skl) = apply(identity_relation(sK4_skl),sK0_skl(sK10_skl,sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f12925]) ).
fof(f12932,plain,
( ~ sQ760_spl
| sK1_skl(sK10_skl,sK4_skl) = apply(sK4_skl,sK0_skl(sK10_skl,sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f1144,f12931]) ).
fof(f12933,plain,
( ~ sQ760_spl
| ~ sQ26_spl
| sK1_skl(sK10_skl,sK4_skl) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f2956,f12932]) ).
fof(f12934,plain,
( ~ sQ759_spl
| sK1_skl(sK10_skl,sK4_skl) = apply(sK4_skl,sK0_skl(sK10_skl,identity_relation(sK4_skl))) ),
inference(forward_demodulation,[status(thm)],[f1144,f12921]) ).
fof(f12935,plain,
( ~ sQ759_spl
| ~ sQ26_spl
| sK1_skl(sK10_skl,sK4_skl) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f2956,f12934]) ).
fof(f13224,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| ~ empty(sK4_skl)
| ~ relation(sK4_skl)
| X0 = sK4_skl ),
inference(paramodulation,[status(thm)],[f1163,f6408]) ).
fof(f13227,definition,
! [X0] :
( sQ771_spl
<=> ( ~ empty(relation_dom(X0))
| ~ relation(X0)
| X0 = sK4_skl ) ),
introduced(definition,[new_symbols(definition,[sQ771_spl])],[split_symbol_definition]) ).
fof(f13230,plain,
( ~ sQ50_spl
| ~ sQ51_spl
| sQ771_spl ),
inference(split_clause,[status(thm)],[f13224,f13227,f737,f732]) ).
fof(f13458,definition,
( sQ790_spl
<=> relation(identity_relation(relation_dom(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ790_spl])],[split_symbol_definition]) ).
fof(f13460,plain,
( sQ790_spl
| ~ relation(identity_relation(relation_dom(sK3_skl))) ),
inference(component_clause,[status(thm)],[f13458]) ).
fof(f13461,definition,
( sQ791_spl
<=> function(identity_relation(relation_dom(sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ791_spl])],[split_symbol_definition]) ).
fof(f13463,plain,
( sQ791_spl
| ~ function(identity_relation(relation_dom(sK3_skl))) ),
inference(component_clause,[status(thm)],[f13461]) ).
fof(f13469,plain,
( sQ791_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13463,f79]) ).
fof(f13470,plain,
sQ791_spl,
inference(contradiction_clause,[status(thm)],[f13469]) ).
fof(f13471,plain,
( sQ790_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13460,f69]) ).
fof(f13472,plain,
sQ790_spl,
inference(contradiction_clause,[status(thm)],[f13471]) ).
fof(f14389,definition,
! [X0,X1] :
( sQ864_spl
<=> ( X0 = X1
| apply(sK9_skl,X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ864_spl])],[split_symbol_definition]) ).
fof(f14390,plain,
! [X0,X1] :
( ~ sQ864_spl
| X0 = X1
| apply(sK9_skl,X0) = X0 ),
inference(component_clause,[status(thm)],[f14389]) ).
fof(f14404,plain,
( ~ sQ113_spl
| ~ sQ760_spl
| ~ sQ26_spl
| sK4_skl = identity_relation(sK10_skl)
| sK0_skl(sK10_skl,sK4_skl) = sK4_skl ),
inference(paramodulation,[status(thm)],[f1368,f12933]) ).
fof(f14412,plain,
( ~ sQ113_spl
| ~ sQ760_spl
| ~ sQ26_spl
| sQ54_spl
| sQ566_spl ),
inference(split_clause,[status(thm)],[f14404,f8610,f759,f400,f12924,f1367]) ).
fof(f14459,plain,
( ~ sQ113_spl
| ~ sQ759_spl
| ~ sQ26_spl
| sK4_skl = identity_relation(sK10_skl)
| sK0_skl(sK10_skl,sK4_skl) = sK4_skl ),
inference(paramodulation,[status(thm)],[f1368,f12935]) ).
fof(f14467,plain,
( ~ sQ113_spl
| ~ sQ759_spl
| ~ sQ26_spl
| sQ54_spl
| sQ566_spl ),
inference(split_clause,[status(thm)],[f14459,f8610,f759,f400,f12920,f1367]) ).
fof(f14498,plain,
( ~ sQ2_spl
| apply(sK9_skl,sK0_skl(sK10_skl,relation_rng(sK4_skl))) = sK0_skl(sK10_skl,relation_rng(sK4_skl))
| relation_rng(sK4_skl) = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f8934,f98]) ).
fof(f14502,definition,
( sQ870_spl
<=> relation_rng(sK4_skl) = identity_relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ870_spl])],[split_symbol_definition]) ).
fof(f14503,plain,
( ~ sQ870_spl
| relation_rng(sK4_skl) = identity_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f14502]) ).
fof(f14505,definition,
( sQ871_spl
<=> apply(sK9_skl,sK0_skl(sK10_skl,relation_rng(sK4_skl))) = sK0_skl(sK10_skl,relation_rng(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ871_spl])],[split_symbol_definition]) ).
fof(f14508,plain,
( ~ sQ2_spl
| sQ871_spl
| sQ870_spl ),
inference(split_clause,[status(thm)],[f14498,f14502,f14505,f148]) ).
fof(f14509,plain,
( ~ sQ870_spl
| sK4_skl = identity_relation(sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f949,f14503]) ).
fof(f14510,plain,
( ~ sQ870_spl
| sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14509,f761]) ).
fof(f14511,plain,
( ~ sQ870_spl
| sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f14510]) ).
fof(f14596,plain,
( ~ sQ2_spl
| apply(sK9_skl,sK0_skl(sK10_skl,relation_dom(sK4_skl))) = sK0_skl(sK10_skl,relation_dom(sK4_skl))
| relation_dom(sK4_skl) = identity_relation(sK10_skl) ),
inference(resolution,[status(thm)],[f8936,f98]) ).
fof(f14600,definition,
( sQ874_spl
<=> relation_dom(sK4_skl) = identity_relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ874_spl])],[split_symbol_definition]) ).
fof(f14601,plain,
( ~ sQ874_spl
| relation_dom(sK4_skl) = identity_relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f14600]) ).
fof(f14603,definition,
( sQ875_spl
<=> apply(sK9_skl,sK0_skl(sK10_skl,relation_dom(sK4_skl))) = sK0_skl(sK10_skl,relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ875_spl])],[split_symbol_definition]) ).
fof(f14606,plain,
( ~ sQ2_spl
| sQ875_spl
| sQ874_spl ),
inference(split_clause,[status(thm)],[f14596,f14600,f14603,f148]) ).
fof(f14607,plain,
( ~ sQ874_spl
| sK4_skl = identity_relation(sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f1163,f14601]) ).
fof(f14608,plain,
( ~ sQ874_spl
| sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14607,f761]) ).
fof(f14609,plain,
( ~ sQ874_spl
| sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f14608]) ).
fof(f14830,definition,
( sQ896_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(relation_rng(sK3_skl))),sK0_skl(sK10_skl,identity_relation(relation_rng(sK3_skl)))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ896_spl])],[split_symbol_definition]) ).
fof(f14831,plain,
( ~ sQ896_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(relation_rng(sK3_skl))),sK0_skl(sK10_skl,identity_relation(relation_rng(sK3_skl)))),sK4_skl) ),
inference(component_clause,[status(thm)],[f14830]) ).
fof(f14846,definition,
( sQ900_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,identity_relation(relation_rng(sK3_skl))),sK1_skl(sK10_skl,identity_relation(relation_rng(sK3_skl)))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ900_spl])],[split_symbol_definition]) ).
fof(f14847,plain,
( ~ sQ900_spl
| in(ordered_pair(sK0_skl(sK10_skl,identity_relation(relation_rng(sK3_skl))),sK1_skl(sK10_skl,identity_relation(relation_rng(sK3_skl)))),sK4_skl) ),
inference(component_clause,[status(thm)],[f14846]) ).
fof(f14918,definition,
( sQ906_spl
<=> in(ordered_pair(sK0_skl(relation_rng(sK3_skl),sK9_skl),sK0_skl(relation_rng(sK3_skl),sK9_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ906_spl])],[split_symbol_definition]) ).
fof(f14919,plain,
( ~ sQ906_spl
| in(ordered_pair(sK0_skl(relation_rng(sK3_skl),sK9_skl),sK0_skl(relation_rng(sK3_skl),sK9_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f14918]) ).
fof(f14980,definition,
( sQ908_spl
<=> in(ordered_pair(sK2_skl(relation_rng(sK3_skl)),sK2_skl(relation_rng(sK3_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ908_spl])],[split_symbol_definition]) ).
fof(f14981,plain,
( ~ sQ908_spl
| in(ordered_pair(sK2_skl(relation_rng(sK3_skl)),sK2_skl(relation_rng(sK3_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f14980]) ).
fof(f14984,definition,
( sQ909_spl
<=> in(ordered_pair(sK2_skl(relation_rng(sK3_skl)),apply(identity_relation(relation_rng(sK3_skl)),sK2_skl(relation_rng(sK3_skl)))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ909_spl])],[split_symbol_definition]) ).
fof(f14985,plain,
( ~ sQ909_spl
| in(ordered_pair(sK2_skl(relation_rng(sK3_skl)),apply(identity_relation(relation_rng(sK3_skl)),sK2_skl(relation_rng(sK3_skl)))),sK4_skl) ),
inference(component_clause,[status(thm)],[f14984]) ).
fof(f15002,plain,
( ~ sQ909_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14985,f1274]) ).
fof(f15003,plain,
~ sQ909_spl,
inference(contradiction_clause,[status(thm)],[f15002]) ).
fof(f15004,plain,
( ~ sQ908_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14981,f1274]) ).
fof(f15005,plain,
~ sQ908_spl,
inference(contradiction_clause,[status(thm)],[f15004]) ).
fof(f15007,plain,
( ~ sQ906_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14919,f1274]) ).
fof(f15008,plain,
~ sQ906_spl,
inference(contradiction_clause,[status(thm)],[f15007]) ).
fof(f15009,plain,
( ~ sQ900_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14847,f1274]) ).
fof(f15010,plain,
~ sQ900_spl,
inference(contradiction_clause,[status(thm)],[f15009]) ).
fof(f15011,plain,
( ~ sQ896_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14831,f1274]) ).
fof(f15012,plain,
~ sQ896_spl,
inference(contradiction_clause,[status(thm)],[f15011]) ).
fof(f15021,plain,
! [X0] :
( sQ3_spl
| ~ sQ99_spl
| ~ sQ864_spl
| sK11_skl = X0
| sK4_skl = sK11_skl ),
inference(paramodulation,[status(thm)],[f8938,f14390]) ).
fof(f15041,definition,
! [X0] :
( sQ911_spl
<=> sK11_skl = X0 ),
introduced(definition,[new_symbols(definition,[sQ911_spl])],[split_symbol_definition]) ).
fof(f15042,plain,
! [X0] :
( ~ sQ911_spl
| sK11_skl = X0 ),
inference(component_clause,[status(thm)],[f15041]) ).
fof(f15044,plain,
( sQ3_spl
| ~ sQ99_spl
| ~ sQ864_spl
| sQ911_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f15021,f3073,f15041,f14389,f1196,f152]) ).
fof(f15080,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ in(sK9_skl,ordered_pair(sK11_skl,sK11_skl))
| ~ in(sK11_skl,sK10_skl) ),
inference(paramodulation,[status(thm)],[f157,f1277]) ).
fof(f15088,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ243_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f15080,f152,f3858,f188,f156]) ).
fof(f15094,plain,
( sQ24_spl
| ~ sQ911_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f517,f15042]) ).
fof(f15098,plain,
( sQ24_spl
| ~ sQ911_spl ),
inference(contradiction_clause,[status(thm)],[f15094]) ).
fof(f15218,plain,
! [X0] :
( ~ sQ680_spl
| ~ sQ1_spl
| ~ sQ145_spl
| apply(sK9_skl,relation_dom(sK3_skl)) = sK4_skl
| ~ in(ordered_pair(sK10_skl,X0),sK3_skl) ),
inference(resolution,[status(thm)],[f1768,f10270]) ).
fof(f15222,plain,
( ~ sQ680_spl
| ~ sQ1_spl
| ~ sQ145_spl
| sQ314_spl
| sQ498_spl ),
inference(split_clause,[status(thm)],[f15218,f7638,f5173,f1767,f144,f10259]) ).
fof(f15453,plain,
( ~ sQ217_spl
| ~ sQ417_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3106,f6812]) ).
fof(f15457,plain,
( ~ sQ217_spl
| ~ sQ417_spl ),
inference(contradiction_clause,[status(thm)],[f15453]) ).
fof(f15526,plain,
( ~ sQ498_spl
| ~ in(sK10_skl,relation_dom(sK3_skl))
| ~ function(sK3_skl)
| ~ relation(sK3_skl) ),
inference(resolution,[status(thm)],[f7639,f163]) ).
fof(f15528,plain,
( ~ sQ498_spl
| ~ sQ447_spl
| ~ sQ43_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f15526,f252,f641,f6964,f7638]) ).
fof(f15892,plain,
! [X0] :
( sQ3_spl
| ~ in(ordered_pair(sK11_skl,X0),relation_dom(identity_relation(identity_relation(sK10_skl))))
| ~ function(identity_relation(identity_relation(sK10_skl)))
| ~ relation(identity_relation(identity_relation(sK10_skl))) ),
inference(resolution,[status(thm)],[f3129,f163]) ).
fof(f15895,definition,
! [X0] :
( sQ973_spl
<=> ~ in(ordered_pair(sK11_skl,X0),relation_dom(identity_relation(identity_relation(sK10_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ973_spl])],[split_symbol_definition]) ).
fof(f15898,plain,
( sQ3_spl
| sQ973_spl
| ~ sQ574_spl
| ~ sQ573_spl ),
inference(split_clause,[status(thm)],[f15892,f8662,f8665,f15895,f152]) ).
fof(f15920,plain,
( sQ3_spl
| ~ sQ100_spl
| ~ in(sK11_skl,relation_dom(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f3869,f163]) ).
fof(f15922,plain,
( sQ3_spl
| ~ sQ100_spl
| ~ sQ244_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f15920,f182,f185,f3861,f1203,f152]) ).
fof(f16052,plain,
( ~ sQ102_spl
| ~ sQ18_spl
| sQ383_spl ),
inference(split_clause,[status(thm)],[f2470,f6275,f293,f1247]) ).
fof(f16133,plain,
( sQ383_spl
| ~ sQ19_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f12828,f60]) ).
fof(f16134,plain,
( sQ383_spl
| ~ sQ19_spl
| sQ18_spl
| sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f16133,f182,f141,f293,f296,f6275]) ).
fof(f16135,plain,
( ~ sQ140_spl
| ~ sQ19_spl
| sK0_skl(sK10_skl,sK9_skl) = sK1_skl(sK10_skl,sK9_skl)
| sK9_skl = identity_relation(sK10_skl)
| sK1_skl(sK10_skl,sK9_skl) = sK0_skl(sK10_skl,sK9_skl) ),
inference(paramodulation,[status(thm)],[f1700,f297]) ).
fof(f16145,plain,
( ~ sQ140_spl
| ~ sQ19_spl
| sQ0_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f16135,f4873,f141,f296,f1699]) ).
fof(f16161,plain,
( sQ18_spl
| sK9_skl = identity_relation(sK10_skl)
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),apply(identity_relation(sK10_skl),sK0_skl(sK10_skl,sK9_skl))),identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f295,f357]) ).
fof(f16164,plain,
( sQ18_spl
| sQ0_spl
| sQ379_spl ),
inference(split_clause,[status(thm)],[f16161,f5988,f141,f293]) ).
fof(f16175,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK0_skl(sK10_skl,sK9_skl)),sK9_skl) ),
inference(forward_demodulation,[status(thm)],[f297,f486]) ).
fof(f16187,plain,
( sQ18_spl
| ~ sQ383_spl
| ~ sQ19_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK0_skl(sK10_skl,sK9_skl)),sK9_skl) ),
inference(backward_demodulation,[status(thm)],[f12801,f295]) ).
fof(f16199,plain,
( sQ18_spl
| ~ sQ383_spl
| ~ sQ19_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16187,f16175]) ).
fof(f16200,plain,
( sQ18_spl
| ~ sQ383_spl
| ~ sQ19_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f16199]) ).
fof(f16201,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f151,f155,f159,f191,f202,f205,f208,f228,f241,f258,f260,f272,f277,f301,f403,f488,f519,f565,f569,f571,f573,f599,f650,f686,f717,f719,f720,f748,f752,f768,f770,f801,f814,f817,f847,f902,f1036,f1111,f1156,f1172,f1199,f1206,f1230,f1250,f1254,f1265,f1271,f1347,f1370,f1374,f1378,f1410,f1411,f1412,f1413,f1433,f1434,f1499,f1503,f1507,f1570,f1574,f1578,f1588,f1592,f1596,f1624,f1628,f1632,f1702,f1706,f1710,f1762,f1766,f1770,f1782,f1786,f1790,f1900,f1904,f1908,f1981,f2014,f2035,f2119,f2120,f2129,f2133,f2137,f2278,f2282,f2286,f2352,f2362,f2386,f2390,f2396,f2508,f2522,f2526,f2530,f2534,f2566,f2573,f2589,f2595,f2625,f2628,f2631,f2656,f2666,f2670,f2722,f2726,f2731,f2775,f2859,f2860,f3076,f3081,f3085,f3086,f3088,f3119,f3130,f3144,f3325,f3376,f3633,f3662,f3742,f3750,f3752,f3857,f3918,f4149,f4151,f4157,f4162,f4165,f4168,f4571,f4578,f4579,f4587,f4594,f4595,f4807,f4876,f4917,f4920,f4923,f4926,f4949,f4953,f4969,f5179,f5380,f5404,f5420,f5469,f5473,f5520,f5555,f5568,f5704,f5706,f5938,f5942,f5946,f5950,f5991,f6006,f6021,f6381,f6395,f6404,f6513,f6578,f6587,f6714,f6741,f6778,f6781,f6794,f6801,f6958,f6967,f6971,f7011,f7014,f7026,f7029,f7036,f7040,f7094,f7098,f7102,f7142,f7157,f7275,f7279,f7378,f7379,f7442,f7446,f7450,f7499,f7509,f7513,f7517,f7532,f7536,f7540,f7617,f7619,f7621,f7628,f7632,f7637,f7641,f7649,f7787,f7824,f7938,f7942,f7982,f8216,f8251,f8586,f8589,f8629,f8633,f8638,f8640,f8646,f8647,f8668,f8672,f8674,f8676,f8687,f8861,f8862,f8875,f8877,f9124,f9142,f9283,f9284,f9298,f9299,f9306,f9317,f9430,f9523,f9526,f9554,f9712,f9983,f10094,f10164,f10231,f10258,f10262,f10266,f10307,f10399,f10652,f10656,f10662,f10666,f11099,f12586,f12593,f12647,f12651,f12655,f12682,f12759,f12763,f12767,f12775,f12812,f13230,f13470,f13472,f14412,f14467,f14508,f14511,f14606,f14609,f15003,f15005,f15008,f15010,f15012,f15044,f15088,f15098,f15222,f15457,f15528,f15898,f15922,f16052,f16134,f16145,f16164,f16200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:58:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 284.61/36.39 % Refutation found
% 284.61/36.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 284.61/36.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 108.29/37.69 % Elapsed time: 37.093881 seconds
% 108.29/37.69 % CPU time: 276.804099 seconds
% 108.29/37.69 % Total memory used: 1.299 GB
% 108.29/37.69 % Net memory used: 1.256 GB
%------------------------------------------------------------------------------