%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU207+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:40 PM UTC 2026
% Result : Theorem 12.69s 2.14s
% Output : CNFRefutation 12.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 90
% Syntax : Number of formulae : 398 ( 13 unt; 80 def)
% Number of atoms : 1712 ( 146 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 2463 (1149 ~;1158 |; 51 &)
% ( 92 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 86 ( 84 usr; 81 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-5 aty)
% Number of variables : 714 ( 685 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f33,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f39,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
! [A] :
( ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK2_skl(C,B,A),B)
& in(ordered_pair(sK2_skl(C,B,A),sK1_skl(C,B,A)),A) )
| in(sK1_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,sK1_skl(C,B,A)),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ( in(sK0_skl(D,C,B,A),B)
& in(ordered_pair(sK0_skl(D,C,B,A),D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(D,sK1_skl(C,B,A)),skolemize(E,sK2_skl(C,B,A))],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK0_skl(X3,X1,X2,X0),X3),X0)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( in(sK0_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,sK1_skl(X1,X2,X0)),X0)
| ~ in(sK1_skl(X1,X2,X0),X1)
| X1 = relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X1,X2,X0),sK1_skl(X1,X2,X0)),X0)
| in(sK1_skl(X1,X2,X0),X1)
| X1 = relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f52,plain,
! [X0,X1,X2] :
( in(sK2_skl(X1,X2,X0),X2)
| in(sK1_skl(X1,X2,X0),X1)
| X1 = relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f53,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK5_skl(B,A),sK4_skl(B,A)),A)
| in(sK4_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK4_skl(B,A)),A)
| ~ in(sK4_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK3_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(D,sK3_skl(C,B,A)),skolemize(C,sK4_skl(B,A)),skolemize(D,sK5_skl(B,A))],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK3_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK4_skl(X1,X0)),X0)
| ~ in(sK4_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [X0,X1] :
( in(ordered_pair(sK5_skl(X1,X0),sK4_skl(X1,X0)),X0)
| in(sK4_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f62,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f63,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ! [D,E] :
( ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ( ( in(ordered_pair(sK9_skl(C,B,A),sK8_skl(C,B,A)),B)
& in(ordered_pair(sK7_skl(C,B,A),sK9_skl(C,B,A)),A) )
| in(ordered_pair(sK7_skl(C,B,A),sK8_skl(C,B,A)),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,sK8_skl(C,B,A)),B)
| ~ in(ordered_pair(sK7_skl(C,B,A),F),A) )
| ~ in(ordered_pair(sK7_skl(C,B,A),sK8_skl(C,B,A)),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(sK6_skl(E,D,C,B,A),E),B)
& in(ordered_pair(D,sK6_skl(E,D,C,B,A)),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(F,sK6_skl(E,D,C,B,A)),skolemize(D,sK7_skl(C,B,A)),skolemize(E,sK8_skl(C,B,A)),skolemize(F,sK9_skl(C,B,A))],[f64]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,sK6_skl(X4,X3,X2,X1,X0)),X0)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK6_skl(X4,X3,X2,X1,X0),X4),X1)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0)
| in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f70,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X2,X1,X0),sK9_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X2)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f71,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK9_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X1)
| in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X2)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f72,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f73,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f80,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f85,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f86,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f98,plain,
( relation(sK13_skl)
& ~ empty(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f28]) ).
fof(f99,plain,
~ empty(sK13_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f103,plain,
? [A] :
( ? [B] :
( relation_rng(relation_composition(A,B)) != relation_image(B,relation_rng(A))
& relation(B) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f104,plain,
( relation_rng(relation_composition(sK15_skl,sK16_skl)) != relation_image(sK16_skl,relation_rng(sK15_skl))
& relation(sK16_skl)
& relation(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(A,sK15_skl),skolemize(B,sK16_skl)],[f103]) ).
fof(f105,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
relation(sK16_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
relation_rng(relation_composition(sK15_skl,sK16_skl)) != relation_image(sK16_skl,relation_rng(sK15_skl)),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f110,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f111,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f125,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X1,relation_image(X0,X2),X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f47]) ).
fof(f126,plain,
! [X0,X1,X2] :
( in(sK0_skl(X1,relation_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f49]) ).
fof(f128,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,sK6_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK6_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f132,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X0)
| in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f133,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X0)
| in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f132,f73]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK6_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f131,f73]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,sK6_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f130,f73]) ).
fof(f136,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,relation_rng(X0)),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f39,f129]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| ~ relation(X0)
| ~ in(relation_rng(X0),X1) ),
inference(resolution,[status(thm)],[f39,f129]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(ordered_pair(X1,relation_image(X0,X2)),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f39,f127]) ).
fof(f139,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X2),X0)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),X2) ),
inference(resolution,[status(thm)],[f39,f127]) ).
fof(f158,plain,
! [X0,X1] :
( ~ in(X0,ordered_pair(sK5_skl(X1,X0),sK4_skl(X1,X0)))
| in(sK4_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f60,f39]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ~ in(X2,ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)))
| in(ordered_pair(sK7_skl(X2,X1,X0),sK9_skl(X2,X1,X0)),X0)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f70,f39]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ~ in(X2,ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)))
| in(ordered_pair(sK9_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X1)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f71,f39]) ).
fof(f174,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(relation_composition(X0,X1),ordered_pair(X2,X4))
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f133,f39]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,relation_rng(relation_composition(X0,X1))),X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_composition(X0,X1)) ),
inference(resolution,[status(thm)],[f136,f133]) ).
fof(f184,plain,
! [X0,X1] :
( empty(X0)
| ~ element(ordered_pair(X1,relation_rng(X0)),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f136,f111]) ).
fof(f186,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,relation_rng(relation_composition(X0,X1))),X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f73]) ).
fof(f187,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X1),relation_composition(X2,X0))
| ~ relation(X0)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),X1) ),
inference(resolution,[status(thm)],[f137,f134]) ).
fof(f190,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK9_skl(X0,X1,X2),sK8_skl(X0,X1,X2)),X1)
| X0 = relation_composition(X2,X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f137,f71]) ).
fof(f191,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,X1,X2),sK9_skl(X0,X1,X2)),X2)
| X0 = relation_composition(X2,X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f137,f70]) ).
fof(f192,plain,
! [X0,X1] :
( in(sK4_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK4_skl(X1,X0)) ),
inference(resolution,[status(thm)],[f137,f60]) ).
fof(f198,plain,
! [X0,X1,X2] :
( empty(X0)
| ~ element(ordered_pair(X2,X1),X0)
| ~ relation(X0)
| ~ in(relation_rng(X0),X1) ),
inference(resolution,[status(thm)],[f137,f111]) ).
fof(f199,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X1),relation_composition(X2,X0))
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f187]) ).
fof(f202,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK9_skl(X0,X1,X2),sK8_skl(X0,X1,X2)),X1)
| X0 = relation_composition(X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f190]) ).
fof(f203,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X0,X1,X2),sK9_skl(X0,X1,X2)),X2)
| X0 = relation_composition(X2,X1)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f191]) ).
fof(f204,plain,
! [X0,X1] :
( in(sK4_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK4_skl(X1,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f192]) ).
fof(f208,plain,
! [X0,X1] :
( ~ in(X1,sK4_skl(X1,X0))
| X1 = relation_rng(X0)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK4_skl(X1,X0)) ),
inference(resolution,[status(thm)],[f204,f39]) ).
fof(f224,plain,
! [X0,X1,X2] :
( empty(X0)
| ~ element(ordered_pair(X1,relation_image(X0,X2)),X0)
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f138,f111]) ).
fof(f243,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK9_skl(X0,X2,X3),sK8_skl(X0,X2,X3)),X2)
| X0 = relation_composition(X3,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(sK7_skl(X0,X2,X3),X1)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),sK8_skl(X0,X2,X3)) ),
inference(resolution,[status(thm)],[f139,f71]) ).
fof(f244,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK7_skl(X0,X2,X3),sK9_skl(X0,X2,X3)),X3)
| X0 = relation_composition(X3,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(sK7_skl(X0,X2,X3),X1)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),sK8_skl(X0,X2,X3)) ),
inference(resolution,[status(thm)],[f139,f70]) ).
fof(f245,plain,
! [X0,X1,X2] :
( in(sK4_skl(X2,X0),X2)
| X2 = relation_rng(X0)
| ~ relation(X0)
| ~ in(sK5_skl(X2,X0),X1)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),sK4_skl(X2,X0)) ),
inference(resolution,[status(thm)],[f139,f60]) ).
fof(f260,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK9_skl(X1,X3,X4),sK8_skl(X1,X3,X4)),X3)
| X1 = relation_composition(X4,X3)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(ordered_pair(ordered_pair(sK7_skl(X1,X3,X4),sK8_skl(X1,X3,X4)),X2),X0)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),X2) ),
inference(resolution,[status(thm)],[f139,f71]) ).
fof(f261,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK7_skl(X1,X3,X4),sK9_skl(X1,X3,X4)),X4)
| X1 = relation_composition(X4,X3)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(ordered_pair(ordered_pair(sK7_skl(X1,X3,X4),sK8_skl(X1,X3,X4)),X2),X0)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),X2) ),
inference(resolution,[status(thm)],[f139,f70]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( in(sK4_skl(X3,X1),X3)
| X3 = relation_rng(X1)
| ~ relation(X1)
| ~ in(ordered_pair(ordered_pair(sK5_skl(X3,X1),sK4_skl(X3,X1)),X2),X0)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),X2) ),
inference(resolution,[status(thm)],[f139,f60]) ).
fof(f279,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK9_skl(X0,X2,X3),sK8_skl(X0,X2,X3)),X2)
| X0 = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(sK7_skl(X0,X2,X3),X1)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),sK8_skl(X0,X2,X3)) ),
inference(duplicate_literals_removal,[status(thm)],[f243]) ).
fof(f280,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK7_skl(X0,X2,X3),sK9_skl(X0,X2,X3)),X3)
| X0 = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(sK7_skl(X0,X2,X3),X1)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),sK8_skl(X0,X2,X3)) ),
inference(duplicate_literals_removal,[status(thm)],[f244]) ).
fof(f281,plain,
! [X0,X1,X2] :
( in(sK4_skl(X2,X0),X2)
| X2 = relation_rng(X0)
| ~ in(sK5_skl(X2,X0),X1)
| ~ relation(X0)
| ~ in(relation_image(X0,X1),sK4_skl(X2,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f245]) ).
fof(f340,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK9_skl(X0,X2,X3),sK8_skl(X0,X2,X3)),X2)
| X0 = relation_composition(X3,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(relation_composition(X0,X1),ordered_pair(sK7_skl(X0,X2,X3),X4))
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),X4),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f174,f71]) ).
fof(f341,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK7_skl(X0,X2,X3),sK9_skl(X0,X2,X3)),X3)
| X0 = relation_composition(X3,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(relation_composition(X0,X1),ordered_pair(sK7_skl(X0,X2,X3),X4))
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),X4),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f174,f70]) ).
fof(f342,plain,
! [X0,X1,X2,X3] :
( in(sK4_skl(X2,X0),X2)
| X2 = relation_rng(X0)
| ~ relation(X0)
| ~ in(relation_composition(X0,X1),ordered_pair(sK5_skl(X2,X0),X3))
| ~ in(ordered_pair(sK4_skl(X2,X0),X3),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f174,f60]) ).
fof(f362,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK9_skl(X1,X3,X4),sK8_skl(X1,X3,X4)),X3)
| X1 = relation_composition(X4,X3)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(relation_composition(X0,X1),ordered_pair(X2,sK8_skl(X1,X3,X4)))
| ~ in(ordered_pair(X2,sK7_skl(X1,X3,X4)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f174,f71]) ).
fof(f363,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK7_skl(X1,X3,X4),sK9_skl(X1,X3,X4)),X4)
| X1 = relation_composition(X4,X3)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(relation_composition(X0,X1),ordered_pair(X2,sK8_skl(X1,X3,X4)))
| ~ in(ordered_pair(X2,sK7_skl(X1,X3,X4)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f174,f70]) ).
fof(f364,plain,
! [X0,X1,X2,X3] :
( in(sK4_skl(X3,X1),X3)
| X3 = relation_rng(X1)
| ~ relation(X1)
| ~ in(relation_composition(X0,X1),ordered_pair(X2,sK4_skl(X3,X1)))
| ~ in(ordered_pair(X2,sK5_skl(X3,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f174,f60]) ).
fof(f381,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK9_skl(X0,X2,X3),sK8_skl(X0,X2,X3)),X2)
| X0 = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(relation_composition(X0,X1),ordered_pair(sK7_skl(X0,X2,X3),X4))
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),X4),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f340]) ).
fof(f382,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK7_skl(X0,X2,X3),sK9_skl(X0,X2,X3)),X3)
| X0 = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(relation_composition(X0,X1),ordered_pair(sK7_skl(X0,X2,X3),X4))
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),X4),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f341]) ).
fof(f383,plain,
! [X0,X1,X2,X3] :
( in(sK4_skl(X2,X0),X2)
| X2 = relation_rng(X0)
| ~ in(relation_composition(X0,X1),ordered_pair(sK5_skl(X2,X0),X3))
| ~ in(ordered_pair(sK4_skl(X2,X0),X3),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f342]) ).
fof(f401,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK9_skl(X1,X3,X4),sK8_skl(X1,X3,X4)),X3)
| X1 = relation_composition(X4,X3)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(relation_composition(X0,X1),ordered_pair(X2,sK8_skl(X1,X3,X4)))
| ~ in(ordered_pair(X2,sK7_skl(X1,X3,X4)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f362]) ).
fof(f402,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK7_skl(X1,X3,X4),sK9_skl(X1,X3,X4)),X4)
| X1 = relation_composition(X4,X3)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(relation_composition(X0,X1),ordered_pair(X2,sK8_skl(X1,X3,X4)))
| ~ in(ordered_pair(X2,sK7_skl(X1,X3,X4)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f363]) ).
fof(f403,plain,
! [X0,X1,X2,X3] :
( in(sK4_skl(X3,X1),X3)
| X3 = relation_rng(X1)
| ~ in(relation_composition(X0,X1),ordered_pair(X2,sK4_skl(X3,X1)))
| ~ in(ordered_pair(X2,sK5_skl(X3,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f364]) ).
fof(f450,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK9_skl(relation_composition(X1,X0),X2,X3),sK8_skl(relation_composition(X1,X0),X2,X3)),X2)
| relation_composition(X1,X0) = relation_composition(X3,X2)
| ~ relation(relation_composition(X1,X0))
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(relation_composition(X1,X0),X2,X3)) ),
inference(resolution,[status(thm)],[f199,f71]) ).
fof(f451,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK7_skl(relation_composition(X1,X0),X2,X3),sK9_skl(relation_composition(X1,X0),X2,X3)),X3)
| relation_composition(X1,X0) = relation_composition(X3,X2)
| ~ relation(relation_composition(X1,X0))
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(relation_composition(X1,X0),X2,X3)) ),
inference(resolution,[status(thm)],[f199,f70]) ).
fof(f452,plain,
! [X0,X1,X2] :
( in(sK4_skl(X1,relation_composition(X2,X0)),X1)
| X1 = relation_rng(relation_composition(X2,X0))
| ~ relation(relation_composition(X2,X0))
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK4_skl(X1,relation_composition(X2,X0))) ),
inference(resolution,[status(thm)],[f199,f60]) ).
fof(f468,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK9_skl(relation_composition(X1,X0),X2,X3),sK8_skl(relation_composition(X1,X0),X2,X3)),X2)
| relation_composition(X1,X0) = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(relation_composition(X1,X0),X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f450,f73]) ).
fof(f469,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK7_skl(relation_composition(X1,X0),X2,X3),sK9_skl(relation_composition(X1,X0),X2,X3)),X3)
| relation_composition(X1,X0) = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(relation_composition(X1,X0),X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f73]) ).
fof(f470,plain,
! [X0,X1,X2] :
( in(sK4_skl(X1,relation_composition(X2,X0)),X1)
| X1 = relation_rng(relation_composition(X2,X0))
| ~ relation(X2)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK4_skl(X1,relation_composition(X2,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f73]) ).
fof(f474,plain,
( ~ in(relation_image(sK16_skl,relation_rng(sK15_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))
| ~ relation(relation_composition(sK15_skl,sK16_skl))
| ~ in(relation_rng(relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f208,f107]) ).
fof(f475,definition,
( sQ0_spl
<=> in(relation_rng(relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ0_spl
| ~ in(relation_rng(relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,definition,
( sQ1_spl
<=> relation(relation_composition(sK15_skl,sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ1_spl
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,definition,
( sQ2_spl
<=> in(relation_image(sK16_skl,relation_rng(sK15_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ2_spl
| ~ in(relation_image(sK16_skl,relation_rng(sK15_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f474,f475,f478,f481]) ).
fof(f498,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK9_skl(X0,X2,X3),sK8_skl(X0,X2,X3)),X2)
| X0 = relation_composition(X3,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),relation_rng(relation_composition(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f186,f71]) ).
fof(f499,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK7_skl(X0,X2,X3),sK9_skl(X0,X2,X3)),X3)
| X0 = relation_composition(X3,X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),relation_rng(relation_composition(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f186,f70]) ).
fof(f500,plain,
! [X0,X1,X2] :
( in(sK4_skl(X2,X0),X2)
| X2 = relation_rng(X0)
| ~ relation(X0)
| ~ in(ordered_pair(sK4_skl(X2,X0),relation_rng(relation_composition(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f186,f60]) ).
fof(f527,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK9_skl(X0,X2,X3),sK8_skl(X0,X2,X3)),X2)
| X0 = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),relation_rng(relation_composition(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f498]) ).
fof(f528,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK7_skl(X0,X2,X3),sK9_skl(X0,X2,X3)),X3)
| X0 = relation_composition(X3,X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(ordered_pair(sK8_skl(X0,X2,X3),relation_rng(relation_composition(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f499]) ).
fof(f529,plain,
! [X0,X1,X2] :
( in(sK4_skl(X2,X0),X2)
| X2 = relation_rng(X0)
| ~ in(ordered_pair(sK4_skl(X2,X0),relation_rng(relation_composition(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f500]) ).
fof(f540,plain,
! [X0,X1] :
( ~ element(ordered_pair(X0,relation_image(sK13_skl,X1)),sK13_skl)
| ~ in(X0,X1)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f99,f224]) ).
fof(f541,plain,
! [X0,X1] :
( ~ element(ordered_pair(X1,X0),sK13_skl)
| ~ relation(sK13_skl)
| ~ in(relation_rng(sK13_skl),X0) ),
inference(resolution,[status(thm)],[f99,f198]) ).
fof(f542,plain,
! [X0] :
( ~ element(ordered_pair(X0,relation_rng(sK13_skl)),sK13_skl)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f99,f184]) ).
fof(f543,plain,
( ~ empty(relation_rng(sK13_skl))
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f99,f86]) ).
fof(f544,definition,
( sQ3_spl
<=> relation(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ3_spl
| ~ relation(sK13_skl) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,definition,
! [X0,X1] :
( sQ4_spl
<=> ( ~ element(ordered_pair(X0,relation_image(sK13_skl,X1)),sK13_skl)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f540,f544,f547]) ).
fof(f551,definition,
! [X0,X1] :
( sQ5_spl
<=> ( ~ element(ordered_pair(X1,X0),sK13_skl)
| ~ in(relation_rng(sK13_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f541,f551,f544]) ).
fof(f555,definition,
! [X0] :
( sQ6_spl
<=> ~ element(ordered_pair(X0,relation_rng(sK13_skl)),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( sQ6_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f542,f544,f555]) ).
fof(f559,definition,
( sQ7_spl
<=> empty(relation_rng(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( ~ sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f543,f544,f559]) ).
fof(f563,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f100]) ).
fof(f564,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f593,plain,
! [X0] :
( ~ in(X0,relation_rng(sK15_skl))
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl)
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(relation_composition(sK15_skl,sK16_skl)))
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f50,f107]) ).
fof(f594,definition,
( sQ8_spl
<=> relation(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ8_spl
| ~ relation(sK16_skl) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,definition,
( sQ9_spl
<=> in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ9_spl
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(relation_composition(sK15_skl,sK16_skl))) ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f600,definition,
! [X0] :
( sQ10_spl
<=> ( ~ in(X0,relation_rng(sK15_skl))
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f601,plain,
! [X0] :
( ~ sQ10_spl
| ~ in(X0,relation_rng(sK15_skl))
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f593,f594,f597,f600]) ).
fof(f604,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f106]) ).
fof(f605,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f720,plain,
( sQ2_spl
| empty(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))
| ~ element(relation_image(sK16_skl,relation_rng(sK15_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f483,f111]) ).
fof(f721,definition,
( sQ11_spl
<=> element(relation_image(sK16_skl,relation_rng(sK15_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f724,definition,
( sQ12_spl
<=> empty(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( sQ2_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f720,f721,f724,f481]) ).
fof(f730,plain,
( sQ1_spl
| ~ relation(sK16_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f480,f73]) ).
fof(f736,definition,
( sQ14_spl
<=> empty(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f739,definition,
( sQ15_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( sQ15_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f743,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f730,f739,f594,f478]) ).
fof(f744,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f741,f105]) ).
fof(f745,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f753,plain,
( sQ9_spl
| in(sK2_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(sK15_skl))
| relation_rng(relation_composition(sK15_skl,sK16_skl)) = relation_image(sK16_skl,relation_rng(sK15_skl))
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f599,f52]) ).
fof(f754,plain,
! [X0] :
( sQ9_spl
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f599,f129]) ).
fof(f759,definition,
( sQ17_spl
<=> relation_rng(relation_composition(sK15_skl,sK16_skl)) = relation_image(sK16_skl,relation_rng(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f760,plain,
( ~ sQ17_spl
| relation_rng(relation_composition(sK15_skl,sK16_skl)) = relation_image(sK16_skl,relation_rng(sK15_skl)) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f787,definition,
( sQ24_spl
<=> in(sK2_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f790,plain,
( sQ9_spl
| sQ24_spl
| sQ17_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f753,f594,f759,f787,f597]) ).
fof(f791,definition,
! [X0] :
( sQ25_spl
<=> ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f792,plain,
! [X0] :
( ~ sQ25_spl
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f794,plain,
( sQ9_spl
| sQ25_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f754,f478,f791,f597]) ).
fof(f802,plain,
( ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f760,f107]) ).
fof(f803,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f802]) ).
fof(f805,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(X1,sK16_skl))
| ~ relation(sK16_skl)
| ~ relation(X1)
| ~ in(sK6_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),X0,relation_composition(X1,sK16_skl),sK16_skl,X1),relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f601,f134]) ).
fof(f806,plain,
( ~ sQ10_spl
| in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(relation_composition(sK15_skl,sK16_skl)))
| relation_rng(relation_composition(sK15_skl,sK16_skl)) = relation_image(sK16_skl,relation_rng(sK15_skl))
| ~ relation(sK16_skl)
| ~ in(sK2_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f601,f51]) ).
fof(f808,definition,
! [X0] :
( sQ28_spl
<=> ( ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0))
| ~ in(sK0_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0),X0,sK16_skl),relation_rng(sK15_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f809,plain,
! [X0] :
( ~ sQ28_spl
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0))
| ~ in(sK0_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0),X0,sK16_skl),relation_rng(sK15_skl)) ),
inference(component_clause,[status(thm)],[f808]) ).
fof(f812,definition,
! [X0,X1] :
( sQ29_spl
<=> ( ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(X1,sK16_skl))
| ~ relation(X1)
| ~ in(sK6_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),X0,relation_composition(X1,sK16_skl),sK16_skl,X1),relation_rng(sK15_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f813,plain,
! [X0,X1] :
( ~ sQ29_spl
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(X1,sK16_skl))
| ~ relation(X1)
| ~ in(sK6_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),X0,relation_composition(X1,sK16_skl),sK16_skl,X1),relation_rng(sK15_skl)) ),
inference(component_clause,[status(thm)],[f812]) ).
fof(f815,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f805,f812,f594,f600]) ).
fof(f816,plain,
( ~ sQ10_spl
| sQ9_spl
| sQ17_spl
| ~ sQ8_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f806,f787,f594,f759,f597,f600]) ).
fof(f826,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ in(ordered_pair(X1,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl)
| ~ relation(sK16_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f792,f133]) ).
fof(f836,definition,
! [X0,X1] :
( sQ33_spl
<=> ( ~ in(ordered_pair(X1,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f837,plain,
! [X0,X1] :
( ~ sQ33_spl
| ~ in(ordered_pair(X1,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl) ),
inference(component_clause,[status(thm)],[f836]) ).
fof(f839,plain,
( ~ sQ25_spl
| sQ33_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f826,f739,f594,f836,f791]) ).
fof(f851,definition,
( sQ37_spl
<=> empty(ordered_pair(sK2_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( ~ sQ37_spl
| empty(ordered_pair(sK2_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl))) ),
inference(component_clause,[status(thm)],[f851]) ).
fof(f855,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f852,f80]) ).
fof(f856,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f855]) ).
fof(f857,plain,
( ~ sQ28_spl
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,relation_rng(sK15_skl)))
| ~ relation(sK16_skl)
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,relation_rng(sK15_skl))) ),
inference(resolution,[status(thm)],[f809,f126]) ).
fof(f860,definition,
( sQ38_spl
<=> in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,relation_rng(sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f862,plain,
( sQ38_spl
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,relation_rng(sK15_skl))) ),
inference(component_clause,[status(thm)],[f860]) ).
fof(f863,plain,
( ~ sQ28_spl
| ~ sQ8_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f857,f860,f594,f808]) ).
fof(f864,definition,
! [X0,X1] :
( sQ39_spl
<=> ( ~ in(ordered_pair(X1,sK0_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0),X0,sK16_skl)),sK15_skl)
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f865,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ in(ordered_pair(X1,sK0_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0),X0,sK16_skl)),sK15_skl)
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0)) ),
inference(component_clause,[status(thm)],[f864]) ).
fof(f900,plain,
( sQ0_spl
| empty(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))
| ~ element(relation_rng(relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f477,f111]) ).
fof(f901,definition,
( sQ47_spl
<=> element(relation_rng(relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f904,plain,
( sQ0_spl
| sQ12_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f900,f901,f724,f475]) ).
fof(f905,plain,
! [X0,X1,X2] :
( ~ sQ29_spl
| ~ in(ordered_pair(X2,sK6_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),X1,relation_composition(X0,sK16_skl),sK16_skl,X0)),sK15_skl)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(X1,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(X0,sK16_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f813,f129]) ).
fof(f907,definition,
! [X0,X1,X2] :
( sQ48_spl
<=> ( ~ in(ordered_pair(X2,sK6_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),X1,relation_composition(X0,sK16_skl),sK16_skl,X0)),sK15_skl)
| ~ in(ordered_pair(X1,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(X0,sK16_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f908,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| ~ in(ordered_pair(X2,sK6_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),X1,relation_composition(X0,sK16_skl),sK16_skl,X0)),sK15_skl)
| ~ in(ordered_pair(X1,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(X0,sK16_skl))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f907]) ).
fof(f910,plain,
( ~ sQ29_spl
| ~ sQ15_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f905,f907,f739,f812]) ).
fof(f927,plain,
! [X0] :
( sQ38_spl
| ~ in(X0,relation_rng(sK15_skl))
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f862,f127]) ).
fof(f929,plain,
( sQ38_spl
| sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f927,f594,f600,f860]) ).
fof(f954,plain,
! [X0] :
( ~ sQ48_spl
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl))
| ~ relation(sK16_skl)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl))
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f908,f135]) ).
fof(f964,definition,
! [X0] :
( sQ58_spl
<=> ( ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl))
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f965,plain,
! [X0] :
( ~ sQ58_spl
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl))
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f964]) ).
fof(f967,plain,
( ~ sQ48_spl
| ~ sQ8_spl
| sQ58_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f954,f739,f964,f594,f907]) ).
fof(f972,plain,
! [X0] :
( ~ sQ58_spl
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),relation_composition(sK15_skl,sK16_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f965]) ).
fof(f1113,plain,
! [X0] :
( ~ sQ39_spl
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0))
| ~ in(sK0_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X0),X0,sK16_skl),relation_rng(sK15_skl))
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f128,f865]) ).
fof(f1133,plain,
( ~ sQ39_spl
| sQ28_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1113,f739,f808,f864]) ).
fof(f1155,plain,
! [X0] :
( ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl))
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,relation_rng(sK15_skl)))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f59,f107]) ).
fof(f1156,definition,
( sQ72_spl
<=> in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,relation_rng(sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1157,plain,
( ~ sQ72_spl
| in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,relation_rng(sK15_skl))) ),
inference(component_clause,[status(thm)],[f1156]) ).
fof(f1158,plain,
( sQ72_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,relation_rng(sK15_skl))) ),
inference(component_clause,[status(thm)],[f1156]) ).
fof(f1159,definition,
! [X0] :
( sQ73_spl
<=> ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1160,plain,
! [X0] :
( ~ sQ73_spl
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f1159]) ).
fof(f1162,plain,
( sQ73_spl
| ~ sQ72_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1155,f478,f1156,f1159]) ).
fof(f1210,plain,
( sQ72_spl
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ relation(sK15_skl)
| ~ relation(sK16_skl)
| ~ in(relation_rng(sK16_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f1158,f470]) ).
fof(f1212,plain,
! [X0,X1] :
( sQ72_spl
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ in(relation_composition(X0,relation_composition(sK15_skl,sK16_skl)),ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))))
| ~ in(ordered_pair(X1,sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),X0)
| ~ relation(relation_composition(sK15_skl,sK16_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1158,f403]) ).
fof(f1213,plain,
! [X0,X1] :
( sQ72_spl
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ in(relation_composition(relation_composition(sK15_skl,sK16_skl),X0),ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X1))
| ~ in(ordered_pair(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X1),X0)
| ~ relation(X0)
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1158,f383]) ).
fof(f1214,plain,
! [X0] :
( sQ72_spl
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ in(ordered_pair(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(relation_composition(relation_composition(sK15_skl,sK16_skl),X0))),X0)
| ~ relation(X0)
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1158,f529]) ).
fof(f1215,plain,
! [X0,X1] :
( sQ72_spl
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ relation(relation_composition(sK15_skl,sK16_skl))
| ~ in(ordered_pair(ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),X1),X0)
| ~ relation(X0)
| ~ in(relation_image(X0,relation_composition(sK15_skl,sK16_skl)),X1) ),
inference(resolution,[status(thm)],[f1158,f262]) ).
fof(f1216,plain,
! [X0] :
( sQ72_spl
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ in(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X0)
| ~ relation(relation_composition(sK15_skl,sK16_skl))
| ~ in(relation_image(relation_composition(sK15_skl,sK16_skl),X0),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f1158,f281]) ).
fof(f1217,plain,
( sQ72_spl
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ relation(relation_composition(sK15_skl,sK16_skl))
| ~ in(relation_rng(relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f1158,f204]) ).
fof(f1218,plain,
( sQ72_spl
| ~ in(relation_composition(sK15_skl,sK16_skl),ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))))
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1158,f158]) ).
fof(f1219,plain,
! [X0] :
( sQ72_spl
| ~ in(X0,relation_rng(sK15_skl))
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f1158,f127]) ).
fof(f1221,definition,
( sQ74_spl
<=> in(relation_rng(sK16_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1223,plain,
( sQ74_spl
| ~ in(relation_rng(sK16_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(component_clause,[status(thm)],[f1221]) ).
fof(f1224,plain,
( sQ72_spl
| sQ17_spl
| ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f1210,f1221,f594,f739,f759,f1156]) ).
fof(f1229,definition,
! [X0,X1] :
( sQ76_spl
<=> ( ~ in(relation_composition(X0,relation_composition(sK15_skl,sK16_skl)),ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))))
| ~ in(ordered_pair(X1,sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1232,plain,
( sQ72_spl
| sQ17_spl
| ~ sQ1_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1212,f1229,f478,f759,f1156]) ).
fof(f1233,definition,
! [X0,X1] :
( sQ77_spl
<=> ( ~ in(relation_composition(relation_composition(sK15_skl,sK16_skl),X0),ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X1))
| ~ in(ordered_pair(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X1),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1236,plain,
( sQ72_spl
| sQ17_spl
| sQ77_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1213,f478,f1233,f759,f1156]) ).
fof(f1237,definition,
! [X0] :
( sQ78_spl
<=> ( ~ in(ordered_pair(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(relation_composition(relation_composition(sK15_skl,sK16_skl),X0))),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1240,plain,
( sQ72_spl
| sQ17_spl
| sQ78_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1214,f478,f1237,f759,f1156]) ).
fof(f1241,definition,
! [X0,X1] :
( sQ79_spl
<=> ( ~ in(ordered_pair(ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),X1),X0)
| ~ relation(X0)
| ~ in(relation_image(X0,relation_composition(sK15_skl,sK16_skl)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1244,plain,
( sQ72_spl
| sQ17_spl
| ~ sQ1_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f1215,f1241,f478,f759,f1156]) ).
fof(f1245,definition,
! [X0] :
( sQ80_spl
<=> ( ~ in(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X0)
| ~ in(relation_image(relation_composition(sK15_skl,sK16_skl),X0),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1248,plain,
( sQ72_spl
| sQ17_spl
| ~ sQ1_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1216,f1245,f478,f759,f1156]) ).
fof(f1249,plain,
( sQ72_spl
| sQ17_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1217,f475,f478,f759,f1156]) ).
fof(f1250,definition,
( sQ81_spl
<=> in(relation_composition(sK15_skl,sK16_skl),ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1252,plain,
( sQ81_spl
| ~ in(relation_composition(sK15_skl,sK16_skl),ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))) ),
inference(component_clause,[status(thm)],[f1250]) ).
fof(f1253,plain,
( sQ72_spl
| ~ sQ81_spl
| sQ17_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1218,f478,f759,f1250,f1156]) ).
fof(f1254,definition,
! [X0] :
( sQ82_spl
<=> ( ~ in(X0,relation_rng(sK15_skl))
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1255,plain,
! [X0] :
( ~ sQ82_spl
| ~ in(X0,relation_rng(sK15_skl))
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(component_clause,[status(thm)],[f1254]) ).
fof(f1257,plain,
( sQ72_spl
| sQ82_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1219,f594,f1254,f1156]) ).
fof(f1262,plain,
( ~ sQ73_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(relation_composition(sK15_skl,sK16_skl)))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1160,f128]) ).
fof(f1263,plain,
! [X0] :
( ~ sQ73_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(relation_composition(sK15_skl,sK16_skl),X0))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1160,f125]) ).
fof(f1264,plain,
! [X0,X1] :
( ~ sQ73_spl
| ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(X0,relation_composition(sK15_skl,sK16_skl)))
| ~ relation(relation_composition(sK15_skl,sK16_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1160,f134]) ).
fof(f1265,plain,
( ~ sQ73_spl
| in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,relation_rng(sK15_skl)))
| relation_image(sK16_skl,relation_rng(sK15_skl)) = relation_rng(relation_composition(sK15_skl,sK16_skl))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1160,f60]) ).
fof(f1266,plain,
! [X0,X1] :
( ~ sQ73_spl
| ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl)
| ~ relation(sK16_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f1160,f133]) ).
fof(f1268,definition,
( sQ84_spl
<=> in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1270,plain,
( sQ84_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(relation_composition(sK15_skl,sK16_skl))) ),
inference(component_clause,[status(thm)],[f1268]) ).
fof(f1271,plain,
( ~ sQ73_spl
| ~ sQ84_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1262,f478,f1268,f1159]) ).
fof(f1272,definition,
! [X0] :
( sQ85_spl
<=> ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(relation_composition(sK15_skl,sK16_skl),X0)) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1273,plain,
! [X0] :
( ~ sQ85_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(relation_composition(sK15_skl,sK16_skl),X0)) ),
inference(component_clause,[status(thm)],[f1272]) ).
fof(f1275,plain,
( ~ sQ73_spl
| sQ85_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1263,f478,f1272,f1159]) ).
fof(f1276,definition,
! [X0,X1] :
( sQ86_spl
<=> ( ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(X0,relation_composition(sK15_skl,sK16_skl)))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1277,plain,
! [X0,X1] :
( ~ sQ86_spl
| ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(X0,relation_composition(sK15_skl,sK16_skl)))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f1276]) ).
fof(f1279,plain,
( ~ sQ73_spl
| ~ sQ1_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1264,f1276,f478,f1159]) ).
fof(f1280,plain,
( ~ sQ73_spl
| sQ72_spl
| sQ17_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1265,f478,f759,f1156,f1159]) ).
fof(f1281,definition,
! [X0,X1] :
( sQ87_spl
<=> ( ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1282,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl) ),
inference(component_clause,[status(thm)],[f1281]) ).
fof(f1284,plain,
( ~ sQ73_spl
| sQ87_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1266,f739,f594,f1281,f1159]) ).
fof(f1290,plain,
( ~ sQ72_spl
| ~ in(relation_image(sK16_skl,relation_rng(sK15_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f1157,f39]) ).
fof(f1330,plain,
! [X0] :
( sQ84_spl
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1270,f129]) ).
fof(f1332,plain,
( sQ84_spl
| sQ73_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1330,f478,f1159,f1268]) ).
fof(f1337,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ in(X0,X1)
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f1273,f127]) ).
fof(f1339,definition,
! [X0,X1] :
( sQ97_spl
<=> ( ~ in(X0,X1)
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1342,plain,
( ~ sQ85_spl
| sQ97_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1337,f478,f1339,f1272]) ).
fof(f1346,plain,
! [X0,X1,X2] :
( ~ sQ86_spl
| ~ in(ordered_pair(X2,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(relation_composition(sK15_skl,sK16_skl))
| ~ relation(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1277,f133]) ).
fof(f1348,definition,
! [X0,X1,X2] :
( sQ98_spl
<=> ( ~ in(ordered_pair(X2,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(sK15_skl,sK16_skl))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1351,plain,
( ~ sQ86_spl
| ~ sQ1_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1346,f1348,f478,f1276]) ).
fof(f1353,plain,
! [X0] :
( ~ sQ87_spl
| ~ in(X0,relation_rng(sK15_skl))
| ~ relation(sK15_skl)
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f128]) ).
fof(f1354,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ in(X0,relation_image(sK15_skl,X1))
| ~ relation(sK15_skl)
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f125]) ).
fof(f1355,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| ~ in(ordered_pair(X2,X0),relation_composition(X1,sK15_skl))
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f134]) ).
fof(f1356,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| relation_composition(X0,X1) = relation_composition(X2,sK15_skl)
| ~ relation(sK15_skl)
| ~ relation(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK8_skl(relation_composition(X0,X1),sK15_skl,X2))
| ~ in(ordered_pair(sK8_skl(relation_composition(X0,X1),sK15_skl,X2),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f468]) ).
fof(f1358,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),relation_rng(relation_composition(X0,X2))),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f527]) ).
fof(f1359,plain,
! [X0,X1,X2,X3] :
( ~ sQ87_spl
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ in(relation_composition(X2,X0),ordered_pair(X3,sK8_skl(X0,sK15_skl,X1)))
| ~ in(ordered_pair(X3,sK7_skl(X0,sK15_skl,X1)),X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f401]) ).
fof(f1360,plain,
! [X0,X1,X2,X3] :
( ~ sQ87_spl
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ in(relation_composition(X0,X2),ordered_pair(sK7_skl(X0,sK15_skl,X1),X3))
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),X3),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f381]) ).
fof(f1361,plain,
! [X0,X1,X2,X3] :
( ~ sQ87_spl
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(X0)
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ in(ordered_pair(ordered_pair(sK7_skl(X0,sK15_skl,X1),sK8_skl(X0,sK15_skl,X1)),X3),X2)
| ~ relation(X2)
| ~ in(relation_image(X2,X0),X3)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f260]) ).
fof(f1362,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ in(sK7_skl(X0,sK15_skl,X1),X2)
| ~ relation(X0)
| ~ in(relation_image(X0,X2),sK8_skl(X0,sK15_skl,X1))
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f279]) ).
fof(f1363,plain,
! [X0,X1] :
( ~ sQ87_spl
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,sK15_skl,X1))
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f202]) ).
fof(f1364,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ in(X0,ordered_pair(sK7_skl(X0,sK15_skl,X1),sK8_skl(X0,sK15_skl,X1)))
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(X0)
| ~ relation(sK15_skl)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f162]) ).
fof(f1365,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| relation_composition(X0,X1) = relation_composition(sK15_skl,X2)
| ~ relation(X2)
| ~ relation(sK15_skl)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK8_skl(relation_composition(X0,X1),X2,sK15_skl))
| ~ in(ordered_pair(sK9_skl(relation_composition(X0,X1),X2,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f469]) ).
fof(f1367,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(sK8_skl(X0,X1,sK15_skl),relation_rng(relation_composition(X0,X2))),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f528]) ).
fof(f1368,plain,
! [X0,X1,X2,X3] :
( ~ sQ87_spl
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ relation(sK15_skl)
| ~ in(relation_composition(X2,X0),ordered_pair(X3,sK8_skl(X0,X1,sK15_skl)))
| ~ in(ordered_pair(X3,sK7_skl(X0,X1,sK15_skl)),X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f402]) ).
fof(f1369,plain,
! [X0,X1,X2,X3] :
( ~ sQ87_spl
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ relation(sK15_skl)
| ~ in(relation_composition(X0,X2),ordered_pair(sK7_skl(X0,X1,sK15_skl),X3))
| ~ in(ordered_pair(sK8_skl(X0,X1,sK15_skl),X3),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f382]) ).
fof(f1370,plain,
! [X0,X1,X2,X3] :
( ~ sQ87_spl
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(ordered_pair(sK7_skl(X0,X1,sK15_skl),sK8_skl(X0,X1,sK15_skl)),X3),X2)
| ~ relation(X2)
| ~ in(relation_image(X2,X0),X3)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f261]) ).
fof(f1371,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ relation(sK15_skl)
| ~ in(sK7_skl(X0,X1,sK15_skl),X2)
| ~ relation(X0)
| ~ in(relation_image(X0,X2),sK8_skl(X0,X1,sK15_skl))
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f280]) ).
fof(f1372,plain,
! [X0,X1] :
( ~ sQ87_spl
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ relation(sK15_skl)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,X1,sK15_skl))
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f203]) ).
fof(f1373,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ in(X0,ordered_pair(sK7_skl(X0,X1,sK15_skl),sK8_skl(X0,X1,sK15_skl)))
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f160]) ).
fof(f1374,plain,
! [X0,X1] :
( ~ sQ87_spl
| in(ordered_pair(sK9_skl(sK15_skl,X0,X1),sK8_skl(sK15_skl,X0,X1)),X0)
| sK15_skl = relation_composition(X1,X0)
| ~ relation(sK15_skl)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f71]) ).
fof(f1375,plain,
! [X0,X1] :
( ~ sQ87_spl
| in(ordered_pair(sK7_skl(sK15_skl,X0,X1),sK9_skl(sK15_skl,X0,X1)),X1)
| sK15_skl = relation_composition(X1,X0)
| ~ relation(sK15_skl)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f70]) ).
fof(f1376,plain,
! [X0] :
( ~ sQ87_spl
| in(sK4_skl(X0,sK15_skl),X0)
| X0 = relation_rng(sK15_skl)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(sK4_skl(X0,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f60]) ).
fof(f1377,plain,
! [X0,X1] :
( ~ sQ87_spl
| in(sK1_skl(X0,X1,sK15_skl),X0)
| X0 = relation_image(sK15_skl,X1)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(sK1_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f51]) ).
fof(f1378,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| ~ in(ordered_pair(X1,X0),relation_composition(sK15_skl,X2))
| ~ relation(X2)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(sK6_skl(X0,X1,relation_composition(sK15_skl,X2),X2,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1282,f135]) ).
fof(f1380,plain,
! [X0] :
( ~ sQ87_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(sK16_skl))
| ~ relation(sK16_skl)
| ~ in(ordered_pair(X0,sK3_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(sK16_skl),sK16_skl)),sK15_skl) ),
inference(resolution,[status(thm)],[f1282,f128]) ).
fof(f1381,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X1))
| ~ relation(sK16_skl)
| ~ in(ordered_pair(X0,sK0_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X1),X1,sK16_skl)),sK15_skl) ),
inference(resolution,[status(thm)],[f1282,f125]) ).
fof(f1382,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(X2,sK16_skl))
| ~ relation(sK16_skl)
| ~ relation(X2)
| ~ in(ordered_pair(X0,sK6_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X1,relation_composition(X2,sK16_skl),sK16_skl,X2)),sK15_skl) ),
inference(resolution,[status(thm)],[f1282,f134]) ).
fof(f1383,plain,
! [X0,X1] :
( ~ sQ87_spl
| empty(sK16_skl)
| ~ element(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl) ),
inference(resolution,[status(thm)],[f1282,f111]) ).
fof(f1384,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1353,f1254,f739,f1281]) ).
fof(f1385,definition,
! [X0,X1] :
( sQ99_spl
<=> ( ~ in(X0,relation_image(sK15_skl,X1))
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1388,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1354,f1385,f739,f1281]) ).
fof(f1389,definition,
! [X0,X1,X2] :
( sQ100_spl
<=> ( ~ in(ordered_pair(X2,X0),relation_composition(X1,sK15_skl))
| ~ relation(X1)
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1355,f1389,f739,f1281]) ).
fof(f1393,definition,
! [X0,X1,X2] :
( sQ101_spl
<=> ( relation_composition(X0,X1) = relation_composition(X2,sK15_skl)
| ~ relation(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK8_skl(relation_composition(X0,X1),sK15_skl,X2))
| ~ in(ordered_pair(sK8_skl(relation_composition(X0,X1),sK15_skl,X2),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1396,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1356,f1393,f739,f1281]) ).
fof(f1401,definition,
! [X0,X1,X2] :
( sQ103_spl
<=> ( X0 = relation_composition(X1,sK15_skl)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),relation_rng(relation_composition(X0,X2))),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1404,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1358,f1401,f739,f1281]) ).
fof(f1405,definition,
! [X0,X1,X2,X3] :
( sQ104_spl
<=> ( X0 = relation_composition(X1,sK15_skl)
| ~ relation(X1)
| ~ in(relation_composition(X2,X0),ordered_pair(X3,sK8_skl(X0,sK15_skl,X1)))
| ~ in(ordered_pair(X3,sK7_skl(X0,sK15_skl,X1)),X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1408,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f1359,f1405,f739,f1281]) ).
fof(f1409,definition,
! [X0,X1,X2,X3] :
( sQ105_spl
<=> ( X0 = relation_composition(X1,sK15_skl)
| ~ relation(X1)
| ~ in(relation_composition(X0,X2),ordered_pair(sK7_skl(X0,sK15_skl,X1),X3))
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),X3),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1412,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1360,f1409,f739,f1281]) ).
fof(f1413,definition,
! [X0,X1,X2,X3] :
( sQ106_spl
<=> ( X0 = relation_composition(X1,sK15_skl)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(ordered_pair(sK7_skl(X0,sK15_skl,X1),sK8_skl(X0,sK15_skl,X1)),X3),X2)
| ~ relation(X2)
| ~ in(relation_image(X2,X0),X3)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1416,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1361,f1413,f739,f1281]) ).
fof(f1417,definition,
! [X0,X1,X2] :
( sQ107_spl
<=> ( X0 = relation_composition(X1,sK15_skl)
| ~ relation(X1)
| ~ in(sK7_skl(X0,sK15_skl,X1),X2)
| ~ relation(X0)
| ~ in(relation_image(X0,X2),sK8_skl(X0,sK15_skl,X1))
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1420,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1362,f1417,f739,f1281]) ).
fof(f1421,definition,
! [X0,X1] :
( sQ108_spl
<=> ( X0 = relation_composition(X1,sK15_skl)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,sK15_skl,X1))
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1424,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f1363,f1421,f739,f1281]) ).
fof(f1425,definition,
! [X0,X1] :
( sQ109_spl
<=> ( ~ in(X0,ordered_pair(sK7_skl(X0,sK15_skl,X1),sK8_skl(X0,sK15_skl,X1)))
| X0 = relation_composition(X1,sK15_skl)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(X0,sK15_skl,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1428,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1364,f1425,f739,f1281]) ).
fof(f1429,definition,
! [X0,X1,X2] :
( sQ110_spl
<=> ( relation_composition(X0,X1) = relation_composition(sK15_skl,X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(relation_rng(X1),sK8_skl(relation_composition(X0,X1),X2,sK15_skl))
| ~ in(ordered_pair(sK9_skl(relation_composition(X0,X1),X2,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1432,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1365,f1429,f739,f1281]) ).
fof(f1437,definition,
! [X0,X1,X2] :
( sQ112_spl
<=> ( X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(X0,X1,sK15_skl),relation_rng(relation_composition(X0,X2))),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1440,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1367,f1437,f739,f1281]) ).
fof(f1441,definition,
! [X0,X1,X2,X3] :
( sQ113_spl
<=> ( X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ in(relation_composition(X2,X0),ordered_pair(X3,sK8_skl(X0,X1,sK15_skl)))
| ~ in(ordered_pair(X3,sK7_skl(X0,X1,sK15_skl)),X2)
| ~ relation(X0)
| ~ relation(X2)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1444,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f1368,f1441,f739,f1281]) ).
fof(f1445,definition,
! [X0,X1,X2,X3] :
( sQ114_spl
<=> ( X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ in(relation_composition(X0,X2),ordered_pair(sK7_skl(X0,X1,sK15_skl),X3))
| ~ in(ordered_pair(sK8_skl(X0,X1,sK15_skl),X3),X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1448,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1369,f1445,f739,f1281]) ).
fof(f1449,definition,
! [X0,X1,X2,X3] :
( sQ115_spl
<=> ( X0 = relation_composition(sK15_skl,X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(ordered_pair(sK7_skl(X0,X1,sK15_skl),sK8_skl(X0,X1,sK15_skl)),X3),X2)
| ~ relation(X2)
| ~ in(relation_image(X2,X0),X3)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1452,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1370,f1449,f739,f1281]) ).
fof(f1453,definition,
! [X0,X1,X2] :
( sQ116_spl
<=> ( X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ in(sK7_skl(X0,X1,sK15_skl),X2)
| ~ relation(X0)
| ~ in(relation_image(X0,X2),sK8_skl(X0,X1,sK15_skl))
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1456,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1371,f1453,f739,f1281]) ).
fof(f1457,definition,
! [X0,X1] :
( sQ117_spl
<=> ( X0 = relation_composition(sK15_skl,X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(relation_rng(X0),sK8_skl(X0,X1,sK15_skl))
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1460,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f1372,f1457,f739,f1281]) ).
fof(f1461,definition,
! [X0,X1] :
( sQ118_spl
<=> ( ~ in(X0,ordered_pair(sK7_skl(X0,X1,sK15_skl),sK8_skl(X0,X1,sK15_skl)))
| X0 = relation_composition(sK15_skl,X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK9_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1464,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f1373,f1461,f739,f1281]) ).
fof(f1465,definition,
! [X0,X1] :
( sQ119_spl
<=> ( in(ordered_pair(sK9_skl(sK15_skl,X0,X1),sK8_skl(sK15_skl,X0,X1)),X0)
| sK15_skl = relation_composition(X1,X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1466,plain,
! [X0,X1] :
( ~ sQ119_spl
| in(ordered_pair(sK9_skl(sK15_skl,X0,X1),sK8_skl(sK15_skl,X0,X1)),X0)
| sK15_skl = relation_composition(X1,X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(component_clause,[status(thm)],[f1465]) ).
fof(f1468,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1374,f1465,f739,f1281]) ).
fof(f1469,definition,
! [X0,X1] :
( sQ120_spl
<=> ( in(ordered_pair(sK7_skl(sK15_skl,X0,X1),sK9_skl(sK15_skl,X0,X1)),X1)
| sK15_skl = relation_composition(X1,X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1470,plain,
! [X0,X1] :
( ~ sQ120_spl
| in(ordered_pair(sK7_skl(sK15_skl,X0,X1),sK9_skl(sK15_skl,X0,X1)),X1)
| sK15_skl = relation_composition(X1,X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,X1),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(component_clause,[status(thm)],[f1469]) ).
fof(f1472,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f1375,f1469,f739,f1281]) ).
fof(f1473,definition,
! [X0] :
( sQ121_spl
<=> ( in(sK4_skl(X0,sK15_skl),X0)
| X0 = relation_rng(sK15_skl)
| ~ in(ordered_pair(sK4_skl(X0,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1476,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1376,f1473,f739,f1281]) ).
fof(f1477,definition,
! [X0,X1] :
( sQ122_spl
<=> ( in(sK1_skl(X0,X1,sK15_skl),X0)
| X0 = relation_image(sK15_skl,X1)
| ~ in(ordered_pair(sK1_skl(X0,X1,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1480,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1377,f1477,f739,f1281]) ).
fof(f1481,definition,
! [X0,X1,X2] :
( sQ123_spl
<=> ( ~ in(ordered_pair(X1,X0),relation_composition(sK15_skl,X2))
| ~ relation(X2)
| ~ in(ordered_pair(sK6_skl(X0,X1,relation_composition(sK15_skl,X2),X2,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1484,plain,
( ~ sQ87_spl
| ~ sQ15_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1378,f1481,f739,f1281]) ).
fof(f1489,definition,
! [X0] :
( sQ125_spl
<=> ~ in(ordered_pair(X0,sK3_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(sK16_skl),sK16_skl)),sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1492,definition,
( sQ126_spl
<=> in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1495,plain,
( ~ sQ87_spl
| ~ sQ126_spl
| ~ sQ8_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1380,f1489,f594,f1492,f1281]) ).
fof(f1496,definition,
! [X0,X1] :
( sQ127_spl
<=> ( ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X1))
| ~ in(ordered_pair(X0,sK0_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X1),X1,sK16_skl)),sK15_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1499,plain,
( ~ sQ87_spl
| ~ sQ8_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f1381,f1496,f594,f1281]) ).
fof(f1500,definition,
! [X0,X1,X2] :
( sQ128_spl
<=> ( ~ in(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(X2,sK16_skl))
| ~ relation(X2)
| ~ in(ordered_pair(X0,sK6_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X1,relation_composition(X2,sK16_skl),sK16_skl,X2)),sK15_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1503,plain,
( ~ sQ87_spl
| ~ sQ8_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f1382,f1500,f594,f1281]) ).
fof(f1504,definition,
! [X0,X1] :
( sQ129_spl
<=> ( ~ element(ordered_pair(X1,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ in(ordered_pair(X0,X1),sK15_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1507,plain,
( ~ sQ87_spl
| sQ14_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1383,f1504,f736,f1281]) ).
fof(f1508,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ119_spl
| ~ in(ordered_pair(sK8_skl(sK15_skl,sK15_skl,X0),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| sK15_skl = relation_composition(X0,sK15_skl)
| ~ relation(sK15_skl)
| ~ relation(X0)
| ~ in(ordered_pair(sK8_skl(sK15_skl,sK15_skl,X0),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1466,f1282]) ).
fof(f1519,definition,
! [X0] :
( sQ130_spl
<=> ( ~ in(ordered_pair(sK8_skl(sK15_skl,sK15_skl,X0),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| sK15_skl = relation_composition(X0,sK15_skl)
| ~ relation(X0)
| ~ in(ordered_pair(sK8_skl(sK15_skl,sK15_skl,X0),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1522,plain,
( ~ sQ87_spl
| ~ sQ119_spl
| ~ sQ15_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f1508,f1519,f739,f1465,f1281]) ).
fof(f1531,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ120_spl
| ~ in(ordered_pair(sK9_skl(sK15_skl,X0,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| sK15_skl = relation_composition(sK15_skl,X0)
| ~ relation(X0)
| ~ relation(sK15_skl)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ),
inference(resolution,[status(thm)],[f1470,f1282]) ).
fof(f1542,definition,
! [X0] :
( sQ131_spl
<=> ( ~ in(ordered_pair(sK9_skl(sK15_skl,X0,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| sK15_skl = relation_composition(sK15_skl,X0)
| ~ relation(X0)
| ~ in(ordered_pair(sK8_skl(sK15_skl,X0,sK15_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1545,plain,
( ~ sQ87_spl
| ~ sQ120_spl
| ~ sQ15_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1531,f1542,f739,f1469,f1281]) ).
fof(f1566,plain,
( ~ sQ72_spl
| empty(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))
| ~ element(relation_image(sK16_skl,relation_rng(sK15_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f1290,f111]) ).
fof(f1567,plain,
( ~ sQ72_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1566,f721,f724,f1156]) ).
fof(f1568,plain,
( ~ sQ58_spl
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_rng(relation_composition(sK15_skl,sK16_skl)))
| ~ relation(relation_composition(sK15_skl,sK16_skl)) ),
inference(resolution,[status(thm)],[f972,f128]) ).
fof(f1573,plain,
( ~ sQ58_spl
| ~ sQ9_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1568,f478,f597,f964]) ).
fof(f1578,plain,
( sQ74_spl
| empty(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))
| ~ element(relation_rng(sK16_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
inference(resolution,[status(thm)],[f1223,f111]) ).
fof(f1579,definition,
( sQ132_spl
<=> element(relation_rng(sK16_skl),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1582,plain,
( sQ74_spl
| sQ12_spl
| ~ sQ132_spl ),
inference(split_clause,[status(thm)],[f1578,f1579,f724,f1221]) ).
fof(f1642,plain,
( ~ sQ82_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(sK16_skl))
| ~ relation(sK16_skl)
| ~ in(sK3_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(sK16_skl),sK16_skl),relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f1255,f128]) ).
fof(f1643,plain,
! [X0] :
( ~ sQ82_spl
| ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X0))
| ~ relation(sK16_skl)
| ~ in(sK0_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X0),X0,sK16_skl),relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f1255,f125]) ).
fof(f1644,plain,
! [X0,X1] :
( ~ sQ82_spl
| ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(X1,sK16_skl))
| ~ relation(sK16_skl)
| ~ relation(X1)
| ~ in(sK6_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X0,relation_composition(X1,sK16_skl),sK16_skl,X1),relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f1255,f134]) ).
fof(f1645,plain,
! [X0] :
( ~ sQ82_spl
| empty(sK16_skl)
| ~ element(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ in(X0,relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f1255,f111]) ).
fof(f1646,definition,
( sQ135_spl
<=> in(sK3_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_rng(sK16_skl),sK16_skl),relation_rng(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1649,plain,
( ~ sQ82_spl
| ~ sQ126_spl
| ~ sQ8_spl
| ~ sQ135_spl ),
inference(split_clause,[status(thm)],[f1642,f1646,f594,f1492,f1254]) ).
fof(f1650,definition,
! [X0] :
( sQ136_spl
<=> ( ~ in(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X0))
| ~ in(sK0_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),relation_image(sK16_skl,X0),X0,sK16_skl),relation_rng(sK15_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1653,plain,
( ~ sQ82_spl
| ~ sQ8_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1643,f1650,f594,f1254]) ).
fof(f1654,definition,
! [X0,X1] :
( sQ137_spl
<=> ( ~ in(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),relation_composition(X1,sK16_skl))
| ~ relation(X1)
| ~ in(sK6_skl(sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),X0,relation_composition(X1,sK16_skl),sK16_skl,X1),relation_rng(sK15_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1657,plain,
( ~ sQ82_spl
| ~ sQ8_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1644,f1654,f594,f1254]) ).
fof(f1658,definition,
! [X0] :
( sQ138_spl
<=> ( ~ element(ordered_pair(X0,sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))),sK16_skl)
| ~ in(X0,relation_rng(sK15_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1661,plain,
( ~ sQ82_spl
| sQ14_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f1645,f1658,f736,f1254]) ).
fof(f1662,plain,
( sQ81_spl
| empty(ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl))))
| ~ element(relation_composition(sK15_skl,sK16_skl),ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))) ),
inference(resolution,[status(thm)],[f1252,f111]) ).
fof(f1663,definition,
( sQ139_spl
<=> element(relation_composition(sK15_skl,sK16_skl),ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1666,definition,
( sQ140_spl
<=> empty(ordered_pair(sK5_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)),sK4_skl(relation_image(sK16_skl,relation_rng(sK15_skl)),relation_composition(sK15_skl,sK16_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1669,plain,
( sQ81_spl
| sQ140_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f1662,f1663,f1666,f1250]) ).
fof(f1695,plain,
! [X0] :
( ~ sQ33_spl
| ~ in(X0,relation_rng(sK15_skl))
| ~ relation(sK15_skl)
| ~ in(ordered_pair(X0,sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl)),sK16_skl) ),
inference(resolution,[status(thm)],[f837,f128]) ).
fof(f1721,plain,
! [X0,X1] :
( ~ sQ33_spl
| ~ in(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X1))
| ~ relation(sK16_skl)
| ~ in(ordered_pair(X0,sK0_skl(sK1_skl(relation_rng(relation_composition(sK15_skl,sK16_skl)),relation_rng(sK15_skl),sK16_skl),relation_image(sK16_skl,X1),X1,sK16_skl)),sK15_skl) ),
inference(resolution,[status(thm)],[f837,f125]) ).
fof(f1725,plain,
( ~ sQ33_spl
| ~ sQ15_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1695,f600,f739,f836]) ).
fof(f1826,plain,
( ~ sQ33_spl
| ~ sQ8_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f1721,f864,f594,f836]) ).
fof(f1836,plain,
$false,
inference(sat_refutation,[status(thm)],[f484,f550,f554,f558,f562,f564,f603,f605,f727,f743,f745,f790,f794,f803,f815,f816,f839,f856,f863,f904,f910,f929,f967,f1133,f1162,f1224,f1232,f1236,f1240,f1244,f1248,f1249,f1253,f1257,f1271,f1275,f1279,f1280,f1284,f1332,f1342,f1351,f1384,f1388,f1392,f1396,f1404,f1408,f1412,f1416,f1420,f1424,f1428,f1432,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1495,f1499,f1503,f1507,f1522,f1545,f1567,f1573,f1582,f1649,f1653,f1657,f1661,f1669,f1725,f1826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU207+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:57:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 12.69/2.14 % Refutation found
% 12.69/2.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.69/2.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.69/2.17 % Elapsed time: 1.793365 seconds
% 12.69/2.17 % CPU time: 13.937918 seconds
% 12.69/2.17 % Total memory used: 240.775 MB
% 12.69/2.17 % Net memory used: 221.028 MB
%------------------------------------------------------------------------------