%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU061+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 02:19:10 PM UTC 2026
% Result : Theorem 0.28s 0.59s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 103
% Syntax : Number of formulae : 442 ( 47 unt; 81 def)
% Number of atoms : 1308 ( 271 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 1337 ( 471 ~; 694 |; 67 &)
% ( 95 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 91 ( 89 usr; 82 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-4 aty)
% Number of variables : 544 ( 511 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] : ~ empty(singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f43,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f53,plain,
! [A] :
( ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f54,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK2_skl(C,B,A),B)
& in(ordered_pair(sK1_skl(C,B,A),sK2_skl(C,B,A)),A) )
| in(sK1_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK1_skl(C,B,A),E),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ( in(sK0_skl(D,C,B,A),B)
& in(ordered_pair(D,sK0_skl(D,C,B,A)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_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))],[f55]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,sK0_skl(X3,X1,X2,X0)),X0)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( in(sK0_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X0)
| in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(sK1_skl(X1,X2,X0),X3),X0)
| ~ in(sK1_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f61,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK1_skl(X1,X2,X0),sK2_skl(X1,X2,X0)),X0)
| in(sK1_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f62,plain,
! [X0,X1,X2] :
( in(sK2_skl(X1,X2,X0),X2)
| in(sK1_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f63,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f64,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
( ! [A,B] :
( ( ( sK3_skl(B,A) = A
| in(sK3_skl(B,A),B) )
& ( sK3_skl(B,A) != A
| ~ in(sK3_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B,A))],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X0,X1] :
( sK3_skl(X0,X1) = X1
| in(sK3_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f70,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f71,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f72,plain,
( ! [A] :
( in(sK4_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(B,sK4_skl(A))],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0] :
( in(sK4_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,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)],[f9]) ).
fof(f76,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)],[f75]) ).
fof(f77,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)],[f76]) ).
fof(f78,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK7_skl(B,A),sK6_skl(B,A)),A)
| in(sK6_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK6_skl(B,A)),A)
| ~ in(sK6_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK5_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(D,sK5_skl(C,B,A)),skolemize(C,sK6_skl(B,A)),skolemize(D,sK7_skl(B,A))],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK5_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,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)],[f78]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK6_skl(X1,X0)),X0)
| ~ in(sK6_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
! [X0,X1] :
( in(ordered_pair(sK7_skl(X1,X0),sK6_skl(X1,X0)),X0)
| in(sK6_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f84,plain,
! [A] : element(sK8_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B,sK8_skl(A))],[f11]) ).
fof(f85,plain,
! [X0] : element(sK8_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f89,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f92,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f98,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f99,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
( function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f21]) ).
fof(f102,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f104,plain,
( relation(sK10_skl)
& empty(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f22]) ).
fof(f105,plain,
empty(sK10_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f113,plain,
( function(sK13_skl)
& empty(sK13_skl)
& relation(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f25]) ).
fof(f114,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
empty(sK13_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f117,plain,
( relation(sK14_skl)
& ~ empty(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(A,sK14_skl)],[f26]) ).
fof(f119,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f125,plain,
( one_to_one(sK17_skl)
& function(sK17_skl)
& relation(sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(A,sK17_skl)],[f29]) ).
fof(f126,plain,
relation(sK17_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
( relation_empty_yielding(sK18_skl)
& relation(sK18_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(A,sK18_skl)],[f30]) ).
fof(f130,plain,
relation(sK18_skl),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f133,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
? [A,B] :
( ( in(A,relation_rng(B))
<~> relation_inverse_image(B,singleton(A)) != empty_set )
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f135,plain,
? [A,B] :
( ( relation_inverse_image(B,singleton(A)) = empty_set
| ~ in(A,relation_rng(B)) )
& ( relation_inverse_image(B,singleton(A)) != empty_set
| in(A,relation_rng(B)) )
& relation(B) ),
inference(NNF_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
? [B] :
( ? [A] :
( ( relation_inverse_image(B,singleton(A)) = empty_set
| ~ in(A,relation_rng(B)) )
& ( relation_inverse_image(B,singleton(A)) != empty_set
| in(A,relation_rng(B)) ) )
& relation(B) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
( ( relation_inverse_image(sK19_skl,singleton(sK20_skl)) = empty_set
| ~ in(sK20_skl,relation_rng(sK19_skl)) )
& ( relation_inverse_image(sK19_skl,singleton(sK20_skl)) != empty_set
| in(sK20_skl,relation_rng(sK19_skl)) )
& relation(sK19_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(B,sK19_skl),skolemize(A,sK20_skl)],[f136]) ).
fof(f138,plain,
relation(sK19_skl),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
( relation_inverse_image(sK19_skl,singleton(sK20_skl)) != empty_set
| in(sK20_skl,relation_rng(sK19_skl)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f140,plain,
( relation_inverse_image(sK19_skl,singleton(sK20_skl)) = empty_set
| ~ in(sK20_skl,relation_rng(sK19_skl)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f141,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f142,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f144,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f146,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f148,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f152,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f153,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f156,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f163,definition,
( sQ0_spl
<=> in(sK20_skl,relation_rng(sK19_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ0_spl
| in(sK20_skl,relation_rng(sK19_skl)) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,definition,
( sQ1_spl
<=> relation_inverse_image(sK19_skl,singleton(sK20_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ1_spl
| relation_inverse_image(sK19_skl,singleton(sK20_skl)) = empty_set ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ1_spl
| relation_inverse_image(sK19_skl,singleton(sK20_skl)) != empty_set ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f139,f163,f166]) ).
fof(f170,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f140,f163,f166]) ).
fof(f171,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0)),X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f172,plain,
! [X0,X1,X2] :
( in(sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),X0)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f59]) ).
fof(f174,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f175,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f176,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f73]) ).
fof(f177,plain,
! [X0,X1] :
( in(ordered_pair(sK5_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f79]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f80]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| in(X0,relation_inverse_image(singleton(ordered_pair(X0,X1)),X2))
| ~ relation(singleton(ordered_pair(X0,X1))) ),
inference(resolution,[status(thm)],[f175,f173]) ).
fof(f187,plain,
! [X0,X1] :
( in(X1,relation_rng(singleton(ordered_pair(X0,X1))))
| ~ relation(singleton(ordered_pair(X0,X1))) ),
inference(resolution,[status(thm)],[f178,f175]) ).
fof(f188,plain,
sK10_skl = empty_set,
inference(resolution,[status(thm)],[f156,f105]) ).
fof(f190,plain,
! [X0] :
( X0 = sK10_skl
| ~ empty(X0) ),
inference(backward_demodulation,[status(thm)],[f188,f156]) ).
fof(f191,plain,
! [X0] : ~ in(X0,sK10_skl),
inference(backward_demodulation,[status(thm)],[f188,f176]) ).
fof(f192,plain,
( sQ1_spl
| relation_inverse_image(sK19_skl,singleton(sK20_skl)) != sK10_skl ),
inference(backward_demodulation,[status(thm)],[f188,f168]) ).
fof(f197,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X0,X1,sK13_skl),sK2_skl(X0,X1,sK13_skl)),sK13_skl)
| in(sK1_skl(X0,X1,sK13_skl),X0)
| X0 = relation_inverse_image(sK13_skl,X1) ),
inference(resolution,[status(thm)],[f61,f114]) ).
fof(f199,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X0,X1,sK9_skl),sK2_skl(X0,X1,sK9_skl)),sK9_skl)
| in(sK1_skl(X0,X1,sK9_skl),X0)
| X0 = relation_inverse_image(sK9_skl,X1) ),
inference(resolution,[status(thm)],[f61,f102]) ).
fof(f200,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X0,X1,sK19_skl),sK2_skl(X0,X1,sK19_skl)),sK19_skl)
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ),
inference(resolution,[status(thm)],[f61,f138]) ).
fof(f204,plain,
! [X0,X1,X2] :
( sK2_skl(X1,singleton(X2),X0) = X2
| in(sK1_skl(X1,singleton(X2),X0),X1)
| X1 = relation_inverse_image(X0,singleton(X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f62,f174]) ).
fof(f206,plain,
! [X0,X1] :
( in(sK2_skl(X0,X1,sK19_skl),relation_rng(sK19_skl))
| ~ relation(sK19_skl)
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ),
inference(resolution,[status(thm)],[f200,f178]) ).
fof(f207,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(X0,X1,sK19_skl),X2)
| in(sK1_skl(X0,X1,sK19_skl),relation_inverse_image(sK19_skl,X2))
| ~ relation(sK19_skl)
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ),
inference(resolution,[status(thm)],[f200,f173]) ).
fof(f209,definition,
! [X0,X1] :
( sQ2_spl
<=> ( in(sK2_skl(X0,X1,sK19_skl),relation_rng(sK19_skl))
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f210,plain,
! [X0,X1] :
( ~ sQ2_spl
| in(sK2_skl(X0,X1,sK19_skl),relation_rng(sK19_skl))
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,definition,
( sQ3_spl
<=> relation(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ3_spl
| ~ relation(sK19_skl) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f206,f209,f212]) ).
fof(f216,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( ~ in(sK2_skl(X0,X1,sK19_skl),X2)
| in(sK1_skl(X0,X1,sK19_skl),relation_inverse_image(sK19_skl,X2))
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ in(sK2_skl(X0,X1,sK19_skl),X2)
| in(sK1_skl(X0,X1,sK19_skl),relation_inverse_image(sK19_skl,X2))
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f207,f216,f212]) ).
fof(f220,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f138]) ).
fof(f221,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( ~ sQ1_spl
| relation_inverse_image(sK19_skl,singleton(sK20_skl)) = sK10_skl ),
inference(forward_demodulation,[status(thm)],[f188,f167]) ).
fof(f225,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK10_skl ),
inference(resolution,[status(thm)],[f190,f99]) ).
fof(f227,plain,
sK13_skl = sK10_skl,
inference(resolution,[status(thm)],[f115,f190]) ).
fof(f233,plain,
! [X0] :
( in(sK4_skl(X0),X0)
| X0 = sK10_skl ),
inference(forward_demodulation,[status(thm)],[f188,f74]) ).
fof(f235,plain,
! [X0,X1] :
( in(ordered_pair(sK4_skl(relation_inverse_image(X0,X1)),sK0_skl(sK4_skl(relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1),X1,X0)),X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = sK10_skl ),
inference(resolution,[status(thm)],[f233,f171]) ).
fof(f236,plain,
! [X0] :
( sK4_skl(singleton(X0)) = X0
| singleton(X0) = sK10_skl ),
inference(resolution,[status(thm)],[f233,f174]) ).
fof(f238,plain,
! [X0] :
( relation_rng(X0) = sK10_skl
| in(ordered_pair(sK5_skl(sK4_skl(relation_rng(X0)),relation_rng(X0),X0),sK4_skl(relation_rng(X0))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f177,f233]) ).
fof(f241,plain,
( ~ sQ0_spl
| in(ordered_pair(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),sK20_skl),sK19_skl)
| ~ relation(sK19_skl) ),
inference(resolution,[status(thm)],[f164,f177]) ).
fof(f243,definition,
( sQ5_spl
<=> in(ordered_pair(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),sK20_skl),sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ5_spl
| in(ordered_pair(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),sK20_skl),sK19_skl) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f241,f212,f243,f163]) ).
fof(f259,plain,
! [X0] :
( in(sK4_skl(X0),X0)
| X0 = sK13_skl ),
inference(backward_demodulation,[status(thm)],[f227,f233]) ).
fof(f265,plain,
! [X0] : ~ in(X0,sK13_skl),
inference(forward_demodulation,[status(thm)],[f227,f191]) ).
fof(f266,plain,
! [X0] :
( sK3_skl(sK13_skl,X0) = X0
| sK13_skl = singleton(X0) ),
inference(resolution,[status(thm)],[f265,f69]) ).
fof(f267,plain,
! [X0,X1] :
( in(sK1_skl(X1,sK13_skl,X0),X1)
| X1 = relation_inverse_image(X0,sK13_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f265,f62]) ).
fof(f268,plain,
( sQ1_spl
| relation_inverse_image(sK19_skl,singleton(sK20_skl)) != sK13_skl ),
inference(forward_demodulation,[status(thm)],[f227,f192]) ).
fof(f269,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X0,X1,sK14_skl),sK2_skl(X0,X1,sK14_skl)),sK14_skl)
| in(sK1_skl(X0,X1,sK14_skl),X0)
| X0 = relation_inverse_image(sK14_skl,X1) ),
inference(resolution,[status(thm)],[f119,f61]) ).
fof(f270,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X0,X1,sK17_skl),sK2_skl(X0,X1,sK17_skl)),sK17_skl)
| in(sK1_skl(X0,X1,sK17_skl),X0)
| X0 = relation_inverse_image(sK17_skl,X1) ),
inference(resolution,[status(thm)],[f126,f61]) ).
fof(f271,plain,
! [X0] :
( in(ordered_pair(sK7_skl(X0,sK17_skl),sK6_skl(X0,sK17_skl)),sK17_skl)
| in(sK6_skl(X0,sK17_skl),X0)
| X0 = relation_rng(sK17_skl) ),
inference(resolution,[status(thm)],[f82,f126]) ).
fof(f272,plain,
! [X0] :
( in(ordered_pair(sK7_skl(X0,sK14_skl),sK6_skl(X0,sK14_skl)),sK14_skl)
| in(sK6_skl(X0,sK14_skl),X0)
| X0 = relation_rng(sK14_skl) ),
inference(resolution,[status(thm)],[f82,f119]) ).
fof(f274,plain,
! [X0] :
( in(ordered_pair(sK7_skl(X0,sK13_skl),sK6_skl(X0,sK13_skl)),sK13_skl)
| in(sK6_skl(X0,sK13_skl),X0)
| X0 = relation_rng(sK13_skl) ),
inference(resolution,[status(thm)],[f82,f114]) ).
fof(f275,plain,
! [X0] :
( in(ordered_pair(sK7_skl(X0,sK9_skl),sK6_skl(X0,sK9_skl)),sK9_skl)
| in(sK6_skl(X0,sK9_skl),X0)
| X0 = relation_rng(sK9_skl) ),
inference(resolution,[status(thm)],[f82,f102]) ).
fof(f276,plain,
! [X0] :
( in(ordered_pair(sK7_skl(X0,sK19_skl),sK6_skl(X0,sK19_skl)),sK19_skl)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(resolution,[status(thm)],[f82,f138]) ).
fof(f278,plain,
! [X0] :
( in(sK6_skl(X0,sK13_skl),X0)
| X0 = relation_rng(sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f265]) ).
fof(f286,plain,
( ~ sQ5_spl
| in(sK20_skl,relation_rng(sK19_skl))
| ~ relation(sK19_skl) ),
inference(resolution,[status(thm)],[f244,f178]) ).
fof(f287,plain,
! [X0] :
( ~ sQ5_spl
| ~ in(sK20_skl,X0)
| in(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),relation_inverse_image(sK19_skl,X0))
| ~ relation(sK19_skl) ),
inference(resolution,[status(thm)],[f244,f173]) ).
fof(f289,plain,
( ~ sQ5_spl
| sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f286,f212,f163,f243]) ).
fof(f290,definition,
! [X0] :
( sQ8_spl
<=> ( ~ in(sK20_skl,X0)
| in(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),relation_inverse_image(sK19_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f291,plain,
! [X0] :
( ~ sQ8_spl
| ~ in(sK20_skl,X0)
| in(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),relation_inverse_image(sK19_skl,X0)) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( ~ sQ5_spl
| sQ8_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f287,f212,f290,f243]) ).
fof(f296,plain,
( ~ sQ1_spl
| relation_inverse_image(sK19_skl,singleton(sK20_skl)) = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f227,f222]) ).
fof(f305,plain,
! [X0] :
( in(ordered_pair(sK7_skl(X0,sK18_skl),sK6_skl(X0,sK18_skl)),sK18_skl)
| in(sK6_skl(X0,sK18_skl),X0)
| X0 = relation_rng(sK18_skl) ),
inference(resolution,[status(thm)],[f130,f82]) ).
fof(f306,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X0,X1,sK18_skl),sK2_skl(X0,X1,sK18_skl)),sK18_skl)
| in(sK1_skl(X0,X1,sK18_skl),X0)
| X0 = relation_inverse_image(sK18_skl,X1) ),
inference(resolution,[status(thm)],[f130,f61]) ).
fof(f328,plain,
! [X0] :
( in(sK6_skl(X0,sK19_skl),relation_rng(sK19_skl))
| ~ relation(sK19_skl)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(resolution,[status(thm)],[f276,f178]) ).
fof(f329,plain,
! [X0,X1] :
( ~ in(sK6_skl(X0,sK19_skl),X1)
| in(sK7_skl(X0,sK19_skl),relation_inverse_image(sK19_skl,X1))
| ~ relation(sK19_skl)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(resolution,[status(thm)],[f276,f173]) ).
fof(f331,definition,
! [X0] :
( sQ11_spl
<=> ( in(sK6_skl(X0,sK19_skl),relation_rng(sK19_skl))
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f332,plain,
! [X0] :
( ~ sQ11_spl
| in(sK6_skl(X0,sK19_skl),relation_rng(sK19_skl))
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( ~ sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f328,f331,f212]) ).
fof(f335,definition,
! [X0,X1] :
( sQ12_spl
<=> ( ~ in(sK6_skl(X0,sK19_skl),X1)
| in(sK7_skl(X0,sK19_skl),relation_inverse_image(sK19_skl,X1))
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f336,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ in(sK6_skl(X0,sK19_skl),X1)
| in(sK7_skl(X0,sK19_skl),relation_inverse_image(sK19_skl,X1))
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,plain,
( ~ sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f329,f335,f212]) ).
fof(f340,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f227,f225]) ).
fof(f341,plain,
relation_rng(sK13_skl) = sK13_skl,
inference(resolution,[status(thm)],[f340,f115]) ).
fof(f346,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,singleton(X2))
| ~ in(ordered_pair(sK1_skl(X1,singleton(X2),X0),X3),X0)
| X1 = relation_inverse_image(X0,singleton(X2))
| ~ relation(X0)
| sK2_skl(X1,singleton(X2),X0) = X2
| X1 = relation_inverse_image(X0,singleton(X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f204,f60]) ).
fof(f347,plain,
! [X0,X1] :
( sK2_skl(sK13_skl,singleton(X1),X0) = X1
| sK13_skl = relation_inverse_image(X0,singleton(X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f204,f265]) ).
fof(f353,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,singleton(X2))
| ~ in(ordered_pair(sK1_skl(X1,singleton(X2),X0),X3),X0)
| sK2_skl(X1,singleton(X2),X0) = X2
| X1 = relation_inverse_image(X0,singleton(X2))
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f346]) ).
fof(f354,plain,
! [X0] :
( in(ordered_pair(sK5_skl(X0,relation_rng(sK13_skl),sK13_skl),X0),sK13_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f341,f177]) ).
fof(f355,plain,
( relation(sK13_skl)
| ~ empty(sK13_skl) ),
inference(paramodulation,[status(thm)],[f341,f100]) ).
fof(f358,definition,
( sQ13_spl
<=> relation(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f361,definition,
! [X0] :
( sQ14_spl
<=> ( in(ordered_pair(sK5_skl(X0,relation_rng(sK13_skl),sK13_skl),X0),sK13_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f354,f358,f361]) ).
fof(f365,definition,
( sQ15_spl
<=> empty(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( sQ15_spl
| ~ empty(sK13_skl) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( sQ13_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f355,f365,f358]) ).
fof(f371,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f115]) ).
fof(f372,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f371]) ).
fof(f380,plain,
! [X0] :
( in(sK8_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f144,f85]) ).
fof(f396,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f148,f144]) ).
fof(f397,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f89]) ).
fof(f399,plain,
! [X0,X1] :
( ~ element(X1,powerset(sK13_skl))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f154,f115]) ).
fof(f401,plain,
! [X0,X1] :
( ~ sQ2_spl
| in(ordered_pair(sK5_skl(sK2_skl(X0,X1,sK19_skl),relation_rng(sK19_skl),sK19_skl),sK2_skl(X0,X1,sK19_skl)),sK19_skl)
| ~ relation(sK19_skl)
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ),
inference(resolution,[status(thm)],[f210,f177]) ).
fof(f403,definition,
! [X0,X1] :
( sQ16_spl
<=> ( in(ordered_pair(sK5_skl(sK2_skl(X0,X1,sK19_skl),relation_rng(sK19_skl),sK19_skl),sK2_skl(X0,X1,sK19_skl)),sK19_skl)
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f401,f403,f212,f209]) ).
fof(f441,plain,
! [X0] :
( ~ in(X0,sK8_skl(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f380,f43]) ).
fof(f452,plain,
! [X0,X1] :
( in(sK1_skl(X0,X1,sK13_skl),X0)
| X0 = relation_inverse_image(sK13_skl,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f265]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(sK1_skl(X0,X1,sK13_skl),X2),sK13_skl)
| X0 = relation_inverse_image(sK13_skl,X1)
| ~ relation(sK13_skl)
| X0 = relation_inverse_image(sK13_skl,X1) ),
inference(resolution,[status(thm)],[f452,f60]) ).
fof(f454,plain,
! [X0] : sK13_skl = relation_inverse_image(sK13_skl,X0),
inference(resolution,[status(thm)],[f452,f265]) ).
fof(f460,definition,
! [X0,X1,X2] :
( sQ17_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(sK1_skl(X0,X1,sK13_skl),X2),sK13_skl)
| X0 = relation_inverse_image(sK13_skl,X1)
| X0 = relation_inverse_image(sK13_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ13_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f453,f460,f358]) ).
fof(f470,plain,
! [X0,X1] :
( in(sK2_skl(X0,X1,sK9_skl),relation_rng(sK9_skl))
| ~ relation(sK9_skl)
| in(sK1_skl(X0,X1,sK9_skl),X0)
| X0 = relation_inverse_image(sK9_skl,X1) ),
inference(resolution,[status(thm)],[f199,f178]) ).
fof(f471,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(X0,X1,sK9_skl),X2)
| in(sK1_skl(X0,X1,sK9_skl),relation_inverse_image(sK9_skl,X2))
| ~ relation(sK9_skl)
| in(sK1_skl(X0,X1,sK9_skl),X0)
| X0 = relation_inverse_image(sK9_skl,X1) ),
inference(resolution,[status(thm)],[f199,f173]) ).
fof(f473,definition,
! [X0,X1] :
( sQ18_spl
<=> ( in(sK2_skl(X0,X1,sK9_skl),relation_rng(sK9_skl))
| in(sK1_skl(X0,X1,sK9_skl),X0)
| X0 = relation_inverse_image(sK9_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f476,definition,
( sQ19_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ19_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( ~ sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f470,f473,f476]) ).
fof(f480,definition,
! [X0,X1,X2] :
( sQ20_spl
<=> ( ~ in(sK2_skl(X0,X1,sK9_skl),X2)
| in(sK1_skl(X0,X1,sK9_skl),relation_inverse_image(sK9_skl,X2))
| in(sK1_skl(X0,X1,sK9_skl),X0)
| X0 = relation_inverse_image(sK9_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ19_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f471,f480,f476]) ).
fof(f484,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f102]) ).
fof(f485,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f487,plain,
( ~ sQ8_spl
| in(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),relation_inverse_image(sK19_skl,singleton(sK20_skl))) ),
inference(resolution,[status(thm)],[f291,f175]) ).
fof(f488,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| in(sK5_skl(sK20_skl,relation_rng(sK19_skl),sK19_skl),sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f296,f487]) ).
fof(f489,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f265]) ).
fof(f490,plain,
( ~ sQ8_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f493,plain,
! [X0,X1] :
( in(sK1_skl(X0,X1,sK13_skl),X0)
| X0 = sK13_skl ),
inference(backward_demodulation,[status(thm)],[f454,f452]) ).
fof(f494,plain,
! [X0,X1] :
( in(sK0_skl(X0,relation_inverse_image(sK13_skl,X1),X1,sK13_skl),X1)
| ~ in(X0,sK13_skl)
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f454,f172]) ).
fof(f495,plain,
! [X0,X1] :
( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK13_skl,X1),X1,sK13_skl)),sK13_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f454,f171]) ).
fof(f496,definition,
! [X0,X1] :
( sQ21_spl
<=> ( in(sK0_skl(X0,relation_inverse_image(sK13_skl,X1),X1,sK13_skl),X1)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ21_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f494,f358,f496]) ).
fof(f500,definition,
! [X0,X1] :
( sQ22_spl
<=> ( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK13_skl,X1),X1,sK13_skl)),sK13_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ22_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f495,f358,f500]) ).
fof(f515,plain,
! [X0,X1] :
( in(ordered_pair(sK4_skl(relation_inverse_image(X0,X1)),sK0_skl(sK4_skl(relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1),X1,X0)),X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f227,f235]) ).
fof(f522,plain,
! [X0] :
( in(ordered_pair(sK4_skl(relation_inverse_image(sK19_skl,X0)),sK0_skl(sK4_skl(relation_inverse_image(sK19_skl,X0)),relation_inverse_image(sK19_skl,X0),X0,sK19_skl)),sK19_skl)
| relation_inverse_image(sK19_skl,X0) = sK13_skl ),
inference(resolution,[status(thm)],[f515,f138]) ).
fof(f573,plain,
! [X0,X1] :
( ~ sQ4_spl
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1)
| ~ relation(sK19_skl)
| in(sK1_skl(X0,X1,sK19_skl),relation_inverse_image(sK19_skl,X1))
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ),
inference(resolution,[status(thm)],[f217,f62]) ).
fof(f576,definition,
! [X0,X1] :
( sQ23_spl
<=> ( in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1)
| in(sK1_skl(X0,X1,sK19_skl),relation_inverse_image(sK19_skl,X1))
| in(sK1_skl(X0,X1,sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f573,f576,f212,f216]) ).
fof(f581,plain,
! [X0] :
( sK4_skl(singleton(X0)) = X0
| singleton(X0) = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f227,f236]) ).
fof(f585,plain,
! [X0,X1] :
( sK4_skl(singleton(ordered_pair(X1,X0))) = ordered_pair(X1,X0)
| in(X0,relation_rng(singleton(ordered_pair(X1,X0))))
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f581,f187]) ).
fof(f586,plain,
! [X0,X1,X2] :
( sK4_skl(singleton(ordered_pair(X0,X1))) = ordered_pair(X0,X1)
| ~ in(X1,X2)
| in(X0,relation_inverse_image(singleton(ordered_pair(X0,X1)),X2))
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f581,f184]) ).
fof(f594,plain,
! [X0] :
( sK4_skl(singleton(X0)) = X0
| ~ empty(sK13_skl) ),
inference(paramodulation,[status(thm)],[f581,f92]) ).
fof(f597,definition,
( sQ24_spl
<=> relation_inverse_image(sK19_skl,sK13_skl) = sK13_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ24_spl
| relation_inverse_image(sK19_skl,sK13_skl) != sK13_skl ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f604,definition,
! [X0,X1] :
( sQ26_spl
<=> ( sK4_skl(singleton(ordered_pair(X1,X0))) = ordered_pair(X1,X0)
| in(X0,relation_rng(singleton(ordered_pair(X1,X0)))) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f585,f358,f604]) ).
fof(f608,definition,
! [X0,X1,X2] :
( sQ27_spl
<=> ( sK4_skl(singleton(ordered_pair(X0,X1))) = ordered_pair(X0,X1)
| ~ in(X1,X2)
| in(X0,relation_inverse_image(singleton(ordered_pair(X0,X1)),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( sQ27_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f586,f358,f608]) ).
fof(f612,definition,
! [X0] :
( sQ28_spl
<=> sK4_skl(singleton(X0)) = X0 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ28_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f594,f365,f612]) ).
fof(f624,plain,
! [X0] :
( relation_rng(X0) = sK13_skl
| in(ordered_pair(sK5_skl(sK4_skl(relation_rng(X0)),relation_rng(X0),X0),sK4_skl(relation_rng(X0))),X0)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f227,f238]) ).
fof(f629,plain,
( relation_rng(sK13_skl) = sK13_skl
| in(ordered_pair(sK5_skl(sK4_skl(relation_rng(sK13_skl)),relation_rng(sK13_skl),sK13_skl),sK4_skl(relation_rng(sK13_skl))),sK13_skl) ),
inference(resolution,[status(thm)],[f624,f114]) ).
fof(f654,definition,
( sQ35_spl
<=> in(ordered_pair(sK5_skl(sK4_skl(relation_rng(sK13_skl)),relation_rng(sK13_skl),sK13_skl),sK4_skl(relation_rng(sK13_skl))),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( ~ sQ35_spl
| in(ordered_pair(sK5_skl(sK4_skl(relation_rng(sK13_skl)),relation_rng(sK13_skl),sK13_skl),sK4_skl(relation_rng(sK13_skl))),sK13_skl) ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f657,definition,
( sQ36_spl
<=> relation_rng(sK13_skl) = sK13_skl ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f629,f654,f657]) ).
fof(f675,plain,
( ~ sQ35_spl
| in(ordered_pair(sK5_skl(sK4_skl(sK13_skl),relation_rng(sK13_skl),sK13_skl),sK4_skl(relation_rng(sK13_skl))),sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f341,f655]) ).
fof(f676,plain,
( ~ sQ35_spl
| in(ordered_pair(sK5_skl(sK4_skl(sK13_skl),sK13_skl,sK13_skl),sK4_skl(relation_rng(sK13_skl))),sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f341,f675]) ).
fof(f677,plain,
( ~ sQ35_spl
| in(ordered_pair(sK5_skl(sK4_skl(sK13_skl),sK13_skl,sK13_skl),sK4_skl(sK13_skl)),sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f341,f676]) ).
fof(f678,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f265]) ).
fof(f679,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f686,plain,
! [X0,X1] :
( sK3_skl(sK13_skl,ordered_pair(X1,X0)) = ordered_pair(X1,X0)
| in(X0,relation_rng(singleton(ordered_pair(X1,X0))))
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f266,f187]) ).
fof(f687,plain,
! [X0,X1,X2] :
( sK3_skl(sK13_skl,ordered_pair(X0,X1)) = ordered_pair(X0,X1)
| ~ in(X1,X2)
| in(X0,relation_inverse_image(singleton(ordered_pair(X0,X1)),X2))
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f266,f184]) ).
fof(f696,plain,
! [X0] :
( sK3_skl(sK13_skl,X0) = X0
| ~ empty(sK13_skl) ),
inference(paramodulation,[status(thm)],[f266,f92]) ).
fof(f703,definition,
! [X0,X1] :
( sQ42_spl
<=> ( sK3_skl(sK13_skl,ordered_pair(X1,X0)) = ordered_pair(X1,X0)
| in(X0,relation_rng(singleton(ordered_pair(X1,X0)))) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( sQ42_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f686,f358,f703]) ).
fof(f707,definition,
! [X0,X1,X2] :
( sQ43_spl
<=> ( sK3_skl(sK13_skl,ordered_pair(X0,X1)) = ordered_pair(X0,X1)
| ~ in(X1,X2)
| in(X0,relation_inverse_image(singleton(ordered_pair(X0,X1)),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( sQ43_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f687,f358,f707]) ).
fof(f711,definition,
! [X0] :
( sQ44_spl
<=> sK3_skl(sK13_skl,X0) = X0 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( sQ44_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f696,f365,f711]) ).
fof(f765,plain,
! [X0] :
( sK13_skl = relation_inverse_image(X0,sK13_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f267,f265]) ).
fof(f779,plain,
! [X0] : in(X0,powerset(X0)),
inference(resolution,[status(thm)],[f397,f133]) ).
fof(f784,plain,
! [X0,X1] :
( in(sK2_skl(X0,X1,sK14_skl),relation_rng(sK14_skl))
| ~ relation(sK14_skl)
| in(sK1_skl(X0,X1,sK14_skl),X0)
| X0 = relation_inverse_image(sK14_skl,X1) ),
inference(resolution,[status(thm)],[f269,f178]) ).
fof(f785,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(X0,X1,sK14_skl),X2)
| in(sK1_skl(X0,X1,sK14_skl),relation_inverse_image(sK14_skl,X2))
| ~ relation(sK14_skl)
| in(sK1_skl(X0,X1,sK14_skl),X0)
| X0 = relation_inverse_image(sK14_skl,X1) ),
inference(resolution,[status(thm)],[f269,f173]) ).
fof(f787,definition,
! [X0,X1] :
( sQ45_spl
<=> ( in(sK2_skl(X0,X1,sK14_skl),relation_rng(sK14_skl))
| in(sK1_skl(X0,X1,sK14_skl),X0)
| X0 = relation_inverse_image(sK14_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f790,definition,
( sQ46_spl
<=> relation(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f792,plain,
( sQ46_spl
| ~ relation(sK14_skl) ),
inference(component_clause,[status(thm)],[f790]) ).
fof(f793,plain,
( ~ sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f784,f787,f790]) ).
fof(f794,definition,
! [X0,X1,X2] :
( sQ47_spl
<=> ( ~ in(sK2_skl(X0,X1,sK14_skl),X2)
| in(sK1_skl(X0,X1,sK14_skl),relation_inverse_image(sK14_skl,X2))
| in(sK1_skl(X0,X1,sK14_skl),X0)
| X0 = relation_inverse_image(sK14_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f797,plain,
( ~ sQ46_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f785,f794,f790]) ).
fof(f798,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f792,f119]) ).
fof(f799,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f798]) ).
fof(f800,plain,
! [X0,X1] :
( in(sK2_skl(X0,X1,sK17_skl),relation_rng(sK17_skl))
| ~ relation(sK17_skl)
| in(sK1_skl(X0,X1,sK17_skl),X0)
| X0 = relation_inverse_image(sK17_skl,X1) ),
inference(resolution,[status(thm)],[f270,f178]) ).
fof(f801,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(X0,X1,sK17_skl),X2)
| in(sK1_skl(X0,X1,sK17_skl),relation_inverse_image(sK17_skl,X2))
| ~ relation(sK17_skl)
| in(sK1_skl(X0,X1,sK17_skl),X0)
| X0 = relation_inverse_image(sK17_skl,X1) ),
inference(resolution,[status(thm)],[f270,f173]) ).
fof(f803,definition,
! [X0,X1] :
( sQ48_spl
<=> ( in(sK2_skl(X0,X1,sK17_skl),relation_rng(sK17_skl))
| in(sK1_skl(X0,X1,sK17_skl),X0)
| X0 = relation_inverse_image(sK17_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f806,definition,
( sQ49_spl
<=> relation(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f808,plain,
( sQ49_spl
| ~ relation(sK17_skl) ),
inference(component_clause,[status(thm)],[f806]) ).
fof(f809,plain,
( ~ sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f800,f803,f806]) ).
fof(f810,definition,
! [X0,X1,X2] :
( sQ50_spl
<=> ( ~ in(sK2_skl(X0,X1,sK17_skl),X2)
| in(sK1_skl(X0,X1,sK17_skl),relation_inverse_image(sK17_skl,X2))
| in(sK1_skl(X0,X1,sK17_skl),X0)
| X0 = relation_inverse_image(sK17_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f813,plain,
( ~ sQ49_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f801,f810,f806]) ).
fof(f814,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f808,f126]) ).
fof(f815,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f814]) ).
fof(f816,plain,
! [X0] :
( in(sK6_skl(X0,sK17_skl),relation_rng(sK17_skl))
| ~ relation(sK17_skl)
| in(sK6_skl(X0,sK17_skl),X0)
| X0 = relation_rng(sK17_skl) ),
inference(resolution,[status(thm)],[f271,f178]) ).
fof(f817,plain,
! [X0,X1] :
( ~ in(sK6_skl(X0,sK17_skl),X1)
| in(sK7_skl(X0,sK17_skl),relation_inverse_image(sK17_skl,X1))
| ~ relation(sK17_skl)
| in(sK6_skl(X0,sK17_skl),X0)
| X0 = relation_rng(sK17_skl) ),
inference(resolution,[status(thm)],[f271,f173]) ).
fof(f819,definition,
! [X0] :
( sQ51_spl
<=> ( in(sK6_skl(X0,sK17_skl),relation_rng(sK17_skl))
| in(sK6_skl(X0,sK17_skl),X0)
| X0 = relation_rng(sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f822,plain,
( ~ sQ49_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f816,f819,f806]) ).
fof(f823,definition,
! [X0,X1] :
( sQ52_spl
<=> ( ~ in(sK6_skl(X0,sK17_skl),X1)
| in(sK7_skl(X0,sK17_skl),relation_inverse_image(sK17_skl,X1))
| in(sK6_skl(X0,sK17_skl),X0)
| X0 = relation_rng(sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( ~ sQ49_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f817,f823,f806]) ).
fof(f828,plain,
! [X0] :
( ~ sQ11_spl
| in(ordered_pair(sK5_skl(sK6_skl(X0,sK19_skl),relation_rng(sK19_skl),sK19_skl),sK6_skl(X0,sK19_skl)),sK19_skl)
| ~ relation(sK19_skl)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(resolution,[status(thm)],[f332,f177]) ).
fof(f840,definition,
! [X0] :
( sQ56_spl
<=> ( in(ordered_pair(sK5_skl(sK6_skl(X0,sK19_skl),relation_rng(sK19_skl),sK19_skl),sK6_skl(X0,sK19_skl)),sK19_skl)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f843,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f828,f840,f212,f331]) ).
fof(f844,plain,
! [X0,X1] :
( ~ sQ12_spl
| in(sK0_skl(sK7_skl(X0,sK19_skl),relation_inverse_image(sK19_skl,X1),X1,sK19_skl),X1)
| ~ relation(sK19_skl)
| ~ in(sK6_skl(X0,sK19_skl),X1)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(resolution,[status(thm)],[f336,f172]) ).
fof(f845,plain,
! [X0,X1] :
( ~ sQ12_spl
| in(ordered_pair(sK7_skl(X0,sK19_skl),sK0_skl(sK7_skl(X0,sK19_skl),relation_inverse_image(sK19_skl,X1),X1,sK19_skl)),sK19_skl)
| ~ relation(sK19_skl)
| ~ in(sK6_skl(X0,sK19_skl),X1)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ),
inference(resolution,[status(thm)],[f336,f171]) ).
fof(f847,definition,
! [X0,X1] :
( sQ57_spl
<=> ( in(sK0_skl(sK7_skl(X0,sK19_skl),relation_inverse_image(sK19_skl,X1),X1,sK19_skl),X1)
| ~ in(sK6_skl(X0,sK19_skl),X1)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f850,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f844,f847,f212,f335]) ).
fof(f851,definition,
! [X0,X1] :
( sQ58_spl
<=> ( in(ordered_pair(sK7_skl(X0,sK19_skl),sK0_skl(sK7_skl(X0,sK19_skl),relation_inverse_image(sK19_skl,X1),X1,sK19_skl)),sK19_skl)
| ~ in(sK6_skl(X0,sK19_skl),X1)
| in(sK6_skl(X0,sK19_skl),X0)
| X0 = relation_rng(sK19_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f854,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f845,f851,f212,f335]) ).
fof(f855,plain,
sK13_skl = relation_inverse_image(sK18_skl,sK13_skl),
inference(resolution,[status(thm)],[f765,f130]) ).
fof(f856,plain,
sK13_skl = relation_inverse_image(sK17_skl,sK13_skl),
inference(resolution,[status(thm)],[f765,f126]) ).
fof(f857,plain,
sK13_skl = relation_inverse_image(sK14_skl,sK13_skl),
inference(resolution,[status(thm)],[f765,f119]) ).
fof(f860,plain,
sK13_skl = relation_inverse_image(sK9_skl,sK13_skl),
inference(resolution,[status(thm)],[f765,f102]) ).
fof(f861,plain,
sK13_skl = relation_inverse_image(sK19_skl,sK13_skl),
inference(resolution,[status(thm)],[f765,f138]) ).
fof(f863,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f861,f599]) ).
fof(f864,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f863]) ).
fof(f865,plain,
! [X0] :
( in(sK0_skl(X0,relation_inverse_image(sK18_skl,sK13_skl),sK13_skl,sK18_skl),sK13_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK18_skl) ),
inference(paramodulation,[status(thm)],[f855,f172]) ).
fof(f866,plain,
! [X0] :
( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK18_skl,sK13_skl),sK13_skl,sK18_skl)),sK18_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK18_skl) ),
inference(paramodulation,[status(thm)],[f855,f171]) ).
fof(f867,definition,
( sQ59_spl
<=> relation(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f869,plain,
( sQ59_spl
| ~ relation(sK18_skl) ),
inference(component_clause,[status(thm)],[f867]) ).
fof(f870,definition,
! [X0] :
( sQ60_spl
<=> ( in(sK0_skl(X0,relation_inverse_image(sK18_skl,sK13_skl),sK13_skl,sK18_skl),sK13_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f873,plain,
( sQ60_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f865,f867,f870]) ).
fof(f874,definition,
! [X0] :
( sQ61_spl
<=> ( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK18_skl,sK13_skl),sK13_skl,sK18_skl)),sK18_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f877,plain,
( sQ61_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f866,f867,f874]) ).
fof(f878,plain,
( sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f869,f130]) ).
fof(f879,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f878]) ).
fof(f882,plain,
! [X0] :
( in(sK6_skl(X0,sK13_skl),X0)
| X0 = sK13_skl ),
inference(forward_demodulation,[status(thm)],[f341,f278]) ).
fof(f883,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,sK6_skl(X0,sK13_skl)),sK13_skl)
| X0 = relation_rng(sK13_skl)
| ~ relation(sK13_skl)
| X0 = sK13_skl ),
inference(resolution,[status(thm)],[f882,f81]) ).
fof(f890,definition,
! [X0,X1] :
( sQ62_spl
<=> ( ~ in(ordered_pair(X1,sK6_skl(X0,sK13_skl)),sK13_skl)
| X0 = relation_rng(sK13_skl)
| X0 = sK13_skl ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f893,plain,
( ~ sQ13_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f883,f890,f358]) ).
fof(f900,plain,
! [X0] :
( in(sK0_skl(X0,relation_inverse_image(sK17_skl,sK13_skl),sK13_skl,sK17_skl),sK13_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK17_skl) ),
inference(paramodulation,[status(thm)],[f856,f172]) ).
fof(f901,plain,
! [X0] :
( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK17_skl,sK13_skl),sK13_skl,sK17_skl)),sK17_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK17_skl) ),
inference(paramodulation,[status(thm)],[f856,f171]) ).
fof(f902,definition,
! [X0] :
( sQ63_spl
<=> ( in(sK0_skl(X0,relation_inverse_image(sK17_skl,sK13_skl),sK13_skl,sK17_skl),sK13_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f905,plain,
( sQ63_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f900,f806,f902]) ).
fof(f906,definition,
! [X0] :
( sQ64_spl
<=> ( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK17_skl,sK13_skl),sK13_skl,sK17_skl)),sK17_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f909,plain,
( sQ64_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f901,f806,f906]) ).
fof(f912,plain,
! [X0] :
( in(sK0_skl(X0,relation_inverse_image(sK14_skl,sK13_skl),sK13_skl,sK14_skl),sK13_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK14_skl) ),
inference(paramodulation,[status(thm)],[f857,f172]) ).
fof(f913,plain,
! [X0] :
( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK14_skl,sK13_skl),sK13_skl,sK14_skl)),sK14_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK14_skl) ),
inference(paramodulation,[status(thm)],[f857,f171]) ).
fof(f914,definition,
! [X0] :
( sQ65_spl
<=> ( in(sK0_skl(X0,relation_inverse_image(sK14_skl,sK13_skl),sK13_skl,sK14_skl),sK13_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f917,plain,
( sQ65_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f912,f790,f914]) ).
fof(f918,definition,
! [X0] :
( sQ66_spl
<=> ( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK14_skl,sK13_skl),sK13_skl,sK14_skl)),sK14_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f921,plain,
( sQ66_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f913,f790,f918]) ).
fof(f924,plain,
! [X0] :
( in(sK0_skl(X0,relation_inverse_image(sK9_skl,sK13_skl),sK13_skl,sK9_skl),sK13_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f860,f172]) ).
fof(f925,plain,
! [X0] :
( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK9_skl,sK13_skl),sK13_skl,sK9_skl)),sK9_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK9_skl) ),
inference(paramodulation,[status(thm)],[f860,f171]) ).
fof(f926,definition,
! [X0] :
( sQ67_spl
<=> ( in(sK0_skl(X0,relation_inverse_image(sK9_skl,sK13_skl),sK13_skl,sK9_skl),sK13_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f929,plain,
( sQ67_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f924,f476,f926]) ).
fof(f930,definition,
! [X0] :
( sQ68_spl
<=> ( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK9_skl,sK13_skl),sK13_skl,sK9_skl)),sK9_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( sQ68_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f925,f476,f930]) ).
fof(f936,plain,
! [X0] :
( in(sK6_skl(X0,sK14_skl),relation_rng(sK14_skl))
| ~ relation(sK14_skl)
| in(sK6_skl(X0,sK14_skl),X0)
| X0 = relation_rng(sK14_skl) ),
inference(resolution,[status(thm)],[f272,f178]) ).
fof(f937,plain,
! [X0,X1] :
( ~ in(sK6_skl(X0,sK14_skl),X1)
| in(sK7_skl(X0,sK14_skl),relation_inverse_image(sK14_skl,X1))
| ~ relation(sK14_skl)
| in(sK6_skl(X0,sK14_skl),X0)
| X0 = relation_rng(sK14_skl) ),
inference(resolution,[status(thm)],[f272,f173]) ).
fof(f939,definition,
! [X0] :
( sQ69_spl
<=> ( in(sK6_skl(X0,sK14_skl),relation_rng(sK14_skl))
| in(sK6_skl(X0,sK14_skl),X0)
| X0 = relation_rng(sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( ~ sQ46_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f936,f939,f790]) ).
fof(f943,definition,
! [X0,X1] :
( sQ70_spl
<=> ( ~ in(sK6_skl(X0,sK14_skl),X1)
| in(sK7_skl(X0,sK14_skl),relation_inverse_image(sK14_skl,X1))
| in(sK6_skl(X0,sK14_skl),X0)
| X0 = relation_rng(sK14_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( ~ sQ46_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f937,f943,f790]) ).
fof(f947,plain,
! [X0] :
( in(sK6_skl(X0,sK9_skl),relation_rng(sK9_skl))
| ~ relation(sK9_skl)
| in(sK6_skl(X0,sK9_skl),X0)
| X0 = relation_rng(sK9_skl) ),
inference(resolution,[status(thm)],[f275,f178]) ).
fof(f948,plain,
! [X0,X1] :
( ~ in(sK6_skl(X0,sK9_skl),X1)
| in(sK7_skl(X0,sK9_skl),relation_inverse_image(sK9_skl,X1))
| ~ relation(sK9_skl)
| in(sK6_skl(X0,sK9_skl),X0)
| X0 = relation_rng(sK9_skl) ),
inference(resolution,[status(thm)],[f275,f173]) ).
fof(f950,definition,
! [X0] :
( sQ71_spl
<=> ( in(sK6_skl(X0,sK9_skl),relation_rng(sK9_skl))
| in(sK6_skl(X0,sK9_skl),X0)
| X0 = relation_rng(sK9_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f953,plain,
( ~ sQ19_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f947,f950,f476]) ).
fof(f954,definition,
! [X0,X1] :
( sQ72_spl
<=> ( ~ in(sK6_skl(X0,sK9_skl),X1)
| in(sK7_skl(X0,sK9_skl),relation_inverse_image(sK9_skl,X1))
| in(sK6_skl(X0,sK9_skl),X0)
| X0 = relation_rng(sK9_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f957,plain,
( ~ sQ19_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f948,f954,f476]) ).
fof(f967,plain,
! [X0] :
( in(sK0_skl(X0,relation_inverse_image(sK19_skl,sK13_skl),sK13_skl,sK19_skl),sK13_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK19_skl) ),
inference(paramodulation,[status(thm)],[f861,f172]) ).
fof(f968,plain,
! [X0] :
( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK19_skl,sK13_skl),sK13_skl,sK19_skl)),sK19_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK19_skl) ),
inference(paramodulation,[status(thm)],[f861,f171]) ).
fof(f969,definition,
! [X0] :
( sQ73_spl
<=> ( in(sK0_skl(X0,relation_inverse_image(sK19_skl,sK13_skl),sK13_skl,sK19_skl),sK13_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f972,plain,
( sQ73_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f967,f212,f969]) ).
fof(f973,definition,
! [X0] :
( sQ74_spl
<=> ( in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK19_skl,sK13_skl),sK13_skl,sK19_skl)),sK19_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( sQ74_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f968,f212,f973]) ).
fof(f989,plain,
! [X0] : ~ in(X0,sK8_skl(powerset(sK13_skl))),
inference(resolution,[status(thm)],[f399,f85]) ).
fof(f992,plain,
! [X0,X1] :
( ~ in(X1,powerset(sK13_skl))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f399,f142]) ).
fof(f1045,plain,
sK8_skl(powerset(sK13_skl)) = sK13_skl,
inference(resolution,[status(thm)],[f989,f882]) ).
fof(f1053,plain,
( ~ in(powerset(sK13_skl),sK13_skl)
| empty(powerset(sK13_skl)) ),
inference(paramodulation,[status(thm)],[f1045,f441]) ).
fof(f1054,plain,
( in(sK13_skl,powerset(sK13_skl))
| empty(powerset(sK13_skl)) ),
inference(paramodulation,[status(thm)],[f1045,f380]) ).
fof(f1056,definition,
( sQ76_spl
<=> empty(powerset(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1057,plain,
( ~ sQ76_spl
| empty(powerset(sK13_skl)) ),
inference(component_clause,[status(thm)],[f1056]) ).
fof(f1059,definition,
( sQ77_spl
<=> in(powerset(sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
( ~ sQ77_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1053,f1056,f1059]) ).
fof(f1063,definition,
( sQ78_spl
<=> in(sK13_skl,powerset(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1066,plain,
( sQ78_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1054,f1056,f1063]) ).
fof(f1067,plain,
( ~ sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1057,f89]) ).
fof(f1068,plain,
~ sQ76_spl,
inference(contradiction_clause,[status(thm)],[f1067]) ).
fof(f1104,plain,
! [X0] :
( in(sK6_skl(X0,sK18_skl),relation_rng(sK18_skl))
| ~ relation(sK18_skl)
| in(sK6_skl(X0,sK18_skl),X0)
| X0 = relation_rng(sK18_skl) ),
inference(resolution,[status(thm)],[f305,f178]) ).
fof(f1105,plain,
! [X0,X1] :
( ~ in(sK6_skl(X0,sK18_skl),X1)
| in(sK7_skl(X0,sK18_skl),relation_inverse_image(sK18_skl,X1))
| ~ relation(sK18_skl)
| in(sK6_skl(X0,sK18_skl),X0)
| X0 = relation_rng(sK18_skl) ),
inference(resolution,[status(thm)],[f305,f173]) ).
fof(f1107,definition,
! [X0] :
( sQ82_spl
<=> ( in(sK6_skl(X0,sK18_skl),relation_rng(sK18_skl))
| in(sK6_skl(X0,sK18_skl),X0)
| X0 = relation_rng(sK18_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1110,plain,
( ~ sQ59_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1104,f1107,f867]) ).
fof(f1111,definition,
! [X0,X1] :
( sQ83_spl
<=> ( ~ in(sK6_skl(X0,sK18_skl),X1)
| in(sK7_skl(X0,sK18_skl),relation_inverse_image(sK18_skl,X1))
| in(sK6_skl(X0,sK18_skl),X0)
| X0 = relation_rng(sK18_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1114,plain,
( ~ sQ59_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1105,f1111,f867]) ).
fof(f1115,plain,
! [X0,X1] :
( in(sK2_skl(X0,X1,sK18_skl),relation_rng(sK18_skl))
| ~ relation(sK18_skl)
| in(sK1_skl(X0,X1,sK18_skl),X0)
| X0 = relation_inverse_image(sK18_skl,X1) ),
inference(resolution,[status(thm)],[f306,f178]) ).
fof(f1116,plain,
! [X0,X1,X2] :
( ~ in(sK2_skl(X0,X1,sK18_skl),X2)
| in(sK1_skl(X0,X1,sK18_skl),relation_inverse_image(sK18_skl,X2))
| ~ relation(sK18_skl)
| in(sK1_skl(X0,X1,sK18_skl),X0)
| X0 = relation_inverse_image(sK18_skl,X1) ),
inference(resolution,[status(thm)],[f306,f173]) ).
fof(f1118,definition,
! [X0,X1] :
( sQ84_spl
<=> ( in(sK2_skl(X0,X1,sK18_skl),relation_rng(sK18_skl))
| in(sK1_skl(X0,X1,sK18_skl),X0)
| X0 = relation_inverse_image(sK18_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1121,plain,
( ~ sQ59_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1115,f1118,f867]) ).
fof(f1122,definition,
! [X0,X1,X2] :
( sQ85_spl
<=> ( ~ in(sK2_skl(X0,X1,sK18_skl),X2)
| in(sK1_skl(X0,X1,sK18_skl),relation_inverse_image(sK18_skl,X2))
| in(sK1_skl(X0,X1,sK18_skl),X0)
| X0 = relation_inverse_image(sK18_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1125,plain,
( ~ sQ59_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1116,f1122,f867]) ).
fof(f1133,plain,
! [X0] :
( in(sK0_skl(sK4_skl(relation_inverse_image(sK19_skl,X0)),relation_inverse_image(sK19_skl,X0),X0,sK19_skl),relation_rng(sK19_skl))
| ~ relation(sK19_skl)
| relation_inverse_image(sK19_skl,X0) = sK13_skl ),
inference(resolution,[status(thm)],[f522,f178]) ).
fof(f1134,plain,
! [X0,X1] :
( ~ in(sK0_skl(sK4_skl(relation_inverse_image(sK19_skl,X0)),relation_inverse_image(sK19_skl,X0),X0,sK19_skl),X1)
| in(sK4_skl(relation_inverse_image(sK19_skl,X0)),relation_inverse_image(sK19_skl,X1))
| ~ relation(sK19_skl)
| relation_inverse_image(sK19_skl,X0) = sK13_skl ),
inference(resolution,[status(thm)],[f522,f173]) ).
fof(f1139,definition,
! [X0] :
( sQ86_spl
<=> ( in(sK0_skl(sK4_skl(relation_inverse_image(sK19_skl,X0)),relation_inverse_image(sK19_skl,X0),X0,sK19_skl),relation_rng(sK19_skl))
| relation_inverse_image(sK19_skl,X0) = sK13_skl ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1142,plain,
( ~ sQ3_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1133,f1139,f212]) ).
fof(f1143,definition,
! [X0,X1] :
( sQ87_spl
<=> ( ~ in(sK0_skl(sK4_skl(relation_inverse_image(sK19_skl,X0)),relation_inverse_image(sK19_skl,X0),X0,sK19_skl),X1)
| in(sK4_skl(relation_inverse_image(sK19_skl,X0)),relation_inverse_image(sK19_skl,X1))
| relation_inverse_image(sK19_skl,X0) = sK13_skl ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1146,plain,
( ~ sQ3_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1134,f1143,f212]) ).
fof(f1159,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(sK1_skl(X0,X1,sK13_skl),X2),sK13_skl)
| X0 = relation_inverse_image(sK13_skl,X1)
| ~ relation(sK13_skl)
| X0 = sK13_skl ),
inference(resolution,[status(thm)],[f493,f60]) ).
fof(f1166,definition,
! [X0,X1,X2] :
( sQ91_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(sK1_skl(X0,X1,sK13_skl),X2),sK13_skl)
| X0 = relation_inverse_image(sK13_skl,X1)
| X0 = sK13_skl ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1169,plain,
( ~ sQ13_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1159,f1166,f358]) ).
fof(f1173,plain,
! [X0,X1] :
( in(sK1_skl(X0,singleton(X1),sK18_skl),X0)
| X0 = relation_inverse_image(sK18_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK18_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK18_skl) = X1
| X0 = relation_inverse_image(sK18_skl,singleton(X1))
| ~ relation(sK18_skl) ),
inference(resolution,[status(thm)],[f353,f306]) ).
fof(f1174,plain,
! [X0,X1] :
( in(sK1_skl(X0,singleton(X1),sK17_skl),X0)
| X0 = relation_inverse_image(sK17_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK17_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK17_skl) = X1
| X0 = relation_inverse_image(sK17_skl,singleton(X1))
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f353,f270]) ).
fof(f1175,plain,
! [X0,X1] :
( in(sK1_skl(X0,singleton(X1),sK14_skl),X0)
| X0 = relation_inverse_image(sK14_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK14_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK14_skl) = X1
| X0 = relation_inverse_image(sK14_skl,singleton(X1))
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f353,f269]) ).
fof(f1176,plain,
! [X0,X1] :
( in(sK1_skl(X0,singleton(X1),sK9_skl),X0)
| X0 = relation_inverse_image(sK9_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK9_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK9_skl) = X1
| X0 = relation_inverse_image(sK9_skl,singleton(X1))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f353,f199]) ).
fof(f1177,plain,
! [X0,X1] :
( in(sK1_skl(X0,singleton(X1),sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK19_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK19_skl) = X1
| X0 = relation_inverse_image(sK19_skl,singleton(X1))
| ~ relation(sK19_skl) ),
inference(resolution,[status(thm)],[f353,f200]) ).
fof(f1180,definition,
! [X0,X1] :
( sQ92_spl
<=> ( in(sK1_skl(X0,singleton(X1),sK18_skl),X0)
| X0 = relation_inverse_image(sK18_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK18_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK18_skl) = X1
| X0 = relation_inverse_image(sK18_skl,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1183,plain,
( sQ92_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f1173,f867,f1180]) ).
fof(f1184,definition,
! [X0,X1] :
( sQ93_spl
<=> ( in(sK1_skl(X0,singleton(X1),sK17_skl),X0)
| X0 = relation_inverse_image(sK17_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK17_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK17_skl) = X1
| X0 = relation_inverse_image(sK17_skl,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1187,plain,
( sQ93_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f1174,f806,f1184]) ).
fof(f1188,definition,
! [X0,X1] :
( sQ94_spl
<=> ( in(sK1_skl(X0,singleton(X1),sK14_skl),X0)
| X0 = relation_inverse_image(sK14_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK14_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK14_skl) = X1
| X0 = relation_inverse_image(sK14_skl,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1191,plain,
( sQ94_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1175,f790,f1188]) ).
fof(f1192,definition,
! [X0,X1] :
( sQ95_spl
<=> ( in(sK1_skl(X0,singleton(X1),sK9_skl),X0)
| X0 = relation_inverse_image(sK9_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK9_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK9_skl) = X1
| X0 = relation_inverse_image(sK9_skl,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1195,plain,
( sQ95_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1176,f476,f1192]) ).
fof(f1196,definition,
! [X0,X1] :
( sQ96_spl
<=> ( in(sK1_skl(X0,singleton(X1),sK19_skl),X0)
| X0 = relation_inverse_image(sK19_skl,singleton(X1))
| ~ in(sK2_skl(X0,singleton(X1),sK19_skl),singleton(X1))
| sK2_skl(X0,singleton(X1),sK19_skl) = X1
| X0 = relation_inverse_image(sK19_skl,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1199,plain,
( sQ96_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1177,f212,f1196]) ).
fof(f1211,plain,
! [X0] :
( sK2_skl(sK13_skl,singleton(X0),sK19_skl) = X0
| sK13_skl = relation_inverse_image(sK19_skl,singleton(X0)) ),
inference(resolution,[status(thm)],[f347,f138]) ).
fof(f1213,plain,
( sQ1_spl
| sK2_skl(sK13_skl,singleton(sK20_skl),sK19_skl) = sK20_skl ),
inference(resolution,[status(thm)],[f1211,f268]) ).
fof(f1223,plain,
! [X0,X1] :
( sK2_skl(sK13_skl,singleton(X1),sK19_skl) = X1
| in(sK0_skl(X0,relation_inverse_image(sK19_skl,singleton(X1)),singleton(X1),sK19_skl),singleton(X1))
| ~ in(X0,sK13_skl)
| ~ relation(sK19_skl) ),
inference(paramodulation,[status(thm)],[f1211,f172]) ).
fof(f1224,plain,
! [X0,X1] :
( sK2_skl(sK13_skl,singleton(X1),sK19_skl) = X1
| in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK19_skl,singleton(X1)),singleton(X1),sK19_skl)),sK19_skl)
| ~ in(X0,sK13_skl)
| ~ relation(sK19_skl) ),
inference(paramodulation,[status(thm)],[f1211,f171]) ).
fof(f1225,definition,
( sQ97_spl
<=> sK13_skl = sK13_skl ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1227,plain,
( sQ97_spl
| sK13_skl != sK13_skl ),
inference(component_clause,[status(thm)],[f1225]) ).
fof(f1233,definition,
! [X0,X1] :
( sQ99_spl
<=> ( sK2_skl(sK13_skl,singleton(X1),sK19_skl) = X1
| in(sK0_skl(X0,relation_inverse_image(sK19_skl,singleton(X1)),singleton(X1),sK19_skl),singleton(X1))
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1236,plain,
( sQ99_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1223,f212,f1233]) ).
fof(f1237,definition,
! [X0,X1] :
( sQ100_spl
<=> ( sK2_skl(sK13_skl,singleton(X1),sK19_skl) = X1
| in(ordered_pair(X0,sK0_skl(X0,relation_inverse_image(sK19_skl,singleton(X1)),singleton(X1),sK19_skl)),sK19_skl)
| ~ in(X0,sK13_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1240,plain,
( sQ100_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1224,f212,f1237]) ).
fof(f1241,plain,
( sQ97_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1227]) ).
fof(f1242,plain,
sQ97_spl,
inference(contradiction_clause,[status(thm)],[f1241]) ).
fof(f1285,plain,
! [X0] :
( powerset(sK13_skl) = sK13_skl
| ~ in(X0,sK6_skl(powerset(sK13_skl),sK13_skl)) ),
inference(resolution,[status(thm)],[f992,f882]) ).
fof(f1286,plain,
! [X0] :
( empty(powerset(sK13_skl))
| ~ in(X0,sK8_skl(powerset(sK13_skl))) ),
inference(resolution,[status(thm)],[f992,f380]) ).
fof(f1290,plain,
! [X0,X1] :
( powerset(sK13_skl) = sK13_skl
| ~ in(X0,sK1_skl(powerset(sK13_skl),X1,sK13_skl)) ),
inference(resolution,[status(thm)],[f992,f493]) ).
fof(f1291,plain,
! [X0] :
( powerset(sK13_skl) = sK13_skl
| ~ in(X0,sK4_skl(powerset(sK13_skl))) ),
inference(resolution,[status(thm)],[f992,f259]) ).
fof(f1303,definition,
! [X0] :
( sQ103_spl
<=> ~ in(X0,sK6_skl(powerset(sK13_skl),sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1306,definition,
( sQ104_spl
<=> powerset(sK13_skl) = sK13_skl ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1307,plain,
( ~ sQ104_spl
| powerset(sK13_skl) = sK13_skl ),
inference(component_clause,[status(thm)],[f1306]) ).
fof(f1309,plain,
( sQ104_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1285,f1303,f1306]) ).
fof(f1310,definition,
! [X0] :
( sQ105_spl
<=> ~ in(X0,sK8_skl(powerset(sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1313,plain,
( sQ76_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1286,f1310,f1056]) ).
fof(f1314,definition,
! [X0,X1] :
( sQ106_spl
<=> ~ in(X0,sK1_skl(powerset(sK13_skl),X1,sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1317,plain,
( sQ104_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1290,f1314,f1306]) ).
fof(f1318,definition,
! [X0] :
( sQ107_spl
<=> ~ in(X0,sK4_skl(powerset(sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1321,plain,
( sQ104_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1291,f1318,f1306]) ).
fof(f1330,plain,
( ~ sQ104_spl
| in(sK13_skl,sK13_skl) ),
inference(paramodulation,[status(thm)],[f1307,f779]) ).
fof(f1345,plain,
( ~ sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1330,f265]) ).
fof(f1346,plain,
~ sQ104_spl,
inference(contradiction_clause,[status(thm)],[f1345]) ).
fof(f1381,plain,
( sQ1_spl
| ~ sQ2_spl
| in(sK20_skl,relation_rng(sK19_skl))
| in(sK1_skl(sK13_skl,singleton(sK20_skl),sK19_skl),sK13_skl)
| sK13_skl = relation_inverse_image(sK19_skl,singleton(sK20_skl)) ),
inference(paramodulation,[status(thm)],[f1213,f210]) ).
fof(f1386,definition,
( sQ110_spl
<=> sK13_skl = relation_inverse_image(sK19_skl,singleton(sK20_skl)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1387,plain,
( ~ sQ110_spl
| sK13_skl = relation_inverse_image(sK19_skl,singleton(sK20_skl)) ),
inference(component_clause,[status(thm)],[f1386]) ).
fof(f1389,definition,
( sQ111_spl
<=> in(sK1_skl(sK13_skl,singleton(sK20_skl),sK19_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1390,plain,
( ~ sQ111_spl
| in(sK1_skl(sK13_skl,singleton(sK20_skl),sK19_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f1389]) ).
fof(f1396,plain,
( sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| sQ111_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1381,f1386,f1389,f163,f209,f166]) ).
fof(f1413,plain,
( ~ sQ110_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1387,f268]) ).
fof(f1414,plain,
( ~ sQ110_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1413]) ).
fof(f1415,plain,
( ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1390,f265]) ).
fof(f1416,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f1415]) ).
fof(f1417,plain,
$false,
inference(sat_refutation,[status(thm)],[f169,f170,f215,f219,f221,f246,f289,f293,f334,f338,f364,f368,f372,f406,f463,f479,f483,f485,f490,f499,f503,f579,f607,f611,f615,f660,f679,f706,f710,f714,f793,f797,f799,f809,f813,f815,f822,f826,f843,f850,f854,f864,f873,f877,f879,f893,f905,f909,f917,f921,f929,f933,f942,f946,f953,f957,f972,f976,f1062,f1066,f1068,f1110,f1114,f1121,f1125,f1142,f1146,f1169,f1183,f1187,f1191,f1195,f1199,f1236,f1240,f1242,f1309,f1313,f1317,f1321,f1346,f1396,f1414,f1416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU061+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n001.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 05:54:13 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 0.28/0.59 % Refutation found
% 0.28/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.28/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.62 % Elapsed time: 0.158547 seconds
% 0.28/0.62 % CPU time: 0.911035 seconds
% 0.28/0.62 % Total memory used: 116.496 MB
% 0.28/0.62 % Net memory used: 115.331 MB
%------------------------------------------------------------------------------