%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU208+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.25s 0.74s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 93
% Syntax : Number of formulae : 377 ( 56 unt; 58 def)
% Number of atoms : 1124 ( 199 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1269 ( 522 ~; 539 |; 108 &)
% ( 79 <=>; 20 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 64 ( 62 usr; 59 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 7 con; 0-4 aty)
% Number of variables : 455 ( 411 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,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(f15,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,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(f54,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f106,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f131]) ).
fof(f133,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f135,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f147,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f151,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f174,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f181,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f184,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f208,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f214,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f231,plain,
! [A] :
( ! [B,C] :
( ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f232,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f232]) ).
fof(f234,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ( ( in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
& in(sK2_skl(B,C,A),B) )
| in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) )
& ( ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
| ~ in(sK2_skl(B,C,A),B)
| ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(D,sK2_skl(B,C,A)),skolemize(E,sK3_skl(B,C,A))],[f233]) ).
fof(f238,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X0)
| ~ in(sK2_skl(X2,X1,X0),X2)
| ~ in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f240,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f241,plain,
! [A,B] :
( ! [C] :
( ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f242,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f241]) ).
fof(f243,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f242]) ).
fof(f244,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( ( ( in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),B)
& in(sK5_skl(A,C,B),A) )
| in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),C) )
& ( ~ in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),B)
| ~ in(sK5_skl(A,C,B),A)
| ~ in(ordered_pair(sK4_skl(A,C,B),sK5_skl(A,C,B)),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(D,sK4_skl(A,C,B)),skolemize(E,sK5_skl(A,C,B))],[f243]) ).
fof(f250,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK4_skl(X2,X1,X0),sK5_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK4_skl(X2,X1,X0),sK5_skl(X2,X1,X0)),X1)
| X1 = relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f261,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)],[f12]) ).
fof(f262,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)],[f261]) ).
fof(f263,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)],[f262]) ).
fof(f264,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK11_skl(C,B,A),B)
& in(ordered_pair(sK10_skl(C,B,A),sK11_skl(C,B,A)),A) )
| in(sK10_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK10_skl(C,B,A),E),A) )
| ~ in(sK10_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(sK9_skl(D,C,B,A),B)
& in(ordered_pair(D,sK9_skl(D,C,B,A)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(E,sK9_skl(D,C,B,A)),skolemize(D,sK10_skl(C,B,A)),skolemize(E,sK11_skl(C,B,A))],[f263]) ).
fof(f265,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,sK9_skl(X3,X1,X2,X0)),X0)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( in(sK9_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f267,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)],[f264]) ).
fof(f290,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)],[f15]) ).
fof(f291,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)],[f290]) ).
fof(f292,plain,
( ! [A,B] :
( ( ( sK18_skl(B,A) = A
| in(sK18_skl(B,A),B) )
& ( sK18_skl(B,A) != A
| ~ in(sK18_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,[sK18_skl]),skolemize(C,sK18_skl(B,A))],[f291]) ).
fof(f293,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f297,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f298,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f297]) ).
fof(f299,plain,
( ! [A] :
( in(sK19_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(B,sK19_skl(A))],[f298]) ).
fof(f301,plain,
! [X0] :
( in(sK19_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f400,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)],[f30]) ).
fof(f401,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)],[f400]) ).
fof(f402,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)],[f401]) ).
fof(f403,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK43_skl(B,A),sK42_skl(B,A)),A)
| in(sK42_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK42_skl(B,A)),A)
| ~ in(sK42_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK41_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl,sK43_skl]),skolemize(D,sK41_skl(C,B,A)),skolemize(C,sK42_skl(B,A)),skolemize(D,sK43_skl(B,A))],[f402]) ).
fof(f405,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)],[f403]) ).
fof(f451,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f452,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f451]) ).
fof(f457,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f478,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f491,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f496,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f497,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f496]) ).
fof(f498,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f499,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f498]) ).
fof(f500,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f498]) ).
fof(f501,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f502,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f501]) ).
fof(f503,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f501]) ).
fof(f509,plain,
! [A] : set_intersection2(A,A) = A,
inference(miniscoping,[status(thm)],[f86]) ).
fof(f510,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f509]) ).
fof(f513,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f88]) ).
fof(f514,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f513]) ).
fof(f519,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f555,plain,
( relation(sK53_skl)
& empty(sK53_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(A,sK53_skl)],[f103]) ).
fof(f556,plain,
empty(sK53_skl),
inference(cnf_transformation,[status(thm)],[f555]) ).
fof(f557,plain,
relation(sK53_skl),
inference(cnf_transformation,[status(thm)],[f555]) ).
fof(f564,plain,
( relation(sK56_skl)
& ~ empty(sK56_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl]),skolemize(A,sK56_skl)],[f106]) ).
fof(f565,plain,
~ empty(sK56_skl),
inference(cnf_transformation,[status(thm)],[f564]) ).
fof(f566,plain,
relation(sK56_skl),
inference(cnf_transformation,[status(thm)],[f564]) ).
fof(f644,plain,
? [A,B,C] :
( ( in(A,relation_inverse_image(C,B))
<~> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) )
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f132]) ).
fof(f645,plain,
? [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f644]) ).
fof(f646,plain,
? [C] :
( ? [A,B] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) ) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f645]) ).
fof(f647,plain,
( ( ! [D] :
( ~ in(D,sK63_skl)
| ~ in(ordered_pair(sK62_skl,D),sK61_skl)
| ~ in(D,relation_rng(sK61_skl)) )
| ~ in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) )
& ( ( in(sK64_skl,sK63_skl)
& in(ordered_pair(sK62_skl,sK64_skl),sK61_skl)
& in(sK64_skl,relation_rng(sK61_skl)) )
| in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) )
& relation(sK61_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61_skl,sK62_skl,sK63_skl,sK64_skl]),skolemize(C,sK61_skl),skolemize(A,sK62_skl),skolemize(B,sK63_skl),skolemize(D,sK64_skl)],[f646]) ).
fof(f648,plain,
relation(sK61_skl),
inference(cnf_transformation,[status(thm)],[f647]) ).
fof(f650,plain,
( in(ordered_pair(sK62_skl,sK64_skl),sK61_skl)
| in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) ),
inference(cnf_transformation,[status(thm)],[f647]) ).
fof(f651,plain,
( in(sK64_skl,sK63_skl)
| in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) ),
inference(cnf_transformation,[status(thm)],[f647]) ).
fof(f652,plain,
! [X0] :
( ~ in(X0,sK63_skl)
| ~ in(ordered_pair(sK62_skl,X0),sK61_skl)
| ~ in(X0,relation_rng(sK61_skl))
| ~ in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) ),
inference(cnf_transformation,[status(thm)],[f647]) ).
fof(f653,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f656,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f662,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f669,plain,
! [A] :
( ! [B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f141]) ).
fof(f671,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f669]) ).
fof(f677,plain,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f685,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f696,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f756,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f777,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f783,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f184]) ).
fof(f785,plain,
! [X0] :
( X0 = empty_set
| relation_rng(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f783]) ).
fof(f795,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f188]) ).
fof(f796,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f795]) ).
fof(f799,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f190]) ).
fof(f801,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f799]) ).
fof(f808,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f192]) ).
fof(f809,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f808]) ).
fof(f810,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f809]) ).
fof(f811,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f862,definition,
( sQ0_spl
<=> in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f863,plain,
( ~ sQ0_spl
| in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) ),
inference(component_clause,[status(thm)],[f862]) ).
fof(f864,plain,
( sQ0_spl
| ~ in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl)) ),
inference(component_clause,[status(thm)],[f862]) ).
fof(f869,definition,
( sQ2_spl
<=> in(ordered_pair(sK62_skl,sK64_skl),sK61_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f870,plain,
( ~ sQ2_spl
| in(ordered_pair(sK62_skl,sK64_skl),sK61_skl) ),
inference(component_clause,[status(thm)],[f869]) ).
fof(f872,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f650,f862,f869]) ).
fof(f873,definition,
( sQ3_spl
<=> in(sK64_skl,sK63_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f874,plain,
( ~ sQ3_spl
| in(sK64_skl,sK63_skl) ),
inference(component_clause,[status(thm)],[f873]) ).
fof(f876,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f651,f862,f873]) ).
fof(f877,definition,
! [X0] :
( sQ4_spl
<=> ( ~ in(X0,sK63_skl)
| ~ in(ordered_pair(sK62_skl,X0),sK61_skl)
| ~ in(X0,relation_rng(sK61_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f878,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,sK63_skl)
| ~ in(ordered_pair(sK62_skl,X0),sK61_skl)
| ~ in(X0,relation_rng(sK61_skl)) ),
inference(component_clause,[status(thm)],[f877]) ).
fof(f880,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f652,f862,f877]) ).
fof(f895,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,sK9_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)],[f265]) ).
fof(f896,plain,
! [X0,X1,X2] :
( in(sK9_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)],[f266]) ).
fof(f897,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)],[f267]) ).
fof(f903,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f293]) ).
fof(f928,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f405]) ).
fof(f947,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sK61_skl)
| in(X0,relation_inverse_image(sK61_skl,X1)) ),
inference(resolution,[status(thm)],[f897,f648]) ).
fof(f948,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,X0),sK61_skl)
| in(X0,relation_rng(sK61_skl)) ),
inference(resolution,[status(thm)],[f928,f648]) ).
fof(f956,plain,
relation(relation_rng(sK53_skl)),
inference(resolution,[status(thm)],[f556,f503]) ).
fof(f957,plain,
empty(relation_rng(sK53_skl)),
inference(resolution,[status(thm)],[f556,f502]) ).
fof(f969,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK64_skl,X0)
| in(sK62_skl,relation_inverse_image(sK61_skl,X0)) ),
inference(resolution,[status(thm)],[f947,f870]) ).
fof(f970,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ in(sK64_skl,sK63_skl) ),
inference(resolution,[status(thm)],[f969,f864]) ).
fof(f972,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f970,f874]) ).
fof(f973,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f972]) ).
fof(f974,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,sK63_skl)
| ~ in(ordered_pair(sK62_skl,X0),sK61_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f878,f948]) ).
fof(f978,plain,
empty(relation_rng(relation_rng(sK53_skl))),
inference(resolution,[status(thm)],[f957,f502]) ).
fof(f985,plain,
relation(relation_rng(relation_rng(relation_rng(sK53_skl)))),
inference(resolution,[status(thm)],[f978,f503]) ).
fof(f989,plain,
( ~ empty(relation_rng(sK56_skl))
| ~ relation(sK56_skl) ),
inference(resolution,[status(thm)],[f497,f565]) ).
fof(f992,definition,
( sQ5_spl
<=> relation(sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f994,plain,
( sQ5_spl
| ~ relation(sK56_skl) ),
inference(component_clause,[status(thm)],[f992]) ).
fof(f995,definition,
( sQ6_spl
<=> empty(relation_rng(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f997,plain,
( sQ6_spl
| ~ empty(relation_rng(sK56_skl)) ),
inference(component_clause,[status(thm)],[f995]) ).
fof(f998,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f989,f992,f995]) ).
fof(f1009,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f994,f566]) ).
fof(f1010,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1009]) ).
fof(f1026,plain,
( sQ6_spl
| ~ empty(relation_rng(relation_rng(sK56_skl)))
| ~ relation(relation_rng(sK56_skl)) ),
inference(resolution,[status(thm)],[f997,f497]) ).
fof(f1027,definition,
( sQ9_spl
<=> relation(relation_rng(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1030,definition,
( sQ10_spl
<=> empty(relation_rng(relation_rng(sK56_skl))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1033,plain,
( sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1026,f1027,f1030,f995]) ).
fof(f1050,plain,
( relation_rng(relation_rng(relation_rng(sK53_skl))) = empty_set
| relation_rng(relation_rng(relation_rng(relation_rng(sK53_skl)))) != empty_set ),
inference(resolution,[status(thm)],[f785,f985]) ).
fof(f1054,plain,
( relation_rng(sK53_skl) = empty_set
| relation_rng(relation_rng(sK53_skl)) != empty_set ),
inference(resolution,[status(thm)],[f785,f956]) ).
fof(f1056,plain,
( empty_set = empty_set
| relation_rng(empty_set) != empty_set ),
inference(resolution,[status(thm)],[f785,f491]) ).
fof(f1073,definition,
( sQ15_spl
<=> relation_rng(relation_rng(relation_rng(relation_rng(sK53_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1075,plain,
( sQ15_spl
| relation_rng(relation_rng(relation_rng(relation_rng(sK53_skl)))) != empty_set ),
inference(component_clause,[status(thm)],[f1073]) ).
fof(f1076,definition,
( sQ16_spl
<=> relation_rng(relation_rng(relation_rng(sK53_skl))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1079,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1050,f1073,f1076]) ).
fof(f1084,definition,
( sQ18_spl
<=> relation_rng(relation_rng(sK53_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f1086,plain,
( sQ18_spl
| relation_rng(relation_rng(sK53_skl)) != empty_set ),
inference(component_clause,[status(thm)],[f1084]) ).
fof(f1092,definition,
( sQ20_spl
<=> relation_rng(sK53_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1095,plain,
( sQ20_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1054,f1084,f1092]) ).
fof(f1096,definition,
( sQ21_spl
<=> sK53_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1097,plain,
( ~ sQ21_spl
| sK53_skl = empty_set ),
inference(component_clause,[status(thm)],[f1096]) ).
fof(f1100,definition,
( sQ22_spl
<=> relation_rng(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1102,plain,
( sQ22_spl
| relation_rng(empty_set) != empty_set ),
inference(component_clause,[status(thm)],[f1100]) ).
fof(f1103,definition,
( sQ23_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1106,plain,
( sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1056,f1100,f1103]) ).
fof(f1114,plain,
( sQ22_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f1102]) ).
fof(f1115,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1114]) ).
fof(f1116,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f1115]) ).
fof(f1139,plain,
! [X0] :
( subset(relation_rng(empty_set),relation_rng(X0))
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f685,f671]) ).
fof(f1140,definition,
( sQ26_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1142,plain,
( sQ26_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f1140]) ).
fof(f1143,definition,
! [X0] :
( sQ27_spl
<=> ( subset(relation_rng(empty_set),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1146,plain,
( sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1139,f1140,f1143]) ).
fof(f1147,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1142,f491]) ).
fof(f1148,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f1147]) ).
fof(f1156,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f214,f656]) ).
fof(f1187,plain,
( sQ18_spl
| ~ sQ21_spl
| relation_rng(relation_rng(empty_set)) != empty_set ),
inference(forward_demodulation,[status(thm)],[f1097,f1086]) ).
fof(f1188,plain,
( sQ18_spl
| ~ sQ21_spl
| relation_rng(empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f1187]) ).
fof(f1189,plain,
( sQ18_spl
| ~ sQ21_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f1188]) ).
fof(f1190,plain,
( sQ18_spl
| ~ sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1189]) ).
fof(f1191,plain,
( sQ18_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1190]) ).
fof(f1235,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f796,f497]) ).
fof(f1304,plain,
! [X0,X1] :
( subset(relation_rng(set_intersection2(X0,X1)),relation_rng(X0))
| ~ relation(X0)
| ~ relation(set_intersection2(X0,X1)) ),
inference(resolution,[status(thm)],[f653,f671]) ).
fof(f1316,plain,
! [X0,X1] :
( subset(relation_rng(set_difference(X0,X1)),relation_rng(X0))
| ~ relation(X0)
| ~ relation(set_difference(X0,X1)) ),
inference(resolution,[status(thm)],[f696,f671]) ).
fof(f1325,plain,
! [X0,X1] :
( ~ empty(relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f810,f497]) ).
fof(f1327,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(set_union2(X0,X1)))
| ~ relation(set_union2(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f811,f671]) ).
fof(f1352,plain,
! [X0] :
( ~ empty(X0)
| ~ relation(identity_relation(X0))
| identity_relation(X0) = empty_set ),
inference(paramodulation,[status(thm)],[f801,f1235]) ).
fof(f1354,plain,
! [X0] :
( ~ empty(X0)
| identity_relation(X0) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f1352,f457]) ).
fof(f1355,definition,
( sQ29_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1357,plain,
( sQ29_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f1355]) ).
fof(f1359,plain,
identity_relation(empty_set) = empty_set,
inference(resolution,[status(thm)],[f1354,f478]) ).
fof(f1360,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| identity_relation(X0) = empty_set ),
inference(resolution,[status(thm)],[f1354,f497]) ).
fof(f1417,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,sK61_skl,X0),sK3_skl(X1,sK61_skl,X0)),X0)
| in(ordered_pair(sK2_skl(X1,sK61_skl,X0),sK3_skl(X1,sK61_skl,X0)),sK61_skl)
| sK61_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f240,f648]) ).
fof(f1421,plain,
! [X0,X1,X2] :
( ~ in(sK3_skl(X1,sK61_skl,X0),X2)
| in(sK2_skl(X1,sK61_skl,X0),relation_inverse_image(sK61_skl,X2))
| in(ordered_pair(sK2_skl(X1,sK61_skl,X0),sK3_skl(X1,sK61_skl,X0)),X0)
| sK61_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1417,f947]) ).
fof(f1425,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0)),sK61_skl)
| sK61_skl = relation_dom_restriction(X0,relation_inverse_image(sK61_skl,X1))
| ~ relation(sK61_skl)
| ~ relation(X0)
| ~ in(sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),X1)
| in(ordered_pair(sK2_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0)),X0)
| sK61_skl = relation_dom_restriction(X0,relation_inverse_image(sK61_skl,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1421,f238]) ).
fof(f1427,definition,
! [X0,X1] :
( sQ30_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0)),sK61_skl)
| sK61_skl = relation_dom_restriction(X0,relation_inverse_image(sK61_skl,X1))
| ~ relation(X0)
| ~ in(sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),X1)
| in(ordered_pair(sK2_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0),sK3_skl(relation_inverse_image(sK61_skl,X1),sK61_skl,X0)),X0)
| sK61_skl = relation_dom_restriction(X0,relation_inverse_image(sK61_skl,X1))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1430,definition,
( sQ31_spl
<=> relation(sK61_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1432,plain,
( sQ31_spl
| ~ relation(sK61_skl) ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1433,plain,
( ~ sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f1425,f1427,f1430]) ).
fof(f1444,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))) != empty_set ),
inference(forward_demodulation,[status(thm)],[f1097,f1075]) ).
fof(f1445,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_rng(relation_rng(relation_rng(empty_set))) != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f1444]) ).
fof(f1446,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_rng(relation_rng(empty_set)) != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f1445]) ).
fof(f1447,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_rng(empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f1446]) ).
fof(f1448,plain,
( sQ15_spl
| ~ sQ21_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f1447]) ).
fof(f1449,plain,
( sQ15_spl
| ~ sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1448]) ).
fof(f1450,plain,
( sQ15_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1449]) ).
fof(f1451,plain,
( ~ relation(sK53_skl)
| sK53_skl = empty_set ),
inference(resolution,[status(thm)],[f957,f1235]) ).
fof(f1457,definition,
( sQ32_spl
<=> relation(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1459,plain,
( sQ32_spl
| ~ relation(sK53_skl) ),
inference(component_clause,[status(thm)],[f1457]) ).
fof(f1460,plain,
( ~ sQ32_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1451,f1096,f1457]) ).
fof(f1478,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f1459]) ).
fof(f1479,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f1478]) ).
fof(f1532,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ relation(identity_relation(X1))
| ~ in(X0,identity_relation(X1)) ),
inference(paramodulation,[status(thm)],[f801,f1325]) ).
fof(f1533,plain,
! [X0] :
( ~ empty(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f777,f1325]) ).
fof(f1534,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,identity_relation(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1532,f457]) ).
fof(f1535,definition,
! [X0] :
( sQ34_spl
<=> ~ in(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f1538,plain,
( ~ sQ29_spl
| ~ sQ26_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f1533,f1535,f1140,f1355]) ).
fof(f1539,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1357,f478]) ).
fof(f1540,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1539]) ).
fof(f1544,plain,
! [X0] :
( subset(relation_rng(set_intersection2(sK61_skl,X0)),relation_rng(sK61_skl))
| ~ relation(set_intersection2(sK61_skl,X0)) ),
inference(resolution,[status(thm)],[f1304,f648]) ).
fof(f1553,plain,
! [X0] :
( relation_inverse(X0) = empty_set
| relation_rng(relation_inverse(X0)) != empty_set
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f452,f785]) ).
fof(f1554,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),relation_inverse(X0))
| in(X1,relation_rng(relation_inverse(X0)))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f452,f928]) ).
fof(f1555,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),relation_inverse(X0))
| in(X1,relation_inverse_image(relation_inverse(X0),X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f452,f897]) ).
fof(f1557,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f499,f497]) ).
fof(f1560,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| relation(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f500,f497]) ).
fof(f1568,plain,
powerset(empty_set) != empty_set,
inference(paramodulation,[status(thm)],[f662,f519]) ).
fof(f1587,plain,
! [X0,X1] :
( in(ordered_pair(sK4_skl(X1,sK61_skl,X0),sK5_skl(X1,sK61_skl,X0)),X0)
| in(ordered_pair(sK4_skl(X1,sK61_skl,X0),sK5_skl(X1,sK61_skl,X0)),sK61_skl)
| sK61_skl = relation_rng_restriction(X1,X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f250,f648]) ).
fof(f1592,plain,
( subset(relation_rng(set_intersection2(sK61_skl,empty_set)),relation_rng(sK61_skl))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f677,f1544]) ).
fof(f1595,plain,
( subset(relation_rng(set_intersection2(sK61_skl,sK61_skl)),relation_rng(sK61_skl))
| ~ relation(sK61_skl) ),
inference(paramodulation,[status(thm)],[f510,f1544]) ).
fof(f1596,definition,
( sQ37_spl
<=> subset(relation_rng(set_intersection2(sK61_skl,empty_set)),relation_rng(sK61_skl)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1599,plain,
( sQ37_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1592,f1140,f1596]) ).
fof(f1600,definition,
( sQ38_spl
<=> subset(relation_rng(set_intersection2(sK61_skl,sK61_skl)),relation_rng(sK61_skl)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1603,plain,
( sQ38_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1595,f1430,f1600]) ).
fof(f1604,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1432,f648]) ).
fof(f1605,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1604]) ).
fof(f1626,plain,
! [X0,X1,X2] :
( ~ in(sK5_skl(X1,sK61_skl,X0),X2)
| in(sK4_skl(X1,sK61_skl,X0),relation_inverse_image(sK61_skl,X2))
| in(ordered_pair(sK4_skl(X1,sK61_skl,X0),sK5_skl(X1,sK61_skl,X0)),X0)
| sK61_skl = relation_rng_restriction(X1,X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1587,f947]) ).
fof(f1630,plain,
! [X0,X1] :
( ~ empty(relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,identity_relation(X1)) ),
inference(resolution,[status(thm)],[f1534,f497]) ).
fof(f1647,plain,
! [X0] :
( ~ empty(X0)
| ~ relation(identity_relation(X0))
| identity_relation(identity_relation(X0)) = empty_set ),
inference(paramodulation,[status(thm)],[f801,f1360]) ).
fof(f1648,plain,
( ~ empty(empty_set)
| ~ relation(empty_set)
| identity_relation(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f777,f1360]) ).
fof(f1649,plain,
! [X0] :
( ~ empty(X0)
| identity_relation(identity_relation(X0)) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f1647,f457]) ).
fof(f1650,definition,
( sQ40_spl
<=> identity_relation(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1653,plain,
( ~ sQ29_spl
| ~ sQ26_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1648,f1650,f1140,f1355]) ).
fof(f1655,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| identity_relation(identity_relation(X0)) = empty_set ),
inference(resolution,[status(thm)],[f1649,f497]) ).
fof(f1659,plain,
( ~ empty(empty_set)
| ~ relation(empty_set)
| empty(relation_dom(empty_set)) ),
inference(paramodulation,[status(thm)],[f777,f1557]) ).
fof(f1660,definition,
( sQ41_spl
<=> empty(relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1663,plain,
( ~ sQ29_spl
| ~ sQ26_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1659,f1660,f1140,f1355]) ).
fof(f1667,plain,
( ~ empty(empty_set)
| ~ relation(empty_set)
| relation(relation_dom(empty_set)) ),
inference(paramodulation,[status(thm)],[f777,f1560]) ).
fof(f1669,definition,
( sQ42_spl
<=> relation(relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1672,plain,
( ~ sQ29_spl
| ~ sQ26_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1667,f1669,f1140,f1355]) ).
fof(f1675,plain,
! [X0] :
( subset(relation_rng(set_difference(empty_set,X0)),relation_rng(empty_set))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f756,f1316]) ).
fof(f1677,definition,
! [X0] :
( sQ43_spl
<=> subset(relation_rng(set_difference(empty_set,X0)),relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1680,plain,
( sQ43_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1675,f1140,f1677]) ).
fof(f1687,plain,
! [X0] :
( subset(relation_rng(empty_set),relation_rng(set_union2(empty_set,X0)))
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1156,f1327]) ).
fof(f1692,definition,
! [X0] :
( sQ44_spl
<=> ( subset(relation_rng(empty_set),relation_rng(set_union2(empty_set,X0)))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1695,plain,
( sQ44_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1687,f1140,f1692]) ).
fof(f1713,plain,
! [X0] :
( sK19_skl(singleton(X0)) = X0
| singleton(X0) = empty_set ),
inference(resolution,[status(thm)],[f301,f903]) ).
fof(f1715,plain,
! [X0] :
( ~ in(X0,sK19_skl(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f301,f208]) ).
fof(f1716,plain,
! [X0] : sK19_skl(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f1713,f519]) ).
fof(f1717,plain,
sK19_skl(powerset(empty_set)) = empty_set,
inference(paramodulation,[status(thm)],[f662,f1716]) ).
fof(f1719,plain,
( in(empty_set,powerset(empty_set))
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f1717,f301]) ).
fof(f1720,definition,
( sQ45_spl
<=> powerset(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1721,plain,
( ~ sQ45_spl
| powerset(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f1720]) ).
fof(f1723,definition,
( sQ46_spl
<=> in(empty_set,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1726,plain,
( sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1719,f1720,f1723]) ).
fof(f1727,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1721,f1568]) ).
fof(f1728,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f1727]) ).
fof(f1795,plain,
( ~ in(powerset(empty_set),empty_set)
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f1717,f1715]) ).
fof(f1797,definition,
( sQ47_spl
<=> in(powerset(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1800,plain,
( ~ sQ47_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1795,f1720,f1797]) ).
fof(f1809,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ relation(identity_relation(X1))
| ~ in(X0,identity_relation(identity_relation(X1))) ),
inference(paramodulation,[status(thm)],[f801,f1630]) ).
fof(f1810,plain,
! [X0] :
( ~ empty(empty_set)
| ~ relation(empty_set)
| ~ in(X0,identity_relation(empty_set)) ),
inference(paramodulation,[status(thm)],[f777,f1630]) ).
fof(f1811,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,identity_relation(identity_relation(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1809,f457]) ).
fof(f1812,definition,
! [X0] :
( sQ48_spl
<=> ~ in(X0,identity_relation(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1815,plain,
( ~ sQ29_spl
| ~ sQ26_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f1810,f1812,f1140,f1355]) ).
fof(f1818,plain,
! [X0,X1] :
( ~ empty(relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,identity_relation(identity_relation(X1))) ),
inference(resolution,[status(thm)],[f1811,f497]) ).
fof(f1872,plain,
relation_inverse(relation_inverse(sK56_skl)) = sK56_skl,
inference(resolution,[status(thm)],[f514,f566]) ).
fof(f1873,plain,
relation_inverse(relation_inverse(empty_set)) = empty_set,
inference(resolution,[status(thm)],[f514,f491]) ).
fof(f1874,plain,
relation_inverse(relation_inverse(sK61_skl)) = sK61_skl,
inference(resolution,[status(thm)],[f514,f648]) ).
fof(f1877,definition,
( sQ50_spl
<=> relation(relation_inverse(sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1878,plain,
( ~ sQ50_spl
| relation(relation_inverse(sK56_skl)) ),
inference(component_clause,[status(thm)],[f1877]) ).
fof(f1879,plain,
( sQ50_spl
| ~ relation(relation_inverse(sK56_skl)) ),
inference(component_clause,[status(thm)],[f1877]) ).
fof(f1882,definition,
( sQ51_spl
<=> relation(relation_inverse(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1883,plain,
( ~ sQ51_spl
| relation(relation_inverse(empty_set)) ),
inference(component_clause,[status(thm)],[f1882]) ).
fof(f1884,plain,
( sQ51_spl
| ~ relation(relation_inverse(empty_set)) ),
inference(component_clause,[status(thm)],[f1882]) ).
fof(f1887,definition,
( sQ52_spl
<=> relation(relation_inverse(sK61_skl)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1888,plain,
( ~ sQ52_spl
| relation(relation_inverse(sK61_skl)) ),
inference(component_clause,[status(thm)],[f1887]) ).
fof(f1889,plain,
( sQ52_spl
| ~ relation(relation_inverse(sK61_skl)) ),
inference(component_clause,[status(thm)],[f1887]) ).
fof(f1995,plain,
! [X0] :
( relation_inverse(identity_relation(X0)) = empty_set
| relation_rng(relation_inverse(identity_relation(X0))) != empty_set ),
inference(resolution,[status(thm)],[f1553,f457]) ).
fof(f1997,plain,
( relation_inverse(empty_set) = empty_set
| relation_rng(relation_inverse(empty_set)) != empty_set ),
inference(resolution,[status(thm)],[f1553,f491]) ).
fof(f2007,definition,
( sQ55_spl
<=> relation_rng(relation_inverse(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f2010,definition,
( sQ56_spl
<=> relation_inverse(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f2011,plain,
( ~ sQ56_spl
| relation_inverse(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f2010]) ).
fof(f2013,plain,
( sQ56_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f1997,f2007,f2010]) ).
fof(f2024,plain,
( ~ empty(empty_set)
| ~ relation(empty_set)
| identity_relation(identity_relation(empty_set)) = empty_set ),
inference(paramodulation,[status(thm)],[f777,f1655]) ).
fof(f2026,definition,
( sQ59_spl
<=> identity_relation(identity_relation(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f2029,plain,
( ~ sQ29_spl
| ~ sQ26_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f2024,f2026,f1140,f1355]) ).
fof(f2039,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,X0),sK61_skl)
| in(X0,relation_rng(relation_inverse(relation_inverse(sK61_skl))))
| ~ relation(relation_inverse(sK61_skl)) ),
inference(paramodulation,[status(thm)],[f1874,f1554]) ).
fof(f2040,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,X0),empty_set)
| in(X0,relation_rng(relation_inverse(relation_inverse(empty_set))))
| ~ relation(relation_inverse(empty_set)) ),
inference(paramodulation,[status(thm)],[f1873,f1554]) ).
fof(f2041,plain,
! [X0,X1] :
( ~ in(ordered_pair(X1,X0),sK56_skl)
| in(X0,relation_rng(relation_inverse(relation_inverse(sK56_skl))))
| ~ relation(relation_inverse(sK56_skl)) ),
inference(paramodulation,[status(thm)],[f1872,f1554]) ).
fof(f2043,definition,
! [X0,X1] :
( sQ60_spl
<=> ( ~ in(ordered_pair(X1,X0),sK61_skl)
| in(X0,relation_rng(relation_inverse(relation_inverse(sK61_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2046,plain,
( sQ60_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f2039,f1887,f2043]) ).
fof(f2047,definition,
! [X0,X1] :
( sQ61_spl
<=> ( ~ in(ordered_pair(X1,X0),empty_set)
| in(X0,relation_rng(relation_inverse(relation_inverse(empty_set)))) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f2050,plain,
( sQ61_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f2040,f1882,f2047]) ).
fof(f2051,definition,
! [X0,X1] :
( sQ62_spl
<=> ( ~ in(ordered_pair(X1,X0),sK56_skl)
| in(X0,relation_rng(relation_inverse(relation_inverse(sK56_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2054,plain,
( sQ62_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2041,f1877,f2051]) ).
fof(f2056,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sK61_skl)
| in(X0,relation_inverse_image(relation_inverse(relation_inverse(sK61_skl)),X1))
| ~ relation(relation_inverse(sK61_skl)) ),
inference(paramodulation,[status(thm)],[f1874,f1555]) ).
fof(f2057,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),empty_set)
| in(X0,relation_inverse_image(relation_inverse(relation_inverse(empty_set)),X1))
| ~ relation(relation_inverse(empty_set)) ),
inference(paramodulation,[status(thm)],[f1873,f1555]) ).
fof(f2058,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sK56_skl)
| in(X0,relation_inverse_image(relation_inverse(relation_inverse(sK56_skl)),X1))
| ~ relation(relation_inverse(sK56_skl)) ),
inference(paramodulation,[status(thm)],[f1872,f1555]) ).
fof(f2060,definition,
! [X0,X1,X2] :
( sQ63_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sK61_skl)
| in(X0,relation_inverse_image(relation_inverse(relation_inverse(sK61_skl)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2063,plain,
( sQ63_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f2056,f1887,f2060]) ).
fof(f2064,definition,
! [X0,X1,X2] :
( sQ64_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),empty_set)
| in(X0,relation_inverse_image(relation_inverse(relation_inverse(empty_set)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2067,plain,
( sQ64_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f2057,f1882,f2064]) ).
fof(f2068,definition,
! [X0,X1,X2] :
( sQ65_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sK56_skl)
| in(X0,relation_inverse_image(relation_inverse(relation_inverse(sK56_skl)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2071,plain,
( sQ65_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2058,f1877,f2068]) ).
fof(f2072,plain,
( sQ50_spl
| ~ relation(sK56_skl) ),
inference(resolution,[status(thm)],[f1879,f452]) ).
fof(f2074,plain,
( sQ50_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2072,f992,f1877]) ).
fof(f2077,plain,
( sQ51_spl
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1884,f452]) ).
fof(f2079,plain,
( sQ51_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f2077,f1140,f1882]) ).
fof(f2083,plain,
( sQ52_spl
| ~ relation(sK61_skl) ),
inference(resolution,[status(thm)],[f1889,f452]) ).
fof(f2085,plain,
( sQ52_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f2083,f1430,f1887]) ).
fof(f2088,plain,
( ~ sQ50_spl
| relation_inverse(relation_inverse(sK56_skl)) = empty_set
| relation_rng(relation_inverse(relation_inverse(sK56_skl))) != empty_set ),
inference(resolution,[status(thm)],[f1878,f1553]) ).
fof(f2098,definition,
( sQ66_spl
<=> relation_rng(relation_inverse(relation_inverse(sK56_skl))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2101,definition,
( sQ67_spl
<=> relation_inverse(relation_inverse(sK56_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2104,plain,
( ~ sQ50_spl
| sQ67_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f2088,f2098,f2101,f1877]) ).
fof(f2107,plain,
( ~ sQ51_spl
| relation_inverse(relation_inverse(empty_set)) = empty_set
| relation_rng(relation_inverse(relation_inverse(empty_set))) != empty_set ),
inference(resolution,[status(thm)],[f1883,f1553]) ).
fof(f2117,definition,
( sQ68_spl
<=> relation_rng(relation_inverse(relation_inverse(empty_set))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2119,plain,
( sQ68_spl
| relation_rng(relation_inverse(relation_inverse(empty_set))) != empty_set ),
inference(component_clause,[status(thm)],[f2117]) ).
fof(f2120,definition,
( sQ69_spl
<=> relation_inverse(relation_inverse(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2123,plain,
( ~ sQ51_spl
| sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f2107,f2117,f2120,f1882]) ).
fof(f2125,plain,
( sQ68_spl
| relation_rng(empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f1873,f2119]) ).
fof(f2126,plain,
( sQ68_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f777,f2125]) ).
fof(f2127,plain,
( sQ68_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2126]) ).
fof(f2128,plain,
sQ68_spl,
inference(contradiction_clause,[status(thm)],[f2127]) ).
fof(f2130,plain,
( ~ sQ52_spl
| relation_inverse(relation_inverse(sK61_skl)) = empty_set
| relation_rng(relation_inverse(relation_inverse(sK61_skl))) != empty_set ),
inference(resolution,[status(thm)],[f1888,f1553]) ).
fof(f2140,definition,
( sQ70_spl
<=> relation_rng(relation_inverse(relation_inverse(sK61_skl))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f2143,definition,
( sQ71_spl
<=> relation_inverse(relation_inverse(sK61_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f2146,plain,
( ~ sQ52_spl
| sQ71_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f2130,f2140,f2143,f1887]) ).
fof(f2174,plain,
! [X0,X1,X2] :
( ~ in(sK5_skl(X0,sK61_skl,X1),X2)
| in(ordered_pair(sK4_skl(X0,sK61_skl,X1),sK5_skl(X0,sK61_skl,X1)),X1)
| sK61_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(ordered_pair(sK4_skl(X0,sK61_skl,X1),sK9_skl(sK4_skl(X0,sK61_skl,X1),relation_inverse_image(sK61_skl,X2),X2,sK61_skl)),sK61_skl)
| ~ relation(sK61_skl) ),
inference(resolution,[status(thm)],[f895,f1626]) ).
fof(f2181,plain,
! [X0,X1,X2] :
( ~ in(sK3_skl(X0,sK61_skl,X1),X2)
| in(ordered_pair(sK2_skl(X0,sK61_skl,X1),sK3_skl(X0,sK61_skl,X1)),X1)
| sK61_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK2_skl(X0,sK61_skl,X1),sK9_skl(sK2_skl(X0,sK61_skl,X1),relation_inverse_image(sK61_skl,X2),X2,sK61_skl)),sK61_skl)
| ~ relation(sK61_skl) ),
inference(resolution,[status(thm)],[f895,f1421]) ).
fof(f2184,plain,
( ~ sQ0_spl
| in(ordered_pair(sK62_skl,sK9_skl(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl),sK63_skl,sK61_skl)),sK61_skl)
| ~ relation(sK61_skl) ),
inference(resolution,[status(thm)],[f895,f863]) ).
fof(f2185,definition,
! [X0,X1,X2] :
( sQ72_spl
<=> ( ~ in(sK5_skl(X0,sK61_skl,X1),X2)
| in(ordered_pair(sK4_skl(X0,sK61_skl,X1),sK5_skl(X0,sK61_skl,X1)),X1)
| sK61_skl = relation_rng_restriction(X0,X1)
| ~ relation(X1)
| in(ordered_pair(sK4_skl(X0,sK61_skl,X1),sK9_skl(sK4_skl(X0,sK61_skl,X1),relation_inverse_image(sK61_skl,X2),X2,sK61_skl)),sK61_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f2188,plain,
( sQ72_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f2174,f1430,f2185]) ).
fof(f2189,definition,
! [X0,X1,X2] :
( sQ73_spl
<=> ( ~ in(sK3_skl(X0,sK61_skl,X1),X2)
| in(ordered_pair(sK2_skl(X0,sK61_skl,X1),sK3_skl(X0,sK61_skl,X1)),X1)
| sK61_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK2_skl(X0,sK61_skl,X1),sK9_skl(sK2_skl(X0,sK61_skl,X1),relation_inverse_image(sK61_skl,X2),X2,sK61_skl)),sK61_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f2192,plain,
( sQ73_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f2181,f1430,f2189]) ).
fof(f2193,definition,
( sQ74_spl
<=> in(ordered_pair(sK62_skl,sK9_skl(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl),sK63_skl,sK61_skl)),sK61_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f2194,plain,
( ~ sQ74_spl
| in(ordered_pair(sK62_skl,sK9_skl(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl),sK63_skl,sK61_skl)),sK61_skl) ),
inference(component_clause,[status(thm)],[f2193]) ).
fof(f2196,plain,
( ~ sQ0_spl
| sQ74_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f2184,f1430,f2193,f862]) ).
fof(f2237,plain,
( ~ sQ4_spl
| ~ sQ74_spl
| ~ in(sK9_skl(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl),sK63_skl,sK61_skl),sK63_skl) ),
inference(resolution,[status(thm)],[f2194,f974]) ).
fof(f2252,plain,
! [X0] :
( ~ empty(empty_set)
| ~ relation(empty_set)
| ~ in(X0,identity_relation(identity_relation(empty_set))) ),
inference(paramodulation,[status(thm)],[f777,f1818]) ).
fof(f2254,definition,
! [X0] :
( sQ75_spl
<=> ~ in(X0,identity_relation(identity_relation(empty_set))) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f2257,plain,
( ~ sQ29_spl
| ~ sQ26_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f2252,f2254,f1140,f1355]) ).
fof(f2265,plain,
( relation_inverse(empty_set) = empty_set
| relation_rng(relation_inverse(identity_relation(empty_set))) != empty_set ),
inference(paramodulation,[status(thm)],[f1359,f1995]) ).
fof(f2266,definition,
( sQ76_spl
<=> relation_rng(relation_inverse(identity_relation(empty_set))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f2269,plain,
( sQ56_spl
| ~ sQ76_spl ),
inference(split_clause,[status(thm)],[f2265,f2266,f2010]) ).
fof(f2272,plain,
! [X0,X1,X2] :
( ~ sQ56_spl
| ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),empty_set)
| in(X0,relation_inverse_image(relation_inverse(empty_set),X1))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2011,f1555]) ).
fof(f2273,plain,
! [X0,X1] :
( ~ sQ56_spl
| ~ in(ordered_pair(X1,X0),empty_set)
| in(X0,relation_rng(relation_inverse(empty_set)))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2011,f1554]) ).
fof(f2275,definition,
! [X0,X1,X2] :
( sQ77_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),empty_set)
| in(X0,relation_inverse_image(relation_inverse(empty_set),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f2278,plain,
( ~ sQ56_spl
| sQ77_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f2272,f1140,f2275,f2010]) ).
fof(f2279,definition,
! [X0,X1] :
( sQ78_spl
<=> ( ~ in(ordered_pair(X1,X0),empty_set)
| in(X0,relation_rng(relation_inverse(empty_set))) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f2282,plain,
( ~ sQ56_spl
| sQ78_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f2273,f1140,f2279,f2010]) ).
fof(f2357,plain,
( ~ sQ4_spl
| ~ sQ74_spl
| ~ in(sK62_skl,relation_inverse_image(sK61_skl,sK63_skl))
| ~ relation(sK61_skl) ),
inference(resolution,[status(thm)],[f2237,f896]) ).
fof(f2358,plain,
( ~ sQ4_spl
| ~ sQ74_spl
| ~ sQ0_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f2357,f1430,f862,f2193,f877]) ).
fof(f2359,plain,
$false,
inference(sat_refutation,[status(thm)],[f872,f876,f880,f973,f998,f1010,f1033,f1079,f1095,f1106,f1116,f1146,f1148,f1191,f1433,f1450,f1460,f1479,f1538,f1540,f1599,f1603,f1605,f1653,f1663,f1672,f1680,f1695,f1726,f1728,f1800,f1815,f2013,f2029,f2046,f2050,f2054,f2063,f2067,f2071,f2074,f2079,f2085,f2104,f2123,f2128,f2146,f2188,f2192,f2196,f2257,f2269,f2278,f2282,f2358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU208+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.42 % Computer : n007.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.43 % CPULimit : 300
% 0.12/0.43 % WCLimit : 300
% 0.12/0.43 % DateTime : Mon Sep 21 05:56:06 UTC 2026
% 0.12/0.43 % CPUTime :
% 0.12/0.46 % Drodi V4.1.1
% 0.25/0.74 % Refutation found
% 0.25/0.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.25/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.76 % Elapsed time: 0.325712 seconds
% 0.25/0.76 % CPU time: 2.130185 seconds
% 0.25/0.76 % Total memory used: 136.483 MB
% 0.25/0.76 % Net memory used: 133.102 MB
%------------------------------------------------------------------------------