%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU203+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:19:39 PM UTC 2026
% Result : Theorem 0.13s 0.61s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 62
% Syntax : Number of formulae : 263 ( 46 unt; 32 def)
% Number of atoms : 855 ( 167 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 975 ( 383 ~; 409 |; 109 &)
% ( 55 <=>; 18 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 33 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 7 con; 0-4 aty)
% Number of variables : 361 ( 317 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f124,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f125,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f124]) ).
fof(f126,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f131,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f134,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f137,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f140,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f144,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f167,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f174,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f177,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f178,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f181,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f183,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f185,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f208,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f224,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(f225,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)],[f224]) ).
fof(f226,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)],[f225]) ).
fof(f227,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))],[f226]) ).
fof(f231,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)],[f227]) ).
fof(f233,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)],[f227]) ).
fof(f234,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(f235,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)],[f234]) ).
fof(f236,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)],[f235]) ).
fof(f237,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))],[f236]) ).
fof(f241,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK4_skl(X2,X1,X0),sK5_skl(X2,X1,X0)),X0)
| ~ in(sK5_skl(X2,X1,X0),X2)
| ~ 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)],[f237]) ).
fof(f243,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)],[f237]) ).
fof(f244,plain,
! [A] :
( ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f245,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f245]) ).
fof(f247,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK8_skl(C,B,A),B)
& in(ordered_pair(sK8_skl(C,B,A),sK7_skl(C,B,A)),A) )
| in(sK7_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,sK7_skl(C,B,A)),A) )
| ~ in(sK7_skl(C,B,A),C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ( in(sK6_skl(D,C,B,A),B)
& in(ordered_pair(sK6_skl(D,C,B,A),D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(E,sK6_skl(D,C,B,A)),skolemize(D,sK7_skl(C,B,A)),skolemize(E,sK8_skl(C,B,A))],[f246]) ).
fof(f248,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK6_skl(X3,X1,X2,X0),X3),X0)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f249,plain,
! [X0,X1,X2,X3] :
( in(sK6_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f250,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f247]) ).
fof(f273,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)],[f14]) ).
fof(f274,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)],[f273]) ).
fof(f275,plain,
( ! [A,B] :
( ( ( sK15_skl(B,A) = A
| in(sK15_skl(B,A),B) )
& ( sK15_skl(B,A) != A
| ~ in(sK15_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,[sK15_skl]),skolemize(C,sK15_skl(B,A))],[f274]) ).
fof(f276,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f280,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f281,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f280]) ).
fof(f282,plain,
( ! [A] :
( in(sK16_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(B,sK16_skl(A))],[f281]) ).
fof(f284,plain,
! [X0] :
( in(sK16_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f356,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f357,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f356]) ).
fof(f358,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f357]) ).
fof(f359,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK32_skl(B,A),sK33_skl(B,A)),A)
| in(sK32_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK32_skl(B,A),D),A)
| ~ in(sK32_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK31_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31_skl,sK32_skl,sK33_skl]),skolemize(D,sK31_skl(C,B,A)),skolemize(C,sK32_skl(B,A)),skolemize(D,sK33_skl(B,A))],[f358]) ).
fof(f361,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f359]) ).
fof(f440,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f461,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f474,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f477,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f478,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f477]) ).
fof(f481,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f482,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f481]) ).
fof(f483,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f481]) ).
fof(f484,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f485,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f484]) ).
fof(f502,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f538,plain,
( relation(sK50_skl)
& empty(sK50_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50_skl]),skolemize(A,sK50_skl)],[f101]) ).
fof(f539,plain,
empty(sK50_skl),
inference(cnf_transformation,[status(thm)],[f538]) ).
fof(f540,plain,
relation(sK50_skl),
inference(cnf_transformation,[status(thm)],[f538]) ).
fof(f547,plain,
( relation(sK53_skl)
& ~ empty(sK53_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(A,sK53_skl)],[f104]) ).
fof(f548,plain,
~ empty(sK53_skl),
inference(cnf_transformation,[status(thm)],[f547]) ).
fof(f549,plain,
relation(sK53_skl),
inference(cnf_transformation,[status(thm)],[f547]) ).
fof(f609,plain,
? [A,B,C] :
( ( in(A,relation_image(C,B))
<~> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) )
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f125]) ).
fof(f610,plain,
? [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| in(A,relation_image(C,B)) )
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f609]) ).
fof(f611,plain,
? [C] :
( ? [A,B] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| in(A,relation_image(C,B)) ) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f610]) ).
fof(f612,plain,
( ( ! [D] :
( ~ in(D,sK59_skl)
| ~ in(ordered_pair(D,sK58_skl),sK57_skl)
| ~ in(D,relation_dom(sK57_skl)) )
| ~ in(sK58_skl,relation_image(sK57_skl,sK59_skl)) )
& ( ( in(sK60_skl,sK59_skl)
& in(ordered_pair(sK60_skl,sK58_skl),sK57_skl)
& in(sK60_skl,relation_dom(sK57_skl)) )
| in(sK58_skl,relation_image(sK57_skl,sK59_skl)) )
& relation(sK57_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57_skl,sK58_skl,sK59_skl,sK60_skl]),skolemize(C,sK57_skl),skolemize(A,sK58_skl),skolemize(B,sK59_skl),skolemize(D,sK60_skl)],[f611]) ).
fof(f613,plain,
relation(sK57_skl),
inference(cnf_transformation,[status(thm)],[f612]) ).
fof(f615,plain,
( in(ordered_pair(sK60_skl,sK58_skl),sK57_skl)
| in(sK58_skl,relation_image(sK57_skl,sK59_skl)) ),
inference(cnf_transformation,[status(thm)],[f612]) ).
fof(f616,plain,
( in(sK60_skl,sK59_skl)
| in(sK58_skl,relation_image(sK57_skl,sK59_skl)) ),
inference(cnf_transformation,[status(thm)],[f612]) ).
fof(f617,plain,
! [X0] :
( ~ in(X0,sK59_skl)
| ~ in(ordered_pair(X0,sK58_skl),sK57_skl)
| ~ in(X0,relation_dom(sK57_skl))
| ~ in(sK58_skl,relation_image(sK57_skl,sK59_skl)) ),
inference(cnf_transformation,[status(thm)],[f612]) ).
fof(f618,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f627,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f634,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)],[f134]) ).
fof(f635,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f634]) ).
fof(f642,plain,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f650,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f661,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f721,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f741,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f748,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f177]) ).
fof(f749,plain,
! [X0] :
( X0 = empty_set
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f748]) ).
fof(f751,plain,
! [A] :
( ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f178]) ).
fof(f752,plain,
! [A] :
( ( ( relation_rng(A) != empty_set
| relation_dom(A) = empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) != empty_set ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f751]) ).
fof(f754,plain,
! [X0] :
( relation_rng(X0) != empty_set
| relation_dom(X0) = empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f752]) ).
fof(f760,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f181]) ).
fof(f761,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f760]) ).
fof(f764,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f183]) ).
fof(f765,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f764]) ).
fof(f766,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f764]) ).
fof(f773,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f185]) ).
fof(f774,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f773]) ).
fof(f775,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f774]) ).
fof(f827,definition,
( sQ0_spl
<=> in(sK58_skl,relation_image(sK57_skl,sK59_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( sQ0_spl
| ~ in(sK58_skl,relation_image(sK57_skl,sK59_skl)) ),
inference(component_clause,[status(thm)],[f827]) ).
fof(f834,definition,
( sQ2_spl
<=> in(ordered_pair(sK60_skl,sK58_skl),sK57_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f835,plain,
( ~ sQ2_spl
| in(ordered_pair(sK60_skl,sK58_skl),sK57_skl) ),
inference(component_clause,[status(thm)],[f834]) ).
fof(f837,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f615,f827,f834]) ).
fof(f838,definition,
( sQ3_spl
<=> in(sK60_skl,sK59_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f839,plain,
( ~ sQ3_spl
| in(sK60_skl,sK59_skl) ),
inference(component_clause,[status(thm)],[f838]) ).
fof(f841,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f616,f827,f838]) ).
fof(f842,definition,
! [X0] :
( sQ4_spl
<=> ( ~ in(X0,sK59_skl)
| ~ in(ordered_pair(X0,sK58_skl),sK57_skl)
| ~ in(X0,relation_dom(sK57_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f843,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,sK59_skl)
| ~ in(ordered_pair(X0,sK58_skl),sK57_skl)
| ~ in(X0,relation_dom(sK57_skl)) ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f845,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f617,f827,f842]) ).
fof(f857,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK6_skl(X1,relation_image(X0,X2),X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f248]) ).
fof(f858,plain,
! [X0,X1,X2] :
( in(sK6_skl(X1,relation_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f249]) ).
fof(f859,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f250]) ).
fof(f865,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f882,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f361]) ).
fof(f909,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X2,X0),sK57_skl)
| in(X0,relation_image(sK57_skl,X1)) ),
inference(resolution,[status(thm)],[f859,f613]) ).
fof(f910,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK57_skl)
| in(X0,relation_dom(sK57_skl)) ),
inference(resolution,[status(thm)],[f882,f613]) ).
fof(f918,plain,
relation(relation_dom(sK50_skl)),
inference(resolution,[status(thm)],[f539,f483]) ).
fof(f919,plain,
empty(relation_dom(sK50_skl)),
inference(resolution,[status(thm)],[f539,f482]) ).
fof(f931,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK60_skl,X0)
| in(sK58_skl,relation_image(sK57_skl,X0)) ),
inference(resolution,[status(thm)],[f909,f835]) ).
fof(f932,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ in(sK60_skl,sK59_skl) ),
inference(resolution,[status(thm)],[f931,f829]) ).
fof(f934,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f932,f839]) ).
fof(f935,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f934]) ).
fof(f936,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(X0,sK59_skl)
| ~ in(ordered_pair(X0,sK58_skl),sK57_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f843,f910]) ).
fof(f940,plain,
empty(relation_dom(relation_dom(sK50_skl))),
inference(resolution,[status(thm)],[f919,f482]) ).
fof(f947,plain,
relation(relation_dom(relation_dom(relation_dom(sK50_skl)))),
inference(resolution,[status(thm)],[f940,f483]) ).
fof(f951,plain,
( ~ empty(relation_dom(sK53_skl))
| ~ relation(sK53_skl) ),
inference(resolution,[status(thm)],[f478,f548]) ).
fof(f954,definition,
( sQ5_spl
<=> relation(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f956,plain,
( sQ5_spl
| ~ relation(sK53_skl) ),
inference(component_clause,[status(thm)],[f954]) ).
fof(f957,definition,
( sQ6_spl
<=> empty(relation_dom(sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f959,plain,
( sQ6_spl
| ~ empty(relation_dom(sK53_skl)) ),
inference(component_clause,[status(thm)],[f957]) ).
fof(f960,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f951,f954,f957]) ).
fof(f971,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f956,f549]) ).
fof(f972,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f971]) ).
fof(f988,plain,
( sQ6_spl
| ~ empty(relation_dom(relation_dom(sK53_skl)))
| ~ relation(relation_dom(sK53_skl)) ),
inference(resolution,[status(thm)],[f959,f478]) ).
fof(f989,definition,
( sQ9_spl
<=> relation(relation_dom(sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f992,definition,
( sQ10_spl
<=> empty(relation_dom(relation_dom(sK53_skl))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f995,plain,
( sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f988,f989,f992,f957]) ).
fof(f1012,plain,
( relation_dom(relation_dom(relation_dom(sK50_skl))) = empty_set
| relation_dom(relation_dom(relation_dom(relation_dom(sK50_skl)))) != empty_set ),
inference(resolution,[status(thm)],[f749,f947]) ).
fof(f1016,plain,
( relation_dom(sK50_skl) = empty_set
| relation_dom(relation_dom(sK50_skl)) != empty_set ),
inference(resolution,[status(thm)],[f749,f918]) ).
fof(f1018,plain,
( empty_set = empty_set
| relation_dom(empty_set) != empty_set ),
inference(resolution,[status(thm)],[f749,f474]) ).
fof(f1035,definition,
( sQ15_spl
<=> relation_dom(relation_dom(relation_dom(relation_dom(sK50_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1037,plain,
( sQ15_spl
| relation_dom(relation_dom(relation_dom(relation_dom(sK50_skl)))) != empty_set ),
inference(component_clause,[status(thm)],[f1035]) ).
fof(f1038,definition,
( sQ16_spl
<=> relation_dom(relation_dom(relation_dom(sK50_skl))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1041,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1012,f1035,f1038]) ).
fof(f1046,definition,
( sQ18_spl
<=> relation_dom(relation_dom(sK50_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f1048,plain,
( sQ18_spl
| relation_dom(relation_dom(sK50_skl)) != empty_set ),
inference(component_clause,[status(thm)],[f1046]) ).
fof(f1054,definition,
( sQ20_spl
<=> relation_dom(sK50_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1057,plain,
( sQ20_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1016,f1046,f1054]) ).
fof(f1058,definition,
( sQ21_spl
<=> sK50_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1059,plain,
( ~ sQ21_spl
| sK50_skl = empty_set ),
inference(component_clause,[status(thm)],[f1058]) ).
fof(f1062,definition,
( sQ22_spl
<=> relation_dom(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1064,plain,
( sQ22_spl
| relation_dom(empty_set) != empty_set ),
inference(component_clause,[status(thm)],[f1062]) ).
fof(f1065,definition,
( sQ23_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1068,plain,
( sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1018,f1062,f1065]) ).
fof(f1076,plain,
( sQ22_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f741,f1064]) ).
fof(f1077,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1076]) ).
fof(f1078,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f1077]) ).
fof(f1102,plain,
! [X0] :
( subset(relation_dom(empty_set),relation_dom(X0))
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f650,f635]) ).
fof(f1103,definition,
( sQ26_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1105,plain,
( sQ26_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f1103]) ).
fof(f1106,definition,
! [X0] :
( sQ27_spl
<=> ( subset(relation_dom(empty_set),relation_dom(X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1109,plain,
( sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1102,f1103,f1106]) ).
fof(f1110,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1105,f474]) ).
fof(f1111,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f1110]) ).
fof(f1153,plain,
( sQ18_spl
| ~ sQ21_spl
| relation_dom(relation_dom(empty_set)) != empty_set ),
inference(forward_demodulation,[status(thm)],[f1059,f1048]) ).
fof(f1154,plain,
( sQ18_spl
| ~ sQ21_spl
| relation_dom(empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f741,f1153]) ).
fof(f1155,plain,
( sQ18_spl
| ~ sQ21_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f741,f1154]) ).
fof(f1156,plain,
( sQ18_spl
| ~ sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1155]) ).
fof(f1157,plain,
( sQ18_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1156]) ).
fof(f1199,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f761,f478]) ).
fof(f1211,plain,
( relation_dom(identity_relation(empty_set)) = empty_set
| ~ relation(identity_relation(empty_set)) ),
inference(resolution,[status(thm)],[f766,f754]) ).
fof(f1214,definition,
( sQ29_spl
<=> relation(identity_relation(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1216,plain,
( sQ29_spl
| ~ relation(identity_relation(empty_set)) ),
inference(component_clause,[status(thm)],[f1214]) ).
fof(f1217,definition,
( sQ30_spl
<=> relation_dom(identity_relation(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1211,f1214,f1217]) ).
fof(f1221,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1216,f440]) ).
fof(f1222,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1221]) ).
fof(f1282,plain,
! [X0,X1] :
( subset(relation_dom(set_intersection2(X0,X1)),relation_dom(X0))
| ~ relation(X0)
| ~ relation(set_intersection2(X0,X1)) ),
inference(resolution,[status(thm)],[f618,f635]) ).
fof(f1286,plain,
! [X0] : set_intersection2(empty_set,X0) = empty_set,
inference(paramodulation,[status(thm)],[f208,f642]) ).
fof(f1294,plain,
! [X0,X1] :
( subset(relation_dom(set_difference(X0,X1)),relation_dom(X0))
| ~ relation(X0)
| ~ relation(set_difference(X0,X1)) ),
inference(resolution,[status(thm)],[f661,f635]) ).
fof(f1303,plain,
! [X0,X1] :
( ~ empty(relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f775,f478]) ).
fof(f1328,plain,
! [X0] :
( ~ empty(X0)
| ~ relation(identity_relation(X0))
| identity_relation(X0) = empty_set ),
inference(paramodulation,[status(thm)],[f765,f1199]) ).
fof(f1330,plain,
! [X0] :
( ~ empty(X0)
| identity_relation(X0) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f1328,f440]) ).
fof(f1331,definition,
( sQ31_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1333,plain,
( sQ31_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f1331]) ).
fof(f1336,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| identity_relation(X0) = empty_set ),
inference(resolution,[status(thm)],[f1330,f478]) ).
fof(f1388,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,sK57_skl,X0),sK3_skl(X1,sK57_skl,X0)),X0)
| in(ordered_pair(sK2_skl(X1,sK57_skl,X0),sK3_skl(X1,sK57_skl,X0)),sK57_skl)
| sK57_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f233,f613]) ).
fof(f1393,plain,
! [X0,X1] :
( in(sK2_skl(X1,sK57_skl,X0),relation_dom(sK57_skl))
| in(ordered_pair(sK2_skl(X1,sK57_skl,X0),sK3_skl(X1,sK57_skl,X0)),X0)
| sK57_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1388,f910]) ).
fof(f1395,plain,
! [X0] :
( ~ in(ordered_pair(sK2_skl(relation_dom(sK57_skl),sK57_skl,X0),sK3_skl(relation_dom(sK57_skl),sK57_skl,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_dom(sK57_skl),sK57_skl,X0),sK3_skl(relation_dom(sK57_skl),sK57_skl,X0)),sK57_skl)
| sK57_skl = relation_dom_restriction(X0,relation_dom(sK57_skl))
| ~ relation(sK57_skl)
| ~ relation(X0)
| in(ordered_pair(sK2_skl(relation_dom(sK57_skl),sK57_skl,X0),sK3_skl(relation_dom(sK57_skl),sK57_skl,X0)),X0)
| sK57_skl = relation_dom_restriction(X0,relation_dom(sK57_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1393,f231]) ).
fof(f1397,definition,
! [X0] :
( sQ32_spl
<=> ( ~ in(ordered_pair(sK2_skl(relation_dom(sK57_skl),sK57_skl,X0),sK3_skl(relation_dom(sK57_skl),sK57_skl,X0)),X0)
| ~ in(ordered_pair(sK2_skl(relation_dom(sK57_skl),sK57_skl,X0),sK3_skl(relation_dom(sK57_skl),sK57_skl,X0)),sK57_skl)
| sK57_skl = relation_dom_restriction(X0,relation_dom(sK57_skl))
| ~ relation(X0)
| in(ordered_pair(sK2_skl(relation_dom(sK57_skl),sK57_skl,X0),sK3_skl(relation_dom(sK57_skl),sK57_skl,X0)),X0)
| sK57_skl = relation_dom_restriction(X0,relation_dom(sK57_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1400,definition,
( sQ33_spl
<=> relation(sK57_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1402,plain,
( sQ33_spl
| ~ relation(sK57_skl) ),
inference(component_clause,[status(thm)],[f1400]) ).
fof(f1403,plain,
( ~ sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1395,f1397,f1400]) ).
fof(f1417,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) != empty_set ),
inference(forward_demodulation,[status(thm)],[f1059,f1037]) ).
fof(f1418,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_dom(relation_dom(relation_dom(empty_set))) != empty_set ),
inference(forward_demodulation,[status(thm)],[f741,f1417]) ).
fof(f1419,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_dom(relation_dom(empty_set)) != empty_set ),
inference(forward_demodulation,[status(thm)],[f741,f1418]) ).
fof(f1420,plain,
( sQ15_spl
| ~ sQ21_spl
| relation_dom(empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f741,f1419]) ).
fof(f1421,plain,
( sQ15_spl
| ~ sQ21_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f741,f1420]) ).
fof(f1422,plain,
( sQ15_spl
| ~ sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1421]) ).
fof(f1423,plain,
( sQ15_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1422]) ).
fof(f1424,plain,
( ~ relation(sK50_skl)
| sK50_skl = empty_set ),
inference(resolution,[status(thm)],[f919,f1199]) ).
fof(f1430,definition,
( sQ34_spl
<=> relation(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f1432,plain,
( sQ34_spl
| ~ relation(sK50_skl) ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1433,plain,
( ~ sQ34_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1424,f1058,f1430]) ).
fof(f1444,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f1432]) ).
fof(f1445,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f1444]) ).
fof(f1513,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(relation_rng(X0)) ),
inference(resolution,[status(thm)],[f485,f478]) ).
fof(f1524,plain,
powerset(empty_set) != empty_set,
inference(paramodulation,[status(thm)],[f627,f502]) ).
fof(f1543,plain,
! [X0,X1] :
( in(ordered_pair(sK4_skl(X1,sK57_skl,X0),sK5_skl(X1,sK57_skl,X0)),X0)
| in(ordered_pair(sK4_skl(X1,sK57_skl,X0),sK5_skl(X1,sK57_skl,X0)),sK57_skl)
| sK57_skl = relation_rng_restriction(X1,X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f243,f613]) ).
fof(f1547,plain,
! [X0,X1,X2] :
( ~ in(sK4_skl(X1,sK57_skl,X0),X2)
| in(sK5_skl(X1,sK57_skl,X0),relation_image(sK57_skl,X2))
| in(ordered_pair(sK4_skl(X1,sK57_skl,X0),sK5_skl(X1,sK57_skl,X0)),X0)
| sK57_skl = relation_rng_restriction(X1,X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1543,f909]) ).
fof(f1551,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),sK5_skl(relation_image(sK57_skl,X1),sK57_skl,X0)),X0)
| ~ in(ordered_pair(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),sK5_skl(relation_image(sK57_skl,X1),sK57_skl,X0)),sK57_skl)
| sK57_skl = relation_rng_restriction(relation_image(sK57_skl,X1),X0)
| ~ relation(sK57_skl)
| ~ relation(X0)
| ~ in(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),X1)
| in(ordered_pair(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),sK5_skl(relation_image(sK57_skl,X1),sK57_skl,X0)),X0)
| sK57_skl = relation_rng_restriction(relation_image(sK57_skl,X1),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1547,f241]) ).
fof(f1553,definition,
! [X0,X1] :
( sQ38_spl
<=> ( ~ in(ordered_pair(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),sK5_skl(relation_image(sK57_skl,X1),sK57_skl,X0)),X0)
| ~ in(ordered_pair(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),sK5_skl(relation_image(sK57_skl,X1),sK57_skl,X0)),sK57_skl)
| sK57_skl = relation_rng_restriction(relation_image(sK57_skl,X1),X0)
| ~ relation(X0)
| ~ in(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),X1)
| in(ordered_pair(sK4_skl(relation_image(sK57_skl,X1),sK57_skl,X0),sK5_skl(relation_image(sK57_skl,X1),sK57_skl,X0)),X0)
| sK57_skl = relation_rng_restriction(relation_image(sK57_skl,X1),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1556,plain,
( ~ sQ33_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1551,f1553,f1400]) ).
fof(f1557,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1402,f613]) ).
fof(f1558,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f1557]) ).
fof(f1561,plain,
! [X0] :
( ~ empty(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f741,f1303]) ).
fof(f1563,definition,
! [X0] :
( sQ39_spl
<=> ~ in(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1566,plain,
( ~ sQ31_spl
| ~ sQ26_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f1561,f1563,f1103,f1331]) ).
fof(f1567,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1333,f461]) ).
fof(f1568,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1567]) ).
fof(f1588,plain,
( ~ empty(empty_set)
| ~ relation(empty_set)
| identity_relation(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f741,f1336]) ).
fof(f1590,definition,
( sQ40_spl
<=> identity_relation(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1593,plain,
( ~ sQ31_spl
| ~ sQ26_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1588,f1590,f1103,f1331]) ).
fof(f1599,plain,
( ~ empty(empty_set)
| ~ relation(empty_set)
| empty(relation_rng(empty_set)) ),
inference(paramodulation,[status(thm)],[f741,f1513]) ).
fof(f1600,definition,
( sQ41_spl
<=> empty(relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1603,plain,
( ~ sQ31_spl
| ~ sQ26_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1599,f1600,f1103,f1331]) ).
fof(f1606,plain,
! [X0] :
( subset(relation_dom(set_intersection2(empty_set,X0)),relation_dom(empty_set))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1286,f1282]) ).
fof(f1607,plain,
! [X0] :
( subset(relation_dom(set_intersection2(X0,empty_set)),relation_dom(X0))
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f642,f1282]) ).
fof(f1611,definition,
! [X0] :
( sQ42_spl
<=> subset(relation_dom(set_intersection2(empty_set,X0)),relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1614,plain,
( sQ42_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1606,f1103,f1611]) ).
fof(f1615,definition,
! [X0] :
( sQ43_spl
<=> ( subset(relation_dom(set_intersection2(X0,empty_set)),relation_dom(X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1618,plain,
( sQ43_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1607,f1103,f1615]) ).
fof(f1627,plain,
! [X0] :
( subset(relation_dom(set_difference(empty_set,X0)),relation_dom(empty_set))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f721,f1294]) ).
fof(f1629,definition,
! [X0] :
( sQ44_spl
<=> subset(relation_dom(set_difference(empty_set,X0)),relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1632,plain,
( sQ44_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1627,f1103,f1629]) ).
fof(f1649,plain,
! [X0] :
( sK16_skl(singleton(X0)) = X0
| singleton(X0) = empty_set ),
inference(resolution,[status(thm)],[f284,f865]) ).
fof(f1652,plain,
! [X0] : sK16_skl(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f1649,f502]) ).
fof(f1653,plain,
sK16_skl(powerset(empty_set)) = empty_set,
inference(paramodulation,[status(thm)],[f627,f1652]) ).
fof(f1655,plain,
( in(empty_set,powerset(empty_set))
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f1653,f284]) ).
fof(f1656,definition,
( sQ45_spl
<=> powerset(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1657,plain,
( ~ sQ45_spl
| powerset(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f1656]) ).
fof(f1659,definition,
( sQ46_spl
<=> in(empty_set,powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1662,plain,
( sQ46_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1655,f1656,f1659]) ).
fof(f1663,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1657,f1524]) ).
fof(f1664,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f1663]) ).
fof(f1687,plain,
! [X0,X1] :
( in(ordered_pair(sK6_skl(X0,relation_image(sK57_skl,X1),X1,sK57_skl),X0),sK57_skl)
| ~ in(X0,relation_image(sK57_skl,X1)) ),
inference(resolution,[status(thm)],[f857,f613]) ).
fof(f1694,plain,
! [X0] :
( ~ sQ4_spl
| ~ in(sK6_skl(sK58_skl,relation_image(sK57_skl,X0),X0,sK57_skl),sK59_skl)
| ~ in(sK58_skl,relation_image(sK57_skl,X0)) ),
inference(resolution,[status(thm)],[f1687,f936]) ).
fof(f1698,plain,
( ~ sQ4_spl
| ~ in(sK58_skl,relation_image(sK57_skl,sK59_skl))
| ~ relation(sK57_skl)
| ~ in(sK58_skl,relation_image(sK57_skl,sK59_skl)) ),
inference(resolution,[status(thm)],[f1694,f858]) ).
fof(f1699,plain,
( ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1698,f827,f1400,f842]) ).
fof(f1700,plain,
$false,
inference(sat_refutation,[status(thm)],[f837,f841,f845,f935,f960,f972,f995,f1041,f1057,f1068,f1078,f1109,f1111,f1157,f1220,f1222,f1403,f1423,f1433,f1445,f1556,f1558,f1566,f1568,f1593,f1603,f1614,f1618,f1632,f1662,f1664,f1699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU203+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n020.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Mon Sep 21 05:58:19 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.56 % Drodi V4.1.1
% 0.13/0.61 % Refutation found
% 0.13/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.63 % Elapsed time: 0.086446 seconds
% 0.13/0.63 % CPU time: 0.377207 seconds
% 0.13/0.63 % Total memory used: 74.136 MB
% 0.13/0.63 % Net memory used: 73.468 MB
%------------------------------------------------------------------------------