TSTP Solution File: SEU061+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:26:30 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 92 ( 10 unt; 0 def)
% Number of atoms : 368 ( 89 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 447 ( 171 ~; 182 |; 62 &)
% ( 17 <=>; 14 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 219 ( 178 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1048,plain,
$false,
inference(avatar_sat_refutation,[],[f222,f223,f474,f1047]) ).
fof(f1047,plain,
( ~ spl21_1
| ~ spl21_2 ),
inference(avatar_contradiction_clause,[],[f1046]) ).
fof(f1046,plain,
( $false
| ~ spl21_1
| ~ spl21_2 ),
inference(subsumption_resolution,[],[f1034,f213]) ).
fof(f213,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f212]) ).
fof(f212,plain,
! [X2,X0] :
( in(X2,X0)
| singleton(X2) != X0 ),
inference(equality_resolution,[],[f181]) ).
fof(f181,plain,
! [X2,X0,X1] :
( in(X2,X0)
| X1 != X2
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( ~ in(sK17(X0,X1),X0)
| sK17(X0,X1) != X1 )
& ( in(sK17(X0,X1),X0)
| sK17(X0,X1) = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f120,f121]) ).
fof(f121,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) )
=> ( ( ~ in(sK17(X0,X1),X0)
| sK17(X0,X1) != X1 )
& ( in(sK17(X0,X1),X0)
| sK17(X0,X1) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) ) ) ),
inference(rectify,[],[f119]) ).
fof(f119,plain,
! [X1,X0] :
( ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| X0 != X2 )
& ( in(X2,X1)
| X0 = X2 ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( ! [X2] :
( X0 = X2
<=> in(X2,X1) )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f1034,plain,
( ~ in(sK5,singleton(sK5))
| ~ spl21_1
| ~ spl21_2 ),
inference(unit_resulting_resolution,[],[f504,f690]) ).
fof(f690,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6)
| ~ in(X1,singleton(sK5)) )
| ~ spl21_2 ),
inference(superposition,[],[f520,f156]) ).
fof(f156,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f520,plain,
( ! [X4,X5] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),sK6)
| ~ in(X5,singleton(sK5)) )
| ~ spl21_2 ),
inference(forward_demodulation,[],[f519,f156]) ).
fof(f519,plain,
( ! [X4,X5] :
( ~ in(X5,singleton(sK5))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK6) )
| ~ spl21_2 ),
inference(subsumption_resolution,[],[f518,f207]) ).
fof(f207,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f152]) ).
fof(f152,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| in(sK7(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f97,f98]) ).
fof(f98,plain,
! [X0] :
( ? [X2] : in(X2,X0)
=> in(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X2] : in(X2,X0) ) ),
inference(rectify,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X1] : in(X1,X0) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ! [X1] : ~ in(X1,X0)
<=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f518,plain,
( ! [X4,X5] :
( ~ in(X5,singleton(sK5))
| in(X4,empty_set)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK6) )
| ~ spl21_2 ),
inference(subsumption_resolution,[],[f516,f148]) ).
fof(f148,plain,
relation(sK6),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( relation(sK6)
& ( empty_set = relation_inverse_image(sK6,singleton(sK5))
| ~ in(sK5,relation_rng(sK6)) )
& ( empty_set != relation_inverse_image(sK6,singleton(sK5))
| in(sK5,relation_rng(sK6)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f93,f94]) ).
fof(f94,plain,
( ? [X0,X1] :
( relation(X1)
& ( empty_set = relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1)) )
& ( empty_set != relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ) )
=> ( relation(sK6)
& ( empty_set = relation_inverse_image(sK6,singleton(sK5))
| ~ in(sK5,relation_rng(sK6)) )
& ( empty_set != relation_inverse_image(sK6,singleton(sK5))
| in(sK5,relation_rng(sK6)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
? [X0,X1] :
( relation(X1)
& ( empty_set = relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1)) )
& ( empty_set != relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
? [X0,X1] :
( relation(X1)
& ( empty_set = relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1)) )
& ( empty_set != relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
? [X0,X1] :
( relation(X1)
& ( in(X0,relation_rng(X1))
<~> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( empty_set != relation_inverse_image(X1,singleton(X0))
<=> in(X0,relation_rng(X1)) ) ),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> ( empty_set != relation_inverse_image(X1,singleton(X0))
<=> in(X0,relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f516,plain,
( ! [X4,X5] :
( ~ relation(sK6)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK6)
| ~ in(X5,singleton(sK5))
| in(X4,empty_set) )
| ~ spl21_2 ),
inference(superposition,[],[f210,f221]) ).
fof(f221,plain,
( empty_set = relation_inverse_image(sK6,singleton(sK5))
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f219,plain,
( spl21_2
<=> empty_set = relation_inverse_image(sK6,singleton(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).
fof(f210,plain,
! [X3,X0,X1,X5] :
( ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),X0)
| ~ relation(X0)
| in(X3,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f201]) ).
fof(f201,plain,
! [X2,X3,X0,X1,X5] :
( in(X3,X2)
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),X0)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f168,f175]) ).
fof(f175,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f168,plain,
! [X2,X3,X0,X1,X5] :
( in(X3,X2)
| ~ in(X5,X1)
| ~ in(ordered_pair(X3,X5),X0)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1,X2] :
( ( ! [X3] :
( ( ( in(sK12(X0,X1,X3),X1)
& in(ordered_pair(X3,sK12(X0,X1,X3)),X0) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X5] :
( ~ in(X5,X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| relation_inverse_image(X0,X1) != X2 )
& ( relation_inverse_image(X0,X1) = X2
| ( ( ~ in(sK13(X0,X1,X2),X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(sK13(X0,X1,X2),X7),X0) ) )
& ( in(sK13(X0,X1,X2),X2)
| ( in(sK14(X0,X1,X2),X1)
& in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X0) ) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f109,f112,f111,f110]) ).
fof(f110,plain,
! [X0,X1,X3] :
( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
=> ( in(sK12(X0,X1,X3),X1)
& in(ordered_pair(X3,sK12(X0,X1,X3)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ? [X6] :
( ( ~ in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) ) )
& ( in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) ) )
=> ( ( ~ in(sK13(X0,X1,X2),X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(sK13(X0,X1,X2),X7),X0) ) )
& ( in(sK13(X0,X1,X2),X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(sK13(X0,X1,X2),X8),X0) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ? [X8] :
( in(X8,X1)
& in(ordered_pair(sK13(X0,X1,X2),X8),X0) )
=> ( in(sK14(X0,X1,X2),X1)
& in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0] :
( ! [X1,X2] :
( ( ! [X3] :
( ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X5] :
( ~ in(X5,X1)
| ~ in(ordered_pair(X3,X5),X0) ) ) )
| relation_inverse_image(X0,X1) != X2 )
& ( relation_inverse_image(X0,X1) = X2
| ? [X6] :
( ( ~ in(X6,X2)
| ! [X7] :
( ~ in(X7,X1)
| ~ in(ordered_pair(X6,X7),X0) ) )
& ( in(X6,X2)
| ? [X8] :
( in(X8,X1)
& in(ordered_pair(X6,X8),X0) ) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ! [X2,X1] :
( ( ! [X3] :
( ( ? [X4] :
( in(X4,X2)
& in(ordered_pair(X3,X4),X0) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ! [X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X0) ) ) )
| relation_inverse_image(X0,X2) != X1 )
& ( relation_inverse_image(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ! [X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X0) ) )
& ( in(X3,X1)
| ? [X4] :
( in(X4,X2)
& in(ordered_pair(X3,X4),X0) ) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X2,X1] :
( ! [X3] :
( ? [X4] :
( in(X4,X2)
& in(ordered_pair(X3,X4),X0) )
<=> in(X3,X1) )
<=> relation_inverse_image(X0,X2) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( relation(X0)
=> ! [X2,X1] :
( ! [X3] :
( ? [X4] :
( in(X4,X2)
& in(ordered_pair(X3,X4),X0) )
<=> in(X3,X1) )
<=> relation_inverse_image(X0,X2) = X1 ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X2,X1] :
( relation_inverse_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f504,plain,
( in(unordered_pair(singleton(sK1(sK6,sK5)),unordered_pair(sK5,sK1(sK6,sK5))),sK6)
| ~ spl21_1 ),
inference(forward_demodulation,[],[f503,f156]) ).
fof(f503,plain,
( in(unordered_pair(singleton(sK1(sK6,sK5)),unordered_pair(sK1(sK6,sK5),sK5)),sK6)
| ~ spl21_1 ),
inference(forward_demodulation,[],[f480,f156]) ).
fof(f480,plain,
( in(unordered_pair(unordered_pair(sK1(sK6,sK5),sK5),singleton(sK1(sK6,sK5))),sK6)
| ~ spl21_1 ),
inference(unit_resulting_resolution,[],[f148,f216,f206]) ).
fof(f206,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(sK1(X0,X2),X2),singleton(sK1(X0,X2))),X0)
| ~ relation(X0)
| ~ in(X2,relation_rng(X0)) ),
inference(equality_resolution,[],[f197]) ).
fof(f197,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK1(X0,X2),X2),singleton(sK1(X0,X2))),X0)
| ~ in(X2,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f136,f175]) ).
fof(f136,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK1(X0,X2),X2),X0)
| ~ in(X2,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(sK1(X0,X2),X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ( ( ! [X6] : ~ in(ordered_pair(X6,sK2(X0,X1)),X0)
| ~ in(sK2(X0,X1),X1) )
& ( in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0)
| in(sK2(X0,X1),X1) ) ) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f84,f87,f86,f85]) ).
fof(f85,plain,
! [X0,X2] :
( ? [X4] : in(ordered_pair(X4,X2),X0)
=> in(ordered_pair(sK1(X0,X2),X2),X0) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) )
=> ( ( ! [X6] : ~ in(ordered_pair(X6,sK2(X0,X1)),X0)
| ~ in(sK2(X0,X1),X1) )
& ( ? [X7] : in(ordered_pair(X7,sK2(X0,X1)),X0)
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1] :
( ? [X7] : in(ordered_pair(X7,sK2(X0,X1)),X0)
=> in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X5] :
( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| ~ in(X5,X1) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| in(X5,X1) ) ) ) )
| ~ relation(X0) ),
inference(rectify,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 )
& ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) )
<=> relation_rng(X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f216,plain,
( in(sK5,relation_rng(sK6))
| ~ spl21_1 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f215,plain,
( spl21_1
<=> in(sK5,relation_rng(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).
fof(f474,plain,
( spl21_1
| spl21_2 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f473,plain,
( $false
| spl21_1
| spl21_2 ),
inference(subsumption_resolution,[],[f471,f282]) ).
fof(f282,plain,
( ! [X0] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK5)),sK6)
| spl21_1 ),
inference(forward_demodulation,[],[f281,f156]) ).
fof(f281,plain,
( ! [X0] : ~ in(unordered_pair(unordered_pair(X0,sK5),singleton(X0)),sK6)
| spl21_1 ),
inference(subsumption_resolution,[],[f277,f148]) ).
fof(f277,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK5),singleton(X0)),sK6)
| ~ relation(sK6) )
| spl21_1 ),
inference(resolution,[],[f217,f205]) ).
fof(f205,plain,
! [X2,X3,X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| in(X2,relation_rng(X0)) ),
inference(equality_resolution,[],[f196]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f137,f175]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( in(X2,X1)
| ~ in(ordered_pair(X3,X2),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f217,plain,
( ~ in(sK5,relation_rng(sK6))
| spl21_1 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f471,plain,
( in(unordered_pair(singleton(sK13(sK6,singleton(sK5),empty_set)),unordered_pair(sK13(sK6,singleton(sK5),empty_set),sK5)),sK6)
| spl21_2 ),
inference(backward_demodulation,[],[f306,f443]) ).
fof(f443,plain,
( sK14(sK6,singleton(sK5),empty_set) = sK5
| spl21_2 ),
inference(unit_resulting_resolution,[],[f298,f211]) ).
fof(f211,plain,
! [X2,X1] :
( X1 = X2
| ~ in(X2,singleton(X1)) ),
inference(equality_resolution,[],[f182]) ).
fof(f182,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ in(X2,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f298,plain,
( in(sK14(sK6,singleton(sK5),empty_set),singleton(sK5))
| spl21_2 ),
inference(unit_resulting_resolution,[],[f148,f207,f220,f166]) ).
fof(f166,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| ~ relation(X0)
| in(sK14(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f220,plain,
( empty_set != relation_inverse_image(sK6,singleton(sK5))
| spl21_2 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f306,plain,
( in(unordered_pair(singleton(sK13(sK6,singleton(sK5),empty_set)),unordered_pair(sK13(sK6,singleton(sK5),empty_set),sK14(sK6,singleton(sK5),empty_set))),sK6)
| spl21_2 ),
inference(forward_demodulation,[],[f297,f156]) ).
fof(f297,plain,
( in(unordered_pair(unordered_pair(sK13(sK6,singleton(sK5),empty_set),sK14(sK6,singleton(sK5),empty_set)),singleton(sK13(sK6,singleton(sK5),empty_set))),sK6)
| spl21_2 ),
inference(unit_resulting_resolution,[],[f148,f207,f220,f203]) ).
fof(f203,plain,
! [X2,X0,X1] :
( in(sK13(X0,X1,X2),X2)
| in(unordered_pair(unordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),singleton(sK13(X0,X1,X2))),X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = X2 ),
inference(definition_unfolding,[],[f165,f175]) ).
fof(f165,plain,
! [X2,X0,X1] :
( relation_inverse_image(X0,X1) = X2
| in(sK13(X0,X1,X2),X2)
| in(ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f223,plain,
( ~ spl21_2
| spl21_1 ),
inference(avatar_split_clause,[],[f146,f215,f219]) ).
fof(f146,plain,
( in(sK5,relation_rng(sK6))
| empty_set != relation_inverse_image(sK6,singleton(sK5)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f222,plain,
( ~ spl21_1
| spl21_2 ),
inference(avatar_split_clause,[],[f147,f219,f215]) ).
fof(f147,plain,
( empty_set = relation_inverse_image(sK6,singleton(sK5))
| ~ in(sK5,relation_rng(sK6)) ),
inference(cnf_transformation,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU061+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 14:33:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.46 % (8576)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.47 % (8584)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.48 % (8584)Instruction limit reached!
% 0.18/0.48 % (8584)------------------------------
% 0.18/0.48 % (8584)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.48 % (8584)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.48 % (8584)Termination reason: Unknown
% 0.18/0.48 % (8584)Termination phase: Saturation
% 0.18/0.48
% 0.18/0.48 % (8584)Memory used [KB]: 6140
% 0.18/0.48 % (8584)Time elapsed: 0.082 s
% 0.18/0.48 % (8584)Instructions burned: 7 (million)
% 0.18/0.48 % (8584)------------------------------
% 0.18/0.48 % (8584)------------------------------
% 0.18/0.50 % (8573)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.50 % (8571)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.50 % (8576)First to succeed.
% 0.18/0.51 % (8576)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (8576)------------------------------
% 0.18/0.51 % (8576)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (8576)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (8576)Termination reason: Refutation
% 0.18/0.51
% 0.18/0.51 % (8576)Memory used [KB]: 6524
% 0.18/0.51 % (8576)Time elapsed: 0.106 s
% 0.18/0.51 % (8576)Instructions burned: 38 (million)
% 0.18/0.51 % (8576)------------------------------
% 0.18/0.51 % (8576)------------------------------
% 0.18/0.51 % (8568)Success in time 0.17 s
%------------------------------------------------------------------------------