TSTP Solution File: SEU240+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU240+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 : Tue May 21 03:56:27 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 48
% Syntax : Number of formulae : 259 ( 72 unt; 0 def)
% Number of atoms : 744 ( 60 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 849 ( 364 ~; 348 |; 90 &)
% ( 21 <=>; 24 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 13 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-2 aty)
% Number of variables : 365 ( 319 !; 46 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f632,plain,
$false,
inference(avatar_sat_refutation,[],[f151,f207,f218,f236,f247,f317,f324,f328,f544,f631]) ).
fof(f631,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f630,plain,
( $false
| ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(subsumption_resolution,[],[f629,f89]) ).
fof(f89,plain,
relation(sK2),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( ( ( ~ in(ordered_pair(sK3,sK5),sK2)
& in(ordered_pair(sK4,sK5),sK2)
& in(ordered_pair(sK3,sK4),sK2) )
| ~ transitive(sK2) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),sK2)
| ~ in(ordered_pair(X5,X6),sK2)
| ~ in(ordered_pair(X4,X5),sK2) )
| transitive(sK2) )
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f67,f69,f68]) ).
fof(f68,plain,
( ? [X0] :
( ( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
| ~ transitive(X0) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| transitive(X0) )
& relation(X0) )
=> ( ( ? [X3,X2,X1] :
( ~ in(ordered_pair(X1,X3),sK2)
& in(ordered_pair(X2,X3),sK2)
& in(ordered_pair(X1,X2),sK2) )
| ~ transitive(sK2) )
& ( ! [X6,X5,X4] :
( in(ordered_pair(X4,X6),sK2)
| ~ in(ordered_pair(X5,X6),sK2)
| ~ in(ordered_pair(X4,X5),sK2) )
| transitive(sK2) )
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
( ? [X3,X2,X1] :
( ~ in(ordered_pair(X1,X3),sK2)
& in(ordered_pair(X2,X3),sK2)
& in(ordered_pair(X1,X2),sK2) )
=> ( ~ in(ordered_pair(sK3,sK5),sK2)
& in(ordered_pair(sK4,sK5),sK2)
& in(ordered_pair(sK3,sK4),sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0] :
( ( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
| ~ transitive(X0) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| transitive(X0) )
& relation(X0) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
? [X0] :
( ( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
| ~ transitive(X0) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| transitive(X0) )
& relation(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
? [X0] :
( ( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
| ~ transitive(X0) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| transitive(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
? [X0] :
( ( transitive(X0)
<~> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
& relation(X0) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
? [X0] :
( ( transitive(X0)
<~> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f629,plain,
( ~ relation(sK2)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(subsumption_resolution,[],[f628,f145]) ).
fof(f145,plain,
( transitive(sK2)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f144,plain,
( spl15_1
<=> transitive(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f628,plain,
( ~ transitive(sK2)
| ~ relation(sK2)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(subsumption_resolution,[],[f627,f338]) ).
fof(f338,plain,
( in(sK4,relation_field(sK2))
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f334,f89]) ).
fof(f334,plain,
( in(sK4,relation_field(sK2))
| ~ relation(sK2)
| ~ spl15_2 ),
inference(resolution,[],[f150,f127]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f150,plain,
( in(ordered_pair(sK3,sK4),sK2)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f148,plain,
( spl15_2
<=> in(ordered_pair(sK3,sK4),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f627,plain,
( ~ in(sK4,relation_field(sK2))
| ~ transitive(sK2)
| ~ relation(sK2)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(subsumption_resolution,[],[f626,f552]) ).
fof(f552,plain,
( in(sK5,relation_field(sK2))
| ~ spl15_1 ),
inference(subsumption_resolution,[],[f548,f89]) ).
fof(f548,plain,
( in(sK5,relation_field(sK2))
| ~ relation(sK2)
| ~ spl15_1 ),
inference(resolution,[],[f545,f127]) ).
fof(f545,plain,
( in(ordered_pair(sK4,sK5),sK2)
| ~ spl15_1 ),
inference(subsumption_resolution,[],[f92,f145]) ).
fof(f92,plain,
( in(ordered_pair(sK4,sK5),sK2)
| ~ transitive(sK2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f626,plain,
( ~ in(sK5,relation_field(sK2))
| ~ in(sK4,relation_field(sK2))
| ~ transitive(sK2)
| ~ relation(sK2)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(subsumption_resolution,[],[f623,f339]) ).
fof(f339,plain,
( in(sK3,relation_field(sK2))
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f335,f89]) ).
fof(f335,plain,
( in(sK3,relation_field(sK2))
| ~ relation(sK2)
| ~ spl15_2 ),
inference(resolution,[],[f150,f126]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f623,plain,
( ~ in(sK3,relation_field(sK2))
| ~ in(sK5,relation_field(sK2))
| ~ in(sK4,relation_field(sK2))
| ~ transitive(sK2)
| ~ relation(sK2)
| ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(resolution,[],[f622,f97]) ).
fof(f97,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ( ( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0)) )
& ( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f622,plain,
( ! [X0] :
( ~ is_transitive_in(sK2,X0)
| ~ in(sK3,X0)
| ~ in(sK5,X0)
| ~ in(sK4,X0) )
| ~ spl15_1
| ~ spl15_2
| ~ spl15_11 ),
inference(subsumption_resolution,[],[f621,f312]) ).
fof(f312,plain,
( sP1(sK2)
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f311,plain,
( spl15_11
<=> sP1(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f621,plain,
( ! [X0] :
( ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ in(sK5,X0)
| ~ is_transitive_in(sK2,X0)
| ~ sP1(sK2) )
| ~ spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f618,f99]) ).
fof(f99,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ is_transitive_in(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ is_transitive_in(X0,X1) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f618,plain,
( ! [X0] :
( ~ sP0(sK2,X0)
| ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ in(sK5,X0) )
| ~ spl15_1
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f617,f546]) ).
fof(f546,plain,
( ~ in(ordered_pair(sK3,sK5),sK2)
| ~ spl15_1 ),
inference(subsumption_resolution,[],[f93,f145]) ).
fof(f93,plain,
( ~ in(ordered_pair(sK3,sK5),sK2)
| ~ transitive(sK2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f617,plain,
( ! [X0] :
( in(ordered_pair(sK3,sK5),sK2)
| ~ in(sK5,X0)
| ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ sP0(sK2,X0) )
| ~ spl15_1
| ~ spl15_2 ),
inference(resolution,[],[f547,f150]) ).
fof(f547,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,sK4),sK2)
| in(ordered_pair(X0,sK5),sK2)
| ~ in(sK5,X1)
| ~ in(sK4,X1)
| ~ in(X0,X1)
| ~ sP0(sK2,X1) )
| ~ spl15_1 ),
inference(resolution,[],[f545,f101]) ).
fof(f101,plain,
! [X0,X1,X6,X7,X5] :
( ~ in(ordered_pair(X6,X7),X0)
| in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ in(ordered_pair(sK6(X0,X1),sK8(X0,X1)),X0)
& in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
& in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
& in(sK8(X0,X1),X1)
& in(sK7(X0,X1),X1)
& in(sK6(X0,X1),X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f74,f75]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK6(X0,X1),sK8(X0,X1)),X0)
& in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
& in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
& in(sK8(X0,X1),X1)
& in(sK7(X0,X1),X1)
& in(sK6(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f544,plain,
( ~ spl15_2
| ~ spl15_11
| ~ spl15_12 ),
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f543,plain,
( $false
| ~ spl15_2
| ~ spl15_11
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f542,f338]) ).
fof(f542,plain,
( ~ in(sK4,relation_field(sK2))
| ~ spl15_2
| ~ spl15_11
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f541,f339]) ).
fof(f541,plain,
( ~ in(sK3,relation_field(sK2))
| ~ in(sK4,relation_field(sK2))
| ~ spl15_2
| ~ spl15_11
| ~ spl15_12 ),
inference(resolution,[],[f540,f349]) ).
fof(f349,plain,
( in(sK5,relation_field(sK2))
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f345,f89]) ).
fof(f345,plain,
( in(sK5,relation_field(sK2))
| ~ relation(sK2)
| ~ spl15_12 ),
inference(resolution,[],[f332,f127]) ).
fof(f332,plain,
( in(ordered_pair(sK4,sK5),sK2)
| ~ spl15_12 ),
inference(global_subsumption,[],[f89,f94,f128,f129,f130,f132,f134,f135,f108,f113,f114,f95,f110,f115,f138,f139,f142,f125,f91,f119,f120,f122,f116,f117,f157,f158,f161,f156,f124,f97,f98,f99,f100,f102,f180,f181,f183,f103,f104,f121,f188,f189,f179,f184,f186,f96,f191,f192,f198,f197,f193,f209,f208,f194,f220,f118,f222,f223,f225,f226,f227,f219,f196,f238,f237,f221,f250,f251,f253,f254,f255,f256,f126,f224,f257,f258,f259,f260,f261,f262,f263,f252,f266,f267,f268,f269,f270,f271,f272,f127,f105,f276,f277,f279,f273,f283,f274,f282,f284,f106,f107,f286,f290,f275,f288,f101,f318,f319,f316,f329,f90,f330,f93,f331,f92]) ).
fof(f331,plain,
( ~ in(ordered_pair(sK3,sK5),sK2)
| ~ spl15_12 ),
inference(global_subsumption,[],[f92,f89,f94,f128,f129,f130,f132,f134,f135,f108,f113,f114,f95,f110,f115,f138,f139,f142,f125,f91,f119,f120,f122,f116,f117,f157,f158,f161,f156,f124,f97,f98,f99,f100,f102,f180,f181,f183,f103,f104,f121,f188,f189,f179,f184,f186,f96,f191,f192,f198,f197,f193,f209,f208,f194,f220,f118,f222,f223,f225,f226,f227,f219,f196,f238,f237,f221,f250,f251,f253,f254,f255,f256,f126,f224,f257,f258,f259,f260,f261,f262,f263,f252,f266,f267,f268,f269,f270,f271,f272,f127,f105,f276,f277,f279,f273,f283,f274,f282,f284,f106,f107,f286,f290,f275,f288,f101,f318,f319,f316,f329,f90,f330,f93]) ).
fof(f330,plain,
( transitive(sK2)
| ~ spl15_12 ),
inference(global_subsumption,[],[f93,f92,f89,f94,f128,f129,f130,f132,f134,f135,f108,f113,f114,f95,f110,f115,f138,f139,f142,f125,f91,f119,f120,f122,f116,f117,f157,f158,f161,f156,f124,f97,f98,f99,f100,f102,f180,f181,f183,f103,f104,f121,f188,f189,f179,f184,f186,f96,f191,f192,f198,f197,f193,f209,f208,f194,f220,f118,f222,f223,f225,f226,f227,f219,f196,f238,f237,f221,f250,f251,f253,f254,f255,f256,f126,f224,f257,f258,f259,f260,f261,f262,f263,f252,f266,f267,f268,f269,f270,f271,f272,f127,f105,f276,f277,f279,f273,f283,f274,f282,f284,f106,f107,f286,f290,f275,f288,f101,f318,f319,f316,f329,f90]) ).
fof(f90,plain,
! [X6,X4,X5] :
( in(ordered_pair(X4,X6),sK2)
| ~ in(ordered_pair(X5,X6),sK2)
| ~ in(ordered_pair(X4,X5),sK2)
| transitive(sK2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f329,plain,
( transitive(sK2)
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f325,f89]) ).
fof(f325,plain,
( transitive(sK2)
| ~ relation(sK2)
| ~ spl15_12 ),
inference(resolution,[],[f316,f98]) ).
fof(f316,plain,
( ! [X0] : is_transitive_in(sK2,X0)
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f315,plain,
( spl15_12
<=> ! [X0] : is_transitive_in(sK2,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f319,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,sK8(X1,X2)),X1)
| ~ in(ordered_pair(X0,sK7(X1,X2)),X1)
| ~ in(sK8(X1,X2),X3)
| ~ in(sK7(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) ),
inference(resolution,[],[f101,f106]) ).
fof(f318,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,sK7(X1,X2)),X1)
| ~ in(ordered_pair(X0,sK6(X1,X2)),X1)
| ~ in(sK7(X1,X2),X3)
| ~ in(sK6(X1,X2),X3)
| ~ in(X0,X3)
| ~ sP0(X1,X3)
| sP0(X1,X2) ),
inference(resolution,[],[f101,f105]) ).
fof(f288,plain,
! [X0,X1] :
( ~ in(X0,ordered_pair(sK7(X0,X1),sK8(X0,X1)))
| sP0(X0,X1) ),
inference(resolution,[],[f106,f122]) ).
fof(f275,plain,
! [X0,X1] :
( ~ in(X0,ordered_pair(sK6(X0,X1),sK7(X0,X1)))
| sP0(X0,X1) ),
inference(resolution,[],[f105,f122]) ).
fof(f290,plain,
! [X0,X1] :
( ~ in(relation_field(X0),sK8(X0,X1))
| ~ relation(X0)
| sP0(X0,X1) ),
inference(resolution,[],[f286,f122]) ).
fof(f286,plain,
! [X0,X1] :
( in(sK8(X0,X1),relation_field(X0))
| sP0(X0,X1)
| ~ relation(X0) ),
inference(resolution,[],[f106,f127]) ).
fof(f107,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK6(X0,X1),sK8(X0,X1)),X0)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f106,plain,
! [X0,X1] :
( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f284,plain,
! [X0,X1] :
( ~ in(relation_field(X0),sK6(X0,X1))
| ~ relation(X0)
| sP0(X0,X1) ),
inference(resolution,[],[f274,f122]) ).
fof(f282,plain,
! [X0,X1] :
( ~ in(relation_field(X0),sK7(X0,X1))
| ~ relation(X0)
| sP0(X0,X1) ),
inference(resolution,[],[f273,f122]) ).
fof(f274,plain,
! [X0,X1] :
( in(sK6(X0,X1),relation_field(X0))
| sP0(X0,X1)
| ~ relation(X0) ),
inference(resolution,[],[f105,f126]) ).
fof(f283,plain,
! [X0,X1] :
( ~ empty(relation_field(X0))
| ~ relation(X0)
| sP0(X0,X1) ),
inference(resolution,[],[f273,f125]) ).
fof(f273,plain,
! [X0,X1] :
( in(sK7(X0,X1),relation_field(X0))
| sP0(X0,X1)
| ~ relation(X0) ),
inference(resolution,[],[f105,f127]) ).
fof(f279,plain,
! [X0] :
( transitive(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f278,f108]) ).
fof(f278,plain,
! [X0] :
( ~ empty(X0)
| ~ sP1(X0)
| transitive(X0)
| ~ relation(X0) ),
inference(resolution,[],[f277,f98]) ).
fof(f277,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ empty(X0)
| ~ sP1(X0) ),
inference(resolution,[],[f276,f100]) ).
fof(f276,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X0) ),
inference(resolution,[],[f105,f125]) ).
fof(f105,plain,
! [X0,X1] :
( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f272,plain,
! [X0,X1] : unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f118,f252]) ).
fof(f271,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),
inference(superposition,[],[f221,f252]) ).
fof(f270,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f224,f252]) ).
fof(f269,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f252,f252]) ).
fof(f268,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f252,f224]) ).
fof(f267,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f252,f221]) ).
fof(f266,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f252,f118]) ).
fof(f252,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f221,f116]) ).
fof(f263,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f118,f224]) ).
fof(f262,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f221,f224]) ).
fof(f261,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f224,f224]) ).
fof(f260,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f224,f221]) ).
fof(f259,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f224,f118]) ).
fof(f258,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f224,f116]) ).
fof(f257,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f224,f116]) ).
fof(f224,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f118,f116]) ).
fof(f256,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f116,f221]) ).
fof(f255,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f116,f221]) ).
fof(f254,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f118,f221]) ).
fof(f253,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f221,f116]) ).
fof(f251,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))),
inference(superposition,[],[f221,f221]) ).
fof(f250,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f221,f118]) ).
fof(f221,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f118,f116]) ).
fof(f237,plain,
( ~ empty(relation_field(empty_set))
| empty(relation_dom(empty_set)) ),
inference(superposition,[],[f120,f196]) ).
fof(f238,plain,
( ~ empty(relation_field(empty_set))
| empty(relation_rng(empty_set)) ),
inference(superposition,[],[f119,f196]) ).
fof(f196,plain,
relation_field(empty_set) = set_union2(relation_dom(empty_set),relation_rng(empty_set)),
inference(forward_demodulation,[],[f195,f139]) ).
fof(f195,plain,
relation_field(sK14) = set_union2(relation_dom(sK14),relation_rng(sK14)),
inference(resolution,[],[f96,f134]) ).
fof(f219,plain,
( ~ empty(relation_field(sK13))
| empty(relation_dom(sK13)) ),
inference(superposition,[],[f120,f194]) ).
fof(f227,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f116,f118]) ).
fof(f226,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f116,f118]) ).
fof(f225,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f118,f116]) ).
fof(f223,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f118,f118]) ).
fof(f222,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f118,f116]) ).
fof(f118,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f220,plain,
( ~ empty(relation_field(sK13))
| empty(relation_rng(sK13)) ),
inference(superposition,[],[f119,f194]) ).
fof(f194,plain,
relation_field(sK13) = set_union2(relation_dom(sK13),relation_rng(sK13)),
inference(resolution,[],[f96,f132]) ).
fof(f208,plain,
( ~ empty(relation_field(sK12))
| empty(relation_dom(sK12)) ),
inference(superposition,[],[f120,f193]) ).
fof(f209,plain,
( ~ empty(relation_field(sK12))
| empty(relation_rng(sK12)) ),
inference(superposition,[],[f119,f193]) ).
fof(f193,plain,
relation_field(sK12) = set_union2(relation_dom(sK12),relation_rng(sK12)),
inference(resolution,[],[f96,f130]) ).
fof(f197,plain,
( ~ empty(relation_field(sK2))
| empty(relation_dom(sK2)) ),
inference(superposition,[],[f120,f192]) ).
fof(f198,plain,
( ~ empty(relation_field(sK2))
| empty(relation_rng(sK2)) ),
inference(superposition,[],[f119,f192]) ).
fof(f192,plain,
relation_field(sK2) = set_union2(relation_dom(sK2),relation_rng(sK2)),
inference(resolution,[],[f96,f89]) ).
fof(f191,plain,
relation_field(empty_set) = set_union2(relation_dom(empty_set),relation_rng(empty_set)),
inference(resolution,[],[f96,f142]) ).
fof(f96,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f186,plain,
! [X0,X1] :
( ~ in(X1,sK8(X0,X1))
| sP0(X0,X1) ),
inference(resolution,[],[f104,f122]) ).
fof(f184,plain,
! [X0,X1] :
( ~ in(X1,sK7(X0,X1))
| sP0(X0,X1) ),
inference(resolution,[],[f103,f122]) ).
fof(f179,plain,
! [X0,X1] :
( ~ in(X1,sK6(X0,X1))
| sP0(X0,X1) ),
inference(resolution,[],[f102,f122]) ).
fof(f189,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| empty(X0) ),
inference(resolution,[],[f188,f122]) ).
fof(f188,plain,
! [X0] :
( in(sK9(X0),X0)
| empty(X0) ),
inference(resolution,[],[f121,f113]) ).
fof(f121,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f104,plain,
! [X0,X1] :
( in(sK8(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f103,plain,
! [X0,X1] :
( in(sK7(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f183,plain,
! [X0] :
( ~ empty(relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(subsumption_resolution,[],[f182,f108]) ).
fof(f182,plain,
! [X0] :
( ~ empty(relation_field(X0))
| ~ sP1(X0)
| transitive(X0)
| ~ relation(X0) ),
inference(resolution,[],[f181,f98]) ).
fof(f181,plain,
! [X0,X1] :
( is_transitive_in(X1,X0)
| ~ empty(X0)
| ~ sP1(X1) ),
inference(resolution,[],[f180,f100]) ).
fof(f180,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ empty(X1) ),
inference(resolution,[],[f102,f125]) ).
fof(f102,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f100,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| is_transitive_in(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f98,plain,
! [X0] :
( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f124,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f156,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f117,f95]) ).
fof(f161,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f95,f117]) ).
fof(f158,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f95,f117]) ).
fof(f157,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(superposition,[],[f117,f95]) ).
fof(f117,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f116,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f122,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f120,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f119,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f91,plain,
( in(ordered_pair(sK3,sK4),sK2)
| ~ transitive(sK2) ),
inference(cnf_transformation,[],[f70]) ).
fof(f125,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f142,plain,
relation(empty_set),
inference(superposition,[],[f134,f139]) ).
fof(f139,plain,
empty_set = sK14,
inference(resolution,[],[f110,f135]) ).
fof(f138,plain,
empty_set = sK11,
inference(resolution,[],[f110,f129]) ).
fof(f115,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f110,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f95,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f114,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f113,plain,
! [X0] : element(sK9(X0),X0),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] : element(sK9(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f19,f77]) ).
fof(f77,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK9(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f108,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f47,f63,f62]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f135,plain,
empty(sK14),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( function(sK14)
& empty(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f29,f87]) ).
fof(f87,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK14)
& empty(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f134,plain,
relation(sK14),
inference(cnf_transformation,[],[f88]) ).
fof(f132,plain,
relation(sK13),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( function(sK13)
& relation(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f40,f85]) ).
fof(f85,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK13)
& relation(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f31]) ).
fof(f31,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f130,plain,
relation(sK12),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
( function(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f27,f83]) ).
fof(f83,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f129,plain,
empty(sK11),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f28,f81]) ).
fof(f81,plain,
( ? [X0] : empty(X0)
=> empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f128,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
~ empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f30,f79]) ).
fof(f79,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f94,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f540,plain,
( ! [X0] :
( ~ in(sK5,X0)
| ~ in(sK3,X0)
| ~ in(sK4,X0) )
| ~ spl15_2
| ~ spl15_11
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f539,f312]) ).
fof(f539,plain,
( ! [X0] :
( ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ in(sK5,X0)
| ~ sP1(sK2) )
| ~ spl15_2
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f538,f316]) ).
fof(f538,plain,
( ! [X0] :
( ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ in(sK5,X0)
| ~ is_transitive_in(sK2,X0)
| ~ sP1(sK2) )
| ~ spl15_2
| ~ spl15_12 ),
inference(resolution,[],[f535,f99]) ).
fof(f535,plain,
( ! [X0] :
( ~ sP0(sK2,X0)
| ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ in(sK5,X0) )
| ~ spl15_2
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f534,f331]) ).
fof(f534,plain,
( ! [X0] :
( in(ordered_pair(sK3,sK5),sK2)
| ~ in(sK5,X0)
| ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ sP0(sK2,X0) )
| ~ spl15_2
| ~ spl15_12 ),
inference(resolution,[],[f344,f150]) ).
fof(f344,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,sK4),sK2)
| in(ordered_pair(X0,sK5),sK2)
| ~ in(sK5,X1)
| ~ in(sK4,X1)
| ~ in(X0,X1)
| ~ sP0(sK2,X1) )
| ~ spl15_12 ),
inference(resolution,[],[f332,f101]) ).
fof(f328,plain,
( spl15_1
| ~ spl15_12 ),
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f327,plain,
( $false
| spl15_1
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f326,f89]) ).
fof(f326,plain,
( ~ relation(sK2)
| spl15_1
| ~ spl15_12 ),
inference(subsumption_resolution,[],[f325,f146]) ).
fof(f146,plain,
( ~ transitive(sK2)
| spl15_1 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f324,plain,
spl15_11,
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f323,plain,
( $false
| spl15_11 ),
inference(subsumption_resolution,[],[f322,f89]) ).
fof(f322,plain,
( ~ relation(sK2)
| spl15_11 ),
inference(resolution,[],[f313,f108]) ).
fof(f313,plain,
( ~ sP1(sK2)
| spl15_11 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f317,plain,
( ~ spl15_11
| spl15_12
| spl15_1 ),
inference(avatar_split_clause,[],[f309,f144,f315,f311]) ).
fof(f309,plain,
( ! [X0] :
( is_transitive_in(sK2,X0)
| ~ sP1(sK2) )
| spl15_1 ),
inference(resolution,[],[f307,f100]) ).
fof(f307,plain,
( ! [X0] : sP0(sK2,X0)
| spl15_1 ),
inference(subsumption_resolution,[],[f306,f105]) ).
fof(f306,plain,
( ! [X0] :
( ~ in(ordered_pair(sK6(sK2,X0),sK7(sK2,X0)),sK2)
| sP0(sK2,X0) )
| spl15_1 ),
inference(duplicate_literal_removal,[],[f303]) ).
fof(f303,plain,
( ! [X0] :
( ~ in(ordered_pair(sK6(sK2,X0),sK7(sK2,X0)),sK2)
| sP0(sK2,X0)
| sP0(sK2,X0) )
| spl15_1 ),
inference(resolution,[],[f294,f107]) ).
fof(f294,plain,
( ! [X0,X1] :
( in(ordered_pair(X0,sK8(sK2,X1)),sK2)
| ~ in(ordered_pair(X0,sK7(sK2,X1)),sK2)
| sP0(sK2,X1) )
| spl15_1 ),
inference(resolution,[],[f292,f106]) ).
fof(f292,plain,
( ! [X6,X4,X5] :
( ~ in(ordered_pair(X5,X6),sK2)
| in(ordered_pair(X4,X6),sK2)
| ~ in(ordered_pair(X4,X5),sK2) )
| spl15_1 ),
inference(subsumption_resolution,[],[f90,f146]) ).
fof(f247,plain,
( spl15_9
| ~ spl15_10 ),
inference(avatar_split_clause,[],[f237,f244,f240]) ).
fof(f240,plain,
( spl15_9
<=> empty(relation_dom(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f244,plain,
( spl15_10
<=> empty(relation_field(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f236,plain,
( spl15_7
| ~ spl15_8 ),
inference(avatar_split_clause,[],[f219,f233,f229]) ).
fof(f229,plain,
( spl15_7
<=> empty(relation_dom(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f233,plain,
( spl15_8
<=> empty(relation_field(sK13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f218,plain,
( spl15_5
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f208,f215,f211]) ).
fof(f211,plain,
( spl15_5
<=> empty(relation_dom(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f215,plain,
( spl15_6
<=> empty(relation_field(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f207,plain,
( spl15_3
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f197,f204,f200]) ).
fof(f200,plain,
( spl15_3
<=> empty(relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f204,plain,
( spl15_4
<=> empty(relation_field(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f151,plain,
( ~ spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f91,f148,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU240+1 : TPTP v8.2.0. Released v3.3.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n012.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 17:27:23 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (31086)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (31092)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.38 % (31090)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38 % (31087)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 TRYING [1]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 % (31093)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.39 TRYING [3]
% 0.16/0.39 TRYING [1]
% 0.16/0.39 % (31089)WARNING: value z3 for option sas not known
% 0.16/0.39 % (31091)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.39 TRYING [2]
% 0.16/0.39 % (31089)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.41 % (31088)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.41 TRYING [3]
% 0.16/0.42 % (31089)First to succeed.
% 0.16/0.42 TRYING [1]
% 0.16/0.42 TRYING [2]
% 0.16/0.42 TRYING [3]
% 0.16/0.43 % (31089)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31086"
% 0.22/0.43 % (31089)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43 % (31089)------------------------------
% 0.22/0.43 % (31089)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43 % (31089)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (31089)Memory used [KB]: 1103
% 0.22/0.43 % (31089)Time elapsed: 0.033 s
% 0.22/0.43 % (31089)Instructions burned: 46 (million)
% 0.22/0.43 % (31086)Success in time 0.06 s
%------------------------------------------------------------------------------