TSTP Solution File: SET768+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET768+4 : TPTP v8.1.0. Released v2.2.0.
% 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 : n022.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 18:22:10 EDT 2022
% Result : Theorem 1.52s 0.55s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 6 unt; 0 def)
% Number of atoms : 375 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 429 ( 148 ~; 156 |; 84 &)
% ( 16 <=>; 23 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 183 ( 156 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1260,plain,
$false,
inference(avatar_sat_refutation,[],[f147,f158,f321,f956,f1210,f1212,f1259]) ).
fof(f1259,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_contradiction_clause,[],[f1258]) ).
fof(f1258,plain,
( $false
| ~ spl7_1
| spl7_2 ),
inference(subsumption_resolution,[],[f1254,f1238]) ).
fof(f1238,plain,
( ! [X0] : ~ subset(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,X0,sK5))
| spl7_2 ),
inference(unit_resulting_resolution,[],[f176,f1217,f99]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f59,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(X3,X1)
& member(X3,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ~ member(X3,X1)
& member(X3,X0) ) ) ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
! [X1,X0] :
( ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X1,X0)
<=> ! [X2] :
( member(X2,X1)
=> member(X2,X0) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f1217,plain,
( ! [X0] : ~ member(sK4,equivalence_class(sK3,X0,sK5))
| spl7_2 ),
inference(resolution,[],[f145,f108]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( apply(X2,X3,X1)
| ~ member(X1,equivalence_class(X3,X0,X2)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ( member(X1,equivalence_class(X3,X0,X2))
| ~ member(X1,X0)
| ~ apply(X2,X3,X1) )
& ( ( member(X1,X0)
& apply(X2,X3,X1) )
| ~ member(X1,equivalence_class(X3,X0,X2)) ) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
! [X3,X2,X1,X0] :
( ( member(X2,equivalence_class(X0,X3,X1))
| ~ member(X2,X3)
| ~ apply(X1,X0,X2) )
& ( ( member(X2,X3)
& apply(X1,X0,X2) )
| ~ member(X2,equivalence_class(X0,X3,X1)) ) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X3,X2,X1,X0] :
( ( member(X2,equivalence_class(X0,X3,X1))
| ~ member(X2,X3)
| ~ apply(X1,X0,X2) )
& ( ( member(X2,X3)
& apply(X1,X0,X2) )
| ~ member(X2,equivalence_class(X0,X3,X1)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X3,X2,X1,X0] :
( member(X2,equivalence_class(X0,X3,X1))
<=> ( member(X2,X3)
& apply(X1,X0,X2) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X6,X2,X3] :
( member(X2,equivalence_class(X0,X3,X6))
<=> ( apply(X6,X0,X2)
& member(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_class) ).
fof(f145,plain,
( ~ apply(sK5,sK3,sK4)
| spl7_2 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f144,plain,
( spl7_2
<=> apply(sK5,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f176,plain,
member(sK4,equivalence_class(sK4,sK2,sK5)),
inference(unit_resulting_resolution,[],[f106,f138,f110]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( ~ apply(X2,X3,X1)
| member(X1,equivalence_class(X3,X0,X2))
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f138,plain,
apply(sK5,sK4,sK4),
inference(unit_resulting_resolution,[],[f106,f107,f112]) ).
fof(f112,plain,
! [X0,X1,X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1)
| ~ equivalence(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( ~ member(X3,X1)
| apply(X0,X4,X2)
| ~ member(X4,X1)
| ~ apply(X0,X3,X2)
| ~ apply(X0,X4,X3)
| ~ member(X2,X1) )
& ! [X5] :
( ~ member(X5,X1)
| apply(X0,X5,X5) )
& ! [X6,X7] :
( ~ member(X7,X1)
| apply(X0,X7,X6)
| ~ apply(X0,X6,X7)
| ~ member(X6,X1) ) )
| ~ equivalence(X0,X1) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X1,X0] :
( ( ! [X5,X6,X4] :
( ~ member(X6,X0)
| apply(X1,X4,X5)
| ~ member(X4,X0)
| ~ apply(X1,X6,X5)
| ~ apply(X1,X4,X6)
| ~ member(X5,X0) )
& ! [X7] :
( ~ member(X7,X0)
| apply(X1,X7,X7) )
& ! [X3,X2] :
( ~ member(X2,X0)
| apply(X1,X2,X3)
| ~ apply(X1,X3,X2)
| ~ member(X3,X0) ) )
| ~ equivalence(X1,X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( ! [X5,X6,X4] :
( apply(X1,X4,X5)
| ~ apply(X1,X4,X6)
| ~ apply(X1,X6,X5)
| ~ member(X6,X0)
| ~ member(X4,X0)
| ~ member(X5,X0) )
& ! [X3,X2] :
( apply(X1,X2,X3)
| ~ apply(X1,X3,X2)
| ~ member(X2,X0)
| ~ member(X3,X0) )
& ! [X7] :
( ~ member(X7,X0)
| apply(X1,X7,X7) ) )
| ~ equivalence(X1,X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( equivalence(X1,X0)
=> ( ! [X5,X6,X4] :
( ( member(X6,X0)
& member(X4,X0)
& member(X5,X0) )
=> ( ( apply(X1,X4,X6)
& apply(X1,X6,X5) )
=> apply(X1,X4,X5) ) )
& ! [X3,X2] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( apply(X1,X3,X2)
=> apply(X1,X2,X3) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X5,X6,X4] :
( ( member(X6,X0)
& member(X4,X0)
& member(X5,X0) )
=> ( ( apply(X1,X4,X6)
& apply(X1,X6,X5) )
=> apply(X1,X4,X5) ) )
& ! [X3,X2] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( apply(X1,X3,X2)
=> apply(X1,X2,X3) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) )
<=> equivalence(X1,X0) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X6] :
( ( ! [X4,X2] :
( ( member(X2,X0)
& member(X4,X0) )
=> ( apply(X6,X2,X4)
=> apply(X6,X4,X2) ) )
& ! [X2,X5,X4] :
( ( member(X4,X0)
& member(X5,X0)
& member(X2,X0) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X6,X2,X2) ) )
<=> equivalence(X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence) ).
fof(f107,plain,
equivalence(sK5,sK2),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( equivalence(sK5,sK2)
& member(sK4,sK2)
& ( ~ apply(sK5,sK3,sK4)
| ~ equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) )
& ( apply(sK5,sK3,sK4)
| equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) )
& member(sK3,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f67,f68]) ).
fof(f68,plain,
( ? [X0,X1,X2,X3] :
( equivalence(X3,X0)
& member(X2,X0)
& ( ~ apply(X3,X1,X2)
| ~ equal_set(equivalence_class(X1,X0,X3),equivalence_class(X2,X0,X3)) )
& ( apply(X3,X1,X2)
| equal_set(equivalence_class(X1,X0,X3),equivalence_class(X2,X0,X3)) )
& member(X1,X0) )
=> ( equivalence(sK5,sK2)
& member(sK4,sK2)
& ( ~ apply(sK5,sK3,sK4)
| ~ equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) )
& ( apply(sK5,sK3,sK4)
| equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) )
& member(sK3,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0,X1,X2,X3] :
( equivalence(X3,X0)
& member(X2,X0)
& ( ~ apply(X3,X1,X2)
| ~ equal_set(equivalence_class(X1,X0,X3),equivalence_class(X2,X0,X3)) )
& ( apply(X3,X1,X2)
| equal_set(equivalence_class(X1,X0,X3),equivalence_class(X2,X0,X3)) )
& member(X1,X0) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
? [X2,X0,X3,X1] :
( equivalence(X1,X2)
& member(X3,X2)
& ( ~ apply(X1,X0,X3)
| ~ equal_set(equivalence_class(X0,X2,X1),equivalence_class(X3,X2,X1)) )
& ( apply(X1,X0,X3)
| equal_set(equivalence_class(X0,X2,X1),equivalence_class(X3,X2,X1)) )
& member(X0,X2) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
? [X2,X0,X3,X1] :
( equivalence(X1,X2)
& member(X3,X2)
& ( ~ apply(X1,X0,X3)
| ~ equal_set(equivalence_class(X0,X2,X1),equivalence_class(X3,X2,X1)) )
& ( apply(X1,X0,X3)
| equal_set(equivalence_class(X0,X2,X1),equivalence_class(X3,X2,X1)) )
& member(X0,X2) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
? [X2,X0,X3,X1] :
( equivalence(X1,X2)
& member(X3,X2)
& ( equal_set(equivalence_class(X0,X2,X1),equivalence_class(X3,X2,X1))
<~> apply(X1,X0,X3) )
& member(X0,X2) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
? [X0,X2,X1,X3] :
( ( equal_set(equivalence_class(X0,X2,X1),equivalence_class(X3,X2,X1))
<~> apply(X1,X0,X3) )
& equivalence(X1,X2)
& member(X0,X2)
& member(X3,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X2,X1,X3] :
( ( equivalence(X1,X2)
& member(X0,X2)
& member(X3,X2) )
=> ( equal_set(equivalence_class(X0,X2,X1),equivalence_class(X3,X2,X1))
<=> apply(X1,X0,X3) ) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X0,X6,X3,X1] :
( ( member(X1,X3)
& member(X0,X3)
& equivalence(X6,X3) )
=> ( apply(X6,X0,X1)
<=> equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X0,X6,X3,X1] :
( ( member(X1,X3)
& member(X0,X3)
& equivalence(X6,X3) )
=> ( apply(X6,X0,X1)
<=> equal_set(equivalence_class(X0,X3,X6),equivalence_class(X1,X3,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII04) ).
fof(f106,plain,
member(sK4,sK2),
inference(cnf_transformation,[],[f69]) ).
fof(f1254,plain,
( subset(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5))
| ~ spl7_1 ),
inference(resolution,[],[f142,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) )
& ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(rectify,[],[f54]) ).
fof(f54,plain,
! [X1,X0] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X1,X0) )
& ( equal_set(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X1,X0] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X1,X0) )
& ( equal_set(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X1,X0] :
( ( subset(X1,X0)
& subset(X0,X1) )
<=> equal_set(X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> equal_set(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f142,plain,
( equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl7_1
<=> equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f1212,plain,
( ~ spl7_1
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f1211]) ).
fof(f1211,plain,
( $false
| ~ spl7_1
| spl7_6 ),
inference(subsumption_resolution,[],[f142,f965]) ).
fof(f965,plain,
( ~ equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5))
| spl7_6 ),
inference(unit_resulting_resolution,[],[f320,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f320,plain,
( ~ subset(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5))
| spl7_6 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f318,plain,
( spl7_6
<=> subset(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f1210,plain,
( ~ spl7_2
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f1209]) ).
fof(f1209,plain,
( $false
| ~ spl7_2
| spl7_6 ),
inference(subsumption_resolution,[],[f1198,f1011]) ).
fof(f1011,plain,
( ~ apply(sK5,sK4,sK1(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)))
| spl7_6 ),
inference(unit_resulting_resolution,[],[f962,f1002,f110]) ).
fof(f1002,plain,
( member(sK1(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)),sK2)
| spl7_6 ),
inference(resolution,[],[f964,f109]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ member(X1,equivalence_class(X3,X0,X2))
| member(X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f964,plain,
( member(sK1(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)),equivalence_class(sK3,sK2,sK5))
| spl7_6 ),
inference(unit_resulting_resolution,[],[f320,f97]) ).
fof(f97,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f962,plain,
( ~ member(sK1(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)),equivalence_class(sK4,sK2,sK5))
| spl7_6 ),
inference(unit_resulting_resolution,[],[f320,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f1198,plain,
( apply(sK5,sK4,sK1(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)))
| ~ spl7_2
| spl7_6 ),
inference(unit_resulting_resolution,[],[f106,f107,f103,f1002,f991,f188]) ).
fof(f188,plain,
( ! [X0,X1] :
( apply(sK5,sK4,X1)
| ~ member(sK3,X0)
| ~ member(X1,X0)
| ~ apply(sK5,sK3,X1)
| ~ equivalence(sK5,X0)
| ~ member(sK4,X0) )
| ~ spl7_2 ),
inference(resolution,[],[f148,f113]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ equivalence(X0,X1)
| apply(X0,X4,X2)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f148,plain,
( apply(sK5,sK4,sK3)
| ~ spl7_2 ),
inference(unit_resulting_resolution,[],[f103,f107,f106,f146,f111]) ).
fof(f111,plain,
! [X0,X1,X6,X7] :
( ~ apply(X0,X6,X7)
| ~ equivalence(X0,X1)
| ~ member(X7,X1)
| apply(X0,X7,X6)
| ~ member(X6,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f146,plain,
( apply(sK5,sK3,sK4)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f991,plain,
( apply(sK5,sK3,sK1(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)))
| spl7_6 ),
inference(unit_resulting_resolution,[],[f964,f108]) ).
fof(f103,plain,
member(sK3,sK2),
inference(cnf_transformation,[],[f69]) ).
fof(f956,plain,
( ~ spl7_2
| spl7_5 ),
inference(avatar_contradiction_clause,[],[f955]) ).
fof(f955,plain,
( $false
| ~ spl7_2
| spl7_5 ),
inference(subsumption_resolution,[],[f947,f953]) ).
fof(f953,plain,
( apply(sK5,sK3,sK1(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5)))
| ~ spl7_2
| spl7_5 ),
inference(unit_resulting_resolution,[],[f106,f103,f107,f324,f694,f393]) ).
fof(f393,plain,
( ! [X6,X4,X5] :
( apply(sK5,sK3,X5)
| ~ member(sK3,X4)
| ~ member(sK4,X4)
| ~ equivalence(sK5,X4)
| ~ member(X5,equivalence_class(sK4,X6,sK5))
| ~ member(X5,X4) )
| ~ spl7_2 ),
inference(resolution,[],[f150,f108]) ).
fof(f150,plain,
( ! [X0,X1] :
( ~ apply(sK5,sK4,X1)
| ~ member(sK3,X0)
| apply(sK5,sK3,X1)
| ~ member(X1,X0)
| ~ equivalence(sK5,X0)
| ~ member(sK4,X0) )
| ~ spl7_2 ),
inference(resolution,[],[f146,f113]) ).
fof(f694,plain,
( member(sK1(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5)),sK2)
| spl7_5 ),
inference(resolution,[],[f324,f109]) ).
fof(f324,plain,
( member(sK1(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5)),equivalence_class(sK4,sK2,sK5))
| spl7_5 ),
inference(unit_resulting_resolution,[],[f316,f97]) ).
fof(f316,plain,
( ~ subset(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5))
| spl7_5 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f314,plain,
( spl7_5
<=> subset(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f947,plain,
( ~ apply(sK5,sK3,sK1(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5)))
| spl7_5 ),
inference(unit_resulting_resolution,[],[f322,f694,f110]) ).
fof(f322,plain,
( ~ member(sK1(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5)),equivalence_class(sK3,sK2,sK5))
| spl7_5 ),
inference(unit_resulting_resolution,[],[f316,f98]) ).
fof(f321,plain,
( ~ spl7_5
| ~ spl7_6
| spl7_1 ),
inference(avatar_split_clause,[],[f159,f140,f318,f314]) ).
fof(f159,plain,
( ~ subset(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5))
| ~ subset(equivalence_class(sK4,sK2,sK5),equivalence_class(sK3,sK2,sK5))
| spl7_1 ),
inference(resolution,[],[f141,f92]) ).
fof(f92,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f141,plain,
( ~ equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5))
| spl7_1 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f158,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f105,f144,f140]) ).
fof(f105,plain,
( ~ apply(sK5,sK3,sK4)
| ~ equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f147,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f104,f144,f140]) ).
fof(f104,plain,
( apply(sK5,sK3,sK4)
| equal_set(equivalence_class(sK3,sK2,sK5),equivalence_class(sK4,sK2,sK5)) ),
inference(cnf_transformation,[],[f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET768+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % 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 : n022.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 14:18:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 % (4413)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.45 % (4405)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (4421)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.51 % (4405)Instruction limit reached!
% 0.19/0.51 % (4405)------------------------------
% 0.19/0.51 % (4405)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (4405)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (4405)Termination reason: Unknown
% 0.19/0.51 % (4405)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (4405)Memory used [KB]: 6396
% 0.19/0.51 % (4405)Time elapsed: 0.108 s
% 0.19/0.51 % (4405)Instructions burned: 52 (million)
% 0.19/0.51 % (4405)------------------------------
% 0.19/0.51 % (4405)------------------------------
% 0.19/0.51 % (4414)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 1.35/0.52 % (4393)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.35/0.52 % (4408)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.35/0.52 % (4396)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)
% 1.35/0.52 % (4417)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 1.35/0.52 % (4397)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.35/0.52 % (4418)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.35/0.52 % (4392)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.35/0.53 % (4403)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.35/0.53 % (4394)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)
% 1.35/0.53 % (4406)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.35/0.53 % (4404)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 1.35/0.53 % (4394)Instruction limit reached!
% 1.35/0.53 % (4394)------------------------------
% 1.35/0.53 % (4394)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53 % (4400)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.35/0.53 % (4394)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53 % (4394)Termination reason: Unknown
% 1.35/0.53 % (4394)Termination phase: Saturation
% 1.35/0.53
% 1.35/0.53 % (4394)Memory used [KB]: 6012
% 1.35/0.53 % (4394)Time elapsed: 0.132 s
% 1.35/0.53 % (4394)Instructions burned: 3 (million)
% 1.35/0.53 % (4394)------------------------------
% 1.35/0.53 % (4394)------------------------------
% 1.35/0.53 % (4406)Instruction limit reached!
% 1.35/0.53 % (4406)------------------------------
% 1.35/0.53 % (4406)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53 % (4406)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53 % (4406)Termination reason: Unknown
% 1.35/0.53 % (4406)Termination phase: Saturation
% 1.35/0.53
% 1.35/0.53 % (4406)Memory used [KB]: 6012
% 1.35/0.53 % (4406)Time elapsed: 0.002 s
% 1.35/0.53 % (4406)Instructions burned: 3 (million)
% 1.35/0.53 % (4406)------------------------------
% 1.35/0.53 % (4406)------------------------------
% 1.35/0.53 % (4403)Instruction limit reached!
% 1.35/0.53 % (4403)------------------------------
% 1.35/0.53 % (4403)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53 % (4403)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53 % (4403)Termination reason: Unknown
% 1.35/0.53 % (4403)Termination phase: Saturation
% 1.35/0.53
% 1.35/0.53 % (4403)Memory used [KB]: 6012
% 1.35/0.53 % (4403)Time elapsed: 0.127 s
% 1.35/0.53 % (4403)Instructions burned: 8 (million)
% 1.35/0.53 % (4403)------------------------------
% 1.35/0.53 % (4403)------------------------------
% 1.35/0.53 % (4410)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.35/0.53 % (4410)Instruction limit reached!
% 1.35/0.53 % (4410)------------------------------
% 1.35/0.53 % (4410)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53 % (4410)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53 % (4410)Termination reason: Unknown
% 1.35/0.53 % (4410)Termination phase: Saturation
% 1.35/0.53
% 1.35/0.53 % (4410)Memory used [KB]: 1407
% 1.35/0.53 % (4410)Time elapsed: 0.002 s
% 1.35/0.53 % (4410)Instructions burned: 2 (million)
% 1.35/0.53 % (4410)------------------------------
% 1.35/0.53 % (4410)------------------------------
% 1.35/0.53 % (4419)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 1.35/0.53 % (4409)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.35/0.53 % (4395)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.35/0.53 % (4409)Instruction limit reached!
% 1.35/0.53 % (4409)------------------------------
% 1.35/0.53 % (4409)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53 % (4409)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53 % (4409)Termination reason: Unknown
% 1.35/0.53 % (4409)Termination phase: Finite model building preprocessing
% 1.35/0.53
% 1.35/0.53 % (4409)Memory used [KB]: 6012
% 1.35/0.53 % (4409)Time elapsed: 0.003 s
% 1.35/0.53 % (4409)Instructions burned: 4 (million)
% 1.35/0.53 % (4409)------------------------------
% 1.35/0.53 % (4409)------------------------------
% 1.35/0.53 % (4398)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.35/0.54 % (4420)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 1.52/0.54 % (4416)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.52/0.54 % (4411)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 1.52/0.54 % (4401)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 1.52/0.54 % (4402)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 1.52/0.54 % (4399)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)
% 1.52/0.54 % (4412)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 1.52/0.54 % (4396)Instruction limit reached!
% 1.52/0.54 % (4396)------------------------------
% 1.52/0.54 % (4396)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.54 % (4396)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.54 % (4396)Termination reason: Unknown
% 1.52/0.54 % (4396)Termination phase: Saturation
% 1.52/0.54
% 1.52/0.54 % (4396)Memory used [KB]: 6140
% 1.52/0.54 % (4396)Time elapsed: 0.130 s
% 1.52/0.54 % (4396)Instructions burned: 13 (million)
% 1.52/0.54 % (4396)------------------------------
% 1.52/0.54 % (4396)------------------------------
% 1.52/0.55 % (4415)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.52/0.55 % (4413)First to succeed.
% 1.52/0.55 % (4397)Instruction limit reached!
% 1.52/0.55 % (4397)------------------------------
% 1.52/0.55 % (4397)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.55 % (4397)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.55 % (4397)Termination reason: Unknown
% 1.52/0.55 % (4397)Termination phase: Saturation
% 1.52/0.55
% 1.52/0.55 % (4397)Memory used [KB]: 1535
% 1.52/0.55 % (4397)Time elapsed: 0.158 s
% 1.52/0.55 % (4397)Instructions burned: 15 (million)
% 1.52/0.55 % (4397)------------------------------
% 1.52/0.55 % (4397)------------------------------
% 1.52/0.55 % (4413)Refutation found. Thanks to Tanya!
% 1.52/0.55 % SZS status Theorem for theBenchmark
% 1.52/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.52/0.55 % (4413)------------------------------
% 1.52/0.55 % (4413)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.55 % (4413)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.55 % (4413)Termination reason: Refutation
% 1.52/0.55
% 1.52/0.55 % (4413)Memory used [KB]: 7036
% 1.52/0.55 % (4413)Time elapsed: 0.148 s
% 1.52/0.55 % (4413)Instructions burned: 77 (million)
% 1.52/0.55 % (4413)------------------------------
% 1.52/0.55 % (4413)------------------------------
% 1.52/0.55 % (4391)Success in time 0.208 s
%------------------------------------------------------------------------------