%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX054+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:45:46 PM UTC 2026
% Result : Theorem 21.33s 3.78s
% Output : Refutation 22.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 24
% Syntax : Number of formulae : 178 ( 20 unt; 11 def)
% Number of atoms : 720 ( 200 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 926 ( 384 ~; 420 |; 83 &)
% ( 14 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 301 ( 0 sgn 252 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( s(X0) = s(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id6) ).
fof(f58,axiom,
! [X0,X1] :
( permutation_succeeds(X0,X1)
<=> ( ? [X2,X3,X4] :
( X1 = cons(X2,X3)
& delete_succeeds(X2,X0,X4)
& permutation_succeeds(X4,X3) )
| ( X0 = nil
& X1 = nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id58) ).
fof(f256,axiom,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
& list_succeeds(X1) )
=> list_succeeds(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(delete:types:1)') ).
fof(f273,axiom,
! [X0,X1,X2] :
( list_succeeds(X1)
=> ( occ(X0,X1) = X2
<=> occ_succeeds(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','occ/2') ).
fof(f286,axiom,
! [X0] : occ(X0,nil) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:nil)') ).
fof(f287,axiom,
! [X0,X1,X2] :
( ( list_succeeds(X2)
& X0 != X1 )
=> occ(X0,cons(X1,X2)) = occ(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:cons:diff)') ).
fof(f288,axiom,
! [X0,X1] :
( list_succeeds(X1)
=> occ(X0,cons(X0,X1)) = s(occ(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:cons:eq)') ).
fof(f291,axiom,
! [X0,X1,X2,X3] :
( ( list_succeeds(X2)
& delete_succeeds(X0,X2,X3)
& X0 != X1 )
=> occ(X1,X2) = occ(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(delete:occ:diff)') ).
fof(f292,axiom,
! [X0,X1,X2] :
( ( list_succeeds(X1)
& delete_succeeds(X0,X1,X2) )
=> occ(X0,X1) = s(occ(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(delete:occ:eq)') ).
fof(f295,axiom,
! [X0] :
( ( list_succeeds(X0)
& ! [X1] : occ(X1,X0) = '0' )
=> X0 = nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:zero)') ).
fof(f296,axiom,
! [X0,X1,X2] :
( ( list_succeeds(X1)
& occ(X0,X1) = s(X2) )
=> ? [X3] : delete_succeeds(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:successor)') ).
fof(f297,axiom,
( ! [X0] :
( ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2)
& ! [X3] :
( ( list_succeeds(X3)
& ! [X4] : occ(X4,X3) = occ(X4,X2) )
=> permutation_succeeds(X3,X2) ) )
| X0 = nil )
=> ! [X3] :
( ( list_succeeds(X3)
& ! [X4] : occ(X4,X3) = occ(X4,X0) )
=> permutation_succeeds(X3,X0) ) )
=> ! [X0] :
( list_succeeds(X0)
=> ! [X3] :
( ( list_succeeds(X3)
& ! [X4] : occ(X4,X3) = occ(X4,X0) )
=> permutation_succeeds(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
fof(f298,conjecture,
! [X0] :
( list_succeeds(X0)
=> ! [X1] :
( ( list_succeeds(X1)
& ! [X2] : occ(X2,X1) = occ(X2,X0) )
=> permutation_succeeds(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(permutation:completeness)') ).
fof(f299,negated_conjecture,
~ ! [X0] :
( list_succeeds(X0)
=> ! [X1] :
( ( list_succeeds(X1)
& ! [X2] : occ(X2,X1) = occ(X2,X0) )
=> permutation_succeeds(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f298]) ).
fof(f300,plain,
( ! [X0] :
( ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2)
& ! [X3] :
( ( list_succeeds(X3)
& ! [X4] : occ(X4,X3) = occ(X4,X2) )
=> permutation_succeeds(X3,X2) ) )
| X0 = nil )
=> ! [X5] :
( ( list_succeeds(X5)
& ! [X6] : occ(X6,X5) = occ(X6,X0) )
=> permutation_succeeds(X5,X0) ) )
=> ! [X7] :
( list_succeeds(X7)
=> ! [X8] :
( ( list_succeeds(X8)
& ! [X9] : occ(X9,X8) = occ(X9,X7) )
=> permutation_succeeds(X8,X7) ) ) ),
inference(rectify,[],[f297]) ).
fof(f310,plain,
? [X0] :
( ? [X1] :
( ~ permutation_succeeds(X1,X0)
& list_succeeds(X1)
& ! [X2] : occ(X2,X1) = occ(X2,X0) )
& list_succeeds(X0) ),
inference(ennf_transformation,[],[f299]) ).
fof(f311,plain,
? [X0] :
( ? [X1] :
( ~ permutation_succeeds(X1,X0)
& list_succeeds(X1)
& ! [X2] : occ(X2,X1) = occ(X2,X0) )
& list_succeeds(X0) ),
inference(flattening,[],[f310]) ).
fof(f314,plain,
! [X0,X1] :
( X0 = X1
| s(X0) != s(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f315,plain,
( ! [X7] :
( ! [X8] :
( permutation_succeeds(X8,X7)
| ~ list_succeeds(X8)
| ? [X9] : occ(X9,X8) != occ(X9,X7) )
| ~ list_succeeds(X7) )
| ? [X0] :
( ? [X5] :
( ~ permutation_succeeds(X5,X0)
& list_succeeds(X5)
& ! [X6] : occ(X6,X5) = occ(X6,X0) )
& ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2)
& ! [X3] :
( permutation_succeeds(X3,X2)
| ~ list_succeeds(X3)
| ? [X4] : occ(X4,X3) != occ(X4,X2) ) )
| X0 = nil ) ) ),
inference(ennf_transformation,[],[f300]) ).
fof(f316,plain,
( ! [X7] :
( ! [X8] :
( permutation_succeeds(X8,X7)
| ~ list_succeeds(X8)
| ? [X9] : occ(X9,X8) != occ(X9,X7) )
| ~ list_succeeds(X7) )
| ? [X0] :
( ? [X5] :
( ~ permutation_succeeds(X5,X0)
& list_succeeds(X5)
& ! [X6] : occ(X6,X5) = occ(X6,X0) )
& ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2)
& ! [X3] :
( permutation_succeeds(X3,X2)
| ~ list_succeeds(X3)
| ? [X4] : occ(X4,X3) != occ(X4,X2) ) )
| X0 = nil ) ) ),
inference(flattening,[],[f315]) ).
fof(f317,plain,
! [X0,X1,X2] :
( ? [X3] : delete_succeeds(X0,X1,X3)
| ~ list_succeeds(X1)
| s(X2) != occ(X0,X1) ),
inference(ennf_transformation,[],[f296]) ).
fof(f318,plain,
! [X0,X1,X2] :
( ? [X3] : delete_succeeds(X0,X1,X3)
| ~ list_succeeds(X1)
| s(X2) != occ(X0,X1) ),
inference(flattening,[],[f317]) ).
fof(f319,plain,
! [X0] :
( X0 = nil
| ~ list_succeeds(X0)
| ? [X1] : '0' != occ(X1,X0) ),
inference(ennf_transformation,[],[f295]) ).
fof(f320,plain,
! [X0] :
( X0 = nil
| ~ list_succeeds(X0)
| ? [X1] : '0' != occ(X1,X0) ),
inference(flattening,[],[f319]) ).
fof(f322,plain,
! [X0,X1,X2] :
( occ(X0,X1) = s(occ(X0,X2))
| ~ list_succeeds(X1)
| ~ delete_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f292]) ).
fof(f323,plain,
! [X0,X1,X2] :
( occ(X0,X1) = s(occ(X0,X2))
| ~ list_succeeds(X1)
| ~ delete_succeeds(X0,X1,X2) ),
inference(flattening,[],[f322]) ).
fof(f324,plain,
! [X0,X1,X2,X3] :
( occ(X1,X2) = occ(X1,X3)
| ~ list_succeeds(X2)
| ~ delete_succeeds(X0,X2,X3)
| X0 = X1 ),
inference(ennf_transformation,[],[f291]) ).
fof(f325,plain,
! [X0,X1,X2,X3] :
( occ(X1,X2) = occ(X1,X3)
| ~ list_succeeds(X2)
| ~ delete_succeeds(X0,X2,X3)
| X0 = X1 ),
inference(flattening,[],[f324]) ).
fof(f329,plain,
! [X0,X1] :
( occ(X0,cons(X0,X1)) = s(occ(X0,X1))
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f288]) ).
fof(f330,plain,
! [X0,X1,X2] :
( occ(X0,cons(X1,X2)) = occ(X0,X2)
| ~ list_succeeds(X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f287]) ).
fof(f331,plain,
! [X0,X1,X2] :
( occ(X0,cons(X1,X2)) = occ(X0,X2)
| ~ list_succeeds(X2)
| X0 = X1 ),
inference(flattening,[],[f330]) ).
fof(f332,plain,
! [X0,X1,X2] :
( ( occ(X0,X1) = X2
<=> occ_succeeds(X0,X1,X2) )
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f273]) ).
fof(f390,plain,
! [X0,X1,X2] :
( list_succeeds(X2)
| ~ delete_succeeds(X0,X1,X2)
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f256]) ).
fof(f391,plain,
! [X0,X1,X2] :
( list_succeeds(X2)
| ~ delete_succeeds(X0,X1,X2)
| ~ list_succeeds(X1) ),
inference(flattening,[],[f390]) ).
fof(f616,definition,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ? [X5,X6] :
( X1 = cons(X0,X5)
& X2 = s(X6)
& occ_succeeds(X0,X5,X6) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f626,plain,
( ~ permutation_succeeds(sK7,sK6)
& list_succeeds(sK7)
& ! [X2] : occ(X2,sK6) = occ(X2,sK7)
& list_succeeds(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f311]) ).
fof(f627,plain,
( ! [X0] :
( ! [X1] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| ? [X2] : occ(X2,X0) != occ(X2,X1) )
| ~ list_succeeds(X0) )
| ? [X3] :
( ? [X4] :
( ~ permutation_succeeds(X4,X3)
& list_succeeds(X4)
& ! [X5] : occ(X5,X4) = occ(X5,X3) )
& ( ? [X6,X7] :
( cons(X6,X7) = X3
& list_succeeds(X7)
& ! [X8] :
( permutation_succeeds(X8,X7)
| ~ list_succeeds(X8)
| ? [X9] : occ(X9,X8) != occ(X9,X7) ) )
| nil = X3 ) ) ),
inference(rectify,[],[f316]) ).
fof(f628,plain,
( ! [X0] :
( ! [X1] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1) )
| ~ list_succeeds(X0) )
| ( ~ permutation_succeeds(sK10,sK9)
& list_succeeds(sK10)
& ! [X5] : occ(X5,sK10) = occ(X5,sK9)
& ( ( sK9 = cons(sK11,sK12)
& list_succeeds(sK12)
& ! [X8] :
( permutation_succeeds(X8,sK12)
| ~ list_succeeds(X8)
| occ(sK13(X8),X8) != occ(sK13(X8),sK12) ) )
| nil = sK9 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12,sK13]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9),skolemize(X4,sK10),skolemize(X6,sK11),skolemize(X7,sK12),skolemize(X9,sK13(X8))],[f627]) ).
fof(f629,plain,
! [X0,X1,X2] :
( delete_succeeds(X0,X1,sK14(X0,X1))
| ~ list_succeeds(X1)
| s(X2) != occ(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X0,X1))],[f318]) ).
fof(f630,plain,
! [X0] :
( X0 = nil
| ~ list_succeeds(X0)
| '0' != occ(sK15(X0),X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f320]) ).
fof(f631,plain,
! [X0,X1,X2] :
( ( ( occ(X0,X1) = X2
| ~ occ_succeeds(X0,X1,X2) )
& ( occ_succeeds(X0,X1,X2)
| occ(X0,X1) != X2 ) )
| ~ list_succeeds(X1) ),
inference(nnf_transformation,[],[f332]) ).
fof(f632,plain,
! [X0,X1] :
( ( permutation_succeeds(X0,X1)
| ( ! [X2,X3,X4] :
( cons(X2,X3) != X1
| ~ delete_succeeds(X2,X0,X4)
| ~ permutation_succeeds(X4,X3) )
& ( nil != X0
| nil != X1 ) ) )
& ( ? [X2,X3,X4] :
( X1 = cons(X2,X3)
& delete_succeeds(X2,X0,X4)
& permutation_succeeds(X4,X3) )
| ( X0 = nil
& X1 = nil )
| ~ permutation_succeeds(X0,X1) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f633,plain,
! [X0,X1] :
( ( permutation_succeeds(X0,X1)
| ( ! [X2,X3,X4] :
( cons(X2,X3) != X1
| ~ delete_succeeds(X2,X0,X4)
| ~ permutation_succeeds(X4,X3) )
& ( nil != X0
| nil != X1 ) ) )
& ( ? [X2,X3,X4] :
( X1 = cons(X2,X3)
& delete_succeeds(X2,X0,X4)
& permutation_succeeds(X4,X3) )
| ( X0 = nil
& X1 = nil )
| ~ permutation_succeeds(X0,X1) ) ),
inference(flattening,[],[f632]) ).
fof(f634,plain,
! [X0,X1] :
( ( permutation_succeeds(X0,X1)
| ( ! [X2,X3,X4] :
( cons(X2,X3) != X1
| ~ delete_succeeds(X2,X0,X4)
| ~ permutation_succeeds(X4,X3) )
& ( nil != X0
| nil != X1 ) ) )
& ( ? [X5,X6,X7] :
( cons(X5,X6) = X1
& delete_succeeds(X5,X0,X7)
& permutation_succeeds(X7,X6) )
| ( X0 = nil
& X1 = nil )
| ~ permutation_succeeds(X0,X1) ) ),
inference(rectify,[],[f633]) ).
fof(f635,plain,
! [X0,X1] :
( ( permutation_succeeds(X0,X1)
| ( ! [X2,X3,X4] :
( cons(X2,X3) != X1
| ~ delete_succeeds(X2,X0,X4)
| ~ permutation_succeeds(X4,X3) )
& ( nil != X0
| nil != X1 ) ) )
& ( ( cons(sK16(X0,X1),sK17(X0,X1)) = X1
& delete_succeeds(sK16(X0,X1),X0,sK18(X0,X1))
& permutation_succeeds(sK18(X0,X1),sK17(X0,X1)) )
| ( X0 = nil
& X1 = nil )
| ~ permutation_succeeds(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X5,sK16(X0,X1)),skolemize(X6,sK17(X0,X1)),skolemize(X7,sK18(X0,X1))],[f634]) ).
fof(f689,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ! [X5,X6] :
( cons(X0,X5) != X1
| s(X6) != X2
| ~ occ_succeeds(X0,X5,X6) ) )
& ( ? [X5,X6] :
( X1 = cons(X0,X5)
& X2 = s(X6)
& occ_succeeds(X0,X5,X6) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f616]) ).
fof(f690,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ! [X3,X4] :
( cons(X1,X3) != X0
| s(X4) != X2
| ~ occ_succeeds(X1,X3,X4) ) )
& ( ? [X5,X6] :
( cons(X1,X5) = X0
& X2 = s(X6)
& occ_succeeds(X1,X5,X6) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f689]) ).
fof(f691,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ! [X3,X4] :
( cons(X1,X3) != X0
| s(X4) != X2
| ~ occ_succeeds(X1,X3,X4) ) )
& ( ( cons(X1,sK54(X0,X1,X2)) = X0
& s(sK55(X0,X1,X2)) = X2
& occ_succeeds(X1,sK54(X0,X1,X2),sK55(X0,X1,X2)) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55]),skolemize(X5,sK54(X0,X1,X2)),skolemize(X6,sK55(X0,X1,X2))],[f690]) ).
fof(f753,plain,
list_succeeds(sK6),
inference(cnf_transformation,[],[f626]) ).
fof(f754,plain,
! [X2] : occ(X2,sK6) = occ(X2,sK7),
inference(cnf_transformation,[],[f626]) ).
fof(f755,plain,
list_succeeds(sK7),
inference(cnf_transformation,[],[f626]) ).
fof(f756,plain,
~ permutation_succeeds(sK7,sK6),
inference(cnf_transformation,[],[f626]) ).
fof(f760,plain,
! [X0,X1] :
( s(X0) != s(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f314]) ).
fof(f761,plain,
! [X0,X1,X8] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X0)
| permutation_succeeds(X8,sK12)
| ~ list_succeeds(X8)
| occ(sK13(X8),X8) != occ(sK13(X8),sK12)
| nil = sK9 ),
inference(cnf_transformation,[],[f628]) ).
fof(f762,plain,
! [X0,X1] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X0)
| list_succeeds(sK12)
| nil = sK9 ),
inference(cnf_transformation,[],[f628]) ).
fof(f763,plain,
! [X0,X1] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X0)
| sK9 = cons(sK11,sK12)
| nil = sK9 ),
inference(cnf_transformation,[],[f628]) ).
fof(f764,plain,
! [X0,X1,X5] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X0)
| occ(X5,sK10) = occ(X5,sK9) ),
inference(cnf_transformation,[],[f628]) ).
fof(f765,plain,
! [X0,X1] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X0)
| list_succeeds(sK10) ),
inference(cnf_transformation,[],[f628]) ).
fof(f766,plain,
! [X0,X1] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X1)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X0)
| ~ permutation_succeeds(sK10,sK9) ),
inference(cnf_transformation,[],[f628]) ).
fof(f767,plain,
! [X2,X0,X1] :
( s(X2) != occ(X0,X1)
| ~ list_succeeds(X1)
| delete_succeeds(X0,X1,sK14(X0,X1)) ),
inference(cnf_transformation,[],[f629]) ).
fof(f768,plain,
! [X0] :
( '0' != occ(sK15(X0),X0)
| ~ list_succeeds(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f630]) ).
fof(f770,plain,
! [X2,X0,X1] :
( ~ delete_succeeds(X0,X1,X2)
| ~ list_succeeds(X1)
| occ(X0,X1) = s(occ(X0,X2)) ),
inference(cnf_transformation,[],[f323]) ).
fof(f771,plain,
! [X2,X3,X0,X1] :
( ~ delete_succeeds(X0,X2,X3)
| ~ list_succeeds(X2)
| occ(X1,X2) = occ(X1,X3)
| X0 = X1 ),
inference(cnf_transformation,[],[f325]) ).
fof(f774,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| occ(X0,cons(X0,X1)) = s(occ(X0,X1)) ),
inference(cnf_transformation,[],[f329]) ).
fof(f775,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X2)
| occ(X0,cons(X1,X2)) = occ(X0,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f331]) ).
fof(f776,plain,
! [X0] : '0' = occ(X0,nil),
inference(cnf_transformation,[],[f286]) ).
fof(f777,plain,
! [X2,X0,X1] :
( occ_succeeds(X0,X1,X2)
| occ(X0,X1) != X2
| ~ list_succeeds(X1) ),
inference(cnf_transformation,[],[f631]) ).
fof(f788,plain,
! [X0,X1] :
( permutation_succeeds(X0,X1)
| nil != X0
| nil != X1 ),
inference(cnf_transformation,[],[f635]) ).
fof(f789,plain,
! [X2,X3,X0,X1,X4] :
( permutation_succeeds(X0,X1)
| cons(X2,X3) != X1
| ~ delete_succeeds(X2,X0,X4)
| ~ permutation_succeeds(X4,X3) ),
inference(cnf_transformation,[],[f635]) ).
fof(f884,plain,
! [X2,X0,X1] :
( ~ delete_succeeds(X0,X1,X2)
| list_succeeds(X2)
| ~ list_succeeds(X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f975,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| s(sK55(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f691]) ).
fof(f977,plain,
! [X2,X3,X0,X1,X4] :
( sP0(X0,X1,X2)
| cons(X1,X3) != X0
| s(X4) != X2
| ~ occ_succeeds(X1,X3,X4) ),
inference(cnf_transformation,[],[f691]) ).
fof(f1151,plain,
! [X0,X1] :
( occ_succeeds(X0,X1,occ(X0,X1))
| ~ list_succeeds(X1) ),
inference(equality_resolution,[],[f777]) ).
fof(f1152,plain,
! [X2,X3,X0,X4] :
( ~ delete_succeeds(X2,X0,X4)
| permutation_succeeds(X0,cons(X2,X3))
| ~ permutation_succeeds(X4,X3) ),
inference(equality_resolution,[],[f789]) ).
fof(f1153,plain,
! [X1] :
( permutation_succeeds(nil,X1)
| nil != X1 ),
inference(equality_resolution,[],[f788]) ).
fof(f1154,plain,
permutation_succeeds(nil,nil),
inference(equality_resolution,[],[f1153]) ).
fof(f1185,plain,
! [X2,X3,X1,X4] :
( sP0(cons(X1,X3),X1,X2)
| s(X4) != X2
| ~ occ_succeeds(X1,X3,X4) ),
inference(equality_resolution,[],[f977]) ).
fof(f1186,plain,
! [X3,X1,X4] :
( sP0(cons(X1,X3),X1,s(X4))
| ~ occ_succeeds(X1,X3,X4) ),
inference(equality_resolution,[],[f1185]) ).
fof(f1222,definition,
( spl92_1
<=> nil = sK9 ),
introduced(definition,[new_symbols(definition,[spl92_1])],[avatar_definition]) ).
fof(f1224,plain,
( nil = sK9
| ~ spl92_1 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f1226,definition,
( spl92_2
<=> ! [X8] :
( permutation_succeeds(X8,sK12)
| occ(sK13(X8),X8) != occ(sK13(X8),sK12)
| ~ list_succeeds(X8) ) ),
introduced(definition,[new_symbols(definition,[spl92_2])],[avatar_definition]) ).
fof(f1227,plain,
( ! [X8] :
( occ(sK13(X8),X8) != occ(sK13(X8),sK12)
| permutation_succeeds(X8,sK12)
| ~ list_succeeds(X8) )
| ~ spl92_2 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f1229,definition,
( spl92_3
<=> ! [X0,X1] :
( permutation_succeeds(X1,X0)
| ~ list_succeeds(X0)
| occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X1) ) ),
introduced(definition,[new_symbols(definition,[spl92_3])],[avatar_definition]) ).
fof(f1230,plain,
( ! [X0,X1] :
( occ(sK8(X0,X1),X0) != occ(sK8(X0,X1),X1)
| ~ list_succeeds(X0)
| permutation_succeeds(X1,X0)
| ~ list_succeeds(X1) )
| ~ spl92_3 ),
inference(avatar_component_clause,[],[f1229]) ).
fof(f1231,plain,
( spl92_1
| spl92_2
| spl92_3 ),
inference(avatar_split_clause,[],[f761,f1229,f1226,f1222]) ).
fof(f1233,definition,
( spl92_4
<=> list_succeeds(sK12) ),
introduced(definition,[new_symbols(definition,[spl92_4])],[avatar_definition]) ).
fof(f1235,plain,
( list_succeeds(sK12)
| ~ spl92_4 ),
inference(avatar_component_clause,[],[f1233]) ).
fof(f1236,plain,
( spl92_1
| spl92_4
| spl92_3 ),
inference(avatar_split_clause,[],[f762,f1229,f1233,f1222]) ).
fof(f1238,definition,
( spl92_5
<=> sK9 = cons(sK11,sK12) ),
introduced(definition,[new_symbols(definition,[spl92_5])],[avatar_definition]) ).
fof(f1240,plain,
( sK9 = cons(sK11,sK12)
| ~ spl92_5 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f1241,plain,
( spl92_1
| spl92_5
| spl92_3 ),
inference(avatar_split_clause,[],[f763,f1229,f1238,f1222]) ).
fof(f1243,definition,
( spl92_6
<=> ! [X5] : occ(X5,sK10) = occ(X5,sK9) ),
introduced(definition,[new_symbols(definition,[spl92_6])],[avatar_definition]) ).
fof(f1244,plain,
( ! [X5] : occ(X5,sK10) = occ(X5,sK9)
| ~ spl92_6 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f1245,plain,
( spl92_6
| spl92_3 ),
inference(avatar_split_clause,[],[f764,f1229,f1243]) ).
fof(f1247,definition,
( spl92_7
<=> list_succeeds(sK10) ),
introduced(definition,[new_symbols(definition,[spl92_7])],[avatar_definition]) ).
fof(f1249,plain,
( list_succeeds(sK10)
| ~ spl92_7 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f1250,plain,
( spl92_7
| spl92_3 ),
inference(avatar_split_clause,[],[f765,f1229,f1247]) ).
fof(f1252,definition,
( spl92_8
<=> permutation_succeeds(sK10,sK9) ),
introduced(definition,[new_symbols(definition,[spl92_8])],[avatar_definition]) ).
fof(f1254,plain,
( ~ permutation_succeeds(sK10,sK9)
| spl92_8 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f1255,plain,
( ~ spl92_8
| spl92_3 ),
inference(avatar_split_clause,[],[f766,f1229,f1252]) ).
fof(f1259,plain,
( ! [X0] :
( occ(sK8(X0,sK7),sK6) != occ(sK8(X0,sK7),X0)
| ~ list_succeeds(X0)
| permutation_succeeds(sK7,X0)
| ~ list_succeeds(sK7) )
| ~ spl92_3 ),
inference(superposition,[],[f1230,f754]) ).
fof(f1260,plain,
( ! [X0] :
( occ(sK8(X0,sK7),sK6) != occ(sK8(X0,sK7),X0)
| ~ list_succeeds(X0)
| permutation_succeeds(sK7,X0) )
| ~ spl92_3 ),
inference(forward_subsumption_resolution,[],[f1259,f755]) ).
fof(f1263,plain,
( ~ list_succeeds(sK6)
| permutation_succeeds(sK7,sK6)
| ~ spl92_3 ),
inference(equality_resolution,[],[f1260]) ).
fof(f1265,plain,
( permutation_succeeds(sK7,sK6)
| ~ spl92_3 ),
inference(forward_subsumption_resolution,[],[f1263,f753]) ).
fof(f1266,plain,
( $false
| ~ spl92_3 ),
inference(forward_subsumption_resolution,[],[f1265,f756]) ).
fof(f1267,plain,
~ spl92_3,
inference(avatar_contradiction_clause,[],[f1266]) ).
fof(f1268,plain,
( ! [X5] : occ(X5,sK10) = occ(X5,nil)
| ~ spl92_1
| ~ spl92_6 ),
inference(forward_demodulation,[],[f1244,f1224]) ).
fof(f1269,plain,
( ~ permutation_succeeds(sK10,nil)
| ~ spl92_1
| spl92_8 ),
inference(forward_demodulation,[],[f1254,f1224]) ).
fof(f1270,plain,
( ! [X5] : '0' = occ(X5,sK10)
| ~ spl92_1
| ~ spl92_6 ),
inference(forward_demodulation,[],[f1268,f776]) ).
fof(f1787,plain,
( '0' != '0'
| ~ list_succeeds(sK10)
| nil = sK10
| ~ spl92_1
| ~ spl92_6 ),
inference(superposition,[],[f768,f1270]) ).
fof(f1788,plain,
( ~ list_succeeds(sK10)
| nil = sK10
| ~ spl92_1
| ~ spl92_6 ),
inference(trivial_inequality_removal,[],[f1787]) ).
fof(f1791,plain,
( nil = sK10
| ~ spl92_1
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_subsumption_resolution,[],[f1788,f1249]) ).
fof(f1871,plain,
( ~ permutation_succeeds(nil,nil)
| ~ spl92_1
| ~ spl92_6
| ~ spl92_7
| spl92_8 ),
inference(superposition,[],[f1269,f1791]) ).
fof(f1907,plain,
( $false
| ~ spl92_1
| ~ spl92_6
| ~ spl92_7
| spl92_8 ),
inference(forward_subsumption_resolution,[],[f1871,f1154]) ).
fof(f1908,plain,
( ~ spl92_1
| ~ spl92_6
| ~ spl92_7
| spl92_8 ),
inference(avatar_contradiction_clause,[],[f1907]) ).
fof(f1979,plain,
( ! [X0] :
( sP0(sK9,sK11,s(X0))
| ~ occ_succeeds(sK11,sK12,X0) )
| ~ spl92_5 ),
inference(superposition,[],[f1186,f1240]) ).
fof(f1984,plain,
( ! [X0] : occ(X0,cons(X0,sK12)) = s(occ(X0,sK12))
| ~ spl92_4 ),
inference(resolution,[],[f1235,f774]) ).
fof(f1985,plain,
( ! [X0,X1] :
( occ(X0,sK12) = occ(X0,cons(X1,sK12))
| X0 = X1 )
| ~ spl92_4 ),
inference(resolution,[],[f1235,f775]) ).
fof(f2022,plain,
( s(occ(sK11,sK12)) = occ(sK11,sK9)
| ~ spl92_4
| ~ spl92_5 ),
inference(superposition,[],[f1984,f1240]) ).
fof(f2033,plain,
( ! [X0] :
( s(X0) != occ(sK11,sK9)
| occ(sK11,sK12) = X0 )
| ~ spl92_4
| ~ spl92_5 ),
inference(superposition,[],[f760,f2022]) ).
fof(f2036,plain,
( ! [X0] :
( occ(X0,sK9) = occ(X0,sK12)
| sK11 = X0 )
| ~ spl92_4
| ~ spl92_5 ),
inference(superposition,[],[f1985,f1240]) ).
fof(f2098,plain,
( ! [X0] :
( ~ occ_succeeds(sK11,sK12,X0)
| s(X0) = s(sK55(sK9,sK11,s(X0))) )
| ~ spl92_5 ),
inference(resolution,[],[f1979,f975]) ).
fof(f2112,plain,
( s(occ(sK11,sK12)) = s(sK55(sK9,sK11,s(occ(sK11,sK12))))
| ~ list_succeeds(sK12)
| ~ spl92_5 ),
inference(resolution,[],[f2098,f1151]) ).
fof(f2115,plain,
( s(occ(sK11,sK12)) = s(sK55(sK9,sK11,s(occ(sK11,sK12))))
| ~ spl92_4
| ~ spl92_5 ),
inference(forward_subsumption_resolution,[],[f2112,f1235]) ).
fof(f2117,plain,
( occ(sK11,sK9) = s(sK55(sK9,sK11,occ(sK11,sK9)))
| ~ spl92_4
| ~ spl92_5 ),
inference(forward_demodulation,[],[f2115,f2022]) ).
fof(f3771,plain,
( ! [X0,X1] :
( s(X1) != occ(X0,sK9)
| ~ list_succeeds(sK10)
| delete_succeeds(X0,sK10,sK14(X0,sK10)) )
| ~ spl92_6 ),
inference(superposition,[],[f767,f1244]) ).
fof(f3776,plain,
( ! [X0,X1] :
( s(X1) != occ(X0,sK9)
| delete_succeeds(X0,sK10,sK14(X0,sK10)) )
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_subsumption_resolution,[],[f3771,f1249]) ).
fof(f3796,plain,
( ! [X0] :
( occ(X0,sK9) != occ(sK11,sK9)
| delete_succeeds(X0,sK10,sK14(X0,sK10)) )
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(superposition,[],[f3776,f2117]) ).
fof(f3800,plain,
( delete_succeeds(sK11,sK10,sK14(sK11,sK10))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(equality_resolution,[],[f3796]) ).
fof(f3801,plain,
( ! [X0] :
( ~ list_succeeds(sK10)
| occ(X0,sK10) = occ(X0,sK14(sK11,sK10))
| sK11 = X0 )
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(resolution,[],[f3800,f771]) ).
fof(f3803,plain,
( list_succeeds(sK14(sK11,sK10))
| ~ list_succeeds(sK10)
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(resolution,[],[f3800,f884]) ).
fof(f3805,plain,
( ~ list_succeeds(sK10)
| occ(sK11,sK10) = s(occ(sK11,sK14(sK11,sK10)))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(resolution,[],[f3800,f770]) ).
fof(f3806,plain,
( ! [X0] :
( ~ permutation_succeeds(sK14(sK11,sK10),X0)
| permutation_succeeds(sK10,cons(sK11,X0)) )
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(resolution,[],[f3800,f1152]) ).
fof(f3807,plain,
( occ(sK11,sK10) = s(occ(sK11,sK14(sK11,sK10)))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_subsumption_resolution,[],[f3805,f1249]) ).
fof(f3808,plain,
( list_succeeds(sK14(sK11,sK10))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_subsumption_resolution,[],[f3803,f1249]) ).
fof(f3809,plain,
( ! [X0] :
( occ(X0,sK10) = occ(X0,sK14(sK11,sK10))
| sK11 = X0 )
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_subsumption_resolution,[],[f3801,f1249]) ).
fof(f3810,plain,
( occ(sK11,sK9) = s(occ(sK11,sK14(sK11,sK10)))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_demodulation,[],[f3807,f1244]) ).
fof(f3811,plain,
( ! [X0] :
( occ(X0,sK9) = occ(X0,sK14(sK11,sK10))
| sK11 = X0 )
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_demodulation,[],[f3809,f1244]) ).
fof(f3833,plain,
( occ(sK11,sK9) != occ(sK11,sK9)
| occ(sK11,sK12) = occ(sK11,sK14(sK11,sK10))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(superposition,[],[f2033,f3810]) ).
fof(f3839,plain,
( occ(sK11,sK12) = occ(sK11,sK14(sK11,sK10))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(trivial_inequality_removal,[],[f3833]) ).
fof(f3852,plain,
( occ(sK13(sK14(sK11,sK10)),sK9) != occ(sK13(sK14(sK11,sK10)),sK12)
| permutation_succeeds(sK14(sK11,sK10),sK12)
| ~ list_succeeds(sK14(sK11,sK10))
| sK11 = sK13(sK14(sK11,sK10))
| ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(superposition,[],[f1227,f3811]) ).
fof(f3858,plain,
( permutation_succeeds(sK14(sK11,sK10),sK12)
| ~ list_succeeds(sK14(sK11,sK10))
| sK11 = sK13(sK14(sK11,sK10))
| ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_subsumption_resolution,[],[f3852,f2036]) ).
fof(f3877,plain,
( permutation_succeeds(sK14(sK11,sK10),sK12)
| sK11 = sK13(sK14(sK11,sK10))
| ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(forward_subsumption_resolution,[],[f3858,f3808]) ).
fof(f3879,definition,
( spl92_167
<=> sK11 = sK13(sK14(sK11,sK10)) ),
introduced(definition,[new_symbols(definition,[spl92_167])],[avatar_definition]) ).
fof(f3881,plain,
( sK11 = sK13(sK14(sK11,sK10))
| ~ spl92_167 ),
inference(avatar_component_clause,[],[f3879]) ).
fof(f3883,definition,
( spl92_168
<=> permutation_succeeds(sK14(sK11,sK10),sK12) ),
introduced(definition,[new_symbols(definition,[spl92_168])],[avatar_definition]) ).
fof(f3885,plain,
( permutation_succeeds(sK14(sK11,sK10),sK12)
| ~ spl92_168 ),
inference(avatar_component_clause,[],[f3883]) ).
fof(f3891,plain,
( spl92_167
| spl92_168
| ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7 ),
inference(avatar_split_clause,[],[f3877,f1247,f1243,f1238,f1233,f1226,f3883,f3879]) ).
fof(f3893,plain,
( occ(sK11,sK12) != occ(sK11,sK14(sK11,sK10))
| permutation_succeeds(sK14(sK11,sK10),sK12)
| ~ list_succeeds(sK14(sK11,sK10))
| ~ spl92_2
| ~ spl92_167 ),
inference(superposition,[],[f1227,f3881]) ).
fof(f3894,plain,
( permutation_succeeds(sK14(sK11,sK10),sK12)
| ~ list_succeeds(sK14(sK11,sK10))
| ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| ~ spl92_167 ),
inference(forward_subsumption_resolution,[],[f3893,f3839]) ).
fof(f3895,plain,
( permutation_succeeds(sK14(sK11,sK10),sK12)
| ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| ~ spl92_167 ),
inference(forward_subsumption_resolution,[],[f3894,f3808]) ).
fof(f3896,plain,
( spl92_168
| ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| ~ spl92_167 ),
inference(avatar_split_clause,[],[f3895,f3879,f1247,f1243,f1238,f1233,f1226,f3883]) ).
fof(f3951,plain,
( permutation_succeeds(sK10,cons(sK11,sK12))
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| ~ spl92_168 ),
inference(resolution,[],[f3806,f3885]) ).
fof(f3952,plain,
( permutation_succeeds(sK10,sK9)
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| ~ spl92_168 ),
inference(forward_demodulation,[],[f3951,f1240]) ).
fof(f3953,plain,
( $false
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| spl92_8
| ~ spl92_168 ),
inference(forward_subsumption_resolution,[],[f3952,f1254]) ).
fof(f3954,plain,
( ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| spl92_8
| ~ spl92_168 ),
inference(avatar_contradiction_clause,[],[f3953]) ).
cnf(s1,plain,
( spl92_1
| spl92_2
| spl92_3 ),
inference(sat_conversion,[],[f1231]) ).
cnf(s2,plain,
( spl92_1
| spl92_3
| spl92_4 ),
inference(sat_conversion,[],[f1236]) ).
cnf(s3,plain,
( spl92_1
| spl92_3
| spl92_5 ),
inference(sat_conversion,[],[f1241]) ).
cnf(s4,plain,
( spl92_3
| spl92_6 ),
inference(sat_conversion,[],[f1245]) ).
cnf(s5,plain,
( spl92_3
| spl92_7 ),
inference(sat_conversion,[],[f1250]) ).
cnf(s6,plain,
( spl92_3
| ~ spl92_8 ),
inference(sat_conversion,[],[f1255]) ).
cnf(s7,plain,
~ spl92_3,
inference(sat_conversion,[],[f1267]) ).
cnf(s38,plain,
( ~ spl92_1
| ~ spl92_6
| ~ spl92_7
| spl92_8 ),
inference(sat_conversion,[],[f1908]) ).
cnf(s116,plain,
( ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| spl92_167
| spl92_168 ),
inference(sat_conversion,[],[f3891]) ).
cnf(s117,plain,
( ~ spl92_2
| ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| ~ spl92_167
| spl92_168 ),
inference(sat_conversion,[],[f3896]) ).
cnf(s124,plain,
( ~ spl92_4
| ~ spl92_5
| ~ spl92_6
| ~ spl92_7
| spl92_8
| ~ spl92_168 ),
inference(sat_conversion,[],[f3954]) ).
cnf(s130,plain,
~ spl92_8,
inference(rat,[],[s6,s7]) ).
cnf(s131,plain,
spl92_7,
inference(rat,[],[s5,s7]) ).
cnf(s138,plain,
spl92_6,
inference(rat,[],[s4,s7]) ).
cnf(s139,plain,
~ spl92_1,
inference(rat,[],[s38,s130,s131,s138]) ).
cnf(s140,plain,
spl92_5,
inference(rat,[],[s3,s7,s139]) ).
cnf(s141,plain,
spl92_4,
inference(rat,[],[s2,s7,s139]) ).
cnf(s142,plain,
~ spl92_168,
inference(rat,[],[s124,s140,s130,s131,s138,s141]) ).
cnf(s156,plain,
spl92_2,
inference(rat,[],[s1,s7,s139]) ).
cnf(s157,plain,
~ spl92_167,
inference(rat,[],[s117,s142,s141,s131,s138,s140,s156]) ).
cnf(s158,plain,
$false,
inference(rat,[],[s116,s142,s141,s131,s138,s140,s157,s156]) ).
fof(f3955,plain,
$false,
inference(avatar_sat_refutation,[],[s158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX054+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n018.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 14:56:51 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running first-order theorem proving
% 0.11/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.81/2.83 % (3459925)Detected formulas, will run a generic FOF schedule.
% 14.81/2.83 % (3459930)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1450239777:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 14.81/2.83 % (3459933)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=330490309:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 14.81/2.83 % (3459931)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=795695683:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 14.81/2.83 % (3459935)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1297094562:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 14.81/2.83 % (3459932)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2275573841:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 14.81/2.83 % (3459934)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3978155702:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 14.81/2.83 % (3459936)dis-21_1_sil=8000:lcm=predicate:random_seed=1148608206:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 14.81/2.83 % (3459933)Instruction limit reached!
% 14.81/2.83 % (3459933)------------------------------
% 14.81/2.83 % (3459933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.81/2.83 % (3459933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.81/2.83 % (3459933)CaDiCaL version: 2.1.3
% 14.81/2.83 % (3459933)Termination reason: Instruction limit
% 14.81/2.83 % (3459933)Termination phase: Saturation
% 14.81/2.83 % (3459933)Time elapsed: 0.067 s
% 14.81/2.83 % (3459933)Peak memory usage: 89 MB
% 14.81/2.83 % (3459933)Instructions burned: 110 (million)
% 14.81/2.83 % (3459934)Instruction limit reached!
% 14.81/2.83 % (3459934)------------------------------
% 14.81/2.83 % (3459934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.81/2.83 % (3459934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.81/2.83 % (3459934)CaDiCaL version: 2.1.3
% 14.81/2.83 % (3459934)Termination reason: Instruction limit
% 14.81/2.83 % (3459934)Termination phase: Saturation
% 14.81/2.83 % (3459934)Time elapsed: 0.069 s
% 14.81/2.83 % (3459934)Peak memory usage: 88 MB
% 14.81/2.83 % (3459934)Instructions burned: 121 (million)
% 14.81/2.83 % (3459936)Instruction limit reached!
% 14.81/2.83 % (3459936)------------------------------
% 14.81/2.83 % (3459936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.81/2.83 % (3459936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.81/2.83 % (3459936)CaDiCaL version: 2.1.3
% 14.81/2.83 % (3459936)Termination reason: Instruction limit
% 14.81/2.83 % (3459936)Termination phase: Saturation
% 14.81/2.83 % (3459936)Time elapsed: 0.079 s
% 14.81/2.83 % (3459936)Peak memory usage: 90 MB
% 14.81/2.83 % (3459936)Instructions burned: 130 (million)
% 14.81/2.83 % (3459935)Instruction limit reached!
% 14.81/2.83 % (3459935)------------------------------
% 14.81/2.83 % (3459935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.81/2.83 % (3459935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.81/2.83 % (3459935)CaDiCaL version: 2.1.3
% 14.81/2.83 % (3459935)Termination reason: Instruction limit
% 14.81/2.83 % (3459935)Termination phase: Saturation
% 14.81/2.83 % (3459935)Time elapsed: 0.098 s
% 14.81/2.83 % (3459935)Peak memory usage: 90 MB
% 14.81/2.83 % (3459935)Instructions burned: 140 (million)
% 14.81/2.83 % (3459946)lrs+1011_1_sil=32000:sp=occurrence:random_seed=333210907:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 14.81/2.83 % (3459944)lrs+10_1_sil=8000:sp=occurrence:random_seed=1717930010:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 14.81/2.83 % (3459945)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1655023865:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 14.81/2.83 % (3459947)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3976558431:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 14.81/2.83 % (3459945)Refutation not found, incomplete strategy
% 21.33/3.78 % (3459945)------------------------------
% 21.33/3.78 % (3459945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459945)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459945)Termination reason: Refutation not found, incomplete strategy
% 21.33/3.78 % (3459945)Time elapsed: 0.052 s
% 21.33/3.78 % (3459945)Peak memory usage: 90 MB
% 21.33/3.78 % (3459945)Instructions burned: 82 (million)
% 21.33/3.78 % (3459947)Instruction limit reached!
% 21.33/3.78 % (3459947)------------------------------
% 21.33/3.78 % (3459947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459947)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459947)Termination reason: Instruction limit
% 21.33/3.78 % (3459947)Termination phase: Saturation
% 21.33/3.78 % (3459947)Time elapsed: 0.141 s
% 21.33/3.78 % (3459947)Peak memory usage: 93 MB
% 21.33/3.78 % (3459947)Instructions burned: 249 (million)
% 21.33/3.78 % (3459944)Instruction limit reached!
% 21.33/3.78 % (3459944)------------------------------
% 21.33/3.78 % (3459944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459944)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459944)Termination reason: Instruction limit
% 21.33/3.78 % (3459944)Termination phase: Saturation
% 21.33/3.78 % (3459944)Time elapsed: 0.192 s
% 21.33/3.78 % (3459944)Peak memory usage: 92 MB
% 21.33/3.78 % (3459944)Instructions burned: 285 (million)
% 21.33/3.78 % (3459946)Instruction limit reached!
% 21.33/3.78 % (3459946)------------------------------
% 21.33/3.78 % (3459946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459946)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459946)Termination reason: Instruction limit
% 21.33/3.78 % (3459946)Termination phase: Saturation
% 21.33/3.78 % (3459946)Time elapsed: 0.204 s
% 21.33/3.78 % (3459946)Peak memory usage: 90 MB
% 21.33/3.78 % (3459946)Instructions burned: 326 (million)
% 21.33/3.78 % (3459945)------------------------------
% 21.33/3.78 % (3459945)------------------------------
% 21.33/3.78 % (3459952)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3421220043:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 21.33/3.78 % (3459953)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2349548910:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 21.33/3.78 % (3459954)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3248868690:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 21.33/3.78 % (3459954)Instruction limit reached!
% 21.33/3.78 % (3459954)------------------------------
% 21.33/3.78 % (3459954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459954)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459954)Termination reason: Instruction limit
% 21.33/3.78 % (3459954)Termination phase: Saturation
% 21.33/3.78 % (3459954)Time elapsed: 0.073 s
% 21.33/3.78 % (3459954)Peak memory usage: 90 MB
% 21.33/3.78 % (3459954)Instructions burned: 114 (million)
% 21.33/3.78 % (3459955)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=651308803:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 21.33/3.78 % (3459952)Instruction limit reached!
% 21.33/3.78 % (3459952)------------------------------
% 21.33/3.78 % (3459952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459952)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459952)Termination reason: Instruction limit
% 21.33/3.78 % (3459952)Termination phase: Saturation
% 21.33/3.78 % (3459952)Time elapsed: 0.168 s
% 21.33/3.78 % (3459952)Peak memory usage: 90 MB
% 21.33/3.78 % (3459952)Instructions burned: 295 (million)
% 21.33/3.78 % (3459955)Instruction limit reached!
% 21.33/3.78 % (3459955)------------------------------
% 21.33/3.78 % (3459955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459955)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459955)Termination reason: Instruction limit
% 21.33/3.78 % (3459955)Termination phase: Saturation
% 21.33/3.78 % (3459955)Time elapsed: 0.066 s
% 21.33/3.78 % (3459955)Peak memory usage: 90 MB
% 21.33/3.78 % (3459955)Instructions burned: 127 (million)
% 21.33/3.78 % (3459959)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2809402831:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 21.33/3.78 % (3459961)lrs+10_1_sil=8000:sp=occurrence:random_seed=2975031536:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 21.33/3.78 % (3459959)Instruction limit reached!
% 21.33/3.78 % (3459959)------------------------------
% 21.33/3.78 % (3459959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459959)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459959)Termination reason: Instruction limit
% 21.33/3.78 % (3459959)Termination phase: Saturation
% 21.33/3.78 % (3459959)Time elapsed: 0.066 s
% 21.33/3.78 % (3459959)Peak memory usage: 89 MB
% 21.33/3.78 % (3459959)Instructions burned: 115 (million)
% 21.33/3.78 % (3459962)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3301047416:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 21.33/3.78 % (3459965)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2972669147:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 21.33/3.78 % (3459962)Instruction limit reached!
% 21.33/3.78 % (3459962)------------------------------
% 21.33/3.78 % (3459962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459962)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459962)Termination reason: Instruction limit
% 21.33/3.78 % (3459962)Termination phase: Saturation
% 21.33/3.78 % (3459962)Time elapsed: 0.251 s
% 21.33/3.78 % (3459962)Peak memory usage: 92 MB
% 21.33/3.78 % (3459962)Instructions burned: 437 (million)
% 21.33/3.78 % (3459968)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3685203323:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 21.33/3.78 % (3459968)Instruction limit reached!
% 21.33/3.78 % (3459968)------------------------------
% 21.33/3.78 % (3459968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459968)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459968)Termination reason: Instruction limit
% 21.33/3.78 % (3459968)Termination phase: Saturation
% 21.33/3.78 % (3459968)Time elapsed: 0.079 s
% 21.33/3.78 % (3459968)Peak memory usage: 91 MB
% 21.33/3.78 % (3459968)Instructions burned: 137 (million)
% 21.33/3.78 % (3459961)Instruction limit reached!
% 21.33/3.78 % (3459961)------------------------------
% 21.33/3.78 % (3459961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459961)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459961)Termination reason: Instruction limit
% 21.33/3.78 % (3459961)Termination phase: Saturation
% 21.33/3.78 % (3459961)Time elapsed: 0.592 s
% 21.33/3.78 % (3459961)Peak memory usage: 101 MB
% 21.33/3.78 % (3459961)Instructions burned: 908 (million)
% 21.33/3.78 % (3459970)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=92570381:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 21.33/3.78 % (3459970)Refutation not found, incomplete strategy
% 21.33/3.78 % (3459970)------------------------------
% 21.33/3.78 % (3459970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459970)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459970)Termination reason: Refutation not found, incomplete strategy
% 21.33/3.78 % (3459970)Time elapsed: 0.016 s
% 21.33/3.78 % (3459970)Peak memory usage: 89 MB
% 21.33/3.78 % (3459970)Instructions burned: 28 (million)
% 21.33/3.78 % (3459971)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3706732420:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 21.33/3.78 % (3459970)------------------------------
% 21.33/3.78 % (3459970)------------------------------
% 21.33/3.78 % (3459974)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=1388250802:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/125Mi)
% 21.33/3.78 % (3459974)Instruction limit reached!
% 21.33/3.78 % (3459974)------------------------------
% 21.33/3.78 % (3459974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459974)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459974)Termination reason: Instruction limit
% 21.33/3.78 % (3459974)Termination phase: Saturation
% 21.33/3.78 % (3459974)Time elapsed: 0.074 s
% 21.33/3.78 % (3459974)Peak memory usage: 91 MB
% 21.33/3.78 % (3459974)Instructions burned: 125 (million)
% 21.33/3.78 % (3459953)Instruction limit reached!
% 21.33/3.78 % (3459953)------------------------------
% 21.33/3.78 % (3459953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459953)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459953)Termination reason: Instruction limit
% 21.33/3.78 % (3459953)Termination phase: Saturation
% 21.33/3.78 % (3459953)Time elapsed: 1.543 s
% 21.33/3.78 % (3459953)Peak memory usage: 143 MB
% 21.33/3.78 % (3459953)Instructions burned: 2350 (million)
% 21.33/3.78 % (3459976)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3122427532:i=134:gtgl=5:slsql=off:gtg=exists_sym_2977 on theBenchmark for (2977ds/134Mi)
% 21.33/3.78 % (3459977)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2326921965:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2976 on theBenchmark for (2976ds/141Mi)
% 21.33/3.78 % (3459977)Refutation not found, incomplete strategy
% 21.33/3.78 % (3459977)------------------------------
% 21.33/3.78 % (3459977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459977)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459977)Termination reason: Refutation not found, incomplete strategy
% 21.33/3.78 % (3459977)Time elapsed: 0.003 s
% 21.33/3.78 % (3459977)Peak memory usage: 88 MB
% 21.33/3.78 % (3459977)Instructions burned: 3 (million)
% 21.33/3.78 % (3459976)Instruction limit reached!
% 21.33/3.78 % (3459976)------------------------------
% 21.33/3.78 % (3459976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459976)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459976)Termination reason: Instruction limit
% 21.33/3.78 % (3459976)Termination phase: Saturation
% 21.33/3.78 % (3459976)Time elapsed: 0.084 s
% 21.33/3.78 % (3459976)Peak memory usage: 91 MB
% 21.33/3.78 % (3459976)Instructions burned: 134 (million)
% 21.33/3.78 % (3459980)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=3301259260:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2975 on theBenchmark for (2975ds/431Mi)
% 21.33/3.78 % (3459980)Refutation not found, incomplete strategy
% 21.33/3.78 % (3459980)------------------------------
% 21.33/3.78 % (3459980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.33/3.78 % (3459980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.33/3.78 % (3459980)CaDiCaL version: 2.1.3
% 21.33/3.78 % (3459980)Termination reason: Refutation not found, incomplete strategy
% 21.33/3.78 % (3459980)Time elapsed: 0.003 s
% 21.33/3.78 % (3459980)Peak memory usage: 88 MB
% 21.33/3.78 % (3459980)Instructions burned: 2 (million)
% 21.33/3.78 % (3459977)------------------------------
% 21.33/3.78 % (3459977)------------------------------
% 21.33/3.78 % (3459971)First to succeed.
% 21.33/3.78 % (3459971)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3459925"
% 21.33/3.78 % (3459980)------------------------------
% 21.33/3.78 % (3459980)------------------------------
% 21.33/3.78 % (3459982)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=3702872400:i=6060:aac=none:ins=25_2972 on theBenchmark for (2972ds/6060Mi)
% 21.33/3.78 % (3459984)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=2316295979:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2971 on theBenchmark for (2971ds/150Mi)
% 21.33/3.78 % (3459971)Refutation found. Thanks to Tanya!
% 21.33/3.78 % SZS status Theorem for theBenchmark
% 21.33/3.78 % SZS output start Proof for theBenchmark
% See solution above
% 22.44/3.97 % (3459971)------------------------------
% 22.44/3.97 % (3459971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 22.44/3.97 % (3459971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.44/3.97 % (3459971)CaDiCaL version: 2.1.3
% 22.44/3.97 % (3459971)Termination reason: Refutation
% 22.44/3.97 % (3459971)Time elapsed: 1.025 s
% 22.44/3.97 % (3459971)Peak memory usage: 136 MB
% 22.44/3.97 % (3459971)Instructions burned: 1550 (million)
% 22.44/3.97 % (3459971)------------------------------
% 22.44/3.97 % (3459971)------------------------------
% 22.44/3.97 % (3459925)Success in time 3.099 s
% 22.44/3.97 % Vampire exiting
%------------------------------------------------------------------------------