%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX046+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 01:45:45 PM UTC 2026
% Result : Theorem 8.51s 1.78s
% Output : Refutation 9.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of formulae : 147 ( 24 unt; 13 def)
% Number of atoms : 530 ( 74 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 648 ( 265 ~; 287 |; 64 &)
% ( 12 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 182 ( 0 sgn 152 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1] :
( '@=<_succeeds'(X0,X1)
<=> ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@=<_succeeds'(X2,X3) )
| X0 = '0' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id21) ).
fof(f60,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@*'('0',X0) = '0' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(times:zero)') ).
fof(f61,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(times:successor)') ).
fof(f86,axiom,
! [X0,X1] :
( '@=<_succeeds'(X0,X1)
=> nat_succeeds(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(leq:types)') ).
fof(f88,axiom,
! [X0,X1] :
( '@=<_succeeds'(X0,X1)
=> ? [X2] : '@+'(X0,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(leq:plus)') ).
fof(f109,axiom,
! [X0,X1] :
( nat_succeeds(X0)
=> '@=<_succeeds'(X0,'@+'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(leq:plus:first)') ).
fof(f114,axiom,
! [X0,X1,X2,X3] :
( ( '@=<_succeeds'(X0,X2)
& '@=<_succeeds'(X1,X3)
& nat_succeeds(X2) )
=> '@=<_succeeds'('@+'(X0,X1),'@+'(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(plus:leq:leq)') ).
fof(f118,axiom,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( ( nat_succeeds(X3)
& '@=<_succeeds'(X2,X3) )
=> '@=<_succeeds'('@*'(X1,X2),'@*'(X1,X3)) ) )
| X0 = '0' )
=> ! [X2,X3] :
( ( nat_succeeds(X3)
& '@=<_succeeds'(X2,X3) )
=> '@=<_succeeds'('@*'(X0,X2),'@*'(X0,X3)) ) )
=> ! [X0] :
( nat_succeeds(X0)
=> ! [X2,X3] :
( ( nat_succeeds(X3)
& '@=<_succeeds'(X2,X3) )
=> '@=<_succeeds'('@*'(X0,X2),'@*'(X0,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
fof(f119,conjecture,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& '@=<_succeeds'(X1,X2)
& nat_succeeds(X2) )
=> '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(times:leq:second)') ).
fof(f120,negated_conjecture,
~ ! [X0,X1,X2] :
( ( nat_succeeds(X0)
& '@=<_succeeds'(X1,X2)
& nat_succeeds(X2) )
=> '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f119]) ).
fof(f130,plain,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( ( nat_succeeds(X3)
& '@=<_succeeds'(X2,X3) )
=> '@=<_succeeds'('@*'(X1,X2),'@*'(X1,X3)) ) )
| X0 = '0' )
=> ! [X4,X5] :
( ( nat_succeeds(X5)
& '@=<_succeeds'(X4,X5) )
=> '@=<_succeeds'('@*'(X0,X4),'@*'(X0,X5)) ) )
=> ! [X6] :
( nat_succeeds(X6)
=> ! [X7,X8] :
( ( nat_succeeds(X8)
& '@=<_succeeds'(X7,X8) )
=> '@=<_succeeds'('@*'(X6,X7),'@*'(X6,X8)) ) ) ),
inference(rectify,[],[f118]) ).
fof(f192,plain,
! [X0] :
( '@*'('0',X0) = '0'
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f193,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f194,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f193]) ).
fof(f230,plain,
! [X0,X1] :
( nat_succeeds(X0)
| ~ '@=<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f86]) ).
fof(f232,plain,
! [X0,X1] :
( ? [X2] : '@+'(X0,X2) = X1
| ~ '@=<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f88]) ).
fof(f266,plain,
! [X0,X1] :
( '@=<_succeeds'(X0,'@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f109]) ).
fof(f275,plain,
! [X0,X1,X2,X3] :
( '@=<_succeeds'('@+'(X0,X1),'@+'(X2,X3))
| ~ '@=<_succeeds'(X0,X2)
| ~ '@=<_succeeds'(X1,X3)
| ~ nat_succeeds(X2) ),
inference(ennf_transformation,[],[f114]) ).
fof(f276,plain,
! [X0,X1,X2,X3] :
( '@=<_succeeds'('@+'(X0,X1),'@+'(X2,X3))
| ~ '@=<_succeeds'(X0,X2)
| ~ '@=<_succeeds'(X1,X3)
| ~ nat_succeeds(X2) ),
inference(flattening,[],[f275]) ).
fof(f283,plain,
( ! [X6] :
( ! [X7,X8] :
( '@=<_succeeds'('@*'(X6,X7),'@*'(X6,X8))
| ~ nat_succeeds(X8)
| ~ '@=<_succeeds'(X7,X8) )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( ~ '@=<_succeeds'('@*'(X0,X4),'@*'(X0,X5))
& nat_succeeds(X5)
& '@=<_succeeds'(X4,X5) )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@=<_succeeds'('@*'(X1,X2),'@*'(X1,X3))
| ~ nat_succeeds(X3)
| ~ '@=<_succeeds'(X2,X3) ) )
| X0 = '0' ) ) ),
inference(ennf_transformation,[],[f130]) ).
fof(f284,plain,
( ! [X6] :
( ! [X7,X8] :
( '@=<_succeeds'('@*'(X6,X7),'@*'(X6,X8))
| ~ nat_succeeds(X8)
| ~ '@=<_succeeds'(X7,X8) )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( ~ '@=<_succeeds'('@*'(X0,X4),'@*'(X0,X5))
& nat_succeeds(X5)
& '@=<_succeeds'(X4,X5) )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@=<_succeeds'('@*'(X1,X2),'@*'(X1,X3))
| ~ nat_succeeds(X3)
| ~ '@=<_succeeds'(X2,X3) ) )
| X0 = '0' ) ) ),
inference(flattening,[],[f283]) ).
fof(f285,plain,
? [X0,X1,X2] :
( ~ '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
& nat_succeeds(X0)
& '@=<_succeeds'(X1,X2)
& nat_succeeds(X2) ),
inference(ennf_transformation,[],[f120]) ).
fof(f286,plain,
? [X0,X1,X2] :
( ~ '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
& nat_succeeds(X0)
& '@=<_succeeds'(X1,X2)
& nat_succeeds(X2) ),
inference(flattening,[],[f285]) ).
fof(f310,plain,
! [X0,X1] :
( ( '@=<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@=<_succeeds'(X2,X3) )
& '0' != X0 ) )
& ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@=<_succeeds'(X2,X3) )
| X0 = '0'
| ~ '@=<_succeeds'(X0,X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f311,plain,
! [X0,X1] :
( ( '@=<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@=<_succeeds'(X2,X3) )
& '0' != X0 ) )
& ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@=<_succeeds'(X2,X3) )
| X0 = '0'
| ~ '@=<_succeeds'(X0,X1) ) ),
inference(flattening,[],[f310]) ).
fof(f312,plain,
! [X0,X1] :
( ( '@=<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@=<_succeeds'(X2,X3) )
& '0' != X0 ) )
& ( ? [X4,X5] :
( s(X4) = X0
& s(X5) = X1
& '@=<_succeeds'(X4,X5) )
| X0 = '0'
| ~ '@=<_succeeds'(X0,X1) ) ),
inference(rectify,[],[f311]) ).
fof(f313,plain,
! [X0,X1] :
( ( '@=<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@=<_succeeds'(X2,X3) )
& '0' != X0 ) )
& ( ( s(sK12(X0,X1)) = X0
& s(sK13(X0,X1)) = X1
& '@=<_succeeds'(sK12(X0,X1),sK13(X0,X1)) )
| X0 = '0'
| ~ '@=<_succeeds'(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X4,sK12(X0,X1)),skolemize(X5,sK13(X0,X1))],[f312]) ).
fof(f349,plain,
! [X0,X1] :
( '@+'(X0,sK33(X0,X1)) = X1
| ~ '@=<_succeeds'(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(X2,sK33(X0,X1))],[f232]) ).
fof(f352,plain,
( ! [X0] :
( ! [X1,X2] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2) )
| ~ nat_succeeds(X0) )
| ? [X3] :
( ? [X4,X5] :
( ~ '@=<_succeeds'('@*'(X3,X4),'@*'(X3,X5))
& nat_succeeds(X5)
& '@=<_succeeds'(X4,X5) )
& ( ? [X6] :
( s(X6) = X3
& nat_succeeds(X6)
& ! [X7,X8] :
( '@=<_succeeds'('@*'(X6,X7),'@*'(X6,X8))
| ~ nat_succeeds(X8)
| ~ '@=<_succeeds'(X7,X8) ) )
| '0' = X3 ) ) ),
inference(rectify,[],[f284]) ).
fof(f353,plain,
( ! [X0] :
( ! [X1,X2] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2) )
| ~ nat_succeeds(X0) )
| ( ~ '@=<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
& nat_succeeds(sK38)
& '@=<_succeeds'(sK37,sK38)
& ( ( sK36 = s(sK39)
& nat_succeeds(sK39)
& ! [X7,X8] :
( '@=<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ nat_succeeds(X8)
| ~ '@=<_succeeds'(X7,X8) ) )
| '0' = sK36 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36,sK37,sK38,sK39]),skolemize(X3,sK36),skolemize(X4,sK37),skolemize(X5,sK38),skolemize(X6,sK39)],[f352]) ).
fof(f354,plain,
( ~ '@=<_succeeds'('@*'(sK40,sK41),'@*'(sK40,sK42))
& nat_succeeds(sK40)
& '@=<_succeeds'(sK41,sK42)
& nat_succeeds(sK42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41,sK42]),skolemize(X0,sK40),skolemize(X1,sK41),skolemize(X2,sK42)],[f286]) ).
fof(f414,plain,
! [X0,X1] :
( '@=<_succeeds'(X0,X1)
| '0' != X0 ),
inference(cnf_transformation,[],[f313]) ).
fof(f488,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '0' = '@*'('0',X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f489,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1)) ),
inference(cnf_transformation,[],[f194]) ).
fof(f514,plain,
! [X0,X1] :
( ~ '@=<_succeeds'(X0,X1)
| nat_succeeds(X0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f516,plain,
! [X0,X1] :
( ~ '@=<_succeeds'(X0,X1)
| '@+'(X0,sK33(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f349]) ).
fof(f537,plain,
! [X0,X1] :
( '@=<_succeeds'(X0,'@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f542,plain,
! [X2,X3,X0,X1] :
( '@=<_succeeds'('@+'(X0,X1),'@+'(X2,X3))
| ~ '@=<_succeeds'(X0,X2)
| ~ '@=<_succeeds'(X1,X3)
| ~ nat_succeeds(X2) ),
inference(cnf_transformation,[],[f276]) ).
fof(f546,plain,
! [X2,X0,X1,X8,X7] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@=<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ nat_succeeds(X8)
| ~ '@=<_succeeds'(X7,X8)
| '0' = sK36 ),
inference(cnf_transformation,[],[f353]) ).
fof(f547,plain,
! [X2,X0,X1] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| nat_succeeds(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f353]) ).
fof(f548,plain,
! [X2,X0,X1] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| sK36 = s(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f353]) ).
fof(f549,plain,
! [X2,X0,X1] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@=<_succeeds'(sK37,sK38) ),
inference(cnf_transformation,[],[f353]) ).
fof(f550,plain,
! [X2,X0,X1] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| nat_succeeds(sK38) ),
inference(cnf_transformation,[],[f353]) ).
fof(f551,plain,
! [X2,X0,X1] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| ~ '@=<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38)) ),
inference(cnf_transformation,[],[f353]) ).
fof(f552,plain,
nat_succeeds(sK42),
inference(cnf_transformation,[],[f354]) ).
fof(f553,plain,
'@=<_succeeds'(sK41,sK42),
inference(cnf_transformation,[],[f354]) ).
fof(f554,plain,
nat_succeeds(sK40),
inference(cnf_transformation,[],[f354]) ).
fof(f555,plain,
~ '@=<_succeeds'('@*'(sK40,sK41),'@*'(sK40,sK42)),
inference(cnf_transformation,[],[f354]) ).
fof(f576,plain,
! [X1] : '@=<_succeeds'('0',X1),
inference(equality_resolution,[],[f414]) ).
fof(f599,definition,
sF43 = '@*'(sK40,sK41),
introduced(definition,[new_symbols(definition,[sF43])],[function_definition]) ).
fof(f600,plain,
'@*'(sK40,sK41) = sF43,
inference(reorient_equations,[],[f599]) ).
fof(f601,definition,
sF44 = '@*'(sK40,sK42),
introduced(definition,[new_symbols(definition,[sF44])],[function_definition]) ).
fof(f602,plain,
'@*'(sK40,sK42) = sF44,
inference(reorient_equations,[],[f601]) ).
fof(f603,plain,
~ '@=<_succeeds'(sF43,sF44),
inference(definition_folding,[],[f555,f602,f600]) ).
fof(f605,definition,
( spl45_1
<=> '0' = sK36 ),
introduced(definition,[new_symbols(definition,[spl45_1])],[avatar_definition]) ).
fof(f607,plain,
( '0' = sK36
| ~ spl45_1 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f609,definition,
( spl45_2
<=> ! [X8,X7] :
( '@=<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ '@=<_succeeds'(X7,X8)
| ~ nat_succeeds(X8) ) ),
introduced(definition,[new_symbols(definition,[spl45_2])],[avatar_definition]) ).
fof(f610,plain,
( ! [X8,X7] :
( '@=<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ '@=<_succeeds'(X7,X8)
| ~ nat_succeeds(X8) )
| ~ spl45_2 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f612,definition,
( spl45_3
<=> ! [X2,X0,X1] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X0)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X2) ) ),
introduced(definition,[new_symbols(definition,[spl45_3])],[avatar_definition]) ).
fof(f613,plain,
( ! [X2,X0,X1] :
( '@=<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X0)
| ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X2) )
| ~ spl45_3 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f614,plain,
( spl45_1
| spl45_2
| spl45_3 ),
inference(avatar_split_clause,[],[f546,f612,f609,f605]) ).
fof(f616,definition,
( spl45_4
<=> nat_succeeds(sK39) ),
introduced(definition,[new_symbols(definition,[spl45_4])],[avatar_definition]) ).
fof(f618,plain,
( nat_succeeds(sK39)
| ~ spl45_4 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f619,plain,
( spl45_1
| spl45_4
| spl45_3 ),
inference(avatar_split_clause,[],[f547,f612,f616,f605]) ).
fof(f621,definition,
( spl45_5
<=> sK36 = s(sK39) ),
introduced(definition,[new_symbols(definition,[spl45_5])],[avatar_definition]) ).
fof(f623,plain,
( sK36 = s(sK39)
| ~ spl45_5 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f624,plain,
( spl45_1
| spl45_5
| spl45_3 ),
inference(avatar_split_clause,[],[f548,f612,f621,f605]) ).
fof(f626,definition,
( spl45_6
<=> '@=<_succeeds'(sK37,sK38) ),
introduced(definition,[new_symbols(definition,[spl45_6])],[avatar_definition]) ).
fof(f628,plain,
( '@=<_succeeds'(sK37,sK38)
| ~ spl45_6 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f629,plain,
( spl45_6
| spl45_3 ),
inference(avatar_split_clause,[],[f549,f612,f626]) ).
fof(f631,definition,
( spl45_7
<=> nat_succeeds(sK38) ),
introduced(definition,[new_symbols(definition,[spl45_7])],[avatar_definition]) ).
fof(f633,plain,
( nat_succeeds(sK38)
| ~ spl45_7 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f634,plain,
( spl45_7
| spl45_3 ),
inference(avatar_split_clause,[],[f550,f612,f631]) ).
fof(f636,definition,
( spl45_8
<=> '@=<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38)) ),
introduced(definition,[new_symbols(definition,[spl45_8])],[avatar_definition]) ).
fof(f638,plain,
( ~ '@=<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| spl45_8 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f639,plain,
( ~ spl45_8
| spl45_3 ),
inference(avatar_split_clause,[],[f551,f612,f636]) ).
fof(f643,plain,
( ! [X0] :
( '@=<_succeeds'(sF43,'@*'(sK40,X0))
| ~ nat_succeeds(sK40)
| ~ '@=<_succeeds'(sK41,X0)
| ~ nat_succeeds(X0) )
| ~ spl45_3 ),
inference(superposition,[],[f613,f600]) ).
fof(f648,plain,
( ! [X0] :
( '@=<_succeeds'(sF43,'@*'(sK40,X0))
| ~ '@=<_succeeds'(sK41,X0)
| ~ nat_succeeds(X0) )
| ~ spl45_3 ),
inference(forward_subsumption_resolution,[],[f643,f554]) ).
fof(f659,plain,
( '@=<_succeeds'(sF43,sF44)
| ~ '@=<_succeeds'(sK41,sK42)
| ~ nat_succeeds(sK42)
| ~ spl45_3 ),
inference(superposition,[],[f648,f602]) ).
fof(f662,plain,
( ~ '@=<_succeeds'(sK41,sK42)
| ~ nat_succeeds(sK42)
| ~ spl45_3 ),
inference(forward_subsumption_resolution,[],[f659,f603]) ).
fof(f663,plain,
( ~ nat_succeeds(sK42)
| ~ spl45_3 ),
inference(forward_subsumption_resolution,[],[f662,f553]) ).
fof(f664,plain,
( $false
| ~ spl45_3 ),
inference(forward_subsumption_resolution,[],[f663,f552]) ).
fof(f665,plain,
~ spl45_3,
inference(avatar_contradiction_clause,[],[f664]) ).
fof(f672,plain,
( ! [X0] :
( ~ nat_succeeds(X0)
| '@*'(s(X0),sK38) = '@+'(sK38,'@*'(X0,sK38)) )
| ~ spl45_7 ),
inference(resolution,[],[f489,f633]) ).
fof(f776,plain,
( '0' = '@*'('0',sK38)
| ~ spl45_7 ),
inference(resolution,[],[f488,f633]) ).
fof(f953,plain,
( ~ '@=<_succeeds'('@*'('0',sK37),'@*'('0',sK38))
| ~ spl45_1
| spl45_8 ),
inference(superposition,[],[f638,f607]) ).
fof(f977,plain,
( ! [X0,X1] :
( ~ '@=<_succeeds'(X0,X1)
| '@*'(sK39,X1) = '@+'('@*'(sK39,X0),sK33('@*'(sK39,X0),'@*'(sK39,X1)))
| ~ nat_succeeds(X1) )
| ~ spl45_2 ),
inference(resolution,[],[f516,f610]) ).
fof(f990,definition,
( spl45_32
<=> nat_succeeds(sK37) ),
introduced(definition,[new_symbols(definition,[spl45_32])],[avatar_definition]) ).
fof(f991,plain,
( nat_succeeds(sK37)
| ~ spl45_32 ),
inference(avatar_component_clause,[],[f990]) ).
fof(f992,plain,
( ~ nat_succeeds(sK37)
| spl45_32 ),
inference(avatar_component_clause,[],[f990]) ).
fof(f1004,plain,
( '@*'(sK39,sK38) = '@+'('@*'(sK39,sK37),sK33('@*'(sK39,sK37),'@*'(sK39,sK38)))
| ~ nat_succeeds(sK38)
| ~ spl45_2
| ~ spl45_6 ),
inference(resolution,[],[f977,f628]) ).
fof(f1008,plain,
( '@*'(sK39,sK38) = '@+'('@*'(sK39,sK37),sK33('@*'(sK39,sK37),'@*'(sK39,sK38)))
| ~ spl45_2
| ~ spl45_6
| ~ spl45_7 ),
inference(forward_subsumption_resolution,[],[f1004,f633]) ).
fof(f1016,plain,
( '@=<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ nat_succeeds('@*'(sK39,sK37))
| ~ spl45_2
| ~ spl45_6
| ~ spl45_7 ),
inference(superposition,[],[f537,f1008]) ).
fof(f1018,definition,
( spl45_34
<=> nat_succeeds('@*'(sK39,sK37)) ),
introduced(definition,[new_symbols(definition,[spl45_34])],[avatar_definition]) ).
fof(f1020,plain,
( ~ nat_succeeds('@*'(sK39,sK37))
| spl45_34 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f1022,definition,
( spl45_35
<=> '@=<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38)) ),
introduced(definition,[new_symbols(definition,[spl45_35])],[avatar_definition]) ).
fof(f1024,plain,
( '@=<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ spl45_35 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f1025,plain,
( ~ spl45_34
| spl45_35
| ~ spl45_2
| ~ spl45_6
| ~ spl45_7 ),
inference(avatar_split_clause,[],[f1016,f631,f626,f609,f1022,f1018]) ).
fof(f1152,plain,
( ! [X0,X1] :
( ~ '@=<_succeeds'(X0,X1)
| nat_succeeds('@*'(sK39,X0))
| ~ nat_succeeds(X1) )
| ~ spl45_2 ),
inference(resolution,[],[f514,f610]) ).
fof(f1154,plain,
( nat_succeeds(sK37)
| ~ spl45_6 ),
inference(resolution,[],[f514,f628]) ).
fof(f1158,plain,
( $false
| ~ spl45_6
| spl45_32 ),
inference(forward_subsumption_resolution,[],[f1154,f992]) ).
fof(f1159,plain,
( ~ spl45_6
| spl45_32 ),
inference(avatar_contradiction_clause,[],[f1158]) ).
fof(f1177,plain,
( '0' = '@*'('0',sK37)
| ~ spl45_32 ),
inference(resolution,[],[f991,f488]) ).
fof(f1178,plain,
( ! [X0] :
( ~ nat_succeeds(X0)
| '@*'(s(X0),sK37) = '@+'(sK37,'@*'(X0,sK37)) )
| ~ spl45_32 ),
inference(resolution,[],[f991,f489]) ).
fof(f1235,plain,
( nat_succeeds('@*'(sK39,sK37))
| ~ nat_succeeds(sK38)
| ~ spl45_2
| ~ spl45_6 ),
inference(resolution,[],[f1152,f628]) ).
fof(f1239,plain,
( ~ nat_succeeds(sK38)
| ~ spl45_2
| ~ spl45_6
| spl45_34 ),
inference(forward_subsumption_resolution,[],[f1235,f1020]) ).
fof(f1252,plain,
( $false
| ~ spl45_2
| ~ spl45_6
| ~ spl45_7
| spl45_34 ),
inference(forward_subsumption_resolution,[],[f1239,f633]) ).
fof(f1253,plain,
( ~ spl45_2
| ~ spl45_6
| ~ spl45_7
| spl45_34 ),
inference(avatar_contradiction_clause,[],[f1252]) ).
fof(f2437,plain,
( ~ '@=<_succeeds'('@*'('0',sK37),'0')
| ~ spl45_1
| ~ spl45_7
| spl45_8 ),
inference(forward_demodulation,[],[f953,f776]) ).
fof(f2442,plain,
( ~ '@=<_succeeds'('0','0')
| ~ spl45_1
| ~ spl45_7
| spl45_8
| ~ spl45_32 ),
inference(forward_demodulation,[],[f2437,f1177]) ).
fof(f2446,plain,
( $false
| ~ spl45_1
| ~ spl45_7
| spl45_8
| ~ spl45_32 ),
inference(forward_subsumption_resolution,[],[f2442,f576]) ).
fof(f2447,plain,
( ~ spl45_1
| ~ spl45_7
| spl45_8
| ~ spl45_32 ),
inference(avatar_contradiction_clause,[],[f2446]) ).
fof(f2457,plain,
( '@*'(s(sK39),sK38) = '@+'(sK38,'@*'(sK39,sK38))
| ~ spl45_4
| ~ spl45_7 ),
inference(resolution,[],[f618,f672]) ).
fof(f2467,plain,
( '@*'(s(sK39),sK37) = '@+'(sK37,'@*'(sK39,sK37))
| ~ spl45_4
| ~ spl45_32 ),
inference(resolution,[],[f618,f1178]) ).
fof(f2469,plain,
( '@*'(sK36,sK37) = '@+'(sK37,'@*'(sK39,sK37))
| ~ spl45_4
| ~ spl45_5
| ~ spl45_32 ),
inference(forward_demodulation,[],[f2467,f623]) ).
fof(f2472,plain,
( '@*'(sK36,sK38) = '@+'(sK38,'@*'(sK39,sK38))
| ~ spl45_4
| ~ spl45_5
| ~ spl45_7 ),
inference(forward_demodulation,[],[f2457,f623]) ).
fof(f2586,plain,
( ! [X0,X1] :
( '@=<_succeeds'('@+'(X0,X1),'@*'(sK36,sK38))
| ~ '@=<_succeeds'(X0,sK38)
| ~ '@=<_succeeds'(X1,'@*'(sK39,sK38))
| ~ nat_succeeds(sK38) )
| ~ spl45_4
| ~ spl45_5
| ~ spl45_7 ),
inference(superposition,[],[f542,f2472]) ).
fof(f2587,plain,
( ! [X0,X1] :
( '@=<_succeeds'('@+'(X0,X1),'@*'(sK36,sK38))
| ~ '@=<_succeeds'(X0,sK38)
| ~ '@=<_succeeds'(X1,'@*'(sK39,sK38)) )
| ~ spl45_4
| ~ spl45_5
| ~ spl45_7 ),
inference(forward_subsumption_resolution,[],[f2586,f633]) ).
fof(f2845,plain,
( '@=<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| ~ '@=<_succeeds'(sK37,sK38)
| ~ '@=<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ spl45_4
| ~ spl45_5
| ~ spl45_7
| ~ spl45_32 ),
inference(superposition,[],[f2587,f2469]) ).
fof(f2940,plain,
( ~ '@=<_succeeds'(sK37,sK38)
| ~ '@=<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ spl45_4
| ~ spl45_5
| ~ spl45_7
| spl45_8
| ~ spl45_32 ),
inference(forward_subsumption_resolution,[],[f2845,f638]) ).
fof(f2943,plain,
( ~ '@=<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ spl45_4
| ~ spl45_5
| ~ spl45_6
| ~ spl45_7
| spl45_8
| ~ spl45_32 ),
inference(forward_subsumption_resolution,[],[f2940,f628]) ).
fof(f2954,plain,
( $false
| ~ spl45_4
| ~ spl45_5
| ~ spl45_6
| ~ spl45_7
| spl45_8
| ~ spl45_32
| ~ spl45_35 ),
inference(forward_subsumption_resolution,[],[f2943,f1024]) ).
fof(f2955,plain,
( ~ spl45_4
| ~ spl45_5
| ~ spl45_6
| ~ spl45_7
| spl45_8
| ~ spl45_32
| ~ spl45_35 ),
inference(avatar_contradiction_clause,[],[f2954]) ).
cnf(s1,plain,
( spl45_1
| spl45_2
| spl45_3 ),
inference(sat_conversion,[],[f614]) ).
cnf(s2,plain,
( spl45_1
| spl45_3
| spl45_4 ),
inference(sat_conversion,[],[f619]) ).
cnf(s3,plain,
( spl45_1
| spl45_3
| spl45_5 ),
inference(sat_conversion,[],[f624]) ).
cnf(s4,plain,
( spl45_3
| spl45_6 ),
inference(sat_conversion,[],[f629]) ).
cnf(s5,plain,
( spl45_3
| spl45_7 ),
inference(sat_conversion,[],[f634]) ).
cnf(s6,plain,
( spl45_3
| ~ spl45_8 ),
inference(sat_conversion,[],[f639]) ).
cnf(s8,plain,
~ spl45_3,
inference(sat_conversion,[],[f665]) ).
cnf(s23,plain,
( ~ spl45_2
| ~ spl45_6
| ~ spl45_7
| ~ spl45_34
| spl45_35 ),
inference(sat_conversion,[],[f1025]) ).
cnf(s31,plain,
( ~ spl45_6
| spl45_32 ),
inference(sat_conversion,[],[f1159]) ).
cnf(s38,plain,
( ~ spl45_2
| ~ spl45_6
| ~ spl45_7
| spl45_34 ),
inference(sat_conversion,[],[f1253]) ).
cnf(s101,plain,
( ~ spl45_1
| ~ spl45_7
| spl45_8
| ~ spl45_32 ),
inference(sat_conversion,[],[f2447]) ).
cnf(s115,plain,
( ~ spl45_4
| ~ spl45_5
| ~ spl45_6
| ~ spl45_7
| spl45_8
| ~ spl45_32
| ~ spl45_35 ),
inference(sat_conversion,[],[f2955]) ).
cnf(s118,plain,
~ spl45_8,
inference(rat,[],[s6,s8]) ).
cnf(s119,plain,
spl45_7,
inference(rat,[],[s5,s8]) ).
cnf(s136,plain,
spl45_6,
inference(rat,[],[s4,s8]) ).
cnf(s137,plain,
spl45_32,
inference(rat,[],[s31,s136]) ).
cnf(s143,plain,
~ spl45_1,
inference(rat,[],[s101,s119,s118,s137]) ).
cnf(s152,plain,
spl45_5,
inference(rat,[],[s3,s8,s143]) ).
cnf(s153,plain,
spl45_4,
inference(rat,[],[s2,s8,s143]) ).
cnf(s154,plain,
~ spl45_35,
inference(rat,[],[s115,s152,s137,s118,s119,s136,s153]) ).
cnf(s164,plain,
spl45_2,
inference(rat,[],[s1,s8,s143]) ).
cnf(s166,plain,
spl45_34,
inference(rat,[],[s38,s136,s119,s164]) ).
cnf(s168,plain,
$false,
inference(rat,[],[s23,s154,s136,s119,s166,s164]) ).
fof(f2965,plain,
$false,
inference(avatar_sat_refutation,[],[s168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX046+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 14:57:10 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 8.51/1.78 % (3460381)Detected formulas, will run a generic FOF schedule.
% 8.51/1.78 % (3460392)dis-21_1_sil=8000:lcm=predicate:random_seed=2257872373: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)
% 8.51/1.78 % (3460391)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3188264114:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.51/1.78 % (3460390)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1734601435:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.51/1.78 % (3460386)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=1549091521:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.51/1.78 % (3460388)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=1643602494:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.51/1.78 % (3460389)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=624216053:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.51/1.78 % (3460387)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=3964264265:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.51/1.78 % (3460392)Instruction limit reached!
% 8.51/1.78 % (3460392)------------------------------
% 8.51/1.78 % (3460392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460392)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460392)Termination reason: Instruction limit
% 8.51/1.78 % (3460392)Termination phase: Saturation
% 8.51/1.78 % (3460392)Time elapsed: 0.044 s
% 8.51/1.78 % (3460392)Peak memory usage: 90 MB
% 8.51/1.78 % (3460392)Instructions burned: 130 (million)
% 8.51/1.78 % (3460390)Instruction limit reached!
% 8.51/1.78 % (3460390)------------------------------
% 8.51/1.78 % (3460390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460390)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460390)Termination reason: Instruction limit
% 8.51/1.78 % (3460390)Termination phase: Saturation
% 8.51/1.78 % (3460390)Time elapsed: 0.073 s
% 8.51/1.78 % (3460390)Peak memory usage: 88 MB
% 8.51/1.78 % (3460390)Instructions burned: 120 (million)
% 8.51/1.78 % (3460389)Instruction limit reached!
% 8.51/1.78 % (3460389)------------------------------
% 8.51/1.78 % (3460389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460389)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460389)Termination reason: Instruction limit
% 8.51/1.78 % (3460389)Termination phase: Saturation
% 8.51/1.78 % (3460389)Time elapsed: 0.079 s
% 8.51/1.78 % (3460389)Peak memory usage: 89 MB
% 8.51/1.78 % (3460389)Instructions burned: 110 (million)
% 8.51/1.78 % (3460391)Instruction limit reached!
% 8.51/1.78 % (3460391)------------------------------
% 8.51/1.78 % (3460391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460391)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460391)Termination reason: Instruction limit
% 8.51/1.78 % (3460391)Termination phase: Saturation
% 8.51/1.78 % (3460391)Time elapsed: 0.091 s
% 8.51/1.78 % (3460391)Peak memory usage: 90 MB
% 8.51/1.78 % (3460391)Instructions burned: 139 (million)
% 8.51/1.78 % (3460400)lrs+10_1_sil=8000:sp=occurrence:random_seed=243761841:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.51/1.78 % (3460401)lrs+10_1_sil=32000:urr=on:br=off:random_seed=118833118:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.51/1.78 % (3460402)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1834904308:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.51/1.78 % (3460400)Instruction limit reached!
% 8.51/1.78 % (3460400)------------------------------
% 8.51/1.78 % (3460400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460400)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460400)Termination reason: Instruction limit
% 8.51/1.78 % (3460400)Termination phase: Saturation
% 8.51/1.78 % (3460400)Time elapsed: 0.105 s
% 8.51/1.78 % (3460400)Peak memory usage: 92 MB
% 8.51/1.78 % (3460400)Instructions burned: 287 (million)
% 8.51/1.78 % (3460404)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=1475256958:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.51/1.78 % (3460401)Instruction limit reached!
% 8.51/1.78 % (3460401)------------------------------
% 8.51/1.78 % (3460401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460401)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460401)Termination reason: Instruction limit
% 8.51/1.78 % (3460401)Termination phase: Saturation
% 8.51/1.78 % (3460401)Time elapsed: 0.078 s
% 8.51/1.78 % (3460401)Peak memory usage: 92 MB
% 8.51/1.78 % (3460401)Instructions burned: 157 (million)
% 8.51/1.78 % (3460407)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3232235992:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 8.51/1.78 % (3460404)Instruction limit reached!
% 8.51/1.78 % (3460404)------------------------------
% 8.51/1.78 % (3460404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460404)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460404)Termination reason: Instruction limit
% 8.51/1.78 % (3460404)Termination phase: Saturation
% 8.51/1.78 % (3460404)Time elapsed: 0.120 s
% 8.51/1.78 % (3460404)Peak memory usage: 94 MB
% 8.51/1.78 % (3460404)Instructions burned: 248 (million)
% 8.51/1.78 % (3460407)Instruction limit reached!
% 8.51/1.78 % (3460407)------------------------------
% 8.51/1.78 % (3460407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460407)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460407)Termination reason: Instruction limit
% 8.51/1.78 % (3460407)Termination phase: Saturation
% 8.51/1.78 % (3460407)Time elapsed: 0.100 s
% 8.51/1.78 % (3460407)Peak memory usage: 90 MB
% 8.51/1.78 % (3460407)Instructions burned: 295 (million)
% 8.51/1.78 % (3460409)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2858139706:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 8.51/1.78 % (3460402)Instruction limit reached!
% 8.51/1.78 % (3460402)------------------------------
% 8.51/1.78 % (3460402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460402)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460402)Termination reason: Instruction limit
% 8.51/1.78 % (3460402)Termination phase: Saturation
% 8.51/1.78 % (3460402)Time elapsed: 0.217 s
% 8.51/1.78 % (3460402)Peak memory usage: 93 MB
% 8.51/1.78 % (3460402)Instructions burned: 325 (million)
% 8.51/1.78 % (3460412)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2662307863:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 8.51/1.78 % (3460411)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4160245610:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 8.51/1.78 % (3460412)Instruction limit reached!
% 8.51/1.78 % (3460412)------------------------------
% 8.51/1.78 % (3460412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460412)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460412)Termination reason: Instruction limit
% 8.51/1.78 % (3460412)Termination phase: Saturation
% 8.51/1.78 % (3460412)Time elapsed: 0.036 s
% 8.51/1.78 % (3460412)Peak memory usage: 89 MB
% 8.51/1.78 % (3460412)Instructions burned: 131 (million)
% 8.51/1.78 % (3460411)Instruction limit reached!
% 8.51/1.78 % (3460411)------------------------------
% 8.51/1.78 % (3460411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460411)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460411)Termination reason: Instruction limit
% 8.51/1.78 % (3460411)Termination phase: Saturation
% 8.51/1.78 % (3460411)Time elapsed: 0.075 s
% 8.51/1.78 % (3460411)Peak memory usage: 90 MB
% 8.51/1.78 % (3460411)Instructions burned: 114 (million)
% 8.51/1.78 % (3460414)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2126731740:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 8.51/1.78 % (3460417)lrs+10_1_sil=8000:sp=occurrence:random_seed=2821962591:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 8.51/1.78 % (3460414)Instruction limit reached!
% 8.51/1.78 % (3460414)------------------------------
% 8.51/1.78 % (3460414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460414)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460414)Termination reason: Instruction limit
% 8.51/1.78 % (3460414)Termination phase: Saturation
% 8.51/1.78 % (3460414)Time elapsed: 0.072 s
% 8.51/1.78 % (3460414)Peak memory usage: 89 MB
% 8.51/1.78 % (3460414)Instructions burned: 115 (million)
% 8.51/1.78 % (3460418)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4128138233:i=437:sd=1:aac=none:ss=included_2993 on theBenchmark for (2993ds/437Mi)
% 8.51/1.78 % (3460421)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1831280012:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 8.51/1.78 % (3460417)Instruction limit reached!
% 8.51/1.78 % (3460417)------------------------------
% 8.51/1.78 % (3460417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460417)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460417)Termination reason: Instruction limit
% 8.51/1.78 % (3460417)Termination phase: Saturation
% 8.51/1.78 % (3460417)Time elapsed: 0.307 s
% 8.51/1.78 % (3460417)Peak memory usage: 99 MB
% 8.51/1.78 % (3460417)Instructions burned: 908 (million)
% 8.51/1.78 % (3460386)First to succeed.
% 8.51/1.78 % (3460386)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3460381"
% 8.51/1.78 % (3460418)Instruction limit reached!
% 8.51/1.78 % (3460418)------------------------------
% 8.51/1.78 % (3460418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460418)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460418)Termination reason: Instruction limit
% 8.51/1.78 % (3460418)Termination phase: Saturation
% 8.51/1.78 % (3460418)Time elapsed: 0.282 s
% 8.51/1.78 % (3460418)Peak memory usage: 93 MB
% 8.51/1.78 % (3460418)Instructions burned: 438 (million)
% 8.51/1.78 % (3460424)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2949324998:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 8.51/1.78 % (3460424)Instruction limit reached!
% 8.51/1.78 % (3460424)------------------------------
% 8.51/1.78 % (3460424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.51/1.78 % (3460424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.78 % (3460424)CaDiCaL version: 2.1.3
% 8.51/1.78 % (3460424)Termination reason: Instruction limit
% 8.51/1.78 % (3460424)Termination phase: Saturation
% 8.51/1.78 % (3460424)Time elapsed: 0.037 s
% 8.51/1.78 % (3460424)Peak memory usage: 91 MB
% 8.51/1.78 % (3460424)Instructions burned: 136 (million)
% 8.51/1.78 % (3460425)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=343268948:st=8:i=592:sd=3:ep=RST:ss=axioms_2989 on theBenchmark for (2989ds/592Mi)
% 8.51/1.78 % (3460427)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=83029707:st=3:i=13193:sd=3:ss=axioms_2988 on theBenchmark for (2988ds/13193Mi)
% 8.51/1.78 % (3460386)Refutation found. Thanks to Tanya!
% 8.51/1.78 % SZS status Theorem for theBenchmark
% 8.51/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 9.97/1.98 % (3460386)------------------------------
% 9.97/1.98 % (3460386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.97/1.98 % (3460386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.97/1.98 % (3460386)CaDiCaL version: 2.1.3
% 9.97/1.98 % (3460386)Termination reason: Refutation
% 9.97/1.98 % (3460386)Time elapsed: 0.949 s
% 9.97/1.98 % (3460386)Peak memory usage: 134 MB
% 9.97/1.98 % (3460386)Instructions burned: 1441 (million)
% 9.97/1.98 % (3460386)------------------------------
% 9.97/1.98 % (3460386)------------------------------
% 9.97/1.98 % (3460381)Success in time 1.351 s
% 9.97/1.98 % Vampire exiting
%------------------------------------------------------------------------------