%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX047+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 14.03s 2.73s
% Output : Refutation 14.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 25
% Syntax : Number of formulae : 190 ( 26 unt; 19 def)
% Number of atoms : 690 ( 130 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 807 ( 307 ~; 402 |; 61 &)
% ( 19 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 134 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f61,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(times:successor)') ).
fof(f68,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@*'(s('0'),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(times:one)') ).
fof(f73,axiom,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
=> nat_succeeds(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:types)') ).
fof(f117,axiom,
! [X0,X1,X2,X3] :
( ( '@<_succeeds'(X0,X2)
& '@<_succeeds'(X1,X3)
& nat_succeeds(X2) )
=> '@<_succeeds'('@+'(X0,X1),'@+'(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(plus:less:less)') ).
fof(f120,axiom,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( ( nat_succeeds(X3)
& '@<_succeeds'(X2,X3)
& X1 != '0' )
=> '@<_succeeds'('@*'(X1,X2),'@*'(X1,X3)) ) )
| X0 = '0' )
=> ! [X2,X3] :
( ( nat_succeeds(X3)
& '@<_succeeds'(X2,X3)
& X0 != '0' )
=> '@<_succeeds'('@*'(X0,X2),'@*'(X0,X3)) ) )
=> ! [X0] :
( nat_succeeds(X0)
=> ! [X2,X3] :
( ( nat_succeeds(X3)
& '@<_succeeds'(X2,X3)
& X0 != '0' )
=> '@<_succeeds'('@*'(X0,X2),'@*'(X0,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
fof(f121,conjecture,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& X0 != '0'
& '@<_succeeds'(X1,X2)
& nat_succeeds(X2) )
=> '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(times:less:second)') ).
fof(f122,negated_conjecture,
~ ! [X0,X1,X2] :
( ( nat_succeeds(X0)
& X0 != '0'
& '@<_succeeds'(X1,X2)
& nat_succeeds(X2) )
=> '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f121]) ).
fof(f132,plain,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( ( nat_succeeds(X3)
& '@<_succeeds'(X2,X3)
& X1 != '0' )
=> '@<_succeeds'('@*'(X1,X2),'@*'(X1,X3)) ) )
| X0 = '0' )
=> ! [X4,X5] :
( ( nat_succeeds(X5)
& '@<_succeeds'(X4,X5)
& X0 != '0' )
=> '@<_succeeds'('@*'(X0,X4),'@*'(X0,X5)) ) )
=> ! [X6] :
( nat_succeeds(X6)
=> ! [X7,X8] :
( ( nat_succeeds(X8)
& '@<_succeeds'(X7,X8)
& '0' != X6 )
=> '@<_succeeds'('@*'(X6,X7),'@*'(X6,X8)) ) ) ),
inference(rectify,[],[f120]) ).
fof(f195,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f196,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f195]) ).
fof(f208,plain,
! [X0] :
( '@*'(s('0'),X0) = X0
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f214,plain,
! [X0,X1] :
( nat_succeeds(X0)
| ~ '@<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f283,plain,
! [X0,X1,X2,X3] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X2,X3))
| ~ '@<_succeeds'(X0,X2)
| ~ '@<_succeeds'(X1,X3)
| ~ nat_succeeds(X2) ),
inference(ennf_transformation,[],[f117]) ).
fof(f284,plain,
! [X0,X1,X2,X3] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X2,X3))
| ~ '@<_succeeds'(X0,X2)
| ~ '@<_succeeds'(X1,X3)
| ~ nat_succeeds(X2) ),
inference(flattening,[],[f283]) ).
fof(f289,plain,
( ! [X6] :
( ! [X7,X8] :
( '@<_succeeds'('@*'(X6,X7),'@*'(X6,X8))
| ~ nat_succeeds(X8)
| ~ '@<_succeeds'(X7,X8)
| '0' = X6 )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( ~ '@<_succeeds'('@*'(X0,X4),'@*'(X0,X5))
& nat_succeeds(X5)
& '@<_succeeds'(X4,X5)
& X0 != '0' )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'('@*'(X1,X2),'@*'(X1,X3))
| ~ nat_succeeds(X3)
| ~ '@<_succeeds'(X2,X3)
| '0' = X1 ) )
| X0 = '0' ) ) ),
inference(ennf_transformation,[],[f132]) ).
fof(f290,plain,
( ! [X6] :
( ! [X7,X8] :
( '@<_succeeds'('@*'(X6,X7),'@*'(X6,X8))
| ~ nat_succeeds(X8)
| ~ '@<_succeeds'(X7,X8)
| '0' = X6 )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( ~ '@<_succeeds'('@*'(X0,X4),'@*'(X0,X5))
& nat_succeeds(X5)
& '@<_succeeds'(X4,X5)
& X0 != '0' )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'('@*'(X1,X2),'@*'(X1,X3))
| ~ nat_succeeds(X3)
| ~ '@<_succeeds'(X2,X3)
| '0' = X1 ) )
| X0 = '0' ) ) ),
inference(flattening,[],[f289]) ).
fof(f291,plain,
? [X0,X1,X2] :
( ~ '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
& nat_succeeds(X0)
& X0 != '0'
& '@<_succeeds'(X1,X2)
& nat_succeeds(X2) ),
inference(ennf_transformation,[],[f122]) ).
fof(f292,plain,
? [X0,X1,X2] :
( ~ '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
& nat_succeeds(X0)
& X0 != '0'
& '@<_succeeds'(X1,X2)
& nat_succeeds(X2) ),
inference(flattening,[],[f291]) ).
fof(f358,plain,
( ! [X0] :
( ! [X1,X2] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0 )
| ~ nat_succeeds(X0) )
| ? [X3] :
( ? [X4,X5] :
( ~ '@<_succeeds'('@*'(X3,X4),'@*'(X3,X5))
& nat_succeeds(X5)
& '@<_succeeds'(X4,X5)
& '0' != X3 )
& ( ? [X6] :
( s(X6) = X3
& nat_succeeds(X6)
& ! [X7,X8] :
( '@<_succeeds'('@*'(X6,X7),'@*'(X6,X8))
| ~ nat_succeeds(X8)
| ~ '@<_succeeds'(X7,X8)
| '0' = X6 ) )
| '0' = X3 ) ) ),
inference(rectify,[],[f290]) ).
fof(f359,plain,
( ! [X0] :
( ! [X1,X2] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0 )
| ~ nat_succeeds(X0) )
| ( ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
& nat_succeeds(sK38)
& '@<_succeeds'(sK37,sK38)
& '0' != sK36
& ( ( sK36 = s(sK39)
& nat_succeeds(sK39)
& ! [X7,X8] :
( '@<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ nat_succeeds(X8)
| ~ '@<_succeeds'(X7,X8)
| '0' = sK39 ) )
| '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)],[f358]) ).
fof(f360,plain,
( ~ '@<_succeeds'('@*'(sK40,sK41),'@*'(sK40,sK42))
& nat_succeeds(sK40)
& '0' != 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)],[f292]) ).
fof(f495,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(cnf_transformation,[],[f196]) ).
fof(f502,plain,
! [X0] :
( '@*'(s('0'),X0) = X0
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f507,plain,
! [X0,X1] :
( nat_succeeds(X0)
| ~ '@<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f214]) ).
fof(f551,plain,
! [X2,X3,X0,X1] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X2,X3))
| ~ '@<_succeeds'(X0,X2)
| ~ '@<_succeeds'(X1,X3)
| ~ nat_succeeds(X2) ),
inference(cnf_transformation,[],[f284]) ).
fof(f554,plain,
! [X2,X0,X1,X8,X7] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| '@<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ nat_succeeds(X8)
| ~ '@<_succeeds'(X7,X8)
| '0' = sK39
| '0' = sK36 ),
inference(cnf_transformation,[],[f359]) ).
fof(f555,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| nat_succeeds(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f359]) ).
fof(f556,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| sK36 = s(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f359]) ).
fof(f557,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| '0' != sK36 ),
inference(cnf_transformation,[],[f359]) ).
fof(f558,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| '@<_succeeds'(sK37,sK38) ),
inference(cnf_transformation,[],[f359]) ).
fof(f559,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| nat_succeeds(sK38) ),
inference(cnf_transformation,[],[f359]) ).
fof(f560,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38)) ),
inference(cnf_transformation,[],[f359]) ).
fof(f561,plain,
nat_succeeds(sK42),
inference(cnf_transformation,[],[f360]) ).
fof(f562,plain,
'@<_succeeds'(sK41,sK42),
inference(cnf_transformation,[],[f360]) ).
fof(f563,plain,
'0' != sK40,
inference(cnf_transformation,[],[f360]) ).
fof(f564,plain,
nat_succeeds(sK40),
inference(cnf_transformation,[],[f360]) ).
fof(f565,plain,
~ '@<_succeeds'('@*'(sK40,sK41),'@*'(sK40,sK42)),
inference(cnf_transformation,[],[f360]) ).
fof(f611,plain,
! [X8,X7] :
( '@<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ nat_succeeds(X8)
| ~ '@<_succeeds'(X7,X8)
| sP44(X7) ),
inference(cnf_transformation,[],[f611_D]) ).
fof(f611_D,definition,
! [X7] :
( ! [X8] :
( '@<_succeeds'('@*'(sK39,X7),'@*'(sK39,X8))
| ~ nat_succeeds(X8)
| ~ '@<_succeeds'(X7,X8) )
<=> ~ sP44(X7) ),
introduced(definition,[new_symbols(definition,[sP44])],[general_splitting_component_introduction]) ).
fof(f612,plain,
! [X2,X0,X1,X7] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| '0' = sK39
| '0' = sK36
| ~ sP44(X7) ),
inference(general_splitting,[],[f554,f611_D]) ).
fof(f613,plain,
! [X7] :
( ~ sP44(X7)
| sP45 ),
inference(cnf_transformation,[],[f613_D]) ).
fof(f613_D,definition,
( ! [X7] : ~ sP44(X7)
<=> ~ sP45 ),
introduced(definition,[new_symbols(definition,[sP45])],[general_splitting_component_introduction]) ).
fof(f614,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@*'(X0,X1),'@*'(X0,X2))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X1,X2)
| '0' = X0
| ~ nat_succeeds(X0)
| '0' = sK39
| '0' = sK36
| ~ sP45 ),
inference(general_splitting,[],[f612,f613_D]) ).
fof(f616,definition,
( spl46_1
<=> '@<_succeeds'('@*'(sK40,sK41),'@*'(sK40,sK42)) ),
introduced(definition,[new_symbols(definition,[spl46_1])],[avatar_definition]) ).
fof(f618,plain,
( ~ '@<_succeeds'('@*'(sK40,sK41),'@*'(sK40,sK42))
| spl46_1 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f619,plain,
~ spl46_1,
inference(avatar_split_clause,[],[f565,f616]) ).
fof(f620,plain,
( ~ nat_succeeds(sK42)
| ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(resolution,[],[f618,f555]) ).
fof(f621,plain,
( ~ nat_succeeds(sK42)
| ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(resolution,[],[f618,f556]) ).
fof(f622,plain,
( ~ nat_succeeds(sK42)
| ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| '0' != sK36
| spl46_1 ),
inference(resolution,[],[f618,f557]) ).
fof(f623,plain,
( ~ nat_succeeds(sK42)
| ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(resolution,[],[f618,f558]) ).
fof(f624,plain,
( ~ nat_succeeds(sK42)
| ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| nat_succeeds(sK38)
| spl46_1 ),
inference(resolution,[],[f618,f559]) ).
fof(f625,plain,
( ~ nat_succeeds(sK42)
| ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| spl46_1 ),
inference(resolution,[],[f618,f560]) ).
fof(f626,plain,
( ~ nat_succeeds(sK42)
| ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| '0' = sK39
| '0' = sK36
| ~ sP45
| spl46_1 ),
inference(resolution,[],[f618,f614]) ).
fof(f643,plain,
( ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| '0' = sK39
| '0' = sK36
| ~ sP45
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f626,f561]) ).
fof(f644,plain,
( ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f625,f561]) ).
fof(f645,plain,
( ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| nat_succeeds(sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f624,f561]) ).
fof(f646,plain,
( ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f623,f561]) ).
fof(f647,plain,
( ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| '0' != sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f622,f561]) ).
fof(f648,plain,
( ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f621,f561]) ).
fof(f649,plain,
( ~ '@<_succeeds'(sK41,sK42)
| '0' = sK40
| ~ nat_succeeds(sK40)
| nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f620,f561]) ).
fof(f651,plain,
( '0' = sK40
| ~ nat_succeeds(sK40)
| '0' = sK39
| '0' = sK36
| ~ sP45
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f643,f562]) ).
fof(f652,plain,
( '0' = sK40
| ~ nat_succeeds(sK40)
| ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f644,f562]) ).
fof(f653,plain,
( '0' = sK40
| ~ nat_succeeds(sK40)
| nat_succeeds(sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f645,f562]) ).
fof(f654,plain,
( '0' = sK40
| ~ nat_succeeds(sK40)
| '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f646,f562]) ).
fof(f655,plain,
( '0' = sK40
| ~ nat_succeeds(sK40)
| '0' != sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f647,f562]) ).
fof(f656,plain,
( '0' = sK40
| ~ nat_succeeds(sK40)
| sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f648,f562]) ).
fof(f657,plain,
( '0' = sK40
| ~ nat_succeeds(sK40)
| nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f649,f562]) ).
fof(f658,plain,
( ~ nat_succeeds(sK40)
| '0' = sK39
| '0' = sK36
| ~ sP45
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f651,f563]) ).
fof(f659,plain,
( ~ nat_succeeds(sK40)
| ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f652,f563]) ).
fof(f660,plain,
( ~ nat_succeeds(sK40)
| nat_succeeds(sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f653,f563]) ).
fof(f661,plain,
( ~ nat_succeeds(sK40)
| '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f654,f563]) ).
fof(f662,plain,
( ~ nat_succeeds(sK40)
| '0' != sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f655,f563]) ).
fof(f663,plain,
( ~ nat_succeeds(sK40)
| sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f656,f563]) ).
fof(f664,plain,
( ~ nat_succeeds(sK40)
| nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f657,f563]) ).
fof(f665,plain,
( '0' = sK39
| '0' = sK36
| ~ sP45
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f658,f564]) ).
fof(f666,plain,
( ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f659,f564]) ).
fof(f667,plain,
( nat_succeeds(sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f660,f564]) ).
fof(f668,plain,
( '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f661,f564]) ).
fof(f669,plain,
( '0' != sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f662,f564]) ).
fof(f670,plain,
( sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f663,f564]) ).
fof(f671,plain,
( nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f664,f564]) ).
fof(f672,plain,
( '0' = sK39
| ~ sP45
| spl46_1 ),
inference(backward_subsumption_resolution,[],[f665,f669]) ).
fof(f676,plain,
( sK36 = s(sK39)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f670,f669]) ).
fof(f677,plain,
( nat_succeeds(sK39)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f671,f669]) ).
fof(f679,definition,
( spl46_2
<=> '@<_succeeds'(sK37,sK38) ),
introduced(definition,[new_symbols(definition,[spl46_2])],[avatar_definition]) ).
fof(f681,plain,
( '@<_succeeds'(sK37,sK38)
| ~ spl46_2 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f682,plain,
( spl46_2
| spl46_1 ),
inference(avatar_split_clause,[],[f668,f616,f679]) ).
fof(f690,plain,
( nat_succeeds(sK37)
| ~ spl46_2 ),
inference(resolution,[],[f681,f507]) ).
fof(f705,plain,
( ! [X0,X1] :
( '@<_succeeds'('@+'(sK37,X0),'@+'(sK38,X1))
| ~ '@<_succeeds'(X0,X1)
| ~ nat_succeeds(sK38) )
| ~ spl46_2 ),
inference(resolution,[],[f681,f551]) ).
fof(f712,plain,
( '@<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ nat_succeeds(sK38)
| sP44(sK37)
| ~ spl46_2 ),
inference(resolution,[],[f681,f611]) ).
fof(f713,plain,
( '@<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| sP44(sK37)
| spl46_1
| ~ spl46_2 ),
inference(forward_subsumption_resolution,[],[f712,f667]) ).
fof(f714,plain,
( ! [X0,X1] :
( '@<_succeeds'('@+'(sK37,X0),'@+'(sK38,X1))
| ~ '@<_succeeds'(X0,X1) )
| spl46_1
| ~ spl46_2 ),
inference(forward_subsumption_resolution,[],[f705,f667]) ).
fof(f758,definition,
( spl46_4
<=> '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38)) ),
introduced(definition,[new_symbols(definition,[spl46_4])],[avatar_definition]) ).
fof(f760,plain,
( ~ '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| spl46_4 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f761,plain,
( ~ spl46_4
| spl46_1 ),
inference(avatar_split_clause,[],[f666,f616,f758]) ).
fof(f1026,definition,
( spl46_8
<=> sK36 = s(sK39) ),
introduced(definition,[new_symbols(definition,[spl46_8])],[avatar_definition]) ).
fof(f1028,plain,
( sK36 = s(sK39)
| ~ spl46_8 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f1029,plain,
( spl46_8
| spl46_1 ),
inference(avatar_split_clause,[],[f676,f616,f1026]) ).
fof(f1124,definition,
( spl46_11
<=> nat_succeeds(sK38) ),
introduced(definition,[new_symbols(definition,[spl46_11])],[avatar_definition]) ).
fof(f1126,plain,
( nat_succeeds(sK38)
| ~ spl46_11 ),
inference(avatar_component_clause,[],[f1124]) ).
fof(f1127,plain,
( spl46_11
| spl46_1 ),
inference(avatar_split_clause,[],[f667,f616,f1124]) ).
fof(f1328,definition,
( spl46_14
<=> nat_succeeds(sK39) ),
introduced(definition,[new_symbols(definition,[spl46_14])],[avatar_definition]) ).
fof(f1330,plain,
( nat_succeeds(sK39)
| ~ spl46_14 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f1331,plain,
( spl46_14
| spl46_1 ),
inference(avatar_split_clause,[],[f677,f616,f1328]) ).
fof(f1363,plain,
( ! [X0] :
( '@*'(s(sK39),X0) = '@+'(X0,'@*'(sK39,X0))
| ~ nat_succeeds(X0) )
| ~ spl46_14 ),
inference(resolution,[],[f1330,f495]) ).
fof(f1448,plain,
( ! [X0] :
( '@+'(X0,'@*'(sK39,X0)) = '@*'(sK36,X0)
| ~ nat_succeeds(X0) )
| ~ spl46_8
| ~ spl46_14 ),
inference(forward_demodulation,[],[f1363,f1028]) ).
fof(f1583,definition,
( spl46_16
<=> sP44(sK37) ),
introduced(definition,[new_symbols(definition,[spl46_16])],[avatar_definition]) ).
fof(f1585,plain,
( sP44(sK37)
| ~ spl46_16 ),
inference(avatar_component_clause,[],[f1583]) ).
fof(f1587,definition,
( spl46_17
<=> '@<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38)) ),
introduced(definition,[new_symbols(definition,[spl46_17])],[avatar_definition]) ).
fof(f1589,plain,
( '@<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ spl46_17 ),
inference(avatar_component_clause,[],[f1587]) ).
fof(f1590,plain,
( spl46_16
| spl46_17
| spl46_1
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f713,f679,f616,f1587,f1583]) ).
fof(f1591,plain,
( sP45
| ~ spl46_16 ),
inference(resolution,[],[f1585,f613]) ).
fof(f1592,plain,
( '0' = sK39
| spl46_1
| ~ spl46_16 ),
inference(backward_subsumption_resolution,[],[f672,f1591]) ).
fof(f1594,definition,
( spl46_18
<=> '0' = sK39 ),
introduced(definition,[new_symbols(definition,[spl46_18])],[avatar_definition]) ).
fof(f1596,plain,
( '0' = sK39
| ~ spl46_18 ),
inference(avatar_component_clause,[],[f1594]) ).
fof(f1597,plain,
( spl46_18
| spl46_1
| ~ spl46_16 ),
inference(avatar_split_clause,[],[f1592,f1583,f616,f1594]) ).
fof(f1600,plain,
( s('0') = sK36
| ~ spl46_8
| ~ spl46_18 ),
inference(superposition,[],[f1028,f1596]) ).
fof(f2090,definition,
( spl46_32
<=> ! [X0] :
( '@+'(X0,'@*'(sK39,X0)) = '@*'(sK36,X0)
| ~ nat_succeeds(X0) ) ),
introduced(definition,[new_symbols(definition,[spl46_32])],[avatar_definition]) ).
fof(f2091,plain,
( ! [X0] :
( '@+'(X0,'@*'(sK39,X0)) = '@*'(sK36,X0)
| ~ nat_succeeds(X0) )
| ~ spl46_32 ),
inference(avatar_component_clause,[],[f2090]) ).
fof(f2092,plain,
( spl46_32
| ~ spl46_8
| ~ spl46_14 ),
inference(avatar_split_clause,[],[f1448,f1328,f1026,f2090]) ).
fof(f2201,definition,
( spl46_35
<=> s('0') = sK36 ),
introduced(definition,[new_symbols(definition,[spl46_35])],[avatar_definition]) ).
fof(f2203,plain,
( s('0') = sK36
| ~ spl46_35 ),
inference(avatar_component_clause,[],[f2201]) ).
fof(f2204,plain,
( spl46_35
| ~ spl46_8
| ~ spl46_18 ),
inference(avatar_split_clause,[],[f1600,f1594,f1026,f2201]) ).
fof(f2771,definition,
( spl46_50
<=> nat_succeeds(sK37) ),
introduced(definition,[new_symbols(definition,[spl46_50])],[avatar_definition]) ).
fof(f2773,plain,
( nat_succeeds(sK37)
| ~ spl46_50 ),
inference(avatar_component_clause,[],[f2771]) ).
fof(f2774,plain,
( spl46_50
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f690,f679,f2771]) ).
fof(f7284,plain,
( ! [X0] :
( '@*'(sK36,X0) = X0
| ~ nat_succeeds(X0) )
| ~ spl46_35 ),
inference(superposition,[],[f502,f2203]) ).
fof(f8124,definition,
( spl46_82
<=> ! [X0,X1] :
( '@<_succeeds'('@+'(sK37,X0),'@+'(sK38,X1))
| ~ '@<_succeeds'(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl46_82])],[avatar_definition]) ).
fof(f8125,plain,
( ! [X0,X1] :
( '@<_succeeds'('@+'(sK37,X0),'@+'(sK38,X1))
| ~ '@<_succeeds'(X0,X1) )
| ~ spl46_82 ),
inference(avatar_component_clause,[],[f8124]) ).
fof(f8126,plain,
( spl46_82
| spl46_1
| ~ spl46_2 ),
inference(avatar_split_clause,[],[f714,f679,f616,f8124]) ).
fof(f8262,definition,
( spl46_87
<=> ! [X0,X1] :
( nat_succeeds(X0)
| ~ '@<_succeeds'(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl46_87])],[avatar_definition]) ).
fof(f8263,plain,
( ! [X0,X1] :
( nat_succeeds(X0)
| ~ '@<_succeeds'(X0,X1) )
| ~ spl46_87 ),
inference(avatar_component_clause,[],[f8262]) ).
fof(f8264,plain,
spl46_87,
inference(avatar_split_clause,[],[f507,f8262]) ).
fof(f8707,definition,
( spl46_102
<=> ! [X0] :
( '@*'(sK36,X0) = X0
| ~ nat_succeeds(X0) ) ),
introduced(definition,[new_symbols(definition,[spl46_102])],[avatar_definition]) ).
fof(f8708,plain,
( ! [X0] :
( '@*'(sK36,X0) = X0
| ~ nat_succeeds(X0) )
| ~ spl46_102 ),
inference(avatar_component_clause,[],[f8707]) ).
fof(f8709,plain,
( spl46_102
| ~ spl46_35 ),
inference(avatar_split_clause,[],[f7284,f2201,f8707]) ).
fof(f8714,plain,
( ~ '@<_succeeds'(sK37,'@*'(sK36,sK38))
| ~ nat_succeeds(sK37)
| spl46_4
| ~ spl46_102 ),
inference(superposition,[],[f760,f8708]) ).
fof(f8759,plain,
( ~ '@<_succeeds'(sK37,'@*'(sK36,sK38))
| spl46_4
| ~ spl46_87
| ~ spl46_102 ),
inference(forward_subsumption_resolution,[],[f8714,f8263]) ).
fof(f8801,definition,
( spl46_103
<=> '@<_succeeds'(sK37,'@*'(sK36,sK38)) ),
introduced(definition,[new_symbols(definition,[spl46_103])],[avatar_definition]) ).
fof(f8803,plain,
( ~ '@<_succeeds'(sK37,'@*'(sK36,sK38))
| spl46_103 ),
inference(avatar_component_clause,[],[f8801]) ).
fof(f8804,plain,
( ~ spl46_103
| spl46_4
| ~ spl46_87
| ~ spl46_102 ),
inference(avatar_split_clause,[],[f8759,f8707,f8262,f758,f8801]) ).
fof(f8810,plain,
( ~ '@<_succeeds'(sK37,sK38)
| ~ nat_succeeds(sK38)
| ~ spl46_102
| spl46_103 ),
inference(superposition,[],[f8803,f8708]) ).
fof(f8813,plain,
( ~ nat_succeeds(sK38)
| ~ spl46_2
| ~ spl46_102
| spl46_103 ),
inference(forward_subsumption_resolution,[],[f8810,f681]) ).
fof(f8815,plain,
( $false
| ~ spl46_2
| ~ spl46_11
| ~ spl46_102
| spl46_103 ),
inference(forward_subsumption_resolution,[],[f8813,f1126]) ).
fof(f8816,plain,
( ~ spl46_2
| ~ spl46_11
| ~ spl46_102
| spl46_103 ),
inference(avatar_contradiction_clause,[],[f8815]) ).
fof(f9946,plain,
( ! [X0] :
( '@<_succeeds'('@+'(sK37,X0),'@*'(sK36,sK38))
| ~ '@<_succeeds'(X0,'@*'(sK39,sK38))
| ~ nat_succeeds(sK38) )
| ~ spl46_32
| ~ spl46_82 ),
inference(superposition,[],[f8125,f2091]) ).
fof(f9948,plain,
( ! [X0] :
( '@<_succeeds'('@+'(sK37,X0),'@*'(sK36,sK38))
| ~ '@<_succeeds'(X0,'@*'(sK39,sK38)) )
| ~ spl46_11
| ~ spl46_32
| ~ spl46_82 ),
inference(forward_subsumption_resolution,[],[f9946,f1126]) ).
fof(f9962,definition,
( spl46_147
<=> ! [X0] :
( '@<_succeeds'('@+'(sK37,X0),'@*'(sK36,sK38))
| ~ '@<_succeeds'(X0,'@*'(sK39,sK38)) ) ),
introduced(definition,[new_symbols(definition,[spl46_147])],[avatar_definition]) ).
fof(f9963,plain,
( ! [X0] :
( '@<_succeeds'('@+'(sK37,X0),'@*'(sK36,sK38))
| ~ '@<_succeeds'(X0,'@*'(sK39,sK38)) )
| ~ spl46_147 ),
inference(avatar_component_clause,[],[f9962]) ).
fof(f9964,plain,
( spl46_147
| ~ spl46_11
| ~ spl46_32
| ~ spl46_82 ),
inference(avatar_split_clause,[],[f9948,f8124,f2090,f1124,f9962]) ).
fof(f10093,plain,
( '@<_succeeds'('@*'(sK36,sK37),'@*'(sK36,sK38))
| ~ '@<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ nat_succeeds(sK37)
| ~ spl46_32
| ~ spl46_147 ),
inference(superposition,[],[f9963,f2091]) ).
fof(f10097,plain,
( ~ '@<_succeeds'('@*'(sK39,sK37),'@*'(sK39,sK38))
| ~ nat_succeeds(sK37)
| spl46_4
| ~ spl46_32
| ~ spl46_147 ),
inference(forward_subsumption_resolution,[],[f10093,f760]) ).
fof(f10104,plain,
( ~ nat_succeeds(sK37)
| spl46_4
| ~ spl46_17
| ~ spl46_32
| ~ spl46_147 ),
inference(forward_subsumption_resolution,[],[f10097,f1589]) ).
fof(f10108,plain,
( $false
| spl46_4
| ~ spl46_17
| ~ spl46_32
| ~ spl46_50
| ~ spl46_147 ),
inference(forward_subsumption_resolution,[],[f10104,f2773]) ).
fof(f10109,plain,
( spl46_4
| ~ spl46_17
| ~ spl46_32
| ~ spl46_50
| ~ spl46_147 ),
inference(avatar_contradiction_clause,[],[f10108]) ).
cnf(s1,plain,
~ spl46_1,
inference(sat_conversion,[],[f619]) ).
cnf(s2,plain,
( spl46_1
| spl46_2 ),
inference(sat_conversion,[],[f682]) ).
cnf(s4,plain,
( spl46_1
| ~ spl46_4 ),
inference(sat_conversion,[],[f761]) ).
cnf(s8,plain,
( spl46_1
| spl46_8 ),
inference(sat_conversion,[],[f1029]) ).
cnf(s11,plain,
( spl46_1
| spl46_11 ),
inference(sat_conversion,[],[f1127]) ).
cnf(s14,plain,
( spl46_1
| spl46_14 ),
inference(sat_conversion,[],[f1331]) ).
cnf(s16,plain,
( spl46_1
| ~ spl46_2
| spl46_16
| spl46_17 ),
inference(sat_conversion,[],[f1590]) ).
cnf(s17,plain,
( spl46_1
| ~ spl46_16
| spl46_18 ),
inference(sat_conversion,[],[f1597]) ).
cnf(s30,plain,
( ~ spl46_8
| ~ spl46_14
| spl46_32 ),
inference(sat_conversion,[],[f2092]) ).
cnf(s33,plain,
( ~ spl46_8
| ~ spl46_18
| spl46_35 ),
inference(sat_conversion,[],[f2204]) ).
cnf(s49,plain,
( ~ spl46_2
| spl46_50 ),
inference(sat_conversion,[],[f2774]) ).
cnf(s298,plain,
( spl46_1
| ~ spl46_2
| spl46_82 ),
inference(sat_conversion,[],[f8126]) ).
cnf(s305,plain,
spl46_87,
inference(sat_conversion,[],[f8264]) ).
cnf(s319,plain,
( ~ spl46_35
| spl46_102 ),
inference(sat_conversion,[],[f8709]) ).
cnf(s321,plain,
( spl46_4
| ~ spl46_87
| ~ spl46_102
| ~ spl46_103 ),
inference(sat_conversion,[],[f8804]) ).
cnf(s323,plain,
( ~ spl46_2
| ~ spl46_11
| ~ spl46_102
| spl46_103 ),
inference(sat_conversion,[],[f8816]) ).
cnf(s365,plain,
( ~ spl46_11
| ~ spl46_32
| ~ spl46_82
| spl46_147 ),
inference(sat_conversion,[],[f9964]) ).
cnf(s368,plain,
( spl46_4
| ~ spl46_17
| ~ spl46_32
| ~ spl46_50
| ~ spl46_147 ),
inference(sat_conversion,[],[f10109]) ).
cnf(s390,plain,
spl46_14,
inference(rat,[],[s14,s1]) ).
cnf(s391,plain,
spl46_11,
inference(rat,[],[s11,s1]) ).
cnf(s392,plain,
spl46_8,
inference(rat,[],[s8,s1]) ).
cnf(s394,plain,
~ spl46_4,
inference(rat,[],[s4,s1]) ).
cnf(s395,plain,
spl46_2,
inference(rat,[],[s2,s1]) ).
cnf(s411,plain,
spl46_32,
inference(rat,[],[s30,s390,s392]) ).
cnf(s419,plain,
spl46_82,
inference(rat,[],[s298,s1,s395]) ).
cnf(s420,plain,
spl46_50,
inference(rat,[],[s49,s395]) ).
cnf(s434,plain,
spl46_147,
inference(rat,[],[s365,s411,s391,s419]) ).
cnf(s435,plain,
~ spl46_17,
inference(rat,[],[s368,s434,s394,s411,s420]) ).
cnf(s439,plain,
spl46_16,
inference(rat,[],[s16,s395,s1,s435]) ).
cnf(s440,plain,
spl46_18,
inference(rat,[],[s17,s1,s439]) ).
cnf(s442,plain,
spl46_35,
inference(rat,[],[s33,s392,s440]) ).
cnf(s445,plain,
spl46_102,
inference(rat,[],[s319,s442]) ).
cnf(s451,plain,
~ spl46_103,
inference(rat,[],[s321,s394,s305,s445]) ).
cnf(s452,plain,
$false,
inference(rat,[],[s323,s395,s391,s451,s445]) ).
fof(f10112,plain,
$false,
inference(avatar_sat_refutation,[],[s452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX047+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n010.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 14:55:18 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running first-order theorem proving
% 0.09/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.00/2.50 % (1982809)Detected formulas, will run a generic FOF schedule.
% 12.00/2.50 % (1982822)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3432243177:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.00/2.50 % (1982818)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=498070992:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.00/2.50 % (1982821)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1982049036:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.00/2.50 % (1982817)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=3845004964:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.00/2.50 % (1982822)Instruction limit reached!
% 12.00/2.50 % (1982822)------------------------------
% 12.00/2.50 % (1982822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.50 % (1982822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.50 % (1982822)CaDiCaL version: 2.1.3
% 12.00/2.50 % (1982822)Termination reason: Instruction limit
% 12.00/2.50 % (1982822)Termination phase: Saturation
% 12.00/2.50 % (1982822)Time elapsed: 0.039 s
% 12.00/2.50 % (1982822)Peak memory usage: 89 MB
% 12.00/2.50 % (1982822)Instructions burned: 121 (million)
% 12.00/2.50 % (1982819)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=1779752195:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.00/2.50 % (1982824)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3212742465:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.00/2.50 % (1982825)dis-21_1_sil=8000:lcm=predicate:random_seed=3530845957: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)
% 12.00/2.50 % (1982821)Instruction limit reached!
% 12.00/2.50 % (1982821)------------------------------
% 12.00/2.50 % (1982821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.50 % (1982821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.50 % (1982821)CaDiCaL version: 2.1.3
% 12.00/2.50 % (1982821)Termination reason: Instruction limit
% 12.00/2.50 % (1982821)Termination phase: Saturation
% 12.00/2.50 % (1982821)Time elapsed: 0.074 s
% 12.00/2.50 % (1982821)Peak memory usage: 89 MB
% 12.00/2.50 % (1982821)Instructions burned: 110 (million)
% 12.00/2.50 % (1982873)lrs+10_1_sil=8000:sp=occurrence:random_seed=623620686:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.00/2.50 % (1982825)Instruction limit reached!
% 12.00/2.50 % (1982825)------------------------------
% 12.00/2.50 % (1982825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.50 % (1982825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.50 % (1982825)CaDiCaL version: 2.1.3
% 12.00/2.50 % (1982825)Termination reason: Instruction limit
% 12.00/2.50 % (1982825)Termination phase: Saturation
% 12.00/2.50 % (1982825)Time elapsed: 0.079 s
% 12.00/2.50 % (1982825)Peak memory usage: 89 MB
% 12.00/2.50 % (1982825)Instructions burned: 129 (million)
% 12.00/2.50 % (1982824)Instruction limit reached!
% 12.00/2.50 % (1982824)------------------------------
% 12.00/2.50 % (1982824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.50 % (1982824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.50 % (1982824)CaDiCaL version: 2.1.3
% 12.00/2.50 % (1982824)Termination reason: Instruction limit
% 12.00/2.50 % (1982824)Termination phase: Saturation
% 12.00/2.50 % (1982824)Time elapsed: 0.104 s
% 12.00/2.50 % (1982824)Peak memory usage: 90 MB
% 12.00/2.50 % (1982824)Instructions burned: 139 (million)
% 12.00/2.50 % (1982873)Instruction limit reached!
% 12.00/2.50 % (1982873)------------------------------
% 12.00/2.50 % (1982873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.00/2.50 % (1982873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.00/2.50 % (1982873)CaDiCaL version: 2.1.3
% 12.00/2.50 % (1982873)Termination reason: Instruction limit
% 12.00/2.50 % (1982873)Termination phase: Saturation
% 12.00/2.50 % (1982873)Time elapsed: 0.106 s
% 12.00/2.50 % (1982873)Peak memory usage: 92 MB
% 12.00/2.50 % (1982873)Instructions burned: 288 (million)
% 14.03/2.73 % (1982899)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1329326890:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 14.03/2.73 % (1982905)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2560427143:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 14.03/2.73 % (1982908)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=2366519695:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 14.03/2.73 % (1982899)Instruction limit reached!
% 14.03/2.73 % (1982899)------------------------------
% 14.03/2.73 % (1982899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1982899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1982899)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1982899)Termination reason: Instruction limit
% 14.03/2.73 % (1982899)Termination phase: Saturation
% 14.03/2.73 % (1982899)Time elapsed: 0.078 s
% 14.03/2.73 % (1982899)Peak memory usage: 91 MB
% 14.03/2.73 % (1982899)Instructions burned: 158 (million)
% 14.03/2.73 % (1982930)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3124272195:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 14.03/2.73 % (1982908)Instruction limit reached!
% 14.03/2.73 % (1982908)------------------------------
% 14.03/2.73 % (1982908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1982908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1982908)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1982908)Termination reason: Instruction limit
% 14.03/2.73 % (1982908)Termination phase: Saturation
% 14.03/2.73 % (1982908)Time elapsed: 0.125 s
% 14.03/2.73 % (1982908)Peak memory usage: 94 MB
% 14.03/2.73 % (1982908)Instructions burned: 249 (million)
% 14.03/2.73 % (1982930)Instruction limit reached!
% 14.03/2.73 % (1982930)------------------------------
% 14.03/2.73 % (1982930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1982930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1982930)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1982930)Termination reason: Instruction limit
% 14.03/2.73 % (1982930)Termination phase: Saturation
% 14.03/2.73 % (1982930)Time elapsed: 0.097 s
% 14.03/2.73 % (1982930)Peak memory usage: 90 MB
% 14.03/2.73 % (1982930)Instructions burned: 296 (million)
% 14.03/2.73 % (1982945)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1657048456:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 14.03/2.73 % (1982905)Instruction limit reached!
% 14.03/2.73 % (1982905)------------------------------
% 14.03/2.73 % (1982905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1982905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1982905)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1982905)Termination reason: Instruction limit
% 14.03/2.73 % (1982905)Termination phase: Saturation
% 14.03/2.73 % (1982905)Time elapsed: 0.228 s
% 14.03/2.73 % (1982905)Peak memory usage: 92 MB
% 14.03/2.73 % (1982905)Instructions burned: 326 (million)
% 14.03/2.73 % (1982953)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=380818798:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 14.03/2.73 % (1982952)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1013076587:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 14.03/2.73 % (1982953)Instruction limit reached!
% 14.03/2.73 % (1982953)------------------------------
% 14.03/2.73 % (1982953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1982953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1982953)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1982953)Termination reason: Instruction limit
% 14.03/2.73 % (1982953)Termination phase: Saturation
% 14.03/2.73 % (1982953)Time elapsed: 0.036 s
% 14.03/2.73 % (1982953)Peak memory usage: 89 MB
% 14.03/2.73 % (1982953)Instructions burned: 128 (million)
% 14.03/2.73 % (1982952)Instruction limit reached!
% 14.03/2.73 % (1982952)------------------------------
% 14.03/2.73 % (1982952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1982952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1982952)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1982952)Termination reason: Instruction limit
% 14.03/2.73 % (1982952)Termination phase: Saturation
% 14.03/2.73 % (1982952)Time elapsed: 0.075 s
% 14.03/2.73 % (1982952)Peak memory usage: 91 MB
% 14.03/2.73 % (1982952)Instructions burned: 113 (million)
% 14.03/2.73 % (1982982)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=96164193:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 14.03/2.73 % (1983000)lrs+10_1_sil=8000:sp=occurrence:random_seed=2919179935:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 14.03/2.73 % (1982982)Instruction limit reached!
% 14.03/2.73 % (1982982)------------------------------
% 14.03/2.73 % (1982982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1982982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1982982)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1982982)Termination reason: Instruction limit
% 14.03/2.73 % (1982982)Termination phase: Saturation
% 14.03/2.73 % (1982982)Time elapsed: 0.063 s
% 14.03/2.73 % (1982982)Peak memory usage: 89 MB
% 14.03/2.73 % (1982982)Instructions burned: 115 (million)
% 14.03/2.73 % (1983001)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1575274923:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 14.03/2.73 % (1983004)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2266795830:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 14.03/2.73 % (1983000)Instruction limit reached!
% 14.03/2.73 % (1983000)------------------------------
% 14.03/2.73 % (1983000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1983000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1983000)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1983000)Termination reason: Instruction limit
% 14.03/2.73 % (1983000)Termination phase: Saturation
% 14.03/2.73 % (1983000)Time elapsed: 0.309 s
% 14.03/2.73 % (1983000)Peak memory usage: 99 MB
% 14.03/2.73 % (1983000)Instructions burned: 908 (million)
% 14.03/2.73 % (1983001)Instruction limit reached!
% 14.03/2.73 % (1983001)------------------------------
% 14.03/2.73 % (1983001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1983001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1983001)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1983001)Termination reason: Instruction limit
% 14.03/2.73 % (1983001)Termination phase: Saturation
% 14.03/2.73 % (1983001)Time elapsed: 0.267 s
% 14.03/2.73 % (1983001)Peak memory usage: 93 MB
% 14.03/2.73 % (1983001)Instructions burned: 437 (million)
% 14.03/2.73 % (1983007)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2651292752:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 14.03/2.73 % (1983007)Instruction limit reached!
% 14.03/2.73 % (1983007)------------------------------
% 14.03/2.73 % (1983007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1983007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1983007)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1983007)Termination reason: Instruction limit
% 14.03/2.73 % (1983007)Termination phase: Saturation
% 14.03/2.73 % (1983007)Time elapsed: 0.036 s
% 14.03/2.73 % (1983007)Peak memory usage: 91 MB
% 14.03/2.73 % (1983007)Instructions burned: 135 (million)
% 14.03/2.73 % (1983008)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3482351491:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 14.03/2.73 % (1983010)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=615504867:st=3:i=13193:sd=3:ss=axioms_2988 on theBenchmark for (2988ds/13193Mi)
% 14.03/2.73 % (1983008)Instruction limit reached!
% 14.03/2.73 % (1983008)------------------------------
% 14.03/2.73 % (1983008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1983008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1983008)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1983008)Termination reason: Instruction limit
% 14.03/2.73 % (1983008)Termination phase: Saturation
% 14.03/2.73 % (1983008)Time elapsed: 0.362 s
% 14.03/2.73 % (1983008)Peak memory usage: 97 MB
% 14.03/2.73 % (1983008)Instructions burned: 592 (million)
% 14.03/2.73 % (1982819)First to succeed.
% 14.03/2.73 % (1982819)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1982809"
% 14.03/2.73 % (1983013)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=639019484:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/125Mi)
% 14.03/2.73 % (1983013)Instruction limit reached!
% 14.03/2.73 % (1983013)------------------------------
% 14.03/2.73 % (1983013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.03/2.73 % (1983013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.03/2.73 % (1983013)CaDiCaL version: 2.1.3
% 14.03/2.73 % (1983013)Termination reason: Instruction limit
% 14.03/2.73 % (1983013)Termination phase: Saturation
% 14.03/2.73 % (1983013)Time elapsed: 0.070 s
% 14.03/2.73 % (1983013)Peak memory usage: 91 MB
% 14.03/2.73 % (1983013)Instructions burned: 126 (million)
% 14.03/2.73 % (1983015)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=661215327:i=134:gtgl=5:slsql=off:gtg=exists_sym_2982 on theBenchmark for (2982ds/134Mi)
% 14.03/2.73 % (1982819)Refutation found. Thanks to Tanya!
% 14.03/2.73 % SZS status Theorem for theBenchmark
% 14.03/2.73 % SZS output start Proof for theBenchmark
% See solution above
% 14.56/2.92 % (1982819)------------------------------
% 14.56/2.92 % (1982819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.56/2.92 % (1982819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.56/2.92 % (1982819)CaDiCaL version: 2.1.3
% 14.56/2.92 % (1982819)Termination reason: Refutation
% 14.56/2.92 % (1982819)Time elapsed: 1.553 s
% 14.56/2.92 % (1982819)Peak memory usage: 145 MB
% 14.56/2.92 % (1982819)Instructions burned: 2468 (million)
% 14.56/2.92 % (1982819)------------------------------
% 14.56/2.92 % (1982819)------------------------------
% 14.56/2.92 % (1982809)Success in time 1.947 s
% 14.56/2.92 % Vampire exiting
%------------------------------------------------------------------------------