%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX042+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 : n005.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 01:45:44 PM UTC 2026
% Result : Theorem 4.59s 1.37s
% Output : Refutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 108 ( 17 unt; 9 def)
% Number of atoms : 375 ( 81 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 428 ( 161 ~; 195 |; 47 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 155 ( 0 sgn 127 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : '0' != s(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id1) ).
fof(f24,axiom,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
<=> ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@<_succeeds'(X2,X3) )
| ? [X4] :
( X0 = '0'
& X1 = s(X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id24) ).
fof(f45,axiom,
! [X0] : '@+'('0',X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(plus:zero)') ).
fof(f46,axiom,
! [X0,X1] :
( nat_succeeds(X0)
=> '@+'(s(X0),X1) = s('@+'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(plus:successor)') ).
fof(f103,axiom,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'(X2,X3)
=> '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3)) ) )
| X0 = '0' )
=> ! [X2,X3] :
( '@<_succeeds'(X2,X3)
=> '@<_succeeds'('@+'(X0,X2),'@+'(X0,X3)) ) )
=> ! [X0] :
( nat_succeeds(X0)
=> ! [X2,X3] :
( '@<_succeeds'(X2,X3)
=> '@<_succeeds'('@+'(X0,X2),'@+'(X0,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
fof(f104,conjecture,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& '@<_succeeds'(X1,X2) )
=> '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:plus:second)') ).
fof(f105,negated_conjecture,
~ ! [X0,X1,X2] :
( ( nat_succeeds(X0)
& '@<_succeeds'(X1,X2) )
=> '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f104]) ).
fof(f115,plain,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'(X2,X3)
=> '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3)) ) )
| X0 = '0' )
=> ! [X4,X5] :
( '@<_succeeds'(X4,X5)
=> '@<_succeeds'('@+'(X0,X4),'@+'(X0,X5)) ) )
=> ! [X6] :
( nat_succeeds(X6)
=> ! [X7,X8] :
( '@<_succeeds'(X7,X8)
=> '@<_succeeds'('@+'(X6,X7),'@+'(X6,X8)) ) ) ),
inference(rectify,[],[f103]) ).
fof(f153,plain,
! [X0,X1] :
( '@+'(s(X0),X1) = s('@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f240,plain,
( ! [X6] :
( ! [X7,X8] :
( '@<_succeeds'('@+'(X6,X7),'@+'(X6,X8))
| ~ '@<_succeeds'(X7,X8) )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( ~ '@<_succeeds'('@+'(X0,X4),'@+'(X0,X5))
& '@<_succeeds'(X4,X5) )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3))
| ~ '@<_succeeds'(X2,X3) ) )
| X0 = '0' ) ) ),
inference(ennf_transformation,[],[f115]) ).
fof(f241,plain,
? [X0,X1,X2] :
( ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
& nat_succeeds(X0)
& '@<_succeeds'(X1,X2) ),
inference(ennf_transformation,[],[f105]) ).
fof(f242,plain,
? [X0,X1,X2] :
( ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
& nat_succeeds(X0)
& '@<_succeeds'(X1,X2) ),
inference(flattening,[],[f241]) ).
fof(f277,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@<_succeeds'(X2,X3) )
| ? [X4] :
( X0 = '0'
& X1 = s(X4) )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f278,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@<_succeeds'(X2,X3) )
| ? [X4] :
( X0 = '0'
& X1 = s(X4) )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(flattening,[],[f277]) ).
fof(f279,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ? [X5,X6] :
( s(X5) = X0
& s(X6) = X1
& '@<_succeeds'(X5,X6) )
| ? [X7] :
( X0 = '0'
& s(X7) = X1 )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(rectify,[],[f278]) ).
fof(f280,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ( s(sK18(X0,X1)) = X0
& s(sK19(X0,X1)) = X1
& '@<_succeeds'(sK18(X0,X1),sK19(X0,X1)) )
| ( X0 = '0'
& s(sK20(X0,X1)) = X1 )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X5,sK18(X0,X1)),skolemize(X6,sK19(X0,X1)),skolemize(X7,sK20(X0,X1))],[f279]) ).
fof(f308,plain,
( ! [X0] :
( ! [X1,X2] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2) )
| ~ nat_succeeds(X0) )
| ? [X3] :
( ? [X4,X5] :
( ~ '@<_succeeds'('@+'(X3,X4),'@+'(X3,X5))
& '@<_succeeds'(X4,X5) )
& ( ? [X6] :
( s(X6) = X3
& nat_succeeds(X6)
& ! [X7,X8] :
( '@<_succeeds'('@+'(X6,X7),'@+'(X6,X8))
| ~ '@<_succeeds'(X7,X8) ) )
| '0' = X3 ) ) ),
inference(rectify,[],[f240]) ).
fof(f309,plain,
( ! [X0] :
( ! [X1,X2] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2) )
| ~ nat_succeeds(X0) )
| ( ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
& '@<_succeeds'(sK37,sK38)
& ( ( sK36 = s(sK39)
& nat_succeeds(sK39)
& ! [X7,X8] :
( '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,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)],[f308]) ).
fof(f310,plain,
( ~ '@<_succeeds'('@+'(sK40,sK41),'@+'(sK40,sK42))
& nat_succeeds(sK40)
& '@<_succeeds'(sK41,sK42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41,sK42]),skolemize(X0,sK40),skolemize(X1,sK41),skolemize(X2,sK42)],[f242]) ).
fof(f311,plain,
! [X0] : '0' != s(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( '@<_succeeds'(X0,X1)
| s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) ),
inference(cnf_transformation,[],[f280]) ).
fof(f429,plain,
! [X0] : '@+'('0',X0) = X0,
inference(cnf_transformation,[],[f45]) ).
fof(f430,plain,
! [X0,X1] :
( '@+'(s(X0),X1) = s('@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f487,plain,
! [X2,X0,X1,X8,X7] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| ~ '@<_succeeds'(X7,X8)
| '0' = sK36 ),
inference(cnf_transformation,[],[f309]) ).
fof(f488,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| nat_succeeds(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f309]) ).
fof(f489,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| sK36 = s(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f309]) ).
fof(f490,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@<_succeeds'(sK37,sK38) ),
inference(cnf_transformation,[],[f309]) ).
fof(f491,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38)) ),
inference(cnf_transformation,[],[f309]) ).
fof(f492,plain,
'@<_succeeds'(sK41,sK42),
inference(cnf_transformation,[],[f310]) ).
fof(f493,plain,
nat_succeeds(sK40),
inference(cnf_transformation,[],[f310]) ).
fof(f494,plain,
~ '@<_succeeds'('@+'(sK40,sK41),'@+'(sK40,sK42)),
inference(cnf_transformation,[],[f310]) ).
fof(f521,plain,
! [X2,X3,X1] :
( '@<_succeeds'(s(X2),X1)
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) ),
inference(equality_resolution,[],[f388]) ).
fof(f522,plain,
! [X2,X3] :
( '@<_succeeds'(s(X2),s(X3))
| ~ '@<_succeeds'(X2,X3) ),
inference(equality_resolution,[],[f521]) ).
fof(f540,plain,
! [X8,X7] :
( '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| ~ '@<_succeeds'(X7,X8)
| sP44(X7) ),
inference(cnf_transformation,[],[f540_D]) ).
fof(f540_D,definition,
! [X7] :
( ! [X8] :
( '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| ~ '@<_succeeds'(X7,X8) )
<=> ~ sP44(X7) ),
introduced(definition,[new_symbols(definition,[sP44])],[general_splitting_component_introduction]) ).
fof(f541,plain,
! [X2,X0,X1,X7] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '0' = sK36
| ~ sP44(X7) ),
inference(general_splitting,[],[f487,f540_D]) ).
fof(f542,plain,
! [X7] :
( ~ sP44(X7)
| sP45 ),
inference(cnf_transformation,[],[f542_D]) ).
fof(f542_D,definition,
( ! [X7] : ~ sP44(X7)
<=> ~ sP45 ),
introduced(definition,[new_symbols(definition,[sP45])],[general_splitting_component_introduction]) ).
fof(f543,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '0' = sK36
| ~ sP45 ),
inference(general_splitting,[],[f541,f542_D]) ).
fof(f545,definition,
( spl46_1
<=> '@<_succeeds'('@+'(sK40,sK41),'@+'(sK40,sK42)) ),
introduced(definition,[new_symbols(definition,[spl46_1])],[avatar_definition]) ).
fof(f547,plain,
( ~ '@<_succeeds'('@+'(sK40,sK41),'@+'(sK40,sK42))
| spl46_1 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f548,plain,
~ spl46_1,
inference(avatar_split_clause,[],[f494,f545]) ).
fof(f549,plain,
( ~ '@<_succeeds'(sK41,sK42)
| ~ nat_succeeds(sK40)
| nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(resolution,[],[f547,f488]) ).
fof(f550,plain,
( ~ '@<_succeeds'(sK41,sK42)
| ~ nat_succeeds(sK40)
| sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(resolution,[],[f547,f489]) ).
fof(f551,plain,
( ~ '@<_succeeds'(sK41,sK42)
| ~ nat_succeeds(sK40)
| '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(resolution,[],[f547,f490]) ).
fof(f552,plain,
( ~ '@<_succeeds'(sK41,sK42)
| ~ nat_succeeds(sK40)
| ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
| spl46_1 ),
inference(resolution,[],[f547,f491]) ).
fof(f553,plain,
( ~ '@<_succeeds'(sK41,sK42)
| ~ nat_succeeds(sK40)
| '0' = sK36
| ~ sP45
| spl46_1 ),
inference(resolution,[],[f547,f543]) ).
fof(f568,plain,
( ~ nat_succeeds(sK40)
| '0' = sK36
| ~ sP45
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f553,f492]) ).
fof(f569,plain,
( ~ nat_succeeds(sK40)
| ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f552,f492]) ).
fof(f570,plain,
( ~ nat_succeeds(sK40)
| '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f551,f492]) ).
fof(f571,plain,
( ~ nat_succeeds(sK40)
| sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f550,f492]) ).
fof(f572,plain,
( ~ nat_succeeds(sK40)
| nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f549,f492]) ).
fof(f573,plain,
( '0' = sK36
| ~ sP45
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f568,f493]) ).
fof(f574,plain,
( ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f569,f493]) ).
fof(f575,plain,
( '@<_succeeds'(sK37,sK38)
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f570,f493]) ).
fof(f576,plain,
( sK36 = s(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f571,f493]) ).
fof(f577,plain,
( nat_succeeds(sK39)
| '0' = sK36
| spl46_1 ),
inference(forward_subsumption_resolution,[],[f572,f493]) ).
fof(f609,definition,
( spl46_3
<=> '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38)) ),
introduced(definition,[new_symbols(definition,[spl46_3])],[avatar_definition]) ).
fof(f611,plain,
( ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
| spl46_3 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f612,plain,
( ~ spl46_3
| spl46_1 ),
inference(avatar_split_clause,[],[f574,f545,f609]) ).
fof(f645,definition,
( spl46_4
<=> '@<_succeeds'(sK37,sK38) ),
introduced(definition,[new_symbols(definition,[spl46_4])],[avatar_definition]) ).
fof(f647,plain,
( '@<_succeeds'(sK37,sK38)
| ~ spl46_4 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f648,plain,
( spl46_4
| spl46_1 ),
inference(avatar_split_clause,[],[f575,f545,f645]) ).
fof(f762,definition,
( spl46_6
<=> '0' = sK36 ),
introduced(definition,[new_symbols(definition,[spl46_6])],[avatar_definition]) ).
fof(f764,plain,
( '0' = sK36
| ~ spl46_6 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f766,definition,
( spl46_7
<=> sK36 = s(sK39) ),
introduced(definition,[new_symbols(definition,[spl46_7])],[avatar_definition]) ).
fof(f768,plain,
( sK36 = s(sK39)
| ~ spl46_7 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f769,plain,
( spl46_6
| spl46_7
| spl46_1 ),
inference(avatar_split_clause,[],[f576,f545,f766,f762]) ).
fof(f770,plain,
( '0' != sK36
| ~ spl46_7 ),
inference(superposition,[],[f311,f768]) ).
fof(f775,plain,
( ! [X0] :
( s('@+'(sK39,X0)) = '@+'(sK36,X0)
| ~ nat_succeeds(sK39) )
| ~ spl46_7 ),
inference(superposition,[],[f430,f768]) ).
fof(f810,plain,
( nat_succeeds(sK39)
| spl46_1
| ~ spl46_7 ),
inference(backward_subsumption_resolution,[],[f577,f770]) ).
fof(f811,plain,
( ~ sP45
| spl46_1
| ~ spl46_7 ),
inference(backward_subsumption_resolution,[],[f573,f770]) ).
fof(f815,plain,
( ! [X0] : s('@+'(sK39,X0)) = '@+'(sK36,X0)
| spl46_1
| ~ spl46_7 ),
inference(backward_subsumption_resolution,[],[f775,f810]) ).
fof(f822,plain,
( ! [X7] : ~ sP44(X7)
| spl46_1
| ~ spl46_7 ),
inference(backward_subsumption_resolution,[],[f542,f811]) ).
fof(f823,plain,
( ! [X8,X7] :
( '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| ~ '@<_succeeds'(X7,X8) )
| spl46_1
| ~ spl46_7 ),
inference(backward_subsumption_resolution,[],[f540,f822]) ).
fof(f827,definition,
( spl46_8
<=> ! [X8,X7] :
( '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| ~ '@<_succeeds'(X7,X8) ) ),
introduced(definition,[new_symbols(definition,[spl46_8])],[avatar_definition]) ).
fof(f828,plain,
( ! [X8,X7] :
( '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| ~ '@<_succeeds'(X7,X8) )
| ~ spl46_8 ),
inference(avatar_component_clause,[],[f827]) ).
fof(f829,plain,
( spl46_8
| spl46_1
| ~ spl46_7 ),
inference(avatar_split_clause,[],[f823,f766,f545,f827]) ).
fof(f850,plain,
( ! [X0,X1] :
( ~ '@<_succeeds'(X0,X1)
| '@<_succeeds'(s('@+'(sK39,X0)),s('@+'(sK39,X1))) )
| ~ spl46_8 ),
inference(resolution,[],[f828,f522]) ).
fof(f876,plain,
( ! [X0,X1] :
( '@<_succeeds'(s('@+'(sK39,X0)),'@+'(sK36,X1))
| ~ '@<_succeeds'(X0,X1) )
| spl46_1
| ~ spl46_7
| ~ spl46_8 ),
inference(forward_demodulation,[],[f850,f815]) ).
fof(f880,plain,
( ! [X0,X1] :
( '@<_succeeds'('@+'(sK36,X0),'@+'(sK36,X1))
| ~ '@<_succeeds'(X0,X1) )
| spl46_1
| ~ spl46_7
| ~ spl46_8 ),
inference(forward_demodulation,[],[f876,f815]) ).
fof(f924,plain,
( ~ '@<_succeeds'('@+'('0',sK37),'@+'('0',sK38))
| spl46_3
| ~ spl46_6 ),
inference(superposition,[],[f611,f764]) ).
fof(f927,plain,
( ~ '@<_succeeds'('@+'('0',sK37),sK38)
| spl46_3
| ~ spl46_6 ),
inference(forward_demodulation,[],[f924,f429]) ).
fof(f929,plain,
( ~ '@<_succeeds'(sK37,sK38)
| spl46_3
| ~ spl46_6 ),
inference(forward_demodulation,[],[f927,f429]) ).
fof(f931,plain,
( $false
| spl46_3
| ~ spl46_4
| ~ spl46_6 ),
inference(forward_subsumption_resolution,[],[f929,f647]) ).
fof(f932,plain,
( spl46_3
| ~ spl46_4
| ~ spl46_6 ),
inference(avatar_contradiction_clause,[],[f931]) ).
fof(f981,definition,
( spl46_11
<=> ! [X0,X1] :
( '@<_succeeds'('@+'(sK36,X0),'@+'(sK36,X1))
| ~ '@<_succeeds'(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl46_11])],[avatar_definition]) ).
fof(f982,plain,
( ! [X0,X1] :
( '@<_succeeds'('@+'(sK36,X0),'@+'(sK36,X1))
| ~ '@<_succeeds'(X0,X1) )
| ~ spl46_11 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f983,plain,
( spl46_11
| spl46_1
| ~ spl46_7
| ~ spl46_8 ),
inference(avatar_split_clause,[],[f880,f827,f766,f545,f981]) ).
fof(f984,plain,
( ~ '@<_succeeds'(sK37,sK38)
| spl46_3
| ~ spl46_11 ),
inference(resolution,[],[f982,f611]) ).
fof(f1033,plain,
( $false
| spl46_3
| ~ spl46_4
| ~ spl46_11 ),
inference(forward_subsumption_resolution,[],[f984,f647]) ).
fof(f1034,plain,
( spl46_3
| ~ spl46_4
| ~ spl46_11 ),
inference(avatar_contradiction_clause,[],[f1033]) ).
cnf(s1,plain,
~ spl46_1,
inference(sat_conversion,[],[f548]) ).
cnf(s3,plain,
( spl46_1
| ~ spl46_3 ),
inference(sat_conversion,[],[f612]) ).
cnf(s4,plain,
( spl46_1
| spl46_4 ),
inference(sat_conversion,[],[f648]) ).
cnf(s6,plain,
( spl46_1
| spl46_6
| spl46_7 ),
inference(sat_conversion,[],[f769]) ).
cnf(s7,plain,
( spl46_1
| ~ spl46_7
| spl46_8 ),
inference(sat_conversion,[],[f829]) ).
cnf(s10,plain,
( spl46_3
| ~ spl46_4
| ~ spl46_6 ),
inference(sat_conversion,[],[f932]) ).
cnf(s12,plain,
( spl46_1
| ~ spl46_7
| ~ spl46_8
| spl46_11 ),
inference(sat_conversion,[],[f983]) ).
cnf(s13,plain,
( spl46_3
| ~ spl46_4
| ~ spl46_11 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s14,plain,
spl46_4,
inference(rat,[],[s4,s1]) ).
cnf(s15,plain,
~ spl46_3,
inference(rat,[],[s3,s1]) ).
cnf(s16,plain,
~ spl46_11,
inference(rat,[],[s13,s14,s15]) ).
cnf(s17,plain,
~ spl46_6,
inference(rat,[],[s10,s14,s15]) ).
cnf(s18,plain,
spl46_7,
inference(rat,[],[s6,s1,s17]) ).
cnf(s19,plain,
~ spl46_8,
inference(rat,[],[s12,s16,s1,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s7,s1,s19,s18]) ).
fof(f1037,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX042+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n005.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 14:55:47 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 4.59/1.37 % (842353)Detected formulas, will run a generic FOF schedule.
% 4.59/1.37 % (842360)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=586196999:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.59/1.37 % (842358)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=1237547812:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.59/1.37 % (842361)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=544987453:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.59/1.37 % (842362)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3644190015:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.59/1.37 % (842364)dis-21_1_sil=8000:lcm=predicate:random_seed=90770350: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)
% 4.59/1.37 % (842363)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2149946117:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.59/1.37 % (842359)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=2069439649:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.59/1.37 % (842362)Instruction limit reached!
% 4.59/1.37 % (842362)------------------------------
% 4.59/1.37 % (842362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842362)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842362)Termination reason: Instruction limit
% 4.59/1.37 % (842362)Termination phase: Saturation
% 4.59/1.37 % (842362)Time elapsed: 0.070 s
% 4.59/1.37 % (842362)Peak memory usage: 88 MB
% 4.59/1.37 % (842362)Instructions burned: 120 (million)
% 4.59/1.37 % (842364)Instruction limit reached!
% 4.59/1.37 % (842364)------------------------------
% 4.59/1.37 % (842364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842364)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842364)Termination reason: Instruction limit
% 4.59/1.37 % (842364)Termination phase: Saturation
% 4.59/1.37 % (842364)Time elapsed: 0.075 s
% 4.59/1.37 % (842364)Peak memory usage: 89 MB
% 4.59/1.37 % (842364)Instructions burned: 130 (million)
% 4.59/1.37 % (842361)Instruction limit reached!
% 4.59/1.37 % (842361)------------------------------
% 4.59/1.37 % (842361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842361)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842361)Termination reason: Instruction limit
% 4.59/1.37 % (842361)Termination phase: Saturation
% 4.59/1.37 % (842361)Time elapsed: 0.076 s
% 4.59/1.37 % (842361)Peak memory usage: 89 MB
% 4.59/1.37 % (842361)Instructions burned: 110 (million)
% 4.59/1.37 % (842363)Instruction limit reached!
% 4.59/1.37 % (842363)------------------------------
% 4.59/1.37 % (842363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842363)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842363)Termination reason: Instruction limit
% 4.59/1.37 % (842363)Termination phase: Saturation
% 4.59/1.37 % (842363)Time elapsed: 0.097 s
% 4.59/1.37 % (842363)Peak memory usage: 90 MB
% 4.59/1.37 % (842363)Instructions burned: 139 (million)
% 4.59/1.37 % (842372)lrs+10_1_sil=8000:sp=occurrence:random_seed=2476226759:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.59/1.37 % (842373)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1211358413:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.59/1.37 % (842374)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2763698362:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.59/1.37 % (842375)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=1589103014:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.59/1.37 % (842373)Instruction limit reached!
% 4.59/1.37 % (842373)------------------------------
% 4.59/1.37 % (842373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842373)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842373)Termination reason: Instruction limit
% 4.59/1.37 % (842373)Termination phase: Saturation
% 4.59/1.37 % (842373)Time elapsed: 0.075 s
% 4.59/1.37 % (842373)Peak memory usage: 91 MB
% 4.59/1.37 % (842373)Instructions burned: 158 (million)
% 4.59/1.37 % (842360)First to succeed.
% 4.59/1.37 % (842360)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-842353"
% 4.59/1.37 % (842375)Instruction limit reached!
% 4.59/1.37 % (842375)------------------------------
% 4.59/1.37 % (842375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842375)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842375)Termination reason: Instruction limit
% 4.59/1.37 % (842375)Termination phase: Saturation
% 4.59/1.37 % (842375)Time elapsed: 0.131 s
% 4.59/1.37 % (842375)Peak memory usage: 93 MB
% 4.59/1.37 % (842375)Instructions burned: 249 (million)
% 4.59/1.37 % (842372)Instruction limit reached!
% 4.59/1.37 % (842372)------------------------------
% 4.59/1.37 % (842372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842372)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842372)Termination reason: Instruction limit
% 4.59/1.37 % (842372)Termination phase: Saturation
% 4.59/1.37 % (842372)Time elapsed: 0.181 s
% 4.59/1.37 % (842372)Peak memory usage: 92 MB
% 4.59/1.37 % (842372)Instructions burned: 285 (million)
% 4.59/1.37 % (842374)Instruction limit reached!
% 4.59/1.37 % (842374)------------------------------
% 4.59/1.37 % (842374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.37 % (842374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.37 % (842374)CaDiCaL version: 2.1.3
% 4.59/1.37 % (842374)Termination reason: Instruction limit
% 4.59/1.37 % (842374)Termination phase: Saturation
% 4.59/1.37 % (842374)Time elapsed: 0.225 s
% 4.59/1.37 % (842374)Peak memory usage: 92 MB
% 4.59/1.37 % (842374)Instructions burned: 325 (million)
% 4.59/1.37 % (842380)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=352215437:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.59/1.37 % (842360)Refutation found. Thanks to Tanya!
% 4.59/1.37 % SZS status Theorem for theBenchmark
% 4.59/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 5.43/1.53 % (842360)------------------------------
% 5.43/1.53 % (842360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.53 % (842360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.53 % (842360)CaDiCaL version: 2.1.3
% 5.43/1.53 % (842360)Termination reason: Refutation
% 5.43/1.53 % (842360)Time elapsed: 0.387 s
% 5.43/1.53 % (842360)Peak memory usage: 131 MB
% 5.43/1.53 % (842360)Instructions burned: 1029 (million)
% 5.43/1.53 % (842360)------------------------------
% 5.43/1.53 % (842360)------------------------------
% 5.43/1.53 % (842353)Success in time 0.681 s
% 5.43/1.53 % Vampire exiting
%------------------------------------------------------------------------------