%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX044+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 15.36s 2.88s
% Output : Refutation 16.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 39
% Syntax : Number of formulae : 266 ( 32 unt; 19 def)
% Number of atoms : 906 ( 142 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1142 ( 502 ~; 535 |; 56 &)
% ( 20 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 20 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 266 ( 0 sgn 238 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : '0' != s(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id1) ).
fof(f2,axiom,
! [X0,X1] :
( s(X0) = s(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id2) ).
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(f49,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@+'(X0,'0') = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(plus:zero)') ).
fof(f50,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@+'(X0,s(X1)) = '@+'(s(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(plus:successor)') ).
fof(f51,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@+'(X0,X1) = '@+'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(plus:commutative)') ).
fof(f73,axiom,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
=> nat_succeeds(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:types)') ).
fof(f75,axiom,
! [X0,X1,X2] :
( ( '@<_succeeds'(X0,X1)
& '@<_succeeds'(X1,s(X2)) )
=> '@<_succeeds'(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:transitive:successor)') ).
fof(f76,axiom,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
=> '@<_succeeds'(X0,s(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:weakening)') ).
fof(f79,axiom,
! [X0] :
( nat_succeeds(X0)
=> ~ '@<_succeeds'(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(less:strictness)') ).
fof(f80,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@<_succeeds'(X0,s(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:one)') ).
fof(f81,axiom,
! [X0,X1] :
( ( nat_succeeds(X1)
& '@<_succeeds'(X0,s(X1)) )
=> ( '@<_succeeds'(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:axiom:successor)') ).
fof(f82,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> ( '@<_succeeds'(X0,X1)
| X0 = X1
| '@<_succeeds'(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(less:totality)') ).
fof(f104,axiom,
! [X0,X1] :
( nat_succeeds(X0)
=> '@<_succeeds'(X0,'@+'(X0,s(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(less:plus:second)') ).
fof(f105,axiom,
! [X0,X1,X2] :
( ( '@<_succeeds'(X0,X1)
& nat_succeeds(X1)
& nat_succeeds(X2) )
=> '@<_succeeds'('@+'(X0,X2),'@+'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:plus:first)') ).
fof(f106,axiom,
! [X0,X1] :
( ( '@<_succeeds'('0',X1)
& nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@<_succeeds'(X0,'@+'(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(less:plus:first)') ).
fof(f111,axiom,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3))
=> '@<_succeeds'(X2,X3) ) )
| X0 = '0' )
=> ! [X2,X3] :
( '@<_succeeds'('@+'(X0,X2),'@+'(X0,X3))
=> '@<_succeeds'(X2,X3) ) )
=> ! [X0] :
( nat_succeeds(X0)
=> ! [X2,X3] :
( '@<_succeeds'('@+'(X0,X2),'@+'(X0,X3))
=> '@<_succeeds'(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
fof(f112,conjecture,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) )
=> '@<_succeeds'(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(less:plus:inverse)') ).
fof(f113,negated_conjecture,
~ ! [X0,X1,X2] :
( ( nat_succeeds(X0)
& '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) )
=> '@<_succeeds'(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f112]) ).
fof(f123,plain,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3))
=> '@<_succeeds'(X2,X3) ) )
| X0 = '0' )
=> ! [X4,X5] :
( '@<_succeeds'('@+'(X0,X4),'@+'(X0,X5))
=> '@<_succeeds'(X4,X5) ) )
=> ! [X6] :
( nat_succeeds(X6)
=> ! [X7,X8] :
( '@<_succeeds'('@+'(X6,X7),'@+'(X6,X8))
=> '@<_succeeds'(X7,X8) ) ) ),
inference(rectify,[],[f111]) ).
fof(f124,plain,
! [X0,X1] :
( X0 = X1
| s(X0) != s(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f161,plain,
! [X0,X1] :
( '@+'(s(X0),X1) = s('@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f166,plain,
! [X0] :
( '@+'(X0,'0') = X0
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f167,plain,
! [X0,X1] :
( '@+'(X0,s(X1)) = '@+'(s(X0),X1)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f168,plain,
! [X0,X1] :
( '@+'(X0,s(X1)) = '@+'(s(X0),X1)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f167]) ).
fof(f169,plain,
! [X0,X1] :
( '@+'(X0,X1) = '@+'(X1,X0)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f170,plain,
! [X0,X1] :
( '@+'(X0,X1) = '@+'(X1,X0)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f169]) ).
fof(f205,plain,
! [X0,X1] :
( nat_succeeds(X0)
| ~ '@<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f207,plain,
! [X0,X1,X2] :
( '@<_succeeds'(X0,X2)
| ~ '@<_succeeds'(X0,X1)
| ~ '@<_succeeds'(X1,s(X2)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f208,plain,
! [X0,X1,X2] :
( '@<_succeeds'(X0,X2)
| ~ '@<_succeeds'(X0,X1)
| ~ '@<_succeeds'(X1,s(X2)) ),
inference(flattening,[],[f207]) ).
fof(f209,plain,
! [X0,X1] :
( '@<_succeeds'(X0,s(X1))
| ~ '@<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f76]) ).
fof(f213,plain,
! [X0] :
( ~ '@<_succeeds'(X0,X0)
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f214,plain,
! [X0] :
( '@<_succeeds'(X0,s(X0))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f215,plain,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
| X0 = X1
| ~ nat_succeeds(X1)
| ~ '@<_succeeds'(X0,s(X1)) ),
inference(ennf_transformation,[],[f81]) ).
fof(f216,plain,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
| X0 = X1
| ~ nat_succeeds(X1)
| ~ '@<_succeeds'(X0,s(X1)) ),
inference(flattening,[],[f215]) ).
fof(f217,plain,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
| X0 = X1
| '@<_succeeds'(X1,X0)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f82]) ).
fof(f218,plain,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
| X0 = X1
| '@<_succeeds'(X1,X0)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f217]) ).
fof(f250,plain,
! [X0,X1] :
( '@<_succeeds'(X0,'@+'(X0,s(X1)))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f104]) ).
fof(f251,plain,
! [X0,X1,X2] :
( '@<_succeeds'('@+'(X0,X2),'@+'(X1,X2))
| ~ '@<_succeeds'(X0,X1)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X2) ),
inference(ennf_transformation,[],[f105]) ).
fof(f252,plain,
! [X0,X1,X2] :
( '@<_succeeds'('@+'(X0,X2),'@+'(X1,X2))
| ~ '@<_succeeds'(X0,X1)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X2) ),
inference(flattening,[],[f251]) ).
fof(f253,plain,
! [X0,X1] :
( '@<_succeeds'(X0,'@+'(X1,X0))
| ~ '@<_succeeds'('0',X1)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f106]) ).
fof(f254,plain,
! [X0,X1] :
( '@<_succeeds'(X0,'@+'(X1,X0))
| ~ '@<_succeeds'('0',X1)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f253]) ).
fof(f262,plain,
( ! [X6] :
( ! [X7,X8] :
( '@<_succeeds'(X7,X8)
| ~ '@<_succeeds'('@+'(X6,X7),'@+'(X6,X8)) )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( ~ '@<_succeeds'(X4,X5)
& '@<_succeeds'('@+'(X0,X4),'@+'(X0,X5)) )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@<_succeeds'(X2,X3)
| ~ '@<_succeeds'('@+'(X1,X2),'@+'(X1,X3)) ) )
| X0 = '0' ) ) ),
inference(ennf_transformation,[],[f123]) ).
fof(f263,plain,
? [X0,X1,X2] :
( ~ '@<_succeeds'(X1,X2)
& nat_succeeds(X0)
& '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(ennf_transformation,[],[f113]) ).
fof(f264,plain,
? [X0,X1,X2] :
( ~ '@<_succeeds'(X1,X2)
& nat_succeeds(X0)
& '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(flattening,[],[f263]) ).
fof(f299,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(f300,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,[],[f299]) ).
fof(f301,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,[],[f300]) ).
fof(f302,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))],[f301]) ).
fof(f330,plain,
( ! [X0] :
( ! [X1,X2] :
( '@<_succeeds'(X1,X2)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) )
| ~ nat_succeeds(X0) )
| ? [X3] :
( ? [X4,X5] :
( ~ '@<_succeeds'(X4,X5)
& '@<_succeeds'('@+'(X3,X4),'@+'(X3,X5)) )
& ( ? [X6] :
( s(X6) = X3
& nat_succeeds(X6)
& ! [X7,X8] :
( '@<_succeeds'(X7,X8)
| ~ '@<_succeeds'('@+'(X6,X7),'@+'(X6,X8)) ) )
| '0' = X3 ) ) ),
inference(rectify,[],[f262]) ).
fof(f331,plain,
( ! [X0] :
( ! [X1,X2] :
( '@<_succeeds'(X1,X2)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) )
| ~ nat_succeeds(X0) )
| ( ~ '@<_succeeds'(sK37,sK38)
& '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
& ( ( sK36 = s(sK39)
& nat_succeeds(sK39)
& ! [X7,X8] :
( '@<_succeeds'(X7,X8)
| ~ '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,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)],[f330]) ).
fof(f332,plain,
( ~ '@<_succeeds'(sK41,sK42)
& nat_succeeds(sK40)
& '@<_succeeds'('@+'(sK40,sK41),'@+'(sK40,sK42)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41,sK42]),skolemize(X0,sK40),skolemize(X1,sK41),skolemize(X2,sK42)],[f264]) ).
fof(f333,plain,
! [X0] : '0' != s(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f334,plain,
! [X0,X1] :
( s(X0) != s(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f404,plain,
! [X0,X1] :
( '@<_succeeds'(sK18(X0,X1),sK19(X0,X1))
| '0' = X0
| ~ '@<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f302]) ).
fof(f408,plain,
! [X0,X1] :
( ~ '@<_succeeds'(X0,X1)
| '0' = X0
| s(sK18(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f302]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( '@<_succeeds'(X0,X1)
| s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) ),
inference(cnf_transformation,[],[f302]) ).
fof(f451,plain,
! [X0] : '@+'('0',X0) = X0,
inference(cnf_transformation,[],[f45]) ).
fof(f452,plain,
! [X0,X1] :
( ~ nat_succeeds(X0)
| '@+'(s(X0),X1) = s('@+'(X0,X1)) ),
inference(cnf_transformation,[],[f161]) ).
fof(f455,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '@+'(X0,'0') = X0 ),
inference(cnf_transformation,[],[f166]) ).
fof(f456,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| '@+'(s(X0),X1) = '@+'(X0,s(X1)) ),
inference(cnf_transformation,[],[f168]) ).
fof(f457,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| '@+'(X0,X1) = '@+'(X1,X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f479,plain,
! [X0,X1] :
( ~ '@<_succeeds'(X0,X1)
| nat_succeeds(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f481,plain,
! [X2,X0,X1] :
( ~ '@<_succeeds'(X1,s(X2))
| ~ '@<_succeeds'(X0,X1)
| '@<_succeeds'(X0,X2) ),
inference(cnf_transformation,[],[f208]) ).
fof(f482,plain,
! [X0,X1] :
( '@<_succeeds'(X0,s(X1))
| ~ '@<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
fof(f485,plain,
! [X0] :
( ~ nat_succeeds(X0)
| ~ '@<_succeeds'(X0,X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f486,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,s(X0)) ),
inference(cnf_transformation,[],[f214]) ).
fof(f487,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| X0 = X1
| '@<_succeeds'(X0,X1)
| ~ '@<_succeeds'(X0,s(X1)) ),
inference(cnf_transformation,[],[f216]) ).
fof(f488,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| X0 = X1
| '@<_succeeds'(X1,X0)
| ~ nat_succeeds(X0)
| '@<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f218]) ).
fof(f510,plain,
! [X0,X1] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,'@+'(X0,s(X1))) ),
inference(cnf_transformation,[],[f250]) ).
fof(f511,plain,
! [X2,X0,X1] :
( '@<_succeeds'('@+'(X0,X2),'@+'(X1,X2))
| ~ '@<_succeeds'(X0,X1)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X2) ),
inference(cnf_transformation,[],[f252]) ).
fof(f512,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ '@<_succeeds'('0',X1)
| ~ nat_succeeds(X0)
| '@<_succeeds'(X0,'@+'(X1,X0)) ),
inference(cnf_transformation,[],[f254]) ).
fof(f517,plain,
! [X2,X0,X1,X8,X7] :
( '@<_succeeds'(X1,X2)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ nat_succeeds(X0)
| '@<_succeeds'(X7,X8)
| ~ '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| '0' = sK36 ),
inference(cnf_transformation,[],[f331]) ).
fof(f518,plain,
! [X2,X0,X1] :
( '@<_succeeds'(X1,X2)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ nat_succeeds(X0)
| nat_succeeds(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f331]) ).
fof(f519,plain,
! [X2,X0,X1] :
( '@<_succeeds'(X1,X2)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ nat_succeeds(X0)
| sK36 = s(sK39)
| '0' = sK36 ),
inference(cnf_transformation,[],[f331]) ).
fof(f520,plain,
! [X2,X0,X1] :
( '@<_succeeds'(X1,X2)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ nat_succeeds(X0)
| '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f521,plain,
! [X2,X0,X1] :
( '@<_succeeds'(X1,X2)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'(sK37,sK38) ),
inference(cnf_transformation,[],[f331]) ).
fof(f522,plain,
'@<_succeeds'('@+'(sK40,sK41),'@+'(sK40,sK42)),
inference(cnf_transformation,[],[f332]) ).
fof(f523,plain,
nat_succeeds(sK40),
inference(cnf_transformation,[],[f332]) ).
fof(f524,plain,
~ '@<_succeeds'(sK41,sK42),
inference(cnf_transformation,[],[f332]) ).
fof(f551,plain,
! [X2,X3,X1] :
( '@<_succeeds'(s(X2),X1)
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) ),
inference(equality_resolution,[],[f410]) ).
fof(f552,plain,
! [X2,X3] :
( '@<_succeeds'(s(X2),s(X3))
| ~ '@<_succeeds'(X2,X3) ),
inference(equality_resolution,[],[f551]) ).
fof(f569,definition,
( spl43_1
<=> '0' = sK36 ),
introduced(definition,[new_symbols(definition,[spl43_1])],[avatar_definition]) ).
fof(f570,plain,
( '0' = sK36
| ~ spl43_1 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f572,definition,
( spl43_2
<=> ! [X8,X7] :
( '@<_succeeds'(X7,X8)
| ~ '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8)) ) ),
introduced(definition,[new_symbols(definition,[spl43_2])],[avatar_definition]) ).
fof(f573,plain,
( ! [X8,X7] :
( ~ '@<_succeeds'('@+'(sK39,X7),'@+'(sK39,X8))
| '@<_succeeds'(X7,X8) )
| ~ spl43_2 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f575,definition,
( spl43_3
<=> ! [X2,X0,X1] :
( '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ) ),
introduced(definition,[new_symbols(definition,[spl43_3])],[avatar_definition]) ).
fof(f576,plain,
( ! [X2,X0,X1] :
( ~ '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2))
| ~ nat_succeeds(X0)
| '@<_succeeds'(X1,X2) )
| ~ spl43_3 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f577,plain,
( spl43_1
| spl43_2
| spl43_3 ),
inference(avatar_split_clause,[],[f517,f575,f572,f569]) ).
fof(f579,definition,
( spl43_4
<=> nat_succeeds(sK39) ),
introduced(definition,[new_symbols(definition,[spl43_4])],[avatar_definition]) ).
fof(f580,plain,
( nat_succeeds(sK39)
| ~ spl43_4 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f581,plain,
( spl43_1
| spl43_4
| spl43_3 ),
inference(avatar_split_clause,[],[f518,f575,f579,f569]) ).
fof(f583,definition,
( spl43_5
<=> sK36 = s(sK39) ),
introduced(definition,[new_symbols(definition,[spl43_5])],[avatar_definition]) ).
fof(f584,plain,
( sK36 = s(sK39)
| ~ spl43_5 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f585,plain,
( spl43_1
| spl43_5
| spl43_3 ),
inference(avatar_split_clause,[],[f519,f575,f583,f569]) ).
fof(f587,definition,
( spl43_6
<=> '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38)) ),
introduced(definition,[new_symbols(definition,[spl43_6])],[avatar_definition]) ).
fof(f588,plain,
( '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
| ~ spl43_6 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f589,plain,
( spl43_6
| spl43_3 ),
inference(avatar_split_clause,[],[f520,f575,f587]) ).
fof(f591,definition,
( spl43_7
<=> '@<_succeeds'(sK37,sK38) ),
introduced(definition,[new_symbols(definition,[spl43_7])],[avatar_definition]) ).
fof(f592,plain,
( ~ '@<_succeeds'(sK37,sK38)
| spl43_7 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f593,plain,
( ~ spl43_7
| spl43_3 ),
inference(avatar_split_clause,[],[f521,f575,f591]) ).
fof(f597,plain,
( ~ nat_succeeds(sK40)
| '@<_succeeds'(sK41,sK42)
| ~ spl43_3 ),
inference(resolution,[],[f576,f522]) ).
fof(f599,plain,
( '@<_succeeds'(sK41,sK42)
| ~ spl43_3 ),
inference(forward_subsumption_resolution,[],[f597,f523]) ).
fof(f600,plain,
( $false
| ~ spl43_3 ),
inference(forward_subsumption_resolution,[],[f599,f524]) ).
fof(f601,plain,
~ spl43_3,
inference(avatar_contradiction_clause,[],[f600]) ).
fof(f602,plain,
! [X0] : '@+'(s(sK40),X0) = s('@+'(sK40,X0)),
inference(resolution,[],[f452,f523]) ).
fof(f636,plain,
( ! [X0] : '@+'(sK36,X0) = X0
| ~ spl43_1 ),
inference(superposition,[],[f451,f570]) ).
fof(f647,plain,
( '@<_succeeds'(sK37,'@+'(sK36,sK38))
| ~ spl43_1
| ~ spl43_6 ),
inference(superposition,[],[f588,f636]) ).
fof(f658,plain,
( '@<_succeeds'(sK37,sK38)
| ~ spl43_1
| ~ spl43_6 ),
inference(forward_demodulation,[],[f647,f636]) ).
fof(f661,plain,
( $false
| ~ spl43_1
| ~ spl43_6
| spl43_7 ),
inference(forward_subsumption_resolution,[],[f658,f592]) ).
fof(f662,plain,
( ~ spl43_1
| ~ spl43_6
| spl43_7 ),
inference(avatar_contradiction_clause,[],[f661]) ).
fof(f679,plain,
( ! [X0] :
( ~ '@<_succeeds'('0',sK39)
| ~ nat_succeeds(X0)
| '@<_succeeds'(X0,'@+'(sK39,X0)) )
| ~ spl43_4 ),
inference(resolution,[],[f580,f512]) ).
fof(f680,plain,
( ! [X0] : '@+'(s(sK39),X0) = s('@+'(sK39,X0))
| ~ spl43_4 ),
inference(resolution,[],[f580,f452]) ).
fof(f681,plain,
( ! [X0] : '@+'(sK36,X0) = s('@+'(sK39,X0))
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f680,f584]) ).
fof(f683,definition,
( spl43_16
<=> ! [X0] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,'@+'(sK39,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl43_16])],[avatar_definition]) ).
fof(f684,plain,
( ! [X0] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,'@+'(sK39,X0)) )
| ~ spl43_16 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f686,definition,
( spl43_17
<=> '@<_succeeds'('0',sK39) ),
introduced(definition,[new_symbols(definition,[spl43_17])],[avatar_definition]) ).
fof(f687,plain,
( ~ '@<_succeeds'('0',sK39)
| spl43_17 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f688,plain,
( spl43_16
| ~ spl43_17
| ~ spl43_4 ),
inference(avatar_split_clause,[],[f679,f579,f686,f683]) ).
fof(f694,plain,
( ! [X0,X1] :
( ~ '@<_succeeds'(X1,'@+'(sK39,X0))
| '@<_succeeds'(s(X1),'@+'(sK36,X0)) )
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f552,f681]) ).
fof(f705,plain,
( ! [X0] :
( ~ nat_succeeds(X0)
| '@+'(sK39,X0) = '@+'(X0,sK39) )
| ~ spl43_4 ),
inference(resolution,[],[f457,f580]) ).
fof(f706,plain,
( '@+'(sK39,sK40) = '@+'(sK40,sK39)
| ~ spl43_4 ),
inference(resolution,[],[f705,f523]) ).
fof(f708,plain,
! [X0] : '@<_succeeds'(sK40,'@+'(sK40,s(X0))),
inference(resolution,[],[f510,f523]) ).
fof(f709,plain,
( ! [X0] : '@<_succeeds'(sK39,'@+'(sK39,s(X0)))
| ~ spl43_4 ),
inference(resolution,[],[f510,f580]) ).
fof(f720,plain,
( ! [X2,X0,X1] :
( ~ '@<_succeeds'(X1,'@+'(sK36,X0))
| ~ '@<_succeeds'(X2,X1)
| '@<_succeeds'(X2,'@+'(sK39,X0)) )
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f481,f681]) ).
fof(f722,plain,
( ! [X0] :
( '@<_succeeds'(X0,'@+'(sK39,sK38))
| ~ '@<_succeeds'(X0,'@+'(sK36,sK37)) )
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6 ),
inference(resolution,[],[f720,f588]) ).
fof(f741,plain,
( ! [X0] :
( ~ '@<_succeeds'('@+'(sK39,X0),'@+'(sK36,sK37))
| '@<_succeeds'(X0,sK38) )
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6 ),
inference(resolution,[],[f722,f573]) ).
fof(f742,plain,
( '@<_succeeds'(sK37,sK38)
| ~ '@<_succeeds'(sK39,sK36)
| ~ nat_succeeds(sK36)
| ~ nat_succeeds(sK37)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6 ),
inference(resolution,[],[f741,f511]) ).
fof(f763,plain,
( ! [X0,X1] :
( s(X1) != '@+'(sK36,X0)
| '@+'(sK39,X0) = X1 )
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f334,f681]) ).
fof(f821,plain,
( '@<_succeeds'(sK39,'@+'(sK39,sK36))
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f709,f584]) ).
fof(f833,plain,
( ! [X0,X1] :
( ~ '@<_succeeds'(X1,'@+'(sK39,X0))
| '@<_succeeds'(X1,'@+'(sK36,X0)) )
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f482,f681]) ).
fof(f834,plain,
( ! [X0] :
( ~ '@<_succeeds'(X0,sK39)
| '@<_succeeds'(X0,sK36) )
| ~ spl43_5 ),
inference(superposition,[],[f482,f584]) ).
fof(f907,plain,
( '0' = '@+'(sK36,sK37)
| '@+'(sK36,sK37) = s(sK18('@+'(sK36,sK37),'@+'(sK36,sK38)))
| ~ spl43_6 ),
inference(resolution,[],[f408,f588]) ).
fof(f924,definition,
( spl43_33
<=> '0' = sK39 ),
introduced(definition,[new_symbols(definition,[spl43_33])],[avatar_definition]) ).
fof(f925,plain,
( '0' = sK39
| ~ spl43_33 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f951,definition,
( spl43_40
<=> '@+'(sK36,sK37) = s(sK18('@+'(sK36,sK37),'@+'(sK36,sK38))) ),
introduced(definition,[new_symbols(definition,[spl43_40])],[avatar_definition]) ).
fof(f952,plain,
( '@+'(sK36,sK37) = s(sK18('@+'(sK36,sK37),'@+'(sK36,sK38)))
| ~ spl43_40 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f954,definition,
( spl43_41
<=> '0' = '@+'(sK36,sK37) ),
introduced(definition,[new_symbols(definition,[spl43_41])],[avatar_definition]) ).
fof(f955,plain,
( '0' = '@+'(sK36,sK37)
| ~ spl43_41 ),
inference(avatar_component_clause,[],[f954]) ).
fof(f956,plain,
( spl43_40
| spl43_41
| ~ spl43_6 ),
inference(avatar_split_clause,[],[f907,f587,f954,f951]) ).
fof(f965,plain,
( ! [X0] :
( '@+'(sK36,sK37) != '@+'(sK36,X0)
| '@+'(sK39,X0) = sK18('@+'(sK36,sK37),'@+'(sK36,sK38)) )
| ~ spl43_4
| ~ spl43_5
| ~ spl43_40 ),
inference(superposition,[],[f763,f952]) ).
fof(f970,plain,
( '@+'(sK39,sK37) = sK18('@+'(sK36,sK37),'@+'(sK36,sK38))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_40 ),
inference(equality_resolution,[],[f965]) ).
fof(f989,plain,
( ! [X0] :
( ~ nat_succeeds(X0)
| '@+'(s(X0),sK39) = '@+'(X0,s(sK39)) )
| ~ spl43_4 ),
inference(resolution,[],[f456,f580]) ).
fof(f990,plain,
( ! [X0] :
( ~ nat_succeeds(X0)
| '@+'(X0,sK36) = '@+'(s(X0),sK39) )
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f989,f584]) ).
fof(f991,plain,
( '@+'(sK40,sK36) = '@+'(s(sK40),sK39)
| ~ spl43_4
| ~ spl43_5 ),
inference(resolution,[],[f990,f523]) ).
fof(f992,plain,
( '@+'(sK39,sK36) = '@+'(s(sK39),sK39)
| ~ spl43_4
| ~ spl43_5 ),
inference(resolution,[],[f990,f580]) ).
fof(f993,plain,
( '@+'(sK36,sK39) = '@+'(sK39,sK36)
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f992,f584]) ).
fof(f994,plain,
( '@+'(sK40,sK36) = s('@+'(sK40,sK39))
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f991,f602]) ).
fof(f996,plain,
( '@+'(sK40,sK36) = s('@+'(sK39,sK40))
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f994,f706]) ).
fof(f997,plain,
( '@+'(sK40,sK36) = '@+'(sK36,sK40)
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f996,f681]) ).
fof(f1013,definition,
( spl43_42
<=> sK36 = sK39 ),
introduced(definition,[new_symbols(definition,[spl43_42])],[avatar_definition]) ).
fof(f1014,plain,
( sK36 = sK39
| ~ spl43_42 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f1206,plain,
( '@<_succeeds'(sK39,'@+'(sK36,sK39))
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f821,f993]) ).
fof(f1208,plain,
( ! [X0] :
( ~ '@<_succeeds'('@+'(sK39,X0),'@+'(sK36,sK39))
| '@<_succeeds'(X0,sK36) )
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f573,f993]) ).
fof(f1319,plain,
( ! [X0] : '0' != '@+'(sK36,X0)
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f333,f681]) ).
fof(f1615,plain,
( '@<_succeeds'(sK40,'@+'(sK40,sK36))
| ~ spl43_5 ),
inference(superposition,[],[f708,f584]) ).
fof(f1616,plain,
( '@<_succeeds'(sK40,'@+'(sK36,sK40))
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f1615,f997]) ).
fof(f1653,definition,
( spl43_78
<=> '0' = sK40 ),
introduced(definition,[new_symbols(definition,[spl43_78])],[avatar_definition]) ).
fof(f1654,plain,
( '0' = sK40
| ~ spl43_78 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f1677,plain,
( '0' = sK40
| sK40 = s(sK18(sK40,'@+'(sK36,sK40)))
| ~ spl43_4
| ~ spl43_5 ),
inference(resolution,[],[f1616,f408]) ).
fof(f1817,definition,
( spl43_83
<=> sK40 = s(sK18(sK40,'@+'(sK36,sK40))) ),
introduced(definition,[new_symbols(definition,[spl43_83])],[avatar_definition]) ).
fof(f1818,plain,
( sK40 = s(sK18(sK40,'@+'(sK36,sK40)))
| ~ spl43_83 ),
inference(avatar_component_clause,[],[f1817]) ).
fof(f1819,plain,
( spl43_83
| spl43_78
| ~ spl43_4
| ~ spl43_5 ),
inference(avatar_split_clause,[],[f1677,f583,f579,f1653,f1817]) ).
fof(f1842,plain,
( '@<_succeeds'('@+'('0',sK41),'@+'('0',sK42))
| ~ spl43_78 ),
inference(superposition,[],[f522,f1654]) ).
fof(f1887,plain,
( '@<_succeeds'('@+'('0',sK41),sK42)
| ~ spl43_78 ),
inference(forward_demodulation,[],[f1842,f451]) ).
fof(f1899,plain,
( '@<_succeeds'(sK41,sK42)
| ~ spl43_78 ),
inference(forward_demodulation,[],[f1887,f451]) ).
fof(f1902,plain,
( $false
| ~ spl43_78 ),
inference(forward_subsumption_resolution,[],[f1899,f524]) ).
fof(f1903,plain,
~ spl43_78,
inference(avatar_contradiction_clause,[],[f1902]) ).
fof(f1904,plain,
( $false
| ~ spl43_4
| ~ spl43_5
| ~ spl43_41 ),
inference(forward_subsumption_resolution,[],[f955,f1319]) ).
fof(f1905,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_41 ),
inference(avatar_contradiction_clause,[],[f1904]) ).
fof(f1940,definition,
( spl43_89
<=> nat_succeeds(sK37) ),
introduced(definition,[new_symbols(definition,[spl43_89])],[avatar_definition]) ).
fof(f1941,plain,
( ~ nat_succeeds(sK37)
| spl43_89 ),
inference(avatar_component_clause,[],[f1940]) ).
fof(f1965,plain,
( '@<_succeeds'(sK39,'@+'(sK39,sK40))
| ~ spl43_4
| ~ spl43_83 ),
inference(superposition,[],[f709,f1818]) ).
fof(f1985,plain,
( '@<_succeeds'(sK39,'@+'(sK36,sK40))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(resolution,[],[f1965,f833]) ).
fof(f1986,plain,
( '@<_succeeds'(s(sK39),'@+'(sK36,sK40))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(resolution,[],[f1965,f694]) ).
fof(f2000,plain,
( '@<_succeeds'(sK36,'@+'(sK36,sK40))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(forward_demodulation,[],[f1986,f584]) ).
fof(f2018,plain,
( '0' = sK39
| sK39 = s(sK18(sK39,'@+'(sK36,sK40)))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(resolution,[],[f1985,f408]) ).
fof(f2022,definition,
( spl43_97
<=> sK39 = s(sK18(sK39,'@+'(sK36,sK40))) ),
introduced(definition,[new_symbols(definition,[spl43_97])],[avatar_definition]) ).
fof(f2023,plain,
( sK39 = s(sK18(sK39,'@+'(sK36,sK40)))
| ~ spl43_97 ),
inference(avatar_component_clause,[],[f2022]) ).
fof(f2024,plain,
( spl43_97
| spl43_33
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(avatar_split_clause,[],[f2018,f1817,f583,f579,f924,f2022]) ).
fof(f2036,plain,
( '0' != sK39
| ~ spl43_97 ),
inference(superposition,[],[f333,f2023]) ).
fof(f2259,plain,
( sK39 = '@+'(sK39,'0')
| ~ spl43_4 ),
inference(resolution,[],[f455,f580]) ).
fof(f2275,plain,
( ~ '@<_succeeds'(sK39,'@+'(sK36,sK39))
| '@<_succeeds'('0',sK36)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5 ),
inference(superposition,[],[f1208,f2259]) ).
fof(f2290,plain,
( '@<_succeeds'('0',sK36)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_subsumption_resolution,[],[f2275,f1206]) ).
fof(f2475,plain,
( nat_succeeds('@+'(sK36,sK37))
| ~ spl43_6 ),
inference(resolution,[],[f479,f588]) ).
fof(f2484,plain,
( nat_succeeds(sK36)
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(resolution,[],[f479,f2000]) ).
fof(f2554,plain,
( ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK37))
| ~ spl43_6 ),
inference(resolution,[],[f2475,f485]) ).
fof(f2592,plain,
( ~ '@<_succeeds'(sK36,sK36)
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(resolution,[],[f2484,f485]) ).
fof(f3477,plain,
( ! [X0] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(sK39,X0)
| sK39 = X0
| '@<_succeeds'(X0,sK39) )
| ~ spl43_4 ),
inference(resolution,[],[f488,f580]) ).
fof(f3484,plain,
( '@<_succeeds'(sK39,sK36)
| sK36 = sK39
| '@<_succeeds'(sK36,sK39)
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(resolution,[],[f3477,f2484]) ).
fof(f3496,definition,
( spl43_192
<=> '@<_succeeds'(sK36,sK39) ),
introduced(definition,[new_symbols(definition,[spl43_192])],[avatar_definition]) ).
fof(f3497,plain,
( '@<_succeeds'(sK36,sK39)
| ~ spl43_192 ),
inference(avatar_component_clause,[],[f3496]) ).
fof(f3499,definition,
( spl43_193
<=> '@<_succeeds'(sK39,sK36) ),
introduced(definition,[new_symbols(definition,[spl43_193])],[avatar_definition]) ).
fof(f3501,plain,
( spl43_192
| spl43_42
| spl43_193
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83 ),
inference(avatar_split_clause,[],[f3484,f1817,f583,f579,f3499,f1013,f3496]) ).
fof(f4673,plain,
( ! [X0] :
( sK39 = X0
| '@<_succeeds'(X0,sK39)
| ~ '@<_succeeds'(X0,s(sK39)) )
| ~ spl43_4 ),
inference(resolution,[],[f487,f580]) ).
fof(f4675,plain,
( ! [X0] :
( ~ '@<_succeeds'(X0,sK36)
| sK39 = X0
| '@<_succeeds'(X0,sK39) )
| ~ spl43_4
| ~ spl43_5 ),
inference(forward_demodulation,[],[f4673,f584]) ).
fof(f4681,plain,
( '0' = sK39
| '@<_succeeds'('0',sK39)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5 ),
inference(resolution,[],[f4675,f2290]) ).
fof(f4684,plain,
( '@<_succeeds'('0',sK39)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_97 ),
inference(forward_subsumption_resolution,[],[f4681,f2036]) ).
fof(f4685,plain,
( $false
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| spl43_17
| ~ spl43_97 ),
inference(forward_subsumption_resolution,[],[f4684,f687]) ).
fof(f4686,plain,
( ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| spl43_17
| ~ spl43_97 ),
inference(avatar_contradiction_clause,[],[f4685]) ).
fof(f5804,plain,
( '@<_succeeds'('@+'(sK39,sK37),sK19('@+'(sK36,sK37),'@+'(sK36,sK38)))
| '0' = '@+'(sK36,sK37)
| ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_40 ),
inference(superposition,[],[f404,f970]) ).
fof(f5817,plain,
( '@<_succeeds'('@+'(sK39,sK37),sK19('@+'(sK36,sK37),'@+'(sK36,sK38)))
| ~ '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK38))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_40 ),
inference(forward_subsumption_resolution,[],[f5804,f1319]) ).
fof(f5824,plain,
( '@<_succeeds'('@+'(sK39,sK37),sK19('@+'(sK36,sK37),'@+'(sK36,sK38)))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_40 ),
inference(forward_subsumption_resolution,[],[f5817,f588]) ).
fof(f5857,plain,
( nat_succeeds('@+'(sK39,sK37))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_40 ),
inference(resolution,[],[f5824,f479]) ).
fof(f6061,plain,
( '@<_succeeds'('@+'(sK39,sK37),'@+'(sK39,'@+'(sK39,sK37)))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_16
| ~ spl43_40 ),
inference(resolution,[],[f5857,f684]) ).
fof(f6143,plain,
( ~ '@<_succeeds'(sK39,sK36)
| ~ nat_succeeds(sK36)
| ~ nat_succeeds(sK37)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| spl43_7 ),
inference(forward_subsumption_resolution,[],[f742,f592]) ).
fof(f6172,plain,
( ~ '@<_succeeds'(sK39,sK36)
| ~ nat_succeeds(sK37)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| spl43_7
| ~ spl43_83 ),
inference(forward_subsumption_resolution,[],[f6143,f2484]) ).
fof(f6261,plain,
( ~ spl43_89
| ~ spl43_193
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| spl43_7
| ~ spl43_83 ),
inference(avatar_split_clause,[],[f6172,f1817,f591,f587,f583,f579,f572,f3499,f1940]) ).
fof(f7514,plain,
( '@<_succeeds'(sK36,sK36)
| ~ spl43_5
| ~ spl43_192 ),
inference(resolution,[],[f3497,f834]) ).
fof(f7538,plain,
( $false
| ~ spl43_4
| ~ spl43_5
| ~ spl43_83
| ~ spl43_192 ),
inference(forward_subsumption_resolution,[],[f7514,f2592]) ).
fof(f7539,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_83
| ~ spl43_192 ),
inference(avatar_contradiction_clause,[],[f7538]) ).
fof(f8712,plain,
( '@<_succeeds'(sK37,'@+'(sK39,sK37))
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_16
| ~ spl43_40 ),
inference(resolution,[],[f6061,f573]) ).
fof(f9143,plain,
( nat_succeeds(sK37)
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_16
| ~ spl43_40 ),
inference(resolution,[],[f8712,f479]) ).
fof(f9150,plain,
( $false
| ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_16
| ~ spl43_40
| spl43_89 ),
inference(forward_subsumption_resolution,[],[f9143,f1941]) ).
fof(f9151,plain,
( ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_16
| ~ spl43_40
| spl43_89 ),
inference(avatar_contradiction_clause,[],[f9150]) ).
fof(f9276,plain,
( ! [X0] : '@+'(sK39,X0) = X0
| ~ spl43_33 ),
inference(superposition,[],[f451,f925]) ).
fof(f10226,plain,
( nat_succeeds(sK37)
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_33
| ~ spl43_40 ),
inference(superposition,[],[f5857,f9276]) ).
fof(f10275,plain,
( $false
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_33
| ~ spl43_40
| spl43_89 ),
inference(forward_subsumption_resolution,[],[f10226,f1941]) ).
fof(f10276,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_33
| ~ spl43_40
| spl43_89 ),
inference(avatar_contradiction_clause,[],[f10275]) ).
fof(f10899,plain,
( ! [X0] : '@+'(sK36,X0) = s('@+'(sK36,X0))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_42 ),
inference(superposition,[],[f681,f1014]) ).
fof(f13237,plain,
( '@<_succeeds'('@+'(sK36,sK37),s('@+'(sK36,sK37)))
| ~ spl43_6 ),
inference(resolution,[],[f486,f2475]) ).
fof(f13256,plain,
( '@<_succeeds'('@+'(sK36,sK37),'@+'(sK36,sK37))
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_42 ),
inference(forward_demodulation,[],[f13237,f10899]) ).
fof(f13267,plain,
( $false
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_42 ),
inference(forward_subsumption_resolution,[],[f13256,f2554]) ).
fof(f13268,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_42 ),
inference(avatar_contradiction_clause,[],[f13267]) ).
cnf(s1,plain,
( spl43_1
| spl43_2
| spl43_3 ),
inference(sat_conversion,[],[f577]) ).
cnf(s2,plain,
( spl43_1
| spl43_3
| spl43_4 ),
inference(sat_conversion,[],[f581]) ).
cnf(s3,plain,
( spl43_1
| spl43_3
| spl43_5 ),
inference(sat_conversion,[],[f585]) ).
cnf(s4,plain,
( spl43_3
| spl43_6 ),
inference(sat_conversion,[],[f589]) ).
cnf(s5,plain,
( spl43_3
| ~ spl43_7 ),
inference(sat_conversion,[],[f593]) ).
cnf(s7,plain,
~ spl43_3,
inference(sat_conversion,[],[f601]) ).
cnf(s13,plain,
( ~ spl43_1
| ~ spl43_6
| spl43_7 ),
inference(sat_conversion,[],[f662]) ).
cnf(s16,plain,
( ~ spl43_4
| spl43_16
| ~ spl43_17 ),
inference(sat_conversion,[],[f688]) ).
cnf(s34,plain,
( ~ spl43_6
| spl43_40
| spl43_41 ),
inference(sat_conversion,[],[f956]) ).
cnf(s70,plain,
( ~ spl43_4
| ~ spl43_5
| spl43_78
| spl43_83 ),
inference(sat_conversion,[],[f1819]) ).
cnf(s80,plain,
~ spl43_78,
inference(sat_conversion,[],[f1903]) ).
cnf(s81,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_41 ),
inference(sat_conversion,[],[f1905]) ).
cnf(s87,plain,
( ~ spl43_4
| ~ spl43_5
| spl43_33
| ~ spl43_83
| spl43_97 ),
inference(sat_conversion,[],[f2024]) ).
cnf(s150,plain,
( ~ spl43_4
| ~ spl43_5
| spl43_42
| ~ spl43_83
| spl43_192
| spl43_193 ),
inference(sat_conversion,[],[f3501]) ).
cnf(s213,plain,
( ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| spl43_17
| ~ spl43_97 ),
inference(sat_conversion,[],[f4686]) ).
cnf(s293,plain,
( ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| spl43_7
| ~ spl43_83
| ~ spl43_89
| ~ spl43_193 ),
inference(sat_conversion,[],[f6261]) ).
cnf(s341,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_83
| ~ spl43_192 ),
inference(sat_conversion,[],[f7539]) ).
cnf(s437,plain,
( ~ spl43_2
| ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_16
| ~ spl43_40
| spl43_89 ),
inference(sat_conversion,[],[f9151]) ).
cnf(s470,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_33
| ~ spl43_40
| spl43_89 ),
inference(sat_conversion,[],[f10276]) ).
cnf(s564,plain,
( ~ spl43_4
| ~ spl43_5
| ~ spl43_6
| ~ spl43_42 ),
inference(sat_conversion,[],[f13268]) ).
cnf(s577,plain,
( ~ spl43_4
| ~ spl43_5
| spl43_83 ),
inference(rat,[],[s70,s80]) ).
cnf(s580,plain,
~ spl43_7,
inference(rat,[],[s5,s7]) ).
cnf(s581,plain,
spl43_6,
inference(rat,[],[s4,s7]) ).
cnf(s583,plain,
~ spl43_1,
inference(rat,[],[s13,s580,s581]) ).
cnf(s584,plain,
spl43_5,
inference(rat,[],[s3,s7,s583]) ).
cnf(s585,plain,
spl43_4,
inference(rat,[],[s2,s7,s583]) ).
cnf(s586,plain,
~ spl43_42,
inference(rat,[],[s564,s584,s581,s585]) ).
cnf(s589,plain,
~ spl43_41,
inference(rat,[],[s81,s584,s585]) ).
cnf(s595,plain,
spl43_83,
inference(rat,[],[s577,s584,s585]) ).
cnf(s605,plain,
spl43_40,
inference(rat,[],[s34,s581,s589]) ).
cnf(s606,plain,
~ spl43_192,
inference(rat,[],[s341,s585,s584,s595]) ).
cnf(s609,plain,
spl43_193,
inference(rat,[],[s150,s595,s586,s585,s584,s606]) ).
cnf(s610,plain,
spl43_2,
inference(rat,[],[s1,s7,s583]) ).
cnf(s612,plain,
~ spl43_89,
inference(rat,[],[s293,s609,s595,s585,s580,s581,s584,s610]) ).
cnf(s616,plain,
~ spl43_33,
inference(rat,[],[s470,s605,s585,s584,s581,s612]) ).
cnf(s617,plain,
~ spl43_16,
inference(rat,[],[s437,s610,s605,s585,s581,s584,s612]) ).
cnf(s628,plain,
spl43_97,
inference(rat,[],[s87,s595,s585,s584,s616]) ).
cnf(s636,plain,
~ spl43_17,
inference(rat,[],[s16,s585,s617]) ).
cnf(s639,plain,
$false,
inference(rat,[],[s213,s610,s585,s584,s628,s636]) ).
fof(f13282,plain,
$false,
inference(avatar_sat_refutation,[],[s639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX044+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 14:55:32 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 12.52/2.44 % (841885)Detected formulas, will run a generic FOF schedule.
% 12.52/2.44 % (841893)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2567595620:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.52/2.44 % (841892)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=1998386848:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.52/2.44 % (841893)Instruction limit reached!
% 12.52/2.44 % (841893)------------------------------
% 12.52/2.44 % (841893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.44 % (841893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.44 % (841893)CaDiCaL version: 2.1.3
% 12.52/2.44 % (841893)Termination reason: Instruction limit
% 12.52/2.44 % (841893)Termination phase: Saturation
% 12.52/2.44 % (841893)Time elapsed: 0.040 s
% 12.52/2.44 % (841893)Peak memory usage: 89 MB
% 12.52/2.44 % (841893)Instructions burned: 112 (million)
% 12.52/2.44 % (841895)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3283617178:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.52/2.44 % (841890)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=1977783654:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.52/2.44 % (841891)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=2078293293:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.52/2.44 % (841894)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3622229666:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.52/2.44 % (841896)dis-21_1_sil=8000:lcm=predicate:random_seed=297870553: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)
% 12.52/2.44 % (841894)Instruction limit reached!
% 12.52/2.44 % (841894)------------------------------
% 12.52/2.44 % (841894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.44 % (841894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.44 % (841894)CaDiCaL version: 2.1.3
% 12.52/2.44 % (841894)Termination reason: Instruction limit
% 12.52/2.44 % (841894)Termination phase: Saturation
% 12.52/2.44 % (841894)Time elapsed: 0.074 s
% 12.52/2.44 % (841894)Peak memory usage: 88 MB
% 12.52/2.44 % (841894)Instructions burned: 120 (million)
% 12.52/2.44 % (841896)Instruction limit reached!
% 12.52/2.44 % (841896)------------------------------
% 12.52/2.44 % (841896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.44 % (841896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.44 % (841896)CaDiCaL version: 2.1.3
% 12.52/2.44 % (841896)Termination reason: Instruction limit
% 12.52/2.44 % (841896)Termination phase: Saturation
% 12.52/2.44 % (841896)Time elapsed: 0.079 s
% 12.52/2.44 % (841896)Peak memory usage: 89 MB
% 12.52/2.44 % (841896)Instructions burned: 129 (million)
% 12.52/2.44 % (841904)lrs+10_1_sil=8000:sp=occurrence:random_seed=1102665905:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.52/2.44 % (841895)Instruction limit reached!
% 12.52/2.44 % (841895)------------------------------
% 12.52/2.44 % (841895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.44 % (841895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.44 % (841895)CaDiCaL version: 2.1.3
% 12.52/2.44 % (841895)Termination reason: Instruction limit
% 12.52/2.44 % (841895)Termination phase: Saturation
% 12.52/2.44 % (841895)Time elapsed: 0.099 s
% 12.52/2.44 % (841895)Peak memory usage: 90 MB
% 12.52/2.44 % (841895)Instructions burned: 139 (million)
% 12.52/2.44 % (841904)Instruction limit reached!
% 12.52/2.44 % (841904)------------------------------
% 12.52/2.44 % (841904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.52/2.44 % (841904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.52/2.44 % (841904)CaDiCaL version: 2.1.3
% 12.52/2.44 % (841904)Termination reason: Instruction limit
% 12.52/2.44 % (841904)Termination phase: Saturation
% 12.52/2.44 % (841904)Time elapsed: 0.099 s
% 12.52/2.44 % (841904)Peak memory usage: 91 MB
% 12.52/2.44 % (841904)Instructions burned: 287 (million)
% 12.52/2.44 % (841906)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1985368633:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 15.36/2.88 % (841908)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2292961268:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 15.36/2.88 % (841909)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=3717627833:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 15.36/2.88 % (841910)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=991018205:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 15.36/2.88 % (841906)Instruction limit reached!
% 15.36/2.88 % (841906)------------------------------
% 15.36/2.88 % (841906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841906)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841906)Termination reason: Instruction limit
% 15.36/2.88 % (841906)Termination phase: Saturation
% 15.36/2.88 % (841906)Time elapsed: 0.074 s
% 15.36/2.88 % (841906)Peak memory usage: 90 MB
% 15.36/2.88 % (841906)Instructions burned: 159 (million)
% 15.36/2.88 % (841909)Instruction limit reached!
% 15.36/2.88 % (841909)------------------------------
% 15.36/2.88 % (841909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841909)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841909)Termination reason: Instruction limit
% 15.36/2.88 % (841909)Termination phase: Saturation
% 15.36/2.88 % (841909)Time elapsed: 0.137 s
% 15.36/2.88 % (841909)Peak memory usage: 93 MB
% 15.36/2.88 % (841909)Instructions burned: 248 (million)
% 15.36/2.88 % (841910)Instruction limit reached!
% 15.36/2.88 % (841910)------------------------------
% 15.36/2.88 % (841910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841910)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841910)Termination reason: Instruction limit
% 15.36/2.88 % (841910)Termination phase: Saturation
% 15.36/2.88 % (841910)Time elapsed: 0.099 s
% 15.36/2.88 % (841910)Peak memory usage: 90 MB
% 15.36/2.88 % (841910)Instructions burned: 296 (million)
% 15.36/2.88 % (841915)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2583961091:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 15.36/2.88 % (841908)Instruction limit reached!
% 15.36/2.88 % (841908)------------------------------
% 15.36/2.88 % (841908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841908)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841908)Termination reason: Instruction limit
% 15.36/2.88 % (841908)Termination phase: Saturation
% 15.36/2.88 % (841908)Time elapsed: 0.222 s
% 15.36/2.88 % (841908)Peak memory usage: 92 MB
% 15.36/2.88 % (841908)Instructions burned: 325 (million)
% 15.36/2.88 % (841917)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=243508424:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 15.36/2.88 % (841916)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=562704323:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 15.36/2.88 % (841917)Instruction limit reached!
% 15.36/2.88 % (841917)------------------------------
% 15.36/2.88 % (841917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841917)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841917)Termination reason: Instruction limit
% 15.36/2.88 % (841917)Termination phase: Saturation
% 15.36/2.88 % (841917)Time elapsed: 0.035 s
% 15.36/2.88 % (841917)Peak memory usage: 89 MB
% 15.36/2.88 % (841917)Instructions burned: 128 (million)
% 15.36/2.88 % (841916)Instruction limit reached!
% 15.36/2.88 % (841916)------------------------------
% 15.36/2.88 % (841916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841916)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841916)Termination reason: Instruction limit
% 15.36/2.88 % (841916)Termination phase: Saturation
% 15.36/2.88 % (841916)Time elapsed: 0.076 s
% 15.36/2.88 % (841916)Peak memory usage: 90 MB
% 15.36/2.88 % (841916)Instructions burned: 114 (million)
% 15.36/2.88 % (841919)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3203617593:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 15.36/2.88 % (841922)lrs+10_1_sil=8000:sp=occurrence:random_seed=378601120:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 15.36/2.88 % (841919)Instruction limit reached!
% 15.36/2.88 % (841919)------------------------------
% 15.36/2.88 % (841919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841919)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841919)Termination reason: Instruction limit
% 15.36/2.88 % (841919)Termination phase: Saturation
% 15.36/2.88 % (841919)Time elapsed: 0.074 s
% 15.36/2.88 % (841919)Peak memory usage: 89 MB
% 15.36/2.88 % (841919)Instructions burned: 115 (million)
% 15.36/2.88 % (841924)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2926308883:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 15.36/2.88 % (841926)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1029650836:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 15.36/2.88 % (841922)Instruction limit reached!
% 15.36/2.88 % (841922)------------------------------
% 15.36/2.88 % (841922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841922)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841922)Termination reason: Instruction limit
% 15.36/2.88 % (841922)Termination phase: Saturation
% 15.36/2.88 % (841922)Time elapsed: 0.303 s
% 15.36/2.88 % (841922)Peak memory usage: 97 MB
% 15.36/2.88 % (841922)Instructions burned: 910 (million)
% 15.36/2.88 % (841924)Instruction limit reached!
% 15.36/2.88 % (841924)------------------------------
% 15.36/2.88 % (841924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841924)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841924)Termination reason: Instruction limit
% 15.36/2.88 % (841924)Termination phase: Saturation
% 15.36/2.88 % (841924)Time elapsed: 0.273 s
% 15.36/2.88 % (841924)Peak memory usage: 92 MB
% 15.36/2.88 % (841924)Instructions burned: 438 (million)
% 15.36/2.88 % (841929)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1111687957:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 15.36/2.88 % (841929)Instruction limit reached!
% 15.36/2.88 % (841929)------------------------------
% 15.36/2.88 % (841929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841929)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841929)Termination reason: Instruction limit
% 15.36/2.88 % (841929)Termination phase: Saturation
% 15.36/2.88 % (841929)Time elapsed: 0.037 s
% 15.36/2.88 % (841929)Peak memory usage: 91 MB
% 15.36/2.88 % (841929)Instructions burned: 139 (million)
% 15.36/2.88 % (841930)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1629651637:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 15.36/2.88 % (841932)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2459710220:st=3:i=13193:sd=3:ss=axioms_2988 on theBenchmark for (2988ds/13193Mi)
% 15.36/2.88 % (841930)Instruction limit reached!
% 15.36/2.88 % (841930)------------------------------
% 15.36/2.88 % (841930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841930)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841930)Termination reason: Instruction limit
% 15.36/2.88 % (841930)Termination phase: Saturation
% 15.36/2.88 % (841930)Time elapsed: 0.333 s
% 15.36/2.88 % (841930)Peak memory usage: 92 MB
% 15.36/2.88 % (841930)Instructions burned: 593 (million)
% 15.36/2.88 % (841935)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=3291896776:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/125Mi)
% 15.36/2.88 % (841935)Instruction limit reached!
% 15.36/2.88 % (841935)------------------------------
% 15.36/2.88 % (841935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841935)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841935)Termination reason: Instruction limit
% 15.36/2.88 % (841935)Termination phase: Saturation
% 15.36/2.88 % (841935)Time elapsed: 0.068 s
% 15.36/2.88 % (841935)Peak memory usage: 90 MB
% 15.36/2.88 % (841935)Instructions burned: 125 (million)
% 15.36/2.88 % (841937)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=1217705901:i=134:gtgl=5:slsql=off:gtg=exists_sym_2982 on theBenchmark for (2982ds/134Mi)
% 15.36/2.88 % (841891)First to succeed.
% 15.36/2.88 % (841891)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-841885"
% 15.36/2.88 % (841937)Instruction limit reached!
% 15.36/2.88 % (841937)------------------------------
% 15.36/2.88 % (841937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841937)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841937)Termination reason: Instruction limit
% 15.36/2.88 % (841937)Termination phase: Saturation
% 15.36/2.88 % (841937)Time elapsed: 0.085 s
% 15.36/2.88 % (841937)Peak memory usage: 90 MB
% 15.36/2.88 % (841937)Instructions burned: 134 (million)
% 15.36/2.88 % (841915)Instruction limit reached!
% 15.36/2.88 % (841915)------------------------------
% 15.36/2.88 % (841915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.36/2.88 % (841915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.36/2.88 % (841915)CaDiCaL version: 2.1.3
% 15.36/2.88 % (841915)Termination reason: Instruction limit
% 15.36/2.88 % (841915)Termination phase: Saturation
% 15.36/2.88 % (841915)Time elapsed: 1.542 s
% 15.36/2.88 % (841915)Peak memory usage: 143 MB
% 15.36/2.88 % (841915)Instructions burned: 2351 (million)
% 15.36/2.88 % (841939)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=1876303617:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/141Mi)
% 15.36/2.88 % (841891)Refutation found. Thanks to Tanya!
% 15.36/2.88 % SZS status Theorem for theBenchmark
% 15.36/2.88 % SZS output start Proof for theBenchmark
% See solution above
% 16.24/3.07 % (841891)------------------------------
% 16.24/3.07 % (841891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.24/3.07 % (841891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.24/3.07 % (841891)CaDiCaL version: 2.1.3
% 16.24/3.07 % (841891)Termination reason: Refutation
% 16.24/3.07 % (841891)Time elapsed: 1.771 s
% 16.24/3.07 % (841891)Peak memory usage: 145 MB
% 16.24/3.07 % (841891)Instructions burned: 2652 (million)
% 16.24/3.07 % (841891)------------------------------
% 16.24/3.07 % (841891)------------------------------
% 16.24/3.07 % (841885)Success in time 2.209 s
% 16.24/3.07 % Vampire exiting
%------------------------------------------------------------------------------