%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX032+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 : n020.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 01:45:43 PM UTC 2026
% Result : Theorem 4.34s 1.39s
% Output : Refutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 124 ( 21 unt; 10 def)
% Number of atoms : 426 ( 84 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 515 ( 213 ~; 234 |; 44 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 94 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
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(f47,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> nat_succeeds('@+'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(plus:types)') ).
fof(f48,axiom,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( ( nat_succeeds(X3)
& nat_succeeds(X2) )
=> '@+'('@+'(X1,X2),X3) = '@+'(X1,'@+'(X2,X3)) ) )
| X0 = '0' )
=> ! [X2,X3] :
( ( nat_succeeds(X3)
& nat_succeeds(X2) )
=> '@+'('@+'(X0,X2),X3) = '@+'(X0,'@+'(X2,X3)) ) )
=> ! [X0] :
( nat_succeeds(X0)
=> ! [X2,X3] :
( ( nat_succeeds(X3)
& nat_succeeds(X2) )
=> '@+'('@+'(X0,X2),X3) = '@+'(X0,'@+'(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
fof(f49,conjecture,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) )
=> '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem-(plus:associative)') ).
fof(f50,negated_conjecture,
~ ! [X0,X1,X2] :
( ( nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) )
=> '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f51,plain,
( ! [X0] :
( ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( ( nat_succeeds(X3)
& nat_succeeds(X2) )
=> '@+'('@+'(X1,X2),X3) = '@+'(X1,'@+'(X2,X3)) ) )
| X0 = '0' )
=> ! [X4,X5] :
( ( nat_succeeds(X5)
& nat_succeeds(X4) )
=> '@+'('@+'(X0,X4),X5) = '@+'(X0,'@+'(X4,X5)) ) )
=> ! [X6] :
( nat_succeeds(X6)
=> ! [X7,X8] :
( ( nat_succeeds(X8)
& nat_succeeds(X7) )
=> '@+'('@+'(X6,X7),X8) = '@+'(X6,'@+'(X7,X8)) ) ) ),
inference(rectify,[],[f48]) ).
fof(f52,plain,
? [X0,X1,X2] :
( '@+'('@+'(X0,X1),X2) != '@+'(X0,'@+'(X1,X2))
& nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) ),
inference(ennf_transformation,[],[f50]) ).
fof(f53,plain,
? [X0,X1,X2] :
( '@+'('@+'(X0,X1),X2) != '@+'(X0,'@+'(X1,X2))
& nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
( ! [X6] :
( ! [X7,X8] :
( '@+'('@+'(X6,X7),X8) = '@+'(X6,'@+'(X7,X8))
| ~ nat_succeeds(X8)
| ~ nat_succeeds(X7) )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( '@+'('@+'(X0,X4),X5) != '@+'(X0,'@+'(X4,X5))
& nat_succeeds(X5)
& nat_succeeds(X4) )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@+'('@+'(X1,X2),X3) = '@+'(X1,'@+'(X2,X3))
| ~ nat_succeeds(X3)
| ~ nat_succeeds(X2) ) )
| X0 = '0' ) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ! [X6] :
( ! [X7,X8] :
( '@+'('@+'(X6,X7),X8) = '@+'(X6,'@+'(X7,X8))
| ~ nat_succeeds(X8)
| ~ nat_succeeds(X7) )
| ~ nat_succeeds(X6) )
| ? [X0] :
( ? [X4,X5] :
( '@+'('@+'(X0,X4),X5) != '@+'(X0,'@+'(X4,X5))
& nat_succeeds(X5)
& nat_succeeds(X4) )
& ( ? [X1] :
( X0 = s(X1)
& nat_succeeds(X1)
& ! [X2,X3] :
( '@+'('@+'(X1,X2),X3) = '@+'(X1,'@+'(X2,X3))
| ~ nat_succeeds(X3)
| ~ nat_succeeds(X2) ) )
| X0 = '0' ) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( nat_succeeds('@+'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f57,plain,
! [X0,X1] :
( nat_succeeds('@+'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( '@+'(s(X0),X1) = s('@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f60,plain,
( '@+'('@+'(sK0,sK1),sK2) != '@+'(sK0,'@+'(sK1,sK2))
& nat_succeeds(sK0)
& nat_succeeds(sK1)
& nat_succeeds(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f53]) ).
fof(f61,plain,
( ! [X0] :
( ! [X1,X2] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1) )
| ~ nat_succeeds(X0) )
| ? [X3] :
( ? [X4,X5] :
( '@+'('@+'(X3,X4),X5) != '@+'(X3,'@+'(X4,X5))
& nat_succeeds(X5)
& nat_succeeds(X4) )
& ( ? [X6] :
( s(X6) = X3
& nat_succeeds(X6)
& ! [X7,X8] :
( '@+'('@+'(X6,X7),X8) = '@+'(X6,'@+'(X7,X8))
| ~ nat_succeeds(X8)
| ~ nat_succeeds(X7) ) )
| '0' = X3 ) ) ),
inference(rectify,[],[f55]) ).
fof(f62,plain,
( ! [X0] :
( ! [X1,X2] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1) )
| ~ nat_succeeds(X0) )
| ( '@+'('@+'(sK3,sK4),sK5) != '@+'(sK3,'@+'(sK4,sK5))
& nat_succeeds(sK5)
& nat_succeeds(sK4)
& ( ( sK3 = s(sK6)
& nat_succeeds(sK6)
& ! [X7,X8] :
( '@+'('@+'(sK6,X7),X8) = '@+'(sK6,'@+'(X7,X8))
| ~ nat_succeeds(X8)
| ~ nat_succeeds(X7) ) )
| '0' = sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f61]) ).
fof(f68,plain,
nat_succeeds(sK2),
inference(cnf_transformation,[],[f60]) ).
fof(f69,plain,
nat_succeeds(sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f70,plain,
nat_succeeds(sK0),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
'@+'('@+'(sK0,sK1),sK2) != '@+'(sK0,'@+'(sK1,sK2)),
inference(cnf_transformation,[],[f60]) ).
fof(f72,plain,
! [X2,X0,X1,X8,X7] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| '@+'('@+'(sK6,X7),X8) = '@+'(sK6,'@+'(X7,X8))
| ~ nat_succeeds(X8)
| ~ nat_succeeds(X7)
| '0' = sK3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X2,X0,X1] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f74,plain,
! [X2,X0,X1] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(cnf_transformation,[],[f62]) ).
fof(f75,plain,
! [X2,X0,X1] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| nat_succeeds(sK4) ),
inference(cnf_transformation,[],[f62]) ).
fof(f76,plain,
! [X2,X0,X1] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| nat_succeeds(sK5) ),
inference(cnf_transformation,[],[f62]) ).
fof(f77,plain,
! [X2,X0,X1] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| '@+'('@+'(sK3,sK4),sK5) != '@+'(sK3,'@+'(sK4,sK5)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f78,plain,
! [X0,X1] :
( nat_succeeds('@+'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f79,plain,
! [X0,X1] :
( '@+'(s(X0),X1) = s('@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f80,plain,
! [X0] : '@+'('0',X0) = X0,
inference(cnf_transformation,[],[f45]) ).
fof(f87,definition,
~ sP8('@+'('@+'(sK0,sK1),sK2)),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f88,plain,
sP8('@+'(sK0,'@+'(sK1,sK2))),
inference(inequality_splitting,[],[f71,f87]) ).
fof(f89,definition,
~ sP9('@+'('@+'(sK3,sK4),sK5)),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
fof(f90,plain,
! [X2,X0,X1] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| sP9('@+'(sK3,'@+'(sK4,sK5))) ),
inference(inequality_splitting,[],[f77,f89]) ).
fof(f95,plain,
! [X8,X7] :
( '@+'('@+'(sK6,X7),X8) = '@+'(sK6,'@+'(X7,X8))
| ~ nat_succeeds(X8)
| sP11(X7) ),
inference(cnf_transformation,[],[f95_D]) ).
fof(f95_D,definition,
! [X7] :
( ! [X8] :
( '@+'('@+'(sK6,X7),X8) = '@+'(sK6,'@+'(X7,X8))
| ~ nat_succeeds(X8) )
<=> ~ sP11(X7) ),
introduced(definition,[new_symbols(definition,[sP11])],[general_splitting_component_introduction]) ).
fof(f96,plain,
! [X2,X0,X1,X7] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X7)
| '0' = sK3
| ~ sP11(X7) ),
inference(general_splitting,[],[f72,f95_D]) ).
fof(f97,plain,
! [X7] :
( ~ sP11(X7)
| ~ nat_succeeds(X7)
| sP12 ),
inference(cnf_transformation,[],[f97_D]) ).
fof(f97_D,definition,
( ! [X7] :
( ~ sP11(X7)
| ~ nat_succeeds(X7) )
<=> ~ sP12 ),
introduced(definition,[new_symbols(definition,[sP12])],[general_splitting_component_introduction]) ).
fof(f98,plain,
! [X2,X0,X1] :
( '@+'('@+'(X0,X1),X2) = '@+'(X0,'@+'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| '0' = sK3
| ~ sP12 ),
inference(general_splitting,[],[f96,f97_D]) ).
fof(f99,plain,
( ~ sP8('@+'(sK0,'@+'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(superposition,[],[f87,f73]) ).
fof(f100,plain,
( ~ sP8('@+'(sK0,'@+'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(superposition,[],[f87,f74]) ).
fof(f101,plain,
( ~ sP8('@+'(sK0,'@+'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(superposition,[],[f87,f75]) ).
fof(f102,plain,
( ~ sP8('@+'(sK0,'@+'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(superposition,[],[f87,f76]) ).
fof(f103,plain,
( ~ sP8('@+'(sK0,'@+'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sP9('@+'(sK3,'@+'(sK4,sK5))) ),
inference(superposition,[],[f87,f90]) ).
fof(f104,plain,
( ~ sP8('@+'(sK0,'@+'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP12 ),
inference(superposition,[],[f87,f98]) ).
fof(f105,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP12 ),
inference(forward_subsumption_resolution,[],[f104,f88]) ).
fof(f106,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sP9('@+'(sK3,'@+'(sK4,sK5))) ),
inference(forward_subsumption_resolution,[],[f103,f88]) ).
fof(f107,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(forward_subsumption_resolution,[],[f102,f88]) ).
fof(f108,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(forward_subsumption_resolution,[],[f101,f88]) ).
fof(f109,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f100,f88]) ).
fof(f110,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f99,f88]) ).
fof(f111,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP12 ),
inference(forward_subsumption_resolution,[],[f105,f68]) ).
fof(f112,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sP9('@+'(sK3,'@+'(sK4,sK5))) ),
inference(forward_subsumption_resolution,[],[f106,f68]) ).
fof(f113,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(forward_subsumption_resolution,[],[f107,f68]) ).
fof(f114,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(forward_subsumption_resolution,[],[f108,f68]) ).
fof(f115,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f109,f68]) ).
fof(f116,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f110,f68]) ).
fof(f117,plain,
( ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP12 ),
inference(forward_subsumption_resolution,[],[f111,f69]) ).
fof(f118,plain,
( ~ nat_succeeds(sK0)
| sP9('@+'(sK3,'@+'(sK4,sK5))) ),
inference(forward_subsumption_resolution,[],[f112,f69]) ).
fof(f119,plain,
( ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(forward_subsumption_resolution,[],[f113,f69]) ).
fof(f120,plain,
( ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(forward_subsumption_resolution,[],[f114,f69]) ).
fof(f121,plain,
( ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f115,f69]) ).
fof(f122,plain,
( ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f116,f69]) ).
fof(f123,plain,
( '0' = sK3
| ~ sP12 ),
inference(forward_subsumption_resolution,[],[f117,f70]) ).
fof(f124,plain,
sP9('@+'(sK3,'@+'(sK4,sK5))),
inference(forward_subsumption_resolution,[],[f118,f70]) ).
fof(f125,plain,
nat_succeeds(sK5),
inference(forward_subsumption_resolution,[],[f119,f70]) ).
fof(f126,plain,
nat_succeeds(sK4),
inference(forward_subsumption_resolution,[],[f120,f70]) ).
fof(f127,plain,
( sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f121,f70]) ).
fof(f128,plain,
( nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f122,f70]) ).
fof(f130,definition,
( spl13_1
<=> sP12 ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f132,plain,
( ~ sP12
| spl13_1 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,definition,
( spl13_2
<=> '0' = sK3 ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f136,plain,
( '0' = sK3
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f123,f134,f130]) ).
fof(f139,definition,
( spl13_3
<=> sK3 = s(sK6) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f141,plain,
( sK3 = s(sK6)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f127,f139,f134]) ).
fof(f144,definition,
( spl13_4
<=> nat_succeeds(sK6) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f146,plain,
( nat_succeeds(sK6)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl13_2
| spl13_4 ),
inference(avatar_split_clause,[],[f128,f144,f134]) ).
fof(f148,plain,
( ~ sP9('@+'('@+'('0',sK4),sK5))
| ~ spl13_2 ),
inference(superposition,[],[f89,f136]) ).
fof(f149,plain,
( ~ sP9('@+'(sK4,sK5))
| ~ spl13_2 ),
inference(forward_demodulation,[],[f148,f80]) ).
fof(f150,plain,
( sP9('@+'('0','@+'(sK4,sK5)))
| ~ spl13_2 ),
inference(superposition,[],[f124,f136]) ).
fof(f151,plain,
( sP9('@+'(sK4,sK5))
| ~ spl13_2 ),
inference(forward_demodulation,[],[f150,f80]) ).
fof(f152,plain,
( $false
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f151,f149]) ).
fof(f153,plain,
~ spl13_2,
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f155,plain,
( sP9('@+'(s(sK6),'@+'(sK4,sK5)))
| ~ spl13_3 ),
inference(superposition,[],[f124,f141]) ).
fof(f156,plain,
( ~ sP9('@+'('@+'(s(sK6),sK4),sK5))
| ~ spl13_3 ),
inference(superposition,[],[f89,f141]) ).
fof(f157,plain,
( sP9(s('@+'(sK6,'@+'(sK4,sK5))))
| ~ nat_succeeds(sK6)
| ~ spl13_3 ),
inference(superposition,[],[f155,f79]) ).
fof(f158,plain,
( sP9(s('@+'(sK6,'@+'(sK4,sK5))))
| ~ spl13_3
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f157,f146]) ).
fof(f159,plain,
( ~ sP9('@+'(s('@+'(sK6,sK4)),sK5))
| ~ nat_succeeds(sK6)
| ~ spl13_3 ),
inference(superposition,[],[f156,f79]) ).
fof(f166,plain,
( ~ sP9('@+'(s('@+'(sK6,sK4)),sK5))
| ~ spl13_3
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f159,f146]) ).
fof(f167,plain,
( ~ sP9(s('@+'('@+'(sK6,sK4),sK5)))
| ~ nat_succeeds('@+'(sK6,sK4))
| ~ spl13_3
| ~ spl13_4 ),
inference(superposition,[],[f166,f79]) ).
fof(f169,definition,
( spl13_5
<=> nat_succeeds('@+'(sK6,sK4)) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f171,plain,
( ~ nat_succeeds('@+'(sK6,sK4))
| spl13_5 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f173,definition,
( spl13_6
<=> sP9(s('@+'('@+'(sK6,sK4),sK5))) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f175,plain,
( ~ sP9(s('@+'('@+'(sK6,sK4),sK5)))
| spl13_6 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( ~ spl13_5
| ~ spl13_6
| ~ spl13_3
| ~ spl13_4 ),
inference(avatar_split_clause,[],[f167,f144,f139,f173,f169]) ).
fof(f177,plain,
( ~ nat_succeeds(sK6)
| ~ nat_succeeds(sK4)
| spl13_5 ),
inference(resolution,[],[f171,f78]) ).
fof(f178,plain,
( ~ nat_succeeds(sK4)
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f177,f146]) ).
fof(f179,plain,
( $false
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f178,f126]) ).
fof(f180,plain,
( ~ spl13_4
| spl13_5 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f181,plain,
( ~ sP9(s('@+'(sK6,'@+'(sK4,sK5))))
| ~ nat_succeeds(sK5)
| sP11(sK4)
| spl13_6 ),
inference(superposition,[],[f175,f95]) ).
fof(f188,plain,
( ~ nat_succeeds(sK5)
| sP11(sK4)
| ~ spl13_3
| ~ spl13_4
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f181,f158]) ).
fof(f189,plain,
( sP11(sK4)
| ~ spl13_3
| ~ spl13_4
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f188,f125]) ).
fof(f190,plain,
( ~ nat_succeeds(sK4)
| sP12
| ~ spl13_3
| ~ spl13_4
| spl13_6 ),
inference(resolution,[],[f189,f97]) ).
fof(f191,plain,
( sP12
| ~ spl13_3
| ~ spl13_4
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f190,f126]) ).
fof(f192,plain,
( $false
| spl13_1
| ~ spl13_3
| ~ spl13_4
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f191,f132]) ).
fof(f193,plain,
( spl13_1
| ~ spl13_3
| ~ spl13_4
| spl13_6 ),
inference(avatar_contradiction_clause,[],[f192]) ).
cnf(s1,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f137]) ).
cnf(s2,plain,
( spl13_2
| spl13_3 ),
inference(sat_conversion,[],[f142]) ).
cnf(s3,plain,
( spl13_2
| spl13_4 ),
inference(sat_conversion,[],[f147]) ).
cnf(s4,plain,
~ spl13_2,
inference(sat_conversion,[],[f153]) ).
cnf(s5,plain,
( ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_6 ),
inference(sat_conversion,[],[f176]) ).
cnf(s6,plain,
( ~ spl13_4
| spl13_5 ),
inference(sat_conversion,[],[f180]) ).
cnf(s7,plain,
( spl13_1
| ~ spl13_3
| ~ spl13_4
| spl13_6 ),
inference(sat_conversion,[],[f193]) ).
cnf(s8,plain,
spl13_4,
inference(rat,[],[s3,s4]) ).
cnf(s9,plain,
spl13_5,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
spl13_3,
inference(rat,[],[s2,s4]) ).
cnf(s11,plain,
~ spl13_6,
inference(rat,[],[s5,s8,s9,s10]) ).
cnf(s12,plain,
spl13_1,
inference(rat,[],[s7,s10,s8,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s4,s12]) ).
fof(f194,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX032+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n020.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Mon Sep 28 14:53:04 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running first-order theorem proving
% 0.26/0.29 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
% 4.34/1.39 % (220074)Detected formulas, will run a generic FOF schedule.
% 4.34/1.39 % (220085)dis-21_1_sil=8000:lcm=predicate:random_seed=399233395: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)
% 4.34/1.39 % (220079)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=1436916516:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.34/1.39 % (220085)Instruction limit reached!
% 4.34/1.39 % (220085)------------------------------
% 4.34/1.39 % (220085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.39 % (220085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.39 % (220085)CaDiCaL version: 2.1.3
% 4.34/1.39 % (220085)Termination reason: Instruction limit
% 4.34/1.39 % (220085)Termination phase: Saturation
% 4.34/1.39 % (220085)Time elapsed: 0.059 s
% 4.34/1.39 % (220085)Peak memory usage: 89 MB
% 4.34/1.39 % (220085)Instructions burned: 132 (million)
% 4.34/1.39 % (220082)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1575619957:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.34/1.39 % (220081)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=1980918661:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.34/1.39 % (220080)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=1500796608:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.34/1.39 % (220084)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4231006947:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.34/1.39 % (220083)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2687804526:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.34/1.39 % (220082)First to succeed.
% 4.34/1.39 % (220082)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-220074"
% 4.34/1.39 % (220083)Instruction limit reached!
% 4.34/1.39 % (220083)------------------------------
% 4.34/1.39 % (220083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.39 % (220083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.39 % (220083)CaDiCaL version: 2.1.3
% 4.34/1.39 % (220083)Termination reason: Instruction limit
% 4.34/1.39 % (220083)Termination phase: Saturation
% 4.34/1.39 % (220083)Time elapsed: 0.112 s
% 4.34/1.39 % (220083)Peak memory usage: 88 MB
% 4.34/1.39 % (220083)Instructions burned: 119 (million)
% 4.34/1.39 % (220084)Instruction limit reached!
% 4.34/1.39 % (220084)------------------------------
% 4.34/1.39 % (220084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.34/1.39 % (220084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.34/1.39 % (220084)CaDiCaL version: 2.1.3
% 4.34/1.39 % (220084)Termination reason: Instruction limit
% 4.34/1.39 % (220084)Termination phase: Saturation
% 4.34/1.39 % (220084)Time elapsed: 0.152 s
% 4.34/1.39 % (220084)Peak memory usage: 90 MB
% 4.34/1.39 % (220084)Instructions burned: 140 (million)
% 4.34/1.39 % (220088)lrs+10_1_sil=8000:sp=occurrence:random_seed=1675556523:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.34/1.39 % (220094)lrs+10_1_sil=32000:urr=on:br=off:random_seed=38672910:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.34/1.39 % (220095)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4078036840:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 4.34/1.39 % (220082)Refutation found. Thanks to Tanya!
% 4.34/1.39 % SZS status Theorem for theBenchmark
% 4.34/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 5.60/1.66 % (220082)------------------------------
% 5.60/1.66 % (220082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.66 % (220082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.66 % (220082)CaDiCaL version: 2.1.3
% 5.60/1.66 % (220082)Termination reason: Refutation
% 5.60/1.66 % (220082)Time elapsed: 0.010 s
% 5.60/1.66 % (220082)Peak memory usage: 89 MB
% 5.60/1.66 % (220082)Instructions burned: 7 (million)
% 5.60/1.66 % (220082)------------------------------
% 5.60/1.66 % (220082)------------------------------
% 5.60/1.66 % (220074)Success in time 0.681 s
% 5.60/1.66 % Vampire exiting
%------------------------------------------------------------------------------