%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX037+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 2.97s 1.10s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 152 ( 22 unt; 12 def)
% Number of atoms : 508 ( 90 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 624 ( 268 ~; 281 |; 47 &)
% ( 10 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 109 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f60,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@*'('0',X0) = '0' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(times:zero)') ).
fof(f61,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(times:successor)') ).
fof(f62,axiom,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> nat_succeeds('@*'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(times:types)') ).
fof(f63,axiom,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) )
=> '@*'('@+'(X0,X1),X2) = '@+'('@*'(X0,X2),'@*'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(plus:times:distributive)') ).
fof(f64,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/sandbox/benchmark/theBenchmark.p',induction) ).
fof(f65,conjecture,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) )
=> '@*'('@*'(X0,X1),X2) = '@*'(X0,'@*'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem-(times:associative)') ).
fof(f66,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)],[f65]) ).
fof(f67,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,[],[f64]) ).
fof(f68,plain,
? [X0,X1,X2] :
( '@*'('@*'(X0,X1),X2) != '@*'(X0,'@*'(X1,X2))
& nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) ),
inference(ennf_transformation,[],[f66]) ).
fof(f69,plain,
? [X0,X1,X2] :
( '@*'('@*'(X0,X1),X2) != '@*'(X0,'@*'(X1,X2))
& nat_succeeds(X0)
& nat_succeeds(X1)
& nat_succeeds(X2) ),
inference(flattening,[],[f68]) ).
fof(f70,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,[],[f67]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( '@*'('@+'(X0,X1),X2) = '@+'('@*'(X0,X2),'@*'(X1,X2))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X2) ),
inference(ennf_transformation,[],[f63]) ).
fof(f73,plain,
! [X0,X1,X2] :
( '@*'('@+'(X0,X1),X2) = '@+'('@*'(X0,X2),'@*'(X1,X2))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X2) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( nat_succeeds('@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f75,plain,
! [X0,X1] :
( nat_succeeds('@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f77,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0] :
( '@*'('0',X0) = '0'
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f81,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)],[f69]) ).
fof(f82,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,[],[f71]) ).
fof(f83,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)],[f82]) ).
fof(f85,plain,
nat_succeeds(sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f86,plain,
nat_succeeds(sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f87,plain,
nat_succeeds(sK0),
inference(cnf_transformation,[],[f81]) ).
fof(f88,plain,
'@*'('@*'(sK0,sK1),sK2) != '@*'(sK0,'@*'(sK1,sK2)),
inference(cnf_transformation,[],[f81]) ).
fof(f89,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,[],[f83]) ).
fof(f90,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,[],[f83]) ).
fof(f91,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,[],[f83]) ).
fof(f92,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,[],[f83]) ).
fof(f93,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,[],[f83]) ).
fof(f94,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,[],[f83]) ).
fof(f95,plain,
! [X2,X0,X1] :
( '@*'('@+'(X0,X1),X2) = '@+'('@*'(X0,X2),'@*'(X1,X2))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f96,plain,
! [X0,X1] :
( nat_succeeds('@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f97,plain,
! [X0,X1] :
( '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f98,plain,
! [X0] :
( '0' = '@*'('0',X0)
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f101,definition,
~ sP7('@*'('@*'(sK0,sK1),sK2)),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f102,plain,
sP7('@*'(sK0,'@*'(sK1,sK2))),
inference(inequality_splitting,[],[f88,f101]) ).
fof(f103,definition,
~ sP8('@*'('@*'(sK3,sK4),sK5)),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f104,plain,
! [X2,X0,X1] :
( '@*'('@*'(X0,X1),X2) = '@*'(X0,'@*'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| sP8('@*'(sK3,'@*'(sK4,sK5))) ),
inference(inequality_splitting,[],[f94,f103]) ).
fof(f106,plain,
! [X8,X7] :
( '@*'('@*'(sK6,X7),X8) = '@*'(sK6,'@*'(X7,X8))
| ~ nat_succeeds(X8)
| sP9(X7) ),
inference(cnf_transformation,[],[f106_D]) ).
fof(f106_D,definition,
! [X7] :
( ! [X8] :
( '@*'('@*'(sK6,X7),X8) = '@*'(sK6,'@*'(X7,X8))
| ~ nat_succeeds(X8) )
<=> ~ sP9(X7) ),
introduced(definition,[new_symbols(definition,[sP9])],[general_splitting_component_introduction]) ).
fof(f107,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
| ~ sP9(X7) ),
inference(general_splitting,[],[f89,f106_D]) ).
fof(f108,plain,
! [X7] :
( ~ sP9(X7)
| ~ nat_succeeds(X7)
| sP10 ),
inference(cnf_transformation,[],[f108_D]) ).
fof(f108_D,definition,
( ! [X7] :
( ~ sP9(X7)
| ~ nat_succeeds(X7) )
<=> ~ sP10 ),
introduced(definition,[new_symbols(definition,[sP10])],[general_splitting_component_introduction]) ).
fof(f109,plain,
! [X2,X0,X1] :
( '@*'('@*'(X0,X1),X2) = '@*'(X0,'@*'(X1,X2))
| ~ nat_succeeds(X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| '0' = sK3
| ~ sP10 ),
inference(general_splitting,[],[f107,f108_D]) ).
fof(f110,plain,
( ~ sP7('@*'(sK0,'@*'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(superposition,[],[f101,f90]) ).
fof(f111,plain,
( ~ sP7('@*'(sK0,'@*'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(superposition,[],[f101,f91]) ).
fof(f112,plain,
( ~ sP7('@*'(sK0,'@*'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(superposition,[],[f101,f92]) ).
fof(f113,plain,
( ~ sP7('@*'(sK0,'@*'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(superposition,[],[f101,f93]) ).
fof(f114,plain,
( ~ sP7('@*'(sK0,'@*'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sP8('@*'(sK3,'@*'(sK4,sK5))) ),
inference(superposition,[],[f101,f104]) ).
fof(f115,plain,
( ~ sP7('@*'(sK0,'@*'(sK1,sK2)))
| ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP10 ),
inference(superposition,[],[f101,f109]) ).
fof(f116,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP10 ),
inference(forward_subsumption_resolution,[],[f115,f102]) ).
fof(f117,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sP8('@*'(sK3,'@*'(sK4,sK5))) ),
inference(forward_subsumption_resolution,[],[f114,f102]) ).
fof(f118,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(forward_subsumption_resolution,[],[f113,f102]) ).
fof(f119,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(forward_subsumption_resolution,[],[f112,f102]) ).
fof(f120,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f111,f102]) ).
fof(f121,plain,
( ~ nat_succeeds(sK2)
| ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f110,f102]) ).
fof(f122,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP10 ),
inference(forward_subsumption_resolution,[],[f116,f85]) ).
fof(f123,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sP8('@*'(sK3,'@*'(sK4,sK5))) ),
inference(forward_subsumption_resolution,[],[f117,f85]) ).
fof(f124,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(forward_subsumption_resolution,[],[f118,f85]) ).
fof(f125,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(forward_subsumption_resolution,[],[f119,f85]) ).
fof(f126,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f120,f85]) ).
fof(f127,plain,
( ~ nat_succeeds(sK1)
| ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f121,f85]) ).
fof(f128,plain,
( ~ nat_succeeds(sK0)
| '0' = sK3
| ~ sP10 ),
inference(forward_subsumption_resolution,[],[f122,f86]) ).
fof(f129,plain,
( ~ nat_succeeds(sK0)
| sP8('@*'(sK3,'@*'(sK4,sK5))) ),
inference(forward_subsumption_resolution,[],[f123,f86]) ).
fof(f130,plain,
( ~ nat_succeeds(sK0)
| nat_succeeds(sK5) ),
inference(forward_subsumption_resolution,[],[f124,f86]) ).
fof(f131,plain,
( ~ nat_succeeds(sK0)
| nat_succeeds(sK4) ),
inference(forward_subsumption_resolution,[],[f125,f86]) ).
fof(f132,plain,
( ~ nat_succeeds(sK0)
| sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f126,f86]) ).
fof(f133,plain,
( ~ nat_succeeds(sK0)
| nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f127,f86]) ).
fof(f134,plain,
( '0' = sK3
| ~ sP10 ),
inference(forward_subsumption_resolution,[],[f128,f87]) ).
fof(f135,plain,
sP8('@*'(sK3,'@*'(sK4,sK5))),
inference(forward_subsumption_resolution,[],[f129,f87]) ).
fof(f136,plain,
nat_succeeds(sK5),
inference(forward_subsumption_resolution,[],[f130,f87]) ).
fof(f137,plain,
nat_succeeds(sK4),
inference(forward_subsumption_resolution,[],[f131,f87]) ).
fof(f138,plain,
( sK3 = s(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f132,f87]) ).
fof(f139,plain,
( nat_succeeds(sK6)
| '0' = sK3 ),
inference(forward_subsumption_resolution,[],[f133,f87]) ).
fof(f141,definition,
( spl11_1
<=> sP10 ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f143,plain,
( ~ sP10
| spl11_1 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f145,definition,
( spl11_2
<=> '0' = sK3 ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f147,plain,
( '0' = sK3
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f134,f145,f141]) ).
fof(f150,definition,
( spl11_3
<=> sK3 = s(sK6) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f152,plain,
( sK3 = s(sK6)
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl11_2
| spl11_3 ),
inference(avatar_split_clause,[],[f138,f150,f145]) ).
fof(f155,definition,
( spl11_4
<=> nat_succeeds(sK6) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f157,plain,
( nat_succeeds(sK6)
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl11_2
| spl11_4 ),
inference(avatar_split_clause,[],[f139,f155,f145]) ).
fof(f159,plain,
( ~ sP8('@*'('@*'('0',sK4),sK5))
| ~ spl11_2 ),
inference(superposition,[],[f103,f147]) ).
fof(f160,plain,
( sP8('@*'('0','@*'(sK4,sK5)))
| ~ spl11_2 ),
inference(superposition,[],[f135,f147]) ).
fof(f161,plain,
( ~ sP8('@*'('0',sK5))
| ~ nat_succeeds(sK4)
| ~ spl11_2 ),
inference(superposition,[],[f159,f98]) ).
fof(f168,plain,
( ~ sP8('@*'('0',sK5))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f161,f137]) ).
fof(f169,plain,
( ~ sP8('0')
| ~ nat_succeeds(sK5)
| ~ spl11_2 ),
inference(superposition,[],[f168,f98]) ).
fof(f170,plain,
( ~ sP8('0')
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f169,f136]) ).
fof(f171,plain,
( sP8('0')
| ~ nat_succeeds('@*'(sK4,sK5))
| ~ spl11_2 ),
inference(superposition,[],[f160,f98]) ).
fof(f172,plain,
( ~ nat_succeeds('@*'(sK4,sK5))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f171,f170]) ).
fof(f173,plain,
( ~ nat_succeeds(sK4)
| ~ nat_succeeds(sK5)
| ~ spl11_2 ),
inference(resolution,[],[f172,f96]) ).
fof(f174,plain,
( ~ nat_succeeds(sK5)
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f173,f137]) ).
fof(f175,plain,
( $false
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f174,f136]) ).
fof(f176,plain,
~ spl11_2,
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f178,plain,
( sP8('@*'(s(sK6),'@*'(sK4,sK5)))
| ~ spl11_3 ),
inference(superposition,[],[f135,f152]) ).
fof(f179,plain,
( ~ sP8('@*'('@*'(s(sK6),sK4),sK5))
| ~ spl11_3 ),
inference(superposition,[],[f103,f152]) ).
fof(f180,plain,
( sP8('@+'('@*'(sK4,sK5),'@*'(sK6,'@*'(sK4,sK5))))
| ~ nat_succeeds(sK6)
| ~ nat_succeeds('@*'(sK4,sK5))
| ~ spl11_3 ),
inference(superposition,[],[f178,f97]) ).
fof(f181,plain,
( sP8('@+'('@*'(sK4,sK5),'@*'(sK6,'@*'(sK4,sK5))))
| ~ nat_succeeds('@*'(sK4,sK5))
| ~ spl11_3
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f180,f157]) ).
fof(f183,definition,
( spl11_5
<=> nat_succeeds('@*'(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f185,plain,
( ~ nat_succeeds('@*'(sK4,sK5))
| spl11_5 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f187,definition,
( spl11_6
<=> sP8('@+'('@*'(sK4,sK5),'@*'(sK6,'@*'(sK4,sK5)))) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f189,plain,
( sP8('@+'('@*'(sK4,sK5),'@*'(sK6,'@*'(sK4,sK5))))
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,plain,
( ~ spl11_5
| spl11_6
| ~ spl11_3
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f181,f155,f150,f187,f183]) ).
fof(f191,plain,
( ~ nat_succeeds(sK4)
| ~ nat_succeeds(sK5)
| spl11_5 ),
inference(resolution,[],[f185,f96]) ).
fof(f192,plain,
( ~ nat_succeeds(sK5)
| spl11_5 ),
inference(forward_subsumption_resolution,[],[f191,f137]) ).
fof(f193,plain,
( $false
| spl11_5 ),
inference(forward_subsumption_resolution,[],[f192,f136]) ).
fof(f194,plain,
spl11_5,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f195,plain,
( ~ sP8('@*'('@+'(sK4,'@*'(sK6,sK4)),sK5))
| ~ nat_succeeds(sK6)
| ~ nat_succeeds(sK4)
| ~ spl11_3 ),
inference(superposition,[],[f179,f97]) ).
fof(f202,plain,
( ~ sP8('@*'('@+'(sK4,'@*'(sK6,sK4)),sK5))
| ~ nat_succeeds(sK4)
| ~ spl11_3
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f195,f157]) ).
fof(f203,plain,
( ~ sP8('@*'('@+'(sK4,'@*'(sK6,sK4)),sK5))
| ~ spl11_3
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f202,f137]) ).
fof(f204,plain,
( ~ sP8('@+'('@*'(sK4,sK5),'@*'('@*'(sK6,sK4),sK5)))
| ~ nat_succeeds(sK4)
| ~ nat_succeeds('@*'(sK6,sK4))
| ~ nat_succeeds(sK5)
| ~ spl11_3
| ~ spl11_4 ),
inference(superposition,[],[f203,f95]) ).
fof(f205,plain,
( ~ sP8('@+'('@*'(sK4,sK5),'@*'('@*'(sK6,sK4),sK5)))
| ~ nat_succeeds('@*'(sK6,sK4))
| ~ nat_succeeds(sK5)
| ~ spl11_3
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f204,f137]) ).
fof(f206,plain,
( ~ sP8('@+'('@*'(sK4,sK5),'@*'('@*'(sK6,sK4),sK5)))
| ~ nat_succeeds('@*'(sK6,sK4))
| ~ spl11_3
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f205,f136]) ).
fof(f208,definition,
( spl11_7
<=> nat_succeeds('@*'(sK6,sK4)) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
fof(f210,plain,
( ~ nat_succeeds('@*'(sK6,sK4))
| spl11_7 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f212,definition,
( spl11_8
<=> sP8('@+'('@*'(sK4,sK5),'@*'('@*'(sK6,sK4),sK5))) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f214,plain,
( ~ sP8('@+'('@*'(sK4,sK5),'@*'('@*'(sK6,sK4),sK5)))
| spl11_8 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,plain,
( ~ spl11_7
| ~ spl11_8
| ~ spl11_3
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f206,f155,f150,f212,f208]) ).
fof(f216,plain,
( ~ nat_succeeds(sK6)
| ~ nat_succeeds(sK4)
| spl11_7 ),
inference(resolution,[],[f210,f96]) ).
fof(f217,plain,
( ~ nat_succeeds(sK4)
| ~ spl11_4
| spl11_7 ),
inference(forward_subsumption_resolution,[],[f216,f157]) ).
fof(f218,plain,
( $false
| ~ spl11_4
| spl11_7 ),
inference(forward_subsumption_resolution,[],[f217,f137]) ).
fof(f219,plain,
( ~ spl11_4
| spl11_7 ),
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f220,plain,
( ~ sP8('@+'('@*'(sK4,sK5),'@*'(sK6,'@*'(sK4,sK5))))
| ~ nat_succeeds(sK5)
| sP9(sK4)
| spl11_8 ),
inference(superposition,[],[f214,f106]) ).
fof(f227,plain,
( ~ nat_succeeds(sK5)
| sP9(sK4)
| ~ spl11_6
| spl11_8 ),
inference(forward_subsumption_resolution,[],[f220,f189]) ).
fof(f228,plain,
( sP9(sK4)
| ~ spl11_6
| spl11_8 ),
inference(forward_subsumption_resolution,[],[f227,f136]) ).
fof(f229,plain,
( ~ nat_succeeds(sK4)
| sP10
| ~ spl11_6
| spl11_8 ),
inference(resolution,[],[f228,f108]) ).
fof(f230,plain,
( sP10
| ~ spl11_6
| spl11_8 ),
inference(forward_subsumption_resolution,[],[f229,f137]) ).
fof(f231,plain,
( $false
| spl11_1
| ~ spl11_6
| spl11_8 ),
inference(forward_subsumption_resolution,[],[f230,f143]) ).
fof(f232,plain,
( spl11_1
| ~ spl11_6
| spl11_8 ),
inference(avatar_contradiction_clause,[],[f231]) ).
cnf(s1,plain,
( ~ spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f148]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f153]) ).
cnf(s3,plain,
( spl11_2
| spl11_4 ),
inference(sat_conversion,[],[f158]) ).
cnf(s4,plain,
~ spl11_2,
inference(sat_conversion,[],[f176]) ).
cnf(s5,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| spl11_6 ),
inference(sat_conversion,[],[f190]) ).
cnf(s6,plain,
spl11_5,
inference(sat_conversion,[],[f194]) ).
cnf(s7,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_7
| ~ spl11_8 ),
inference(sat_conversion,[],[f215]) ).
cnf(s8,plain,
( ~ spl11_4
| spl11_7 ),
inference(sat_conversion,[],[f219]) ).
cnf(s9,plain,
( spl11_1
| ~ spl11_6
| spl11_8 ),
inference(sat_conversion,[],[f232]) ).
cnf(s10,plain,
( ~ spl11_3
| ~ spl11_4
| spl11_6 ),
inference(rat,[],[s5,s6]) ).
cnf(s11,plain,
spl11_4,
inference(rat,[],[s3,s4]) ).
cnf(s12,plain,
spl11_7,
inference(rat,[],[s8,s11]) ).
cnf(s13,plain,
spl11_3,
inference(rat,[],[s2,s4]) ).
cnf(s14,plain,
~ spl11_8,
inference(rat,[],[s7,s11,s12,s13]) ).
cnf(s15,plain,
spl11_6,
inference(rat,[],[s10,s11,s13]) ).
cnf(s16,plain,
spl11_1,
inference(rat,[],[s9,s14,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s4,s16]) ).
fof(f233,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX037+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 14:55:09 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.97/1.10 % (412702)Detected formulas, will run a generic FOF schedule.
% 2.97/1.10 % (412711)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4100714454:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.97/1.10 % (412708)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=2461570860:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.97/1.10 % (412707)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=3781416257:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.97/1.10 % (412712)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4195648363:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.97/1.10 % (412709)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=2607455680:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.97/1.10 % (412710)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=448296697:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.97/1.10 % (412713)dis-21_1_sil=8000:lcm=predicate:random_seed=3240561319: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)
% 2.97/1.10 % (412710)First to succeed.
% 2.97/1.10 % (412710)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-412702"
% 2.97/1.10 % (412711)Instruction limit reached!
% 2.97/1.10 % (412711)------------------------------
% 2.97/1.10 % (412711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.10 % (412711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.10 % (412711)CaDiCaL version: 2.1.3
% 2.97/1.10 % (412711)Termination reason: Instruction limit
% 2.97/1.10 % (412711)Termination phase: Saturation
% 2.97/1.10 % (412711)Time elapsed: 0.039 s
% 2.97/1.10 % (412711)Peak memory usage: 88 MB
% 2.97/1.10 % (412711)Instructions burned: 120 (million)
% 2.97/1.10 % (412713)Instruction limit reached!
% 2.97/1.10 % (412713)------------------------------
% 2.97/1.10 % (412713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.10 % (412713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.10 % (412713)CaDiCaL version: 2.1.3
% 2.97/1.10 % (412713)Termination reason: Instruction limit
% 2.97/1.10 % (412713)Termination phase: Saturation
% 2.97/1.10 % (412713)Time elapsed: 0.081 s
% 2.97/1.10 % (412713)Peak memory usage: 89 MB
% 2.97/1.10 % (412713)Instructions burned: 129 (million)
% 2.97/1.10 % (412712)Instruction limit reached!
% 2.97/1.10 % (412712)------------------------------
% 2.97/1.10 % (412712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.10 % (412712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.10 % (412712)CaDiCaL version: 2.1.3
% 2.97/1.10 % (412712)Termination reason: Instruction limit
% 2.97/1.10 % (412712)Termination phase: Saturation
% 2.97/1.10 % (412712)Time elapsed: 0.095 s
% 2.97/1.10 % (412712)Peak memory usage: 90 MB
% 2.97/1.10 % (412712)Instructions burned: 140 (million)
% 2.97/1.10 % (412721)lrs+10_1_sil=8000:sp=occurrence:random_seed=4266103005:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.97/1.10 % (412721)Instruction limit reached!
% 2.97/1.10 % (412721)------------------------------
% 2.97/1.10 % (412721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.97/1.10 % (412721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.97/1.10 % (412721)CaDiCaL version: 2.1.3
% 2.97/1.10 % (412721)Termination reason: Instruction limit
% 2.97/1.10 % (412721)Termination phase: Saturation
% 2.97/1.10 % (412721)Time elapsed: 0.089 s
% 2.97/1.10 % (412721)Peak memory usage: 91 MB
% 2.97/1.10 % (412721)Instructions burned: 285 (million)
% 2.97/1.10 % (412722)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3792815909:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.97/1.10 % (412710)Refutation found. Thanks to Tanya!
% 2.97/1.10 % SZS status Theorem for theBenchmark
% 2.97/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.29 % (412710)------------------------------
% 3.63/1.29 % (412710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.29 % (412710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.29 % (412710)CaDiCaL version: 2.1.3
% 3.63/1.29 % (412710)Termination reason: Refutation
% 3.63/1.29 % (412710)Time elapsed: 0.007 s
% 3.63/1.29 % (412710)Peak memory usage: 89 MB
% 3.63/1.29 % (412710)Instructions burned: 8 (million)
% 3.63/1.29 % (412710)------------------------------
% 3.63/1.29 % (412710)------------------------------
% 3.63/1.29 % (412702)Success in time 0.432 s
% 3.63/1.29 % Vampire exiting
%------------------------------------------------------------------------------