%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 02:32:23 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 18
% Syntax : Number of formulae : 84 ( 5 unt; 0 def)
% Number of atoms : 335 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 415 ( 164 ~; 251 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 136 ( 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| iLEQ(suc(X0),suc(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_109) ).
fof(f2,axiom,
! [X0] : 'LE'(f(X0),s(s(s(s('0'))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_104) ).
fof(f3,axiom,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_91) ).
fof(f4,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s('0'))
| 'E'('0',f(suc(X0)))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_114) ).
fof(f5,axiom,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ iLEQ(suc(X0),suc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_71) ).
fof(f8,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s('0')))
| 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f9,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_66) ).
fof(f10,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s(s('0'))))
| 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_84) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_144) ).
fof(f12,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s('0'))),f(X0))
| 'LE'(f(X0),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_127) ).
fof(f13,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_51) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21) ).
fof(f15,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s(s(s('0')))))
| 'E'(s(s(s('0'))),f(suc(X0)))
| 'LE'(f(X0),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_102) ).
fof(f16,axiom,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14) ).
fof(f17,axiom,
! [X0] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_96) ).
fof(f18,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
fof(f19,plain,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f12,f2]) ).
fof(f23,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(suc(X0)))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[],[f15,f2]) ).
fof(f24,plain,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| ~ 'E'(s(s(s('0'))),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[],[f23,f16]) ).
fof(f25,plain,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| iLEQ(suc(X0),suc(X0)) ),
inference(forward_subsumption_resolution,[],[f24,f19]) ).
fof(f26,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| iLEQ(suc(X0),suc(X0))
| 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f25,f13]) ).
fof(f27,plain,
! [X0] :
( iLEQ(suc(suc(X0)),suc(suc(X0)))
| 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[],[f25,f10]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| 'LE'(f(X2),s(s(s('0')))) ),
inference(resolution,[],[f7,f23]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ iLEQ(suc(X1),suc(X0))
| 'LE'(f(X2),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[],[f36,f19]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X2))
| 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(resolution,[],[f38,f23]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[],[f42,f19]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(resolution,[],[f44,f23]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[],[f80,f19]) ).
fof(f118,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X0),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(resolution,[],[f82,f25]) ).
fof(f129,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X0),s(s(s('0'))))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(duplicate_literal_removal,[],[f118]) ).
fof(f135,plain,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| 'LE'(f(X0),s(s(s('0'))))
| 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f129,f26]) ).
fof(f141,plain,
! [X0] :
( 'LE'(f(suc(X0)),s(s(s('0'))))
| 'LE'(f(suc(X0)),s(s(s('0'))))
| 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[],[f129,f27]) ).
fof(f142,plain,
! [X0] :
( 'LE'(f(suc(X0)),s(s(s('0'))))
| 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f148,plain,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literal_removal,[],[f135]) ).
fof(f150,plain,
! [X0] :
( 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[],[f142,f10]) ).
fof(f151,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(forward_subsumption_resolution,[],[f148,f13]) ).
fof(f156,plain,
! [X2,X0,X1] :
( 'LE'(f(X0),s(s('0')))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f150,f6]) ).
fof(f157,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| ~ 'E'(s(s('0')),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[],[f150,f5]) ).
fof(f158,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| iLEQ(suc(X0),suc(X0)) ),
inference(forward_subsumption_resolution,[],[f157,f151]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X1)))
| 'LE'(f(X0),s(s('0')))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(X2)) ),
inference(forward_subsumption_resolution,[],[f156,f151]) ).
fof(f160,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| iLEQ(suc(X0),suc(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f158,f8]) ).
fof(f161,plain,
! [X0] :
( iLEQ(suc(suc(X0)),suc(suc(X0)))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
inference(resolution,[],[f158,f18]) ).
fof(f301,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X2),s(s('0')))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(resolution,[],[f159,f150]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(X0))
| 'LE'(f(X2),s(s('0')))
| ~ iLEQ(suc(X2),suc(X0))
| 'LE'(f(X1),s(s('0'))) ),
inference(forward_subsumption_resolution,[],[f301,f151]) ).
fof(f315,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(X0))
| 'LE'(f(X2),s(s('0')))
| ~ iLEQ(suc(X2),suc(X0))
| 'LE'(f(X1),s(s('0')))
| 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[],[f305,f150]) ).
fof(f319,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| 'LE'(f(X2),s(s('0')))
| ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X1),s(s('0')))
| 'LE'(f(X0),s(s('0'))) ),
inference(forward_subsumption_resolution,[],[f315,f151]) ).
fof(f322,plain,
! [X0,X1] :
( 'LE'(f(X0),s(s('0')))
| ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X1),s(s('0')))
| 'LE'(f(X0),s(s('0')))
| 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[],[f319,f158]) ).
fof(f349,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X0),s(s('0')))
| 'LE'(f(X1),s(s('0'))) ),
inference(duplicate_literal_removal,[],[f322]) ).
fof(f355,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'LE'(f(X0),s(s('0')))
| 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f349,f160]) ).
fof(f365,plain,
! [X0] :
( 'LE'(f(suc(X0)),s(s('0')))
| 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
inference(resolution,[],[f349,f161]) ).
fof(f374,plain,
! [X0] :
( 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
inference(duplicate_literal_removal,[],[f365]) ).
fof(f384,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f355]) ).
fof(f386,plain,
! [X0] :
( 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
inference(forward_subsumption_resolution,[],[f374,f18]) ).
fof(f387,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[],[f384,f8]) ).
fof(f392,plain,
! [X2,X0,X1] :
( 'LE'(f(X0),s('0'))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1)) ),
inference(resolution,[],[f386,f14]) ).
fof(f393,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| ~ 'E'(s('0'),f(X0))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[],[f386,f3]) ).
fof(f394,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| iLEQ(suc(X0),suc(X0)) ),
inference(forward_subsumption_resolution,[],[f393,f387]) ).
fof(f395,plain,
! [X2,X0,X1] :
( ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X0),s('0'))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1)) ),
inference(forward_subsumption_resolution,[],[f392,f387]) ).
fof(f396,plain,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(resolution,[],[f394,f17]) ).
fof(f521,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| 'LE'(f(X2),s('0'))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f395,f386]) ).
fof(f523,plain,
! [X2,X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X2),suc(X0))
| 'LE'(f(X2),s('0'))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(X0))
| 'LE'(f(X1),s('0')) ),
inference(forward_subsumption_resolution,[],[f521,f387]) ).
fof(f525,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X0),s('0'))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(X1))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f523,f386]) ).
fof(f527,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X2))
| 'LE'(f(X0),s('0'))
| ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(forward_subsumption_resolution,[],[f525,f387]) ).
fof(f538,plain,
! [X0,X1] :
( 'LE'(f(X0),s('0'))
| ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X1),s('0'))
| 'LE'(f(X1),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f527,f394]) ).
fof(f567,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X0),s('0'))
| 'LE'(f(X1),s('0')) ),
inference(duplicate_literal_removal,[],[f538]) ).
fof(f586,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'LE'(f(X0),s('0'))
| 'LE'(f(X0),s('0')) ),
inference(resolution,[],[f567,f394]) ).
fof(f587,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(resolution,[],[f567,f396]) ).
fof(f614,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(duplicate_literal_removal,[],[f587]) ).
fof(f615,plain,
! [X0] : 'LE'(f(X0),s('0')),
inference(duplicate_literal_removal,[],[f586]) ).
fof(f623,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0)) ),
inference(forward_subsumption_resolution,[],[f614,f17]) ).
fof(f629,plain,
! [X0] :
( 'E'('0',f(suc(X0)))
| 'LE'(f(X0),'0') ),
inference(resolution,[],[f615,f4]) ).
fof(f636,plain,
! [X0] :
( 'LE'(f(X0),'0')
| ~ 'E'('0',f(X0))
| iLEQ(suc(X0),suc(X0)) ),
inference(resolution,[],[f629,f1]) ).
fof(f643,plain,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| 'LE'(f(X0),'0') ),
inference(forward_subsumption_resolution,[],[f636,f623]) ).
fof(f646,plain,
! [X0,X1] :
( 'LE'(f(X0),'0')
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f643,f11]) ).
fof(f665,plain,
! [X0,X1] :
( 'LE'(f(X0),'0')
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1)) ),
inference(duplicate_literal_removal,[],[f646]) ).
fof(f669,plain,
! [X0,X1] :
( 'LE'(f(X0),'0')
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1)) ),
inference(forward_subsumption_resolution,[],[f665,f623]) ).
fof(f673,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| 'LE'(f(X0),'0')
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1)) ),
inference(forward_subsumption_resolution,[],[f669,f629]) ).
fof(f682,plain,
! [X0] :
( 'LE'(f(X0),'0')
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(resolution,[],[f673,f643]) ).
fof(f698,plain,
! [X0] :
( 'LE'(f(X0),'0')
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(duplicate_literal_removal,[],[f682]) ).
fof(f709,plain,
! [X0] :
( 'LE'(f(X0),'0')
| ~ 'E'('0',f(suc(X0))) ),
inference(forward_subsumption_resolution,[],[f698,f623]) ).
fof(f724,plain,
! [X0] : 'LE'(f(X0),'0'),
inference(forward_subsumption_resolution,[],[f709,f629]) ).
fof(f731,plain,
$false,
inference(resolution,[],[f724,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n009.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 18:03:45 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.29 % (3301833)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (3301841)dis+10_1_sil=32000:sp=arity:random_seed=2836297010:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (3301839)% WARNING: option uhcvi not known.
% 0.19/0.29 % (3301839)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=201411675:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (3301838)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2961523466_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % (3301840)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2474210985:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (3301841) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3301833-3301841"...
% 0.19/0.29 % (3301842)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=315137599:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (3301843)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2110829922:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (3301844)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=480378615:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (3301841)...printing done.
% 0.19/0.29 % (3301841)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (3301841)------------------------------
% 0.19/0.29 % (3301841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (3301841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (3301841)CaDiCaL version: 2.1.3
% 0.19/0.29 % (3301841)Termination reason: Refutation
% 0.19/0.29 % (3301841)Time elapsed: 0.008 s
% 0.19/0.29 % (3301841)Peak memory usage: 11 MB
% 0.19/0.29 % (3301841)Instructions burned: 28 (million)
% 0.19/0.29 % (3301833)Success in time 0.035 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------