%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO630-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 02:32:15 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 7 unt; 0 def)
% Number of atoms : 333 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 305 ( 59 ~; 246 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 107 ( 107 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_01) ).
fof(f2,axiom,
! [X0] : iLEQ(X0,g(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13_02) ).
fof(f4,axiom,
! [X0] : iLEQ(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_04) ).
fof(f5,axiom,
! [X0] : ~ 'E'(f(X0),f(g(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31_05) ).
fof(f6,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s('0'))
| ~ iLEQ(X0,X1)
| 'E'('0',f(X1))
| 'LE'(f(X1),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_06) ).
fof(f7,axiom,
! [X0] : ~ 'LE'(f(X0),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_07) ).
fof(f10,axiom,
! [X0] :
( ~ 'E'(s(s(s(s(s('0'))))),f(X0))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_10) ).
fof(f11,axiom,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21_11) ).
fof(f12,axiom,
! [X0] :
( ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27_12) ).
fof(f13,axiom,
! [X0] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30_13) ).
fof(f15,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s('0'))))
| ~ iLEQ(X0,X1)
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16_15) ).
fof(f16,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s('0'))))))
| ~ iLEQ(X0,X1)
| 'E'(s(s(s(s('0')))),f(X1))
| 'LE'(f(X1),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_16) ).
fof(f17,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s('0')))))
| ~ iLEQ(X0,X1)
| 'E'(s(s(s('0'))),f(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26_17) ).
fof(f24,axiom,
! [X0] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29_24) ).
fof(f30,axiom,
! [X0] :
( ~ 'E'(s(s(s(s('0')))),f(X0))
| ~ 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_30) ).
fof(f32,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s('0')))
| ~ iLEQ(X0,X1)
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17_32) ).
fof(f33,plain,
! [X0] :
( ~ 'E'('0',f(g(X0)))
| ~ 'E'('0',f(X0)) ),
inference(forward_subsumption_resolution,[],[f24,f5]) ).
fof(f34,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s('0'))
| ~ iLEQ(X0,X1)
| 'E'('0',f(X1)) ),
inference(forward_subsumption_resolution,[],[f6,f7]) ).
fof(f35,plain,
! [X0] :
( ~ 'E'(s('0'),f(g(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[],[f13,f5]) ).
fof(f36,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(g(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(forward_subsumption_resolution,[],[f12,f5]) ).
fof(f37,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(g(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f11,f5]) ).
fof(f38,plain,
! [X0] :
( ~ 'E'(s(s(s(s('0')))),f(g(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f30,f5]) ).
fof(f39,plain,
! [X0] :
( ~ 'E'(s(s(s(s(s('0'))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f10,f5]) ).
fof(f40,plain,
! [X0,X1] :
( ~ iLEQ(X0,X1)
| 'E'(s(s(s(s('0')))),f(X1))
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s(s('0'))))),f(X0)) ),
inference(resolution,[],[f16,f1]) ).
fof(f41,plain,
! [X0] :
( 'E'(s(s(s(s(s('0'))))),f(X0))
| 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X0)) ),
inference(resolution,[],[f40,f4]) ).
fof(f42,plain,
! [X0] :
( 'LE'(f(g(X0)),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s(s(s(s('0'))))),f(X0)) ),
inference(resolution,[],[f40,f2]) ).
fof(f43,plain,
! [X0] :
( 'LE'(f(g(X0)),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(X0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X0)) ),
inference(resolution,[],[f41,f39]) ).
fof(f45,plain,
! [X0] :
( 'LE'(f(g(X0)),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(X0))) ),
inference(forward_subsumption_resolution,[],[f43,f42]) ).
fof(f46,plain,
! [X0,X1] :
( ~ iLEQ(g(X0),X1)
| 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s(s('0'))),f(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(resolution,[],[f45,f17]) ).
fof(f47,plain,
! [X0] :
( 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s(s('0'))),f(g(X0)))
| 'LE'(f(g(X0)),s(s(s('0')))) ),
inference(resolution,[],[f46,f4]) ).
fof(f48,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s(s(s('0')))),f(g(X0))) ),
inference(resolution,[],[f46,f2]) ).
fof(f49,plain,
! [X0] :
( ~ 'E'(s(s(s(s('0')))),f(X0))
| 'LE'(f(g(X0)),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(X0))) ),
inference(resolution,[],[f47,f38]) ).
fof(f50,plain,
! [X0,X1] :
( ~ iLEQ(g(g(X0)),X1)
| 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(resolution,[],[f48,f15]) ).
fof(f52,plain,
! [X0] :
( 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(g(g(X0))))
| 'LE'(f(g(g(X0))),s(s('0'))) ),
inference(resolution,[],[f50,f4]) ).
fof(f53,plain,
! [X0] :
( 'LE'(f(g(g(g(X0)))),s(s('0')))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s(s('0')))),f(g(X0))) ),
inference(resolution,[],[f50,f2]) ).
fof(f56,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(g(g(X0))))
| 'LE'(f(g(g(X0))),s(s('0')))
| 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(X0)))) ),
inference(resolution,[],[f52,f49]) ).
fof(f57,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s('0')),f(g(g(X0))))
| 'LE'(f(g(g(X0))),s(s('0')))
| 'E'(s(s(s('0'))),f(g(g(X0)))) ),
inference(duplicate_literal_removal,[],[f56]) ).
fof(f59,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(X0))),X1)
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f53,f32]) ).
fof(f63,plain,
! [X0,X1] :
( ~ iLEQ(g(g(X0)),X1)
| 'LE'(f(g(g(X0))),s(s('0')))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(g(g(X0))))
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(resolution,[],[f57,f15]) ).
fof(f69,plain,
! [X0] :
( 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0')) ),
inference(resolution,[],[f59,f4]) ).
fof(f70,plain,
! [X0] :
( 'LE'(f(g(g(g(g(X0))))),s('0'))
| 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0))))) ),
inference(resolution,[],[f59,f2]) ).
fof(f74,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s('0')))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(g(g(X0))))
| 'E'(s(s('0')),f(g(g(X0))))
| 'LE'(f(g(g(X0))),s(s('0'))) ),
inference(resolution,[],[f63,f4]) ).
fof(f76,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(X0))))
| 'LE'(f(g(g(X0))),s(s('0')))
| 'E'(s(s('0')),f(g(g(X0)))) ),
inference(duplicate_literal_removal,[],[f74]) ).
fof(f78,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(g(X0)))
| 'E'(s(s('0')),f(g(g(X0))))
| 'LE'(f(g(g(X0))),s(s('0'))) ),
inference(resolution,[],[f76,f37]) ).
fof(f81,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(X0)))) ),
inference(resolution,[],[f69,f49]) ).
fof(f82,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s(s('0')),f(g(g(g(X0))))) ),
inference(duplicate_literal_removal,[],[f81]) ).
fof(f87,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(g(X0)))),X1)
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'('0',f(X1)) ),
inference(resolution,[],[f70,f34]) ).
fof(f101,plain,
! [X0,X1] :
( ~ iLEQ(g(g(X0)),X1)
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(resolution,[],[f82,f15]) ).
fof(f106,plain,
! [X0] :
( 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(resolution,[],[f87,f4]) ).
fof(f107,plain,
! [X0] :
( 'E'(s(s(s(s('0')))),f(g(X0)))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(g(X0))))))) ),
inference(resolution,[],[f87,f2]) ).
fof(f116,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(X0)))) ),
inference(resolution,[],[f106,f49]) ).
fof(f117,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0)))))) ),
inference(duplicate_literal_removal,[],[f116]) ).
fof(f124,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(X0)))) ),
inference(resolution,[],[f107,f49]) ).
fof(f125,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s(s('0'))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0)))))) ),
inference(duplicate_literal_removal,[],[f124]) ).
fof(f139,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s(s('0'))) ),
inference(resolution,[],[f101,f2]) ).
fof(f140,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'LE'(f(g(g(g(X0)))),s(s('0'))) ),
inference(duplicate_literal_removal,[],[f139]) ).
fof(f141,plain,
! [X0] :
( 'LE'(f(g(g(g(X0)))),s(s('0')))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s('0'),f(g(g(g(X0))))) ),
inference(forward_subsumption_resolution,[],[f140,f78]) ).
fof(f142,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(X0))),X1)
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f141,f32]) ).
fof(f143,plain,
! [X0,X1] :
( ~ iLEQ(g(g(X0)),X1)
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(resolution,[],[f117,f15]) ).
fof(f156,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0')) ),
inference(resolution,[],[f142,f4]) ).
fof(f158,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s('0'),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s('0')) ),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f162,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(g(g(X0))))
| 'LE'(f(g(g(g(X0)))),s('0'))
| 'E'(s('0'),f(g(g(g(X0))))) ),
inference(resolution,[],[f158,f36]) ).
fof(f163,plain,
! [X0,X1] :
( ~ iLEQ(g(g(X0)),X1)
| 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(resolution,[],[f125,f15]) ).
fof(f212,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s(s('0'))) ),
inference(resolution,[],[f143,f2]) ).
fof(f213,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s(s('0'))) ),
inference(duplicate_literal_removal,[],[f212]) ).
fof(f214,plain,
! [X0] :
( 'LE'(f(g(g(g(X0)))),s(s('0')))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(forward_subsumption_resolution,[],[f213,f78]) ).
fof(f221,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(X0))),X1)
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f214,f32]) ).
fof(f223,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s(s('0'))) ),
inference(resolution,[],[f163,f2]) ).
fof(f224,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(X0))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s(s('0'))) ),
inference(duplicate_literal_removal,[],[f223]) ).
fof(f225,plain,
! [X0] :
( 'LE'(f(g(g(g(X0)))),s(s('0')))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(g(X0))))))) ),
inference(forward_subsumption_resolution,[],[f224,f78]) ).
fof(f253,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(X0))),X1)
| 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f225,f32]) ).
fof(f320,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'LE'(f(g(g(g(g(X0))))),s('0')) ),
inference(resolution,[],[f221,f2]) ).
fof(f321,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'LE'(f(g(g(g(g(X0))))),s('0')) ),
inference(duplicate_literal_removal,[],[f320]) ).
fof(f322,plain,
! [X0] :
( 'LE'(f(g(g(g(g(X0))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(forward_subsumption_resolution,[],[f321,f162]) ).
fof(f323,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(g(X0)))),X1)
| 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(X1)) ),
inference(resolution,[],[f322,f34]) ).
fof(f325,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'LE'(f(g(g(g(g(X0))))),s('0')) ),
inference(resolution,[],[f253,f2]) ).
fof(f326,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'LE'(f(g(g(g(g(X0))))),s('0')) ),
inference(duplicate_literal_removal,[],[f325]) ).
fof(f327,plain,
! [X0] :
( 'LE'(f(g(g(g(g(X0))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(g(g(g(g(g(X0))))))) ),
inference(forward_subsumption_resolution,[],[f326,f162]) ).
fof(f328,plain,
! [X0,X1] :
( 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(g(g(g(g(g(X0)))))))
| ~ iLEQ(g(g(g(g(X0)))),X1)
| 'E'('0',f(X1)) ),
inference(resolution,[],[f327,f34]) ).
fof(f329,plain,
! [X0] :
( 'E'('0',f(g(g(g(g(X0))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(resolution,[],[f323,f4]) ).
fof(f331,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(duplicate_literal_removal,[],[f329]) ).
fof(f335,plain,
! [X0] :
( ~ 'E'(s('0'),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(resolution,[],[f331,f35]) ).
fof(f384,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(g(X0)))),X1)
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'('0',f(X1)) ),
inference(forward_subsumption_resolution,[],[f328,f335]) ).
fof(f386,plain,
! [X0] :
( 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'('0',f(g(g(g(g(g(X0))))))) ),
inference(resolution,[],[f384,f2]) ).
fof(f387,plain,
! [X0] : 'E'('0',f(g(g(g(g(g(X0))))))),
inference(duplicate_literal_removal,[],[f386]) ).
fof(f390,plain,
! [X0] : ~ 'E'('0',f(g(g(g(g(X0)))))),
inference(resolution,[],[f387,f33]) ).
fof(f397,plain,
$false,
inference(resolution,[],[f390,f387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO630-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 18:02:27 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (2851170)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (2851179)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3193520621:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (2851176)% WARNING: option uhcvi not known.
% 0.20/0.27 % (2851175)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1341928366_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (2851176)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4188387351:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (2851180)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=361688093:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (2851177)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3237981527:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (2851178)dis+10_1_sil=32000:sp=arity:random_seed=3934273279:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (2851181)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=681474285:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % TRYING [1]
% 0.20/0.27 % TRYING [2]
% 0.20/0.27 % TRYING [3]
% 0.20/0.27 % TRYING [4]
% 0.20/0.27 % (2851178) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2851170-2851178"...
% 0.20/0.27 % (2851178)...printing done.
% 0.20/0.27 % (2851178)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2851178)------------------------------
% 0.20/0.27 % (2851178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2851178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2851178)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2851178)Termination reason: Refutation
% 0.20/0.27 % (2851178)Time elapsed: 0.014 s
% 0.20/0.27 % (2851178)Peak memory usage: 11 MB
% 0.20/0.27 % (2851178)Instructions burned: 25 (million)
% 0.20/0.27 % (2851170)Success in time 0.048 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------