%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO631-1 : 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 0.40s 0.33s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 26
% Syntax : Number of formulae : 102 ( 9 unt; 0 def)
% Number of atoms : 293 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 281 ( 90 ~; 191 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 12 ( 4 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 : 132 ( 132 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27_01) ).
fof(f2,axiom,
! [X0] : iLEQ(X0,g(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_02) ).
fof(f3,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_8_03) ).
fof(f4,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| ~ iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_48_04) ).
fof(f5,axiom,
! [X0] : ~ 'E'(f(X0),f(g(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19_05) ).
fof(f6,axiom,
! [X0] : iLEQ(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_06) ).
fof(f7,axiom,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_44_07) ).
fof(f11,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s('0')))))))
| ~ iLEQ(X0,X1)
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5_11) ).
fof(f12,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_29_12) ).
fof(f13,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0'))))))))))
| ~ iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_13) ).
fof(f16,axiom,
! [X0] :
( ~ 'E'(s(s(s(s(s(s('0')))))),f(X0))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_16) ).
fof(f19,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| ~ iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s(s('0'))))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s(s('0')))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26_19) ).
fof(f21,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_23_21) ).
fof(f22,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_20_22) ).
fof(f23,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_40_23) ).
fof(f25,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_2_25) ).
fof(f31,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_56_31) ).
fof(f32,axiom,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_42_32) ).
fof(f35,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_35) ).
fof(f36,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_0_36) ).
fof(f39,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_49_39) ).
fof(f45,axiom,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s('0'))))))))
| ~ iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s('0')))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s('0'))))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_54_45) ).
fof(f48,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_55_48) ).
fof(f50,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_51_50) ).
fof(f52,axiom,
! [X0] : ~ 'LE'(f(X0),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_38_52) ).
fof(f54,axiom,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0)))
| 'E'(f(X0),f(g(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31_54) ).
fof(f58,plain,
! [X0] : ~ iLEQ(X0,g(X0)),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f59,plain,
! [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')))) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f60,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f61,plain,
! [X0] : ~ iLEQ(X0,X0),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f64,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s('0')))))))
| iLEQ(X0,X1)
| 'E'(s(s(s(s(s('0'))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s('0')))))) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f65,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0'))))))))))
| iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f69,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s(s('0'))))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s(s('0')))))))) ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f71,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s('0')))
| iLEQ(X0,X1)
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f75,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s('0'))
| iLEQ(X0,X1)
| 'E'('0',f(X1))
| 'LE'(f(X1),'0') ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f78,plain,
! [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'))))) ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f84,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s(s(s(s(s('0'))))))))
| iLEQ(X0,X1)
| 'E'(s(s(s(s(s(s('0')))))),f(X1))
| 'LE'(f(X1),s(s(s(s(s(s('0'))))))) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f87,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s(s(s('0'))))
| iLEQ(X0,X1)
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f90,plain,
! [X0] :
( ~ 'E'('0',f(g(X0)))
| ~ 'E'('0',f(X0)) ),
inference(forward_subsumption_resolution,[],[f25,f5]) ).
fof(f91,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s('0'))
| iLEQ(X0,X1)
| 'E'('0',f(X1)) ),
inference(forward_subsumption_resolution,[],[f75,f52]) ).
fof(f92,plain,
! [X0] :
( ~ 'E'(s('0'),f(g(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[],[f35,f5]) ).
fof(f93,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(g(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(forward_subsumption_resolution,[],[f22,f5]) ).
fof(f94,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(g(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f12,f5]) ).
fof(f95,plain,
! [X0] :
( ~ 'E'(s(s(s(s('0')))),f(g(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f48,f5]) ).
fof(f96,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,[],[f23,f5]) ).
fof(f97,plain,
! [X0] :
( ~ 'E'(s(s(s(s(s(s('0')))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f16,f5]) ).
fof(f98,plain,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f7,f5]) ).
fof(f99,plain,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f54,f5]) ).
fof(f100,plain,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f1,f5]) ).
fof(f101,plain,
! [X0] :
( ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f32,f5]) ).
fof(f102,plain,
! [X0,X1] :
( iLEQ(X0,X1)
| 'LE'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X1)) ),
inference(resolution,[],[f60,f39]) ).
fof(f103,plain,
! [X0] :
( 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0))
| 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0)) ),
inference(resolution,[],[f102,f61]) ).
fof(f104,plain,
! [X0] :
( 'LE'(f(g(X0)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0))) ),
inference(resolution,[],[f102,f58]) ).
fof(f107,plain,
! [X0] :
( 'LE'(f(g(X0)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)) ),
inference(resolution,[],[f103,f101]) ).
fof(f121,plain,
! [X0] :
( 'LE'(f(g(X0)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0))) ),
inference(forward_subsumption_resolution,[],[f107,f104]) ).
fof(f122,plain,
! [X0,X1] :
( 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| iLEQ(g(X0),X1)
| 'LE'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X1)) ),
inference(resolution,[],[f121,f65]) ).
fof(f131,plain,
! [X0] :
( 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| 'LE'(f(g(X0)),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0))) ),
inference(resolution,[],[f122,f61]) ).
fof(f132,plain,
! [X0] :
( 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| 'LE'(f(g(g(X0))),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(X0)))) ),
inference(resolution,[],[f122,f58]) ).
fof(f139,plain,
! [X0] :
( 'LE'(f(g(X0)),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0)) ),
inference(resolution,[],[f131,f100]) ).
fof(f145,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(X0)))) ),
inference(forward_subsumption_resolution,[],[f132,f139]) ).
fof(f152,plain,
! [X0,X1] :
( 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(X0))))
| iLEQ(g(g(X0)),X1)
| 'LE'(f(X1),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(X1)) ),
inference(resolution,[],[f145,f69]) ).
fof(f155,plain,
! [X0] :
( 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(X0))))
| 'LE'(f(g(g(X0))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(X0)))) ),
inference(resolution,[],[f152,f61]) ).
fof(f156,plain,
! [X0] :
( 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(g(X0))))
| 'LE'(f(g(g(g(X0)))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(X0))))) ),
inference(resolution,[],[f152,f58]) ).
fof(f220,plain,
! [X0] :
( 'LE'(f(g(g(X0))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(X0))))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0))) ),
inference(resolution,[],[f155,f99]) ).
fof(f243,plain,
! [X0] :
( 'LE'(f(g(g(g(X0)))),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(X0))))) ),
inference(forward_subsumption_resolution,[],[f156,f220]) ).
fof(f244,plain,
! [X0,X1] :
( 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(X0)))))
| iLEQ(g(g(g(X0))),X1)
| 'LE'(f(X1),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(X1)) ),
inference(resolution,[],[f243,f84]) ).
fof(f260,plain,
! [X0] :
( 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(X0)))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(X0))))) ),
inference(resolution,[],[f244,f61]) ).
fof(f261,plain,
! [X0] :
( 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(g(X0)))))
| 'LE'(f(g(g(g(g(X0))))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[],[f244,f58]) ).
fof(f271,plain,
! [X0] :
( 'LE'(f(g(g(g(X0)))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(X0)))))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(g(X0)))) ),
inference(resolution,[],[f260,f98]) ).
fof(f310,plain,
! [X0] :
( 'LE'(f(g(g(g(g(X0))))),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(X0)))))) ),
inference(forward_subsumption_resolution,[],[f261,f271]) ).
fof(f346,plain,
! [X0,X1] :
( 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(X0))))))
| iLEQ(g(g(g(g(X0)))),X1)
| 'LE'(f(X1),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(X1)) ),
inference(resolution,[],[f310,f64]) ).
fof(f348,plain,
! [X0] :
( 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(X0))))))
| 'LE'(f(g(g(g(g(X0))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[],[f346,f61]) ).
fof(f349,plain,
! [X0] :
( 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(g(X0))))))
| 'LE'(f(g(g(g(g(g(X0)))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[],[f346,f58]) ).
fof(f409,plain,
! [X0] :
( 'LE'(f(g(g(g(g(X0))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(X0))))))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(g(g(g(X0))))) ),
inference(resolution,[],[f348,f97]) ).
fof(f411,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(X0)))))),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(X0))))))) ),
inference(forward_subsumption_resolution,[],[f349,f409]) ).
fof(f430,plain,
! [X0,X1] :
( 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(X0)))))))
| iLEQ(g(g(g(g(g(X0))))),X1)
| 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X1)) ),
inference(resolution,[],[f411,f78]) ).
fof(f484,plain,
! [X0] :
( 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(X0)))))))
| 'LE'(f(g(g(g(g(g(X0)))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[],[f430,f61]) ).
fof(f485,plain,
! [X0] :
( 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(g(X0)))))))
| 'LE'(f(g(g(g(g(g(g(X0))))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(X0)))))))) ),
inference(resolution,[],[f430,f58]) ).
fof(f489,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(X0)))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(X0)))))))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(g(g(g(X0)))))) ),
inference(resolution,[],[f484,f96]) ).
fof(f507,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(g(X0))))))),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(X0)))))))) ),
inference(forward_subsumption_resolution,[],[f485,f489]) ).
fof(f581,plain,
! [X0,X1] :
( 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(X0))))))))
| iLEQ(g(g(g(g(g(g(X0)))))),X1)
| 'E'(s(s(s('0'))),f(X1))
| 'LE'(f(X1),s(s(s('0')))) ),
inference(resolution,[],[f507,f59]) ).
fof(f583,plain,
! [X0] :
( 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(X0))))))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(X0))))))))
| 'LE'(f(g(g(g(g(g(g(X0))))))),s(s(s('0')))) ),
inference(resolution,[],[f581,f61]) ).
fof(f584,plain,
! [X0] :
( 'E'(s(s(s(s('0')))),f(g(g(g(g(g(g(X0))))))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(X0)))))))))
| 'LE'(f(g(g(g(g(g(g(g(X0)))))))),s(s(s('0')))) ),
inference(resolution,[],[f581,f58]) ).
fof(f674,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(g(X0))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(X0))))))))
| ~ 'E'(s(s(s(s('0')))),f(g(g(g(g(g(X0))))))) ),
inference(resolution,[],[f583,f95]) ).
fof(f800,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(g(g(X0)))))))),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(X0))))))))) ),
inference(forward_subsumption_resolution,[],[f584,f674]) ).
fof(f801,plain,
! [X0,X1] :
( 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(X0)))))))))
| iLEQ(g(g(g(g(g(g(g(X0))))))),X1)
| 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0'))) ),
inference(resolution,[],[f800,f87]) ).
fof(f803,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(X0)))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(X0)))))))))
| 'LE'(f(g(g(g(g(g(g(g(X0)))))))),s(s('0'))) ),
inference(resolution,[],[f801,f61]) ).
fof(f804,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(g(g(g(g(g(g(g(X0)))))))))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(X0))))))))))
| 'LE'(f(g(g(g(g(g(g(g(g(X0))))))))),s(s('0'))) ),
inference(resolution,[],[f801,f58]) ).
fof(f914,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(g(g(X0)))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(X0)))))))))
| ~ 'E'(s(s(s('0'))),f(g(g(g(g(g(g(X0)))))))) ),
inference(resolution,[],[f803,f94]) ).
fof(f1081,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(g(g(g(X0))))))))),s(s('0')))
| 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(X0)))))))))) ),
inference(forward_subsumption_resolution,[],[f804,f914]) ).
fof(f1082,plain,
! [X0,X1] :
( 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(X0))))))))))
| iLEQ(g(g(g(g(g(g(g(g(X0)))))))),X1)
| 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0')) ),
inference(resolution,[],[f1081,f71]) ).
fof(f1084,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(X0))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(X0))))))))))
| 'LE'(f(g(g(g(g(g(g(g(g(X0))))))))),s('0')) ),
inference(resolution,[],[f1082,f61]) ).
fof(f1085,plain,
! [X0] :
( 'E'(s(s('0')),f(g(g(g(g(g(g(g(g(X0))))))))))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(X0)))))))))))
| 'LE'(f(g(g(g(g(g(g(g(g(g(X0)))))))))),s('0')) ),
inference(resolution,[],[f1082,f58]) ).
fof(f1096,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(g(g(g(X0))))))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(X0))))))))))
| ~ 'E'(s(s('0')),f(g(g(g(g(g(g(g(X0))))))))) ),
inference(resolution,[],[f1084,f93]) ).
fof(f1125,plain,
! [X0] :
( 'LE'(f(g(g(g(g(g(g(g(g(g(X0)))))))))),s('0'))
| 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(forward_subsumption_resolution,[],[f1085,f1096]) ).
fof(f1126,plain,
! [X0,X1] :
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(X0)))))))))))
| iLEQ(g(g(g(g(g(g(g(g(g(X0))))))))),X1)
| 'E'('0',f(X1)) ),
inference(resolution,[],[f1125,f91]) ).
fof(f1208,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(X0)))))))))))
| 'E'('0',f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(resolution,[],[f1126,f61]) ).
fof(f1209,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(g(g(g(g(g(g(X0)))))))))))
| 'E'('0',f(g(g(g(g(g(g(g(g(g(g(X0)))))))))))) ),
inference(resolution,[],[f1126,f58]) ).
fof(f1242,plain,
! [X0] :
( ~ 'E'(s('0'),f(g(g(g(g(g(g(g(g(X0))))))))))
| 'E'('0',f(g(g(g(g(g(g(g(g(g(X0))))))))))) ),
inference(resolution,[],[f1208,f92]) ).
fof(f1260,plain,
! [X0] : 'E'('0',f(g(g(g(g(g(g(g(g(g(g(X0)))))))))))),
inference(forward_subsumption_resolution,[],[f1209,f1242]) ).
fof(f1261,plain,
! [X0] : ~ 'E'('0',f(g(g(g(g(g(g(g(g(g(X0))))))))))),
inference(resolution,[],[f1260,f90]) ).
fof(f1265,plain,
$false,
inference(backward_subsumption_resolution,[],[f1260,f1261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n015.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 18:02:32 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 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
% 0.40/0.33 % (2851599)Will run a generic schedule for satisfiability detection.
% 0.40/0.33 % (2851604)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1061163883_2999 on theBenchmark for (2999ds/0Mi)
% 0.40/0.33 % TRYING [1]
% 0.40/0.33 % TRYING [2]
% 0.40/0.33 % TRYING [3]
% 0.40/0.33 % (2851606)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=831571941:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.40/0.33 % (2851607)dis+10_1_sil=32000:sp=arity:random_seed=3511348043:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.40/0.33 % (2851608)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1926263339:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.40/0.33 % (2851609)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2178399277:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.40/0.33 % (2851610)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=484041472:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.40/0.33 % (2851605)% WARNING: option uhcvi not known.
% 0.40/0.33 % TRYING [4]
% 0.40/0.33 % (2851605)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3676376048:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.40/0.33 % TRYING [5]
% 0.40/0.33 % (2851608)Instruction limit reached!
% 0.40/0.33 % (2851608)------------------------------
% 0.40/0.33 % (2851608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.33 % (2851608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.33 % (2851608)CaDiCaL version: 2.1.3
% 0.40/0.33 % (2851608)Termination reason: Instruction limit
% 0.40/0.33 % (2851608)Termination phase: Saturation
% 0.40/0.33 % (2851608)Time elapsed: 0.049 s
% 0.40/0.33 % (2851608)Peak memory usage: 11 MB
% 0.40/0.33 % (2851608)Instructions burned: 118 (million)
% 0.40/0.33 % (2851607)Instruction limit reached!
% 0.40/0.33 % (2851607)------------------------------
% 0.40/0.33 % (2851607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.33 % (2851607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.33 % (2851607)CaDiCaL version: 2.1.3
% 0.40/0.33 % (2851607)Termination reason: Instruction limit
% 0.40/0.33 % (2851607)Termination phase: Saturation
% 0.40/0.33 % (2851607)Time elapsed: 0.053 s
% 0.40/0.33 % (2851607)Peak memory usage: 11 MB
% 0.40/0.33 % (2851607)Instructions burned: 103 (million)
% 0.40/0.33 % (2851609)Instruction limit reached!
% 0.40/0.33 % (2851609)------------------------------
% 0.40/0.33 % (2851609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.33 % (2851609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.33 % (2851609)CaDiCaL version: 2.1.3
% 0.40/0.33 % (2851609)Termination reason: Instruction limit
% 0.40/0.33 % (2851609)Termination phase: Saturation
% 0.40/0.33 % (2851609)Time elapsed: 0.061 s
% 0.40/0.33 % (2851609)Peak memory usage: 11 MB
% 0.40/0.33 % (2851609)Instructions burned: 133 (million)
% 0.40/0.33 % (2851618)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=363516092:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.40/0.33 % (2851610)Instruction limit reached!
% 0.40/0.33 % (2851610)------------------------------
% 0.40/0.33 % (2851610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.33 % (2851610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.33 % (2851610)CaDiCaL version: 2.1.3
% 0.40/0.33 % (2851610)Termination reason: Instruction limit
% 0.40/0.33 % (2851610)Termination phase: Saturation
% 0.40/0.33 % (2851610)Time elapsed: 0.071 s
% 0.40/0.33 % (2851610)Peak memory usage: 11 MB
% 0.40/0.33 % (2851610)Instructions burned: 160 (million)
% 0.40/0.33 % (2851619)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=692305759:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.40/0.33 % TRYING [1]
% 0.40/0.33 % TRYING [2]
% 0.40/0.33 % TRYING [3]
% 0.40/0.33 % (2851605) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2851599-2851605"...
% 0.40/0.33 % (2851605)...printing done.
% 0.40/0.33 % (2851620)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3136533069:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.40/0.33 % (2851605)Refutation found. Thanks to Tanya!
% 0.40/0.33 % SZS status Unsatisfiable for theBenchmark
% 0.40/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.40/0.33 % (2851605)------------------------------
% 0.40/0.33 % (2851605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.33 % (2851605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.33 % (2851605)CaDiCaL version: 2.1.3
% 0.40/0.33 % (2851605)Termination reason: Refutation
% 0.40/0.33 % (2851605)Time elapsed: 0.075 s
% 0.40/0.33 % (2851605)Peak memory usage: 12 MB
% 0.40/0.33 % (2851605)Instructions burned: 148 (million)
% 0.40/0.33 % (2851599)Success in time 0.116 s
% 0.40/0.33 % Vampire exiting
%------------------------------------------------------------------------------