%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n008.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 02:28:28 PM UTC 2026
% Result : Unsatisfiable 5.74s 1.57s
% Output : Refutation 6.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% 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 : 304 ( 58 ~; 246 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 106 ( 106 !; 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(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(f25,axiom,
! [X0] : iLEQ(X0,g(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22_25) ).
fof(f29,axiom,
! [X0] : iLEQ(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2_29) ).
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(f31,axiom,
! [X0] : ~ 'E'(f(X0),f(g(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24_31) ).
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'(s(s(s(s('0')))),f(g(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f30,f31]) ).
fof(f34,plain,
! [X0] :
( ~ 'E'('0',f(g(X0)))
| ~ 'E'('0',f(X0)) ),
inference(forward_subsumption_resolution,[],[f24,f31]) ).
fof(f35,plain,
! [X0] :
( ~ 'E'(s('0'),f(g(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[],[f13,f31]) ).
fof(f36,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(g(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(forward_subsumption_resolution,[],[f12,f31]) ).
fof(f37,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(g(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f11,f31]) ).
fof(f38,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,f31]) ).
fof(f39,plain,
! [X0,X1] :
( ~ 'LE'(f(X0),s('0'))
| ~ iLEQ(X0,X1)
| 'E'('0',f(X1)) ),
inference(forward_subsumption_resolution,[],[f6,f7]) ).
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,f29]) ).
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,f25]) ).
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,f38]) ).
fof(f44,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,[],[f44,f17]) ).
fof(f49,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,f29]) ).
fof(f50,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,f25]) ).
fof(f52,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,[],[f49,f33]) ).
fof(f55,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,[],[f50,f15]) ).
fof(f59,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,[],[f55,f29]) ).
fof(f60,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,[],[f55,f25]) ).
fof(f63,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,[],[f59,f52]) ).
fof(f64,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,[],[f63]) ).
fof(f67,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,[],[f60,f32]) ).
fof(f73,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,[],[f64,f15]) ).
fof(f78,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,[],[f67,f29]) ).
fof(f79,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,[],[f67,f25]) ).
fof(f88,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,[],[f73,f29]) ).
fof(f90,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,[],[f88]) ).
fof(f92,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,[],[f90,f37]) ).
fof(f95,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,[],[f78,f52]) ).
fof(f96,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,[],[f95]) ).
fof(f101,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,[],[f79,f39]) ).
fof(f116,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,[],[f96,f15]) ).
fof(f121,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,[],[f101,f29]) ).
fof(f122,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,[],[f101,f25]) ).
fof(f135,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,[],[f121,f52]) ).
fof(f136,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,[],[f135]) ).
fof(f143,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,[],[f122,f52]) ).
fof(f144,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,[],[f143]) ).
fof(f158,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,[],[f116,f25]) ).
fof(f159,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,[],[f158]) ).
fof(f160,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,[],[f159,f92]) ).
fof(f161,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,[],[f160,f32]) ).
fof(f162,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,[],[f136,f15]) ).
fof(f163,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,[],[f161,f29]) ).
fof(f165,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,[],[f163]) ).
fof(f172,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,[],[f165,f36]) ).
fof(f182,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,[],[f144,f15]) ).
fof(f247,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,[],[f162,f25]) ).
fof(f248,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,[],[f247]) ).
fof(f249,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,[],[f248,f92]) ).
fof(f250,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,[],[f249,f32]) ).
fof(f252,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,[],[f182,f25]) ).
fof(f253,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,[],[f252]) ).
fof(f254,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,[],[f253,f92]) ).
fof(f255,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,[],[f254,f32]) ).
fof(f333,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,[],[f250,f25]) ).
fof(f334,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,[],[f333]) ).
fof(f335,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,[],[f334,f172]) ).
fof(f336,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,[],[f335,f39]) ).
fof(f338,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,[],[f255,f25]) ).
fof(f339,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,[],[f338]) ).
fof(f340,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,[],[f339,f172]) ).
fof(f341,plain,
! [X0,X1] :
( ~ iLEQ(g(g(g(g(X0)))),X1)
| 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(X1)) ),
inference(resolution,[],[f340,f39]) ).
fof(f344,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,[],[f336,f29]) ).
fof(f346,plain,
! [X0] :
( 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(duplicate_literal_removal,[],[f344]) ).
fof(f349,plain,
! [X0] :
( ~ 'E'(s('0'),f(g(g(g(X0)))))
| 'E'('0',f(g(g(g(g(X0)))))) ),
inference(resolution,[],[f346,f35]) ).
fof(f391,plain,
! [X0] :
( 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0))))))
| 'E'('0',f(g(g(g(g(g(X0))))))) ),
inference(resolution,[],[f341,f25]) ).
fof(f392,plain,
! [X0] :
( 'E'('0',f(g(g(g(g(g(X0)))))))
| 'E'(s('0'),f(g(g(g(g(X0)))))) ),
inference(duplicate_literal_removal,[],[f391]) ).
fof(f393,plain,
! [X0] : 'E'('0',f(g(g(g(g(g(X0))))))),
inference(forward_subsumption_resolution,[],[f392,f349]) ).
fof(f405,plain,
! [X0] : ~ 'E'('0',f(g(g(g(g(X0)))))),
inference(resolution,[],[f393,f34]) ).
fof(f414,plain,
$false,
inference(resolution,[],[f405,f393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO630-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 17:59:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.74/1.57 % (2477376)Input is clausal, will run a generic CNF schedule.
% 5.74/1.57 % (2477387)dis-21_1_sil=8000:lcm=predicate:random_seed=1254511594:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 5.74/1.57 % (2477387)Instruction limit reached!
% 5.74/1.57 % (2477387)------------------------------
% 5.74/1.57 % (2477387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477387)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477387)Termination reason: Instruction limit
% 5.74/1.57 % (2477387)Termination phase: Saturation
% 5.74/1.57 % (2477387)Time elapsed: 0.030 s
% 5.74/1.57 % (2477387)Peak memory usage: 87 MB
% 5.74/1.57 % (2477387)Instructions burned: 121 (million)
% 5.74/1.57 % (2477382)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2428603685:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.74/1.57 % (2477384)lrs+10_1_sil=8000:sp=occurrence:random_seed=909215703:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.74/1.57 % (2477383)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=703816906:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.74/1.57 % (2477381)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=1774580174:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.74/1.57 % (2477385)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1668799629:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.74/1.57 % (2477384)Refutation not found, incomplete strategy
% 5.74/1.57 % (2477384)------------------------------
% 5.74/1.57 % (2477384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477385)Refutation not found, incomplete strategy
% 5.74/1.57 % (2477385)------------------------------
% 5.74/1.57 % (2477385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477385)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477384)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477385)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.57 % (2477385)Time elapsed: 0.001 s
% 5.74/1.57 % (2477384)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.57 % (2477384)Time elapsed: 0.001 s
% 5.74/1.57 % (2477384)Peak memory usage: 85 MB
% 5.74/1.57 % (2477385)Peak memory usage: 85 MB
% 5.74/1.57 % (2477386)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3537553432:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.74/1.57 % (2477386)Instruction limit reached!
% 5.74/1.57 % (2477386)------------------------------
% 5.74/1.57 % (2477386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477386)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477386)Termination reason: Instruction limit
% 5.74/1.57 % (2477386)Termination phase: Saturation
% 5.74/1.57 % (2477386)Time elapsed: 0.074 s
% 5.74/1.57 % (2477386)Peak memory usage: 88 MB
% 5.74/1.57 % (2477386)Instructions burned: 181 (million)
% 5.74/1.57 % (2477389)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2695759535:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.74/1.57 % (2477389)Refutation not found, incomplete strategy
% 5.74/1.57 % (2477389)------------------------------
% 5.74/1.57 % (2477389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477389)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477389)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.57 % (2477389)Time elapsed: 0.0000 s
% 5.74/1.57 % (2477389)Peak memory usage: 86 MB
% 5.74/1.57 % (2477384)------------------------------
% 5.74/1.57 % (2477384)------------------------------
% 5.74/1.57 % (2477385)------------------------------
% 5.74/1.57 % (2477385)------------------------------
% 5.74/1.57 % (2477389)------------------------------
% 5.74/1.57 % (2477389)------------------------------
% 5.74/1.57 % (2477396)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2213261259:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.74/1.57 % (2477396)Refutation not found, incomplete strategy
% 5.74/1.57 % (2477396)------------------------------
% 5.74/1.57 % (2477396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477396)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477396)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.57 % (2477396)Time elapsed: 0.001 s
% 5.74/1.57 % (2477396)Peak memory usage: 86 MB
% 5.74/1.57 % (2477401)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3024158066:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.74/1.57 % (2477399)lrs+10_64_to=lpo:sil=8000:random_seed=2509452856:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.74/1.57 % (2477398)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2410440379:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.74/1.57 % (2477398)Refutation not found, incomplete strategy
% 5.74/1.57 % (2477398)------------------------------
% 5.74/1.57 % (2477398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477398)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477398)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.57 % (2477398)Time elapsed: 0.0000 s
% 5.74/1.57 % (2477398)Peak memory usage: 86 MB
% 5.74/1.57 % (2477401)Instruction limit reached!
% 5.74/1.57 % (2477401)------------------------------
% 5.74/1.57 % (2477401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477401)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477401)Termination reason: Instruction limit
% 5.74/1.57 % (2477401)Termination phase: Saturation
% 5.74/1.57 % (2477401)Time elapsed: 0.042 s
% 5.74/1.57 % (2477401)Peak memory usage: 88 MB
% 5.74/1.57 % (2477401)Instructions burned: 197 (million)
% 5.74/1.57 % (2477399)Instruction limit reached!
% 5.74/1.57 % (2477399)------------------------------
% 5.74/1.57 % (2477399)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477399)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477399)Termination reason: Instruction limit
% 5.74/1.57 % (2477399)Termination phase: Saturation
% 5.74/1.57 % (2477399)Time elapsed: 0.059 s
% 5.74/1.57 % (2477399)Peak memory usage: 87 MB
% 5.74/1.57 % (2477399)Instructions burned: 126 (million)
% 5.74/1.57 % (2477396)------------------------------
% 5.74/1.57 % (2477396)------------------------------
% 5.74/1.57 % (2477405)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=164262124:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.74/1.57 % (2477405)First to succeed.
% 5.74/1.57 % (2477405)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2477376"
% 5.74/1.57 % (2477382)Refutation not found, incomplete strategy
% 5.74/1.57 % (2477382)------------------------------
% 5.74/1.57 % (2477382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477382)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477382)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.57 % (2477382)Time elapsed: 0.585 s
% 5.74/1.57 % (2477382)Peak memory usage: 125 MB
% 5.74/1.57 % (2477382)Instructions burned: 867 (million)
% 5.74/1.57 % (2477406)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3305271066:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 5.74/1.57 % (2477381)Also succeeded, but the first one will report.
% 5.74/1.57 % (2477398)------------------------------
% 5.74/1.57 % (2477398)------------------------------
% 5.74/1.57 % (2477407)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3168847271:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 5.74/1.57 % (2477407)Refutation not found, incomplete strategy
% 5.74/1.57 % (2477407)------------------------------
% 5.74/1.57 % (2477407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.57 % (2477407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.57 % (2477407)CaDiCaL version: 2.1.3
% 5.74/1.57 % (2477407)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.57 % (2477407)Time elapsed: 0.001 s
% 5.74/1.57 % (2477407)Peak memory usage: 86 MB
% 5.74/1.57 % (2477405)Refutation found. Thanks to Tanya!
% 5.74/1.57 % SZS status Unsatisfiable for theBenchmark
% 5.74/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 6.93/1.76 % (2477405)------------------------------
% 6.93/1.76 % (2477405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.76 % (2477405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.76 % (2477405)CaDiCaL version: 2.1.3
% 6.93/1.76 % (2477405)Termination reason: Refutation
% 6.93/1.76 % (2477405)Time elapsed: 0.008 s
% 6.93/1.76 % (2477405)Peak memory usage: 88 MB
% 6.93/1.76 % (2477405)Instructions burned: 24 (million)
% 6.93/1.76 % (2477405)------------------------------
% 6.93/1.76 % (2477405)------------------------------
% 6.93/1.76 % (2477376)Success in time 0.896 s
% 6.93/1.76 % Vampire exiting
%------------------------------------------------------------------------------