%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO674-1 : 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 : n001.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 02:32:21 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 22
% Syntax : Number of formulae : 148 ( 10 unt; 8 def)
% Number of atoms : 646 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 918 ( 420 ~; 490 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 132 ( 0 sgn 132 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X5),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X5))
| ~ 'E'(s('0'),f(suc(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_193) ).
fof(f2,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_298) ).
fof(f3,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_281) ).
fof(f4,axiom,
! [X0] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_176) ).
fof(f5,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_139) ).
fof(f6,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_126) ).
fof(f7,axiom,
! [X0] : 'LE'(f(X0),s(s(s('0')))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_498) ).
fof(f8,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_204) ).
fof(f9,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_129) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X4),suc(X5))
| ~ iLEQ(suc(X5),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'(s(s('0')),f(X5))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X5)))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_431) ).
fof(f11,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_50) ).
fof(f12,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_84) ).
fof(f13,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_493) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X2))
| ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X2),suc(X5))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X5))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X5)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_453) ).
fof(f15,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(forward_subsumption_resolution,[],[f5,f7]) ).
fof(f16,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f2,f15]) ).
fof(f17,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(X0))
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f16,f4]) ).
fof(f18,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f16,f11]) ).
fof(f19,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f12,f15]) ).
fof(f20,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f9,f7]) ).
fof(f21,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f20,f2]) ).
fof(f22,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0)))) ),
inference(resolution,[],[f20,f12]) ).
fof(f37,plain,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X4))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f14,f3]) ).
fof(f38,plain,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X4))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X4)) ),
inference(duplicate_literal_removal,[],[f37]) ).
fof(f53,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f21,f4]) ).
fof(f54,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f21,f11]) ).
fof(f68,plain,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X0),suc(X4))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f1,f13]) ).
fof(f71,plain,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X0),suc(X4))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2))) ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f85,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f19,f4]) ).
fof(f86,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f19,f11]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f10,f6]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X4))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f99]) ).
fof(f117,plain,
( 'E'(s(s('0')),f(z))
| 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[],[f17,f8]) ).
fof(f119,definition,
( spl0_1
<=> 'E'(s('0'),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f120,plain,
( ~ 'E'(s('0'),f(z))
| spl0_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f123,definition,
( spl0_2
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f124,plain,
( ~ 'E'('0',f(z))
| spl0_2 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( 'E'('0',f(z))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f127,definition,
( spl0_3
<=> 'E'(s(s('0')),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f129,plain,
( 'E'(s(s('0')),f(z))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f117,f127,f123,f119]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f38,f3]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X2)) ),
inference(duplicate_literal_removal,[],[f142]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f71,f13]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2))) ),
inference(duplicate_literal_removal,[],[f165]) ).
fof(f179,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f22,f4]) ).
fof(f180,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(suc(suc(X0)))))
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f22,f11]) ).
fof(f205,plain,
( 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[],[f53,f8]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f104,f6]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X3))) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f230,plain,
( 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f85,f8]) ).
fof(f255,plain,
( 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f18,f8]) ).
fof(f257,definition,
( spl0_4
<=> 'E'(s('0'),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f258,plain,
( ~ 'E'(s('0'),f(suc(z)))
| spl0_4 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( 'E'(s('0'),f(suc(z)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f261,definition,
( spl0_5
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f262,plain,
( ~ 'E'('0',f(suc(z)))
| spl0_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( 'E'('0',f(suc(z)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f265,definition,
( spl0_6
<=> 'E'(s(s('0')),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f266,plain,
( ~ 'E'(s(s('0')),f(suc(z)))
| spl0_6 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f267,plain,
( 'E'(s(s('0')),f(suc(z)))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f268,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f255,f265,f261,f257]) ).
fof(f293,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f86,f8]) ).
fof(f295,definition,
( spl0_7
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f296,plain,
( ~ 'E'(s('0'),f(suc(suc(z))))
| spl0_7 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f299,definition,
( spl0_8
<=> 'E'(s(s('0')),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f300,plain,
( ~ 'E'(s(s('0')),f(suc(suc(z))))
| spl0_8 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f301,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f302,plain,
( spl0_7
| spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f293,f299,f261,f295]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f143,f3]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0)) ),
inference(duplicate_literal_removal,[],[f311]) ).
fof(f321,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f179,f8]) ).
fof(f329,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f168,f13]) ).
fof(f332,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X2))) ),
inference(duplicate_literal_removal,[],[f329]) ).
fof(f340,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f54,f8]) ).
fof(f347,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f220,f6]) ).
fof(f352,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X2),suc(X1))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(suc(X2))) ),
inference(duplicate_literal_removal,[],[f347]) ).
fof(f359,plain,
( 'E'(s(s('0')),f(suc(suc(suc(z)))))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f180,f8]) ).
fof(f383,plain,
! [X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f312,f3]) ).
fof(f384,plain,
! [X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1))) ),
inference(duplicate_literal_removal,[],[f383]) ).
fof(f410,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f384,f3]) ).
fof(f411,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(duplicate_literal_removal,[],[f410]) ).
fof(f432,plain,
( ~ 'E'('0',f(z))
| ~ spl0_5 ),
inference(resolution,[],[f411,f263]) ).
fof(f433,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f432,f125]) ).
fof(f434,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f439,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f332,f13]) ).
fof(f442,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f439]) ).
fof(f448,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f442,f13]) ).
fof(f451,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f448]) ).
fof(f456,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f352,f6]) ).
fof(f461,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literal_removal,[],[f456]) ).
fof(f465,plain,
( ~ 'E'(s('0'),f(z))
| ~ spl0_4 ),
inference(resolution,[],[f451,f259]) ).
fof(f466,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_7 ),
inference(resolution,[],[f451,f297]) ).
fof(f467,plain,
( $false
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f466,f259]) ).
fof(f468,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f469,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f465,f257,f119]) ).
fof(f470,plain,
( 'E'(s(s('0')),f(suc(suc(suc(z)))))
| 'E'(s('0'),f(suc(suc(z))))
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f359,f262]) ).
fof(f471,plain,
( 'E'(s(s('0')),f(suc(suc(suc(z)))))
| spl0_5
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f470,f296]) ).
fof(f484,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f461,f6]) ).
fof(f489,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literal_removal,[],[f484]) ).
fof(f502,plain,
( ~ 'E'(s(s('0')),f(suc(z)))
| ~ spl0_8 ),
inference(resolution,[],[f489,f301]) ).
fof(f503,plain,
( ~ 'E'(s(s('0')),f(suc(suc(z))))
| spl0_5
| spl0_7 ),
inference(resolution,[],[f489,f471]) ).
fof(f504,plain,
( $false
| spl0_5
| spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f503,f301]) ).
fof(f505,plain,
( spl0_5
| spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f506,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f502,f299,f265]) ).
fof(f507,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(z))
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f205,f266]) ).
fof(f508,plain,
( 'E'(s('0'),f(z))
| spl0_2
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f507,f124]) ).
fof(f509,plain,
( $false
| spl0_1
| spl0_2
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f508,f120]) ).
fof(f510,plain,
( spl0_1
| spl0_2
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f509]) ).
fof(f511,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(z)))
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f230,f266]) ).
fof(f512,plain,
( 'E'(s('0'),f(suc(z)))
| spl0_2
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f511,f124]) ).
fof(f513,plain,
( $false
| spl0_2
| spl0_4
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f512,f258]) ).
fof(f514,plain,
( spl0_2
| spl0_4
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f513]) ).
fof(f515,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(z)))
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f321,f300]) ).
fof(f516,plain,
( 'E'(s('0'),f(suc(z)))
| spl0_2
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f515,f124]) ).
fof(f517,plain,
( spl0_4
| spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f516,f299,f123,f257]) ).
fof(f520,plain,
( ~ 'E'(s(s('0')),f(z))
| ~ spl0_6 ),
inference(resolution,[],[f267,f489]) ).
fof(f521,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f520,f129]) ).
fof(f522,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f523,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z)))
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f340,f300]) ).
fof(f524,plain,
( 'E'(s('0'),f(suc(z)))
| spl0_5
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f523,f262]) ).
fof(f525,plain,
( $false
| spl0_4
| spl0_5
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f524,f258]) ).
fof(f526,plain,
( spl0_4
| spl0_5
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f525]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f130]) ).
cnf(s2,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f268]) ).
cnf(s3,plain,
( spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f302]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f434]) ).
cnf(s5,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f468]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f469]) ).
cnf(s7,plain,
( spl0_5
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f505]) ).
cnf(s8,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f506]) ).
cnf(s9,plain,
( spl0_1
| spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f510]) ).
cnf(s10,plain,
( spl0_2
| spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f514]) ).
cnf(s11,plain,
( spl0_2
| spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f517]) ).
cnf(s12,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f522]) ).
cnf(s13,plain,
( spl0_4
| spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f526]) ).
cnf(s14,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s12,s1,s9]) ).
cnf(s15,plain,
( spl0_7
| spl0_5 ),
inference(rat,[],[s3,s7]) ).
cnf(s16,plain,
( spl0_4
| spl0_5 ),
inference(rat,[],[s8,s2,s13]) ).
cnf(s17,plain,
spl0_5,
inference(rat,[],[s16,s5,s15]) ).
cnf(s18,plain,
~ spl0_2,
inference(rat,[],[s4,s17]) ).
cnf(s19,plain,
spl0_1,
inference(rat,[],[s14,s18]) ).
cnf(s20,plain,
~ spl0_4,
inference(rat,[],[s6,s19]) ).
cnf(s21,plain,
spl0_8,
inference(rat,[],[s11,s18,s20]) ).
cnf(s22,plain,
spl0_6,
inference(rat,[],[s10,s18,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s8,s21,s22]) ).
fof(f527,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO674-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.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 18:08:49 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.21/0.28 % (583166)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (583175)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3527321961:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (583172)% WARNING: option uhcvi not known.
% 0.21/0.28 % (583173)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2409077115:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (583171)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4270025444_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (583172)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=393097328:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (583174)dis+10_1_sil=32000:sp=arity:random_seed=1255266236:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (583176)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2416165495:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.28 % (583177)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4001288187:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.28 % (583175) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-583166-583175"...
% 0.21/0.28 % (583175)...printing done.
% 0.21/0.28 % (583175)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (583175)------------------------------
% 0.21/0.28 % (583175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (583175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (583175)CaDiCaL version: 2.1.3
% 0.21/0.28 % (583175)Termination reason: Refutation
% 0.21/0.28 % (583175)Time elapsed: 0.013 s
% 0.21/0.28 % (583175)Peak memory usage: 12 MB
% 0.21/0.28 % (583175)Instructions burned: 55 (million)
% 0.21/0.28 % (583166)Success in time 0.043 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------