%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 02:28:37 PM UTC 2026
% Result : Unsatisfiable 3.08s 1.07s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 133 ( 11 unt; 9 def)
% Number of atoms : 399 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 477 ( 211 ~; 257 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 79 ( 0 sgn 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_109) ).
fof(f2,axiom,
! [X0] : 'LE'(f(X0),s(s(s(s('0'))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_104) ).
fof(f3,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_91) ).
fof(f4,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s('0'))
| 'E'('0',f(suc(X0)))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_114) ).
fof(f5,axiom,
! [X0] :
( 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_5) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_71) ).
fof(f8,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s('0')))
| 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f9,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_66) ).
fof(f10,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s(s('0'))))
| 'E'(s(s('0')),f(suc(X0)))
| 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_84) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_144) ).
fof(f12,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s('0'))),f(X0))
| 'LE'(f(X0),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_127) ).
fof(f13,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_51) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ 'E'(s('0'),f(suc(X2)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X0))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21) ).
fof(f15,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s(s(s('0')))))
| 'E'(s(s(s('0'))),f(suc(X0)))
| 'LE'(f(X0),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_102) ).
fof(f16,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14) ).
fof(f17,axiom,
! [X0] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_96) ).
fof(f18,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
fof(f19,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(X0))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[],[f12,f2]) ).
fof(f20,plain,
! [X0] :
( 'E'(s(s(s('0'))),f(suc(X0)))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(forward_subsumption_resolution,[],[f15,f2]) ).
fof(f22,plain,
! [X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f11]) ).
fof(f25,plain,
! [X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1)) ),
inference(duplicate_literal_removal,[],[f22]) ).
fof(f27,plain,
! [X0,X1] :
( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1)) ),
inference(forward_subsumption_resolution,[],[f25,f1]) ).
fof(f31,plain,
! [X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X0)) ),
inference(factoring,[],[f14]) ).
fof(f33,plain,
! [X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1)) ),
inference(duplicate_literal_removal,[],[f31]) ).
fof(f35,plain,
! [X0,X1] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X1)) ),
inference(forward_subsumption_resolution,[],[f33,f3]) ).
fof(f36,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f27]) ).
fof(f38,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X0)) ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f39,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(forward_subsumption_resolution,[],[f38,f1]) ).
fof(f41,plain,
! [X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(X1)) ),
inference(factoring,[],[f6]) ).
fof(f44,plain,
! [X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s('0')),f(X1)) ),
inference(duplicate_literal_removal,[],[f41]) ).
fof(f46,plain,
! [X0,X1] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s('0')),f(X1)) ),
inference(forward_subsumption_resolution,[],[f44,f5]) ).
fof(f52,plain,
! [X0,X1] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(factoring,[],[f7]) ).
fof(f55,plain,
! [X0,X1] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(forward_subsumption_resolution,[],[f55,f16]) ).
fof(f58,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0)) ),
inference(factoring,[],[f35]) ).
fof(f60,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f58]) ).
fof(f61,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(forward_subsumption_resolution,[],[f60,f3]) ).
fof(f62,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(factoring,[],[f46]) ).
fof(f64,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(duplicate_literal_removal,[],[f62]) ).
fof(f65,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(forward_subsumption_resolution,[],[f64,f5]) ).
fof(f69,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(factoring,[],[f56]) ).
fof(f70,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ iLEQ(suc(X0),suc(X0)) ),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(forward_subsumption_resolution,[],[f70,f16]) ).
fof(f73,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(X0))
| 'LE'(f(X0),s(s(s('0')))) ),
inference(resolution,[],[f71,f20]) ).
fof(f75,plain,
! [X0] : 'LE'(f(X0),s(s(s('0')))),
inference(forward_subsumption_resolution,[],[f73,f19]) ).
fof(f76,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f75,f13]) ).
fof(f77,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f75,f10]) ).
fof(f78,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f76,f8]) ).
fof(f79,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f76,f18]) ).
fof(f80,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f77,f8]) ).
fof(f81,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0)))) ),
inference(resolution,[],[f77,f18]) ).
fof(f82,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(X0))
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f78,f17]) ).
fof(f83,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,[],[f78,f4]) ).
fof(f84,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f80,f17]) ).
fof(f85,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,[],[f80,f4]) ).
fof(f86,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,[],[f79,f17]) ).
fof(f87,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,[],[f79,f4]) ).
fof(f88,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,[],[f81,f17]) ).
fof(f89,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,[],[f81,f4]) ).
fof(f90,plain,
( 'E'(s(s('0')),f(z))
| 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[],[f82,f9]) ).
fof(f92,definition,
( spl0_1
<=> 'E'(s('0'),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f96,definition,
( spl0_2
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f100,definition,
( spl0_3
<=> 'E'(s(s('0')),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f102,plain,
( 'E'(s(s('0')),f(z))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f90,f100,f96,f92]) ).
fof(f104,plain,
( 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[],[f84,f9]) ).
fof(f105,plain,
( 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f86,f9]) ).
fof(f106,plain,
( 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f83,f9]) ).
fof(f108,definition,
( spl0_4
<=> 'E'(s('0'),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f110,plain,
( 'E'(s('0'),f(suc(z)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f112,definition,
( spl0_5
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f114,plain,
( 'E'('0',f(suc(z)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,definition,
( spl0_6
<=> 'E'(s(s('0')),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f118,plain,
( 'E'(s(s('0')),f(suc(z)))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f106,f116,f112,f108]) ).
fof(f120,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f88,f9]) ).
fof(f121,plain,
( ~ 'E'(s('0'),f(z))
| ~ spl0_4 ),
inference(resolution,[],[f110,f61]) ).
fof(f124,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f121,f108,f92]) ).
fof(f125,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f85,f9]) ).
fof(f126,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f87,f9]) ).
fof(f128,definition,
( spl0_7
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f130,plain,
( 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f132,definition,
( spl0_8
<=> 'E'(s(s('0')),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f134,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_7
| spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f126,f132,f112,f128]) ).
fof(f136,plain,
( ~ 'E'('0',f(z))
| ~ spl0_5 ),
inference(resolution,[],[f114,f39]) ).
fof(f142,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f136,f112,f96]) ).
fof(f144,plain,
( 'E'(s(s('0')),f(suc(suc(suc(z)))))
| 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f89,f9]) ).
fof(f146,definition,
( spl0_9
<=> 'E'(s(s('0')),f(suc(suc(suc(z))))) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f148,plain,
( 'E'(s(s('0')),f(suc(suc(suc(z)))))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_7
| spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f144,f146,f112,f128]) ).
fof(f150,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_7 ),
inference(resolution,[],[f130,f61]) ).
fof(f153,plain,
( $false
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f150,f110]) ).
fof(f154,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f153]) ).
fof(f155,plain,
( spl0_4
| spl0_5
| spl0_8 ),
inference(avatar_split_clause,[],[f125,f132,f112,f108]) ).
fof(f156,plain,
( spl0_4
| spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f105,f116,f96,f108]) ).
fof(f157,plain,
( spl0_4
| spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f120,f132,f96,f108]) ).
fof(f158,plain,
( spl0_1
| spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f104,f116,f96,f92]) ).
fof(f165,plain,
( ~ 'E'(s(s('0')),f(z))
| ~ spl0_6 ),
inference(resolution,[],[f118,f65]) ).
fof(f168,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f165,f102]) ).
fof(f169,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f171,plain,
( ~ 'E'(s(s('0')),f(suc(z)))
| ~ spl0_8 ),
inference(resolution,[],[f134,f65]) ).
fof(f174,plain,
( $false
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f171,f118]) ).
fof(f175,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f174]) ).
fof(f177,plain,
( ~ 'E'(s(s('0')),f(suc(suc(z))))
| ~ spl0_9 ),
inference(resolution,[],[f148,f65]) ).
fof(f180,plain,
( $false
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f177,f134]) ).
fof(f181,plain,
( ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f180]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f103]) ).
cnf(s2,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f119]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f124]) ).
cnf(s4,plain,
( spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f135]) ).
cnf(s6,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f142]) ).
cnf(s8,plain,
( spl0_5
| spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f149]) ).
cnf(s9,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f154]) ).
cnf(s11,plain,
( spl0_4
| spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f155]) ).
cnf(s12,plain,
( spl0_2
| spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f156]) ).
cnf(s13,plain,
( spl0_2
| spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f157]) ).
cnf(s14,plain,
( spl0_1
| spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f158]) ).
cnf(s16,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f169]) ).
cnf(s18,plain,
( ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f175]) ).
cnf(s20,plain,
( ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f181]) ).
cnf(s21,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s16,s1,s14]) ).
cnf(s22,plain,
( spl0_7
| spl0_5 ),
inference(rat,[],[s20,s4,s8]) ).
cnf(s23,plain,
( spl0_4
| spl0_5 ),
inference(rat,[],[s18,s2,s11]) ).
cnf(s24,plain,
spl0_5,
inference(rat,[],[s23,s9,s22]) ).
cnf(s25,plain,
~ spl0_2,
inference(rat,[],[s6,s24]) ).
cnf(s26,plain,
spl0_1,
inference(rat,[],[s21,s25]) ).
cnf(s27,plain,
~ spl0_4,
inference(rat,[],[s3,s26]) ).
cnf(s28,plain,
spl0_8,
inference(rat,[],[s13,s25,s27]) ).
cnf(s29,plain,
spl0_6,
inference(rat,[],[s12,s25,s27]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s18,s28,s29]) ).
fof(f182,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO680-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n001.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 18:09:19 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.08/1.07 % (583994)Input is clausal, will run a generic CNF schedule.
% 3.08/1.07 % (584002)lrs+10_1_sil=8000:sp=occurrence:random_seed=3265152545:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.08/1.07 % (584002)Refutation not found, incomplete strategy
% 3.08/1.07 % (584002)------------------------------
% 3.08/1.07 % (584002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.07 % (584002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.07 % (584002)CaDiCaL version: 2.1.3
% 3.08/1.07 % (584002)Termination reason: Refutation not found, incomplete strategy
% 3.08/1.07 % (584002)Time elapsed: 0.0000 s
% 3.08/1.07 % (584002)Peak memory usage: 86 MB
% 3.08/1.07 % (584003)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=758434858:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.08/1.07 % (584003)Refutation not found, incomplete strategy
% 3.08/1.07 % (584003)------------------------------
% 3.08/1.07 % (584003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.07 % (584003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.07 % (584003)CaDiCaL version: 2.1.3
% 3.08/1.07 % (584003)Termination reason: Refutation not found, incomplete strategy
% 3.08/1.07 % (584003)Time elapsed: 0.001 s
% 3.08/1.07 % (584003)Peak memory usage: 86 MB
% 3.08/1.07 % (584000)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3969106929:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.08/1.07 % (583999)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=2378595740:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.08/1.07 % (584001)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3460431933:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.08/1.07 % (584004)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1018637895:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.08/1.07 % (584005)dis-21_1_sil=8000:lcm=predicate:random_seed=3633823732: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)
% 3.08/1.07 % (584004)First to succeed.
% 3.08/1.07 % (584004)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-583994"
% 3.08/1.07 % (584005)Also succeeded, but the first one will report.
% 3.08/1.07 % (584002)------------------------------
% 3.08/1.07 % (584002)------------------------------
% 3.08/1.07 % (584013)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=1653267246:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.08/1.07 % (584013)Refutation not found, incomplete strategy
% 3.08/1.07 % (584013)------------------------------
% 3.08/1.07 % (584013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.07 % (584013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.07 % (584013)CaDiCaL version: 2.1.3
% 3.08/1.07 % (584013)Termination reason: Refutation not found, incomplete strategy
% 3.08/1.07 % (584013)Time elapsed: 0.0000 s
% 3.08/1.07 % (584013)Peak memory usage: 86 MB
% 3.08/1.07 % (584003)------------------------------
% 3.08/1.07 % (584003)------------------------------
% 3.08/1.07 % (584004)Refutation found. Thanks to Tanya!
% 3.08/1.07 % SZS status Unsatisfiable for theBenchmark
% 3.08/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.27 % (584004)------------------------------
% 3.58/1.27 % (584004)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.27 % (584004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.27 % (584004)CaDiCaL version: 2.1.3
% 3.58/1.27 % (584004)Termination reason: Refutation
% 3.58/1.27 % (584004)Time elapsed: 0.007 s
% 3.58/1.27 % (584004)Peak memory usage: 89 MB
% 3.58/1.27 % (584004)Instructions burned: 10 (million)
% 3.58/1.27 % (584004)------------------------------
% 3.58/1.27 % (584004)------------------------------
% 3.58/1.27 % (583994)Success in time 0.42 s
% 3.58/1.27 % Vampire exiting
%------------------------------------------------------------------------------