%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO661-1 : 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 : n003.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 02:32:19 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 123 ( 10 unt; 7 def)
% Number of atoms : 445 ( 0 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 584 ( 262 ~; 315 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_93) ).
fof(f3,axiom,
! [X0] :
( ~ 'LE'(f(suc(suc(X0))),s('0'))
| 'E'('0',f(suc(suc(X0))))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_51) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_106) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s('0'),f(suc(suc(X2))))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
fof(f6,axiom,
! [X0] : 'LE'(f(X0),s(s('0'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_72) ).
fof(f7,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_119) ).
fof(f8,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_57) ).
fof(f9,axiom,
! [X0] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_0) ).
fof(f10,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_85) ).
fof(f15,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_109) ).
fof(f18,axiom,
! [X2,X0,X1] :
( ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(suc(X2))))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X2),f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_204) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X0),suc(X2))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X2),f(suc(X2)))
| 'E'(f(X1),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
fof(f22,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(suc(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_148) ).
fof(f23,axiom,
! [X0] :
( ~ 'LE'(f(suc(suc(X0))),s(s('0')))
| 'E'(s('0'),f(suc(suc(X0))))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_33) ).
fof(f25,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_118) ).
fof(f28,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(suc(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_25) ).
fof(f29,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f25,f6]) ).
fof(f30,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f29,f9]) ).
fof(f31,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f29,f8]) ).
fof(f32,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(suc(X0))))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f29,f3]) ).
fof(f33,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f7,f6]) ).
fof(f34,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[],[f33,f9]) ).
fof(f35,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f33,f8]) ).
fof(f36,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(suc(X0))))
| 'E'(s('0'),f(suc(suc(suc(X0))))) ),
inference(resolution,[],[f33,f3]) ).
fof(f37,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(z)) ),
inference(resolution,[],[f30,f1]) ).
fof(f39,definition,
( spl0_1
<=> 'E'(s('0'),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f41,plain,
( 'E'(s('0'),f(z))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f43,definition,
( spl0_2
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f44,plain,
( ~ 'E'('0',f(z))
| spl0_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( 'E'('0',f(z))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f37,f43,f39]) ).
fof(f47,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f23,f6]) ).
fof(f48,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(X0))
| 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f47,f9]) ).
fof(f49,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(X0)))
| 'E'(s('0'),f(suc(suc(suc(X0))))) ),
inference(resolution,[],[f47,f8]) ).
fof(f50,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'('0',f(suc(suc(X0))))
| 'E'(s('0'),f(suc(suc(suc(suc(X0)))))) ),
inference(resolution,[],[f47,f3]) ).
fof(f51,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f34,f1]) ).
fof(f52,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(z))) ),
inference(resolution,[],[f31,f1]) ).
fof(f54,definition,
( spl0_3
<=> 'E'(s('0'),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f55,plain,
( ~ 'E'(s('0'),f(suc(z)))
| spl0_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( 'E'(s('0'),f(suc(z)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f58,definition,
( spl0_4
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f59,plain,
( ~ 'E'('0',f(suc(z)))
| spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f60,plain,
( 'E'('0',f(suc(z)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f52,f58,f54]) ).
fof(f69,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f20,f15]) ).
fof(f70,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X1),f(suc(X1))) ),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f84,plain,
! [X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f4,f10]) ).
fof(f87,plain,
! [X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| 'E'(f(X1),f(suc(X1)))
| 'E'(f(X0),f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f84]) ).
fof(f94,plain,
( 'E'('0',f(z))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f48,f1]) ).
fof(f100,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(suc(X0)))) ),
inference(resolution,[],[f18,f22]) ).
fof(f105,plain,
! [X0,X1] :
( ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(suc(X1))))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X1),f(suc(X1))) ),
inference(duplicate_literal_removal,[],[f100]) ).
fof(f111,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f35,f1]) ).
fof(f113,definition,
( spl0_5
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f114,plain,
( ~ 'E'(s('0'),f(suc(suc(z))))
| spl0_5 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f111,f58,f113]) ).
fof(f121,plain,
! [X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f5,f28]) ).
fof(f128,plain,
! [X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ 'E'(s('0'),f(suc(suc(X1))))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(f(X1),f(suc(X1)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f121]) ).
fof(f136,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f70,f15]) ).
fof(f137,plain,
! [X0] :
( 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f143,plain,
! [X0] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| 'E'(f(X0),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(resolution,[],[f87,f10]) ).
fof(f146,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f143]) ).
fof(f149,plain,
( 'E'('0',f(suc(suc(z))))
| 'E'(s('0'),f(suc(suc(z)))) ),
inference(resolution,[],[f32,f1]) ).
fof(f151,definition,
( spl0_6
<=> 'E'('0',f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f152,plain,
( ~ 'E'('0',f(suc(suc(z))))
| spl0_6 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( 'E'('0',f(suc(suc(z))))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f149,f151,f113]) ).
fof(f156,plain,
! [X0] :
( ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(suc(X0)))) ),
inference(resolution,[],[f105,f22]) ).
fof(f161,plain,
! [X0] :
( ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'(f(X0),f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f163,plain,
! [X0] :
( ~ 'E'('0',f(suc(suc(X0))))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(forward_subsumption_resolution,[],[f161,f137]) ).
fof(f173,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(suc(X0)))) ),
inference(resolution,[],[f128,f28]) ).
fof(f180,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(f(X0),f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f173]) ).
fof(f182,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(suc(X0))))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(forward_subsumption_resolution,[],[f180,f146]) ).
fof(f183,plain,
( 'E'('0',f(suc(z)))
| 'E'(s('0'),f(suc(suc(suc(z))))) ),
inference(resolution,[],[f49,f1]) ).
fof(f198,plain,
( 'E'('0',f(suc(suc(z))))
| 'E'(s('0'),f(suc(suc(suc(z))))) ),
inference(resolution,[],[f36,f1]) ).
fof(f200,definition,
( spl0_8
<=> 'E'(s('0'),f(suc(suc(suc(z))))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f202,plain,
( 'E'(s('0'),f(suc(suc(suc(z)))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f198,f151,f200]) ).
fof(f205,plain,
( ~ 'E'('0',f(suc(z)))
| ~ 'E'('0',f(z))
| ~ spl0_6 ),
inference(resolution,[],[f153,f163]) ).
fof(f206,plain,
( ~ 'E'('0',f(z))
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f205,f60]) ).
fof(f207,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f206,f45]) ).
fof(f208,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f209,plain,
( 'E'(s('0'),f(suc(suc(suc(z)))))
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f183,f59]) ).
fof(f210,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f209,f58,f200]) ).
fof(f211,plain,
( 'E'('0',f(suc(suc(z))))
| 'E'(s('0'),f(suc(suc(suc(suc(z)))))) ),
inference(resolution,[],[f50,f1]) ).
fof(f212,plain,
( 'E'(s('0'),f(suc(suc(suc(suc(z))))))
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f211,f152]) ).
fof(f213,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_8 ),
inference(resolution,[],[f202,f182]) ).
fof(f214,plain,
( ~ 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f213,f56]) ).
fof(f217,plain,
( ~ 'E'(s('0'),f(suc(suc(z))))
| ~ 'E'(s('0'),f(suc(suc(suc(z)))))
| spl0_6 ),
inference(resolution,[],[f212,f182]) ).
fof(f218,plain,
( ~ 'E'(s('0'),f(suc(suc(suc(z)))))
| ~ spl0_5
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f217,f115]) ).
fof(f219,plain,
( $false
| ~ spl0_5
| spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f218,f202]) ).
fof(f220,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f221,plain,
( 'E'(s('0'),f(suc(z)))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f51,f44]) ).
fof(f222,plain,
( $false
| spl0_2
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f221,f55]) ).
fof(f223,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f224,plain,
( ~ spl0_5
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f214,f200,f54,f113]) ).
fof(f225,plain,
( 'E'(s('0'),f(suc(suc(z))))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f94,f44]) ).
fof(f226,plain,
( $false
| spl0_2
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f225,f114]) ).
fof(f227,plain,
( spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f226]) ).
fof(f230,plain,
( ~ 'E'(s('0'),f(z))
| ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_5 ),
inference(resolution,[],[f115,f182]) ).
fof(f231,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f230,f41]) ).
fof(f232,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f231,f56]) ).
fof(f233,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f232]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f116]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s6,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f203]) ).
cnf(s7,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f208]) ).
cnf(s8,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f210]) ).
cnf(s10,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f220]) ).
cnf(s11,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f223]) ).
cnf(s12,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f224]) ).
cnf(s13,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f227]) ).
cnf(s14,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f233]) ).
cnf(s15,plain,
spl0_6,
inference(rat,[],[s10,s4,s6]) ).
cnf(s16,plain,
spl0_4,
inference(rat,[],[s12,s2,s3,s8]) ).
cnf(s17,plain,
~ spl0_2,
inference(rat,[],[s7,s15,s16]) ).
cnf(s18,plain,
spl0_5,
inference(rat,[],[s13,s17]) ).
cnf(s19,plain,
spl0_3,
inference(rat,[],[s11,s17]) ).
cnf(s20,plain,
spl0_1,
inference(rat,[],[s1,s17]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s14,s20,s18,s19]) ).
fof(f234,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO661-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 18:03:27 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 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
% 0.09/0.24 % (1828342)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (1828357)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2442505629:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.24 % (1828357) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1828342-1828357"...
% 0.09/0.24 % (1828357)...printing done.
% 0.09/0.24 % (1828354)% WARNING: option uhcvi not known.
% 0.09/0.24 % (1828357)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (1828357)------------------------------
% 0.09/0.25 % (1828357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1828357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1828357)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1828357)Termination reason: Refutation
% 0.09/0.25 % (1828357)Time elapsed: 0.005 s
% 0.09/0.25 % (1828357)Peak memory usage: 12 MB
% 0.09/0.25 % (1828357)Instructions burned: 15 (million)
% 0.09/0.25 % (1828342)Success in time 0.036 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------