%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 02:28:38 PM UTC 2026
% Result : Unsatisfiable 0.65s 0.97s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 210 ( 12 unt; 14 def)
% Number of atoms : 758 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 874 ( 326 ~; 534 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 18 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 103 ( 0 sgn 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_469) ).
fof(f2,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_398) ).
fof(f3,axiom,
! [X0] : 'LE'(f(X0),s(s(s(s('0'))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_451) ).
fof(f4,axiom,
! [X0] :
( iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X3),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X4))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(X4)))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_560) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',clause_476) ).
fof(f7,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s('0')),f(X0))
| 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_97) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',clause_443) ).
fof(f9,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_287) ).
fof(f10,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s('0'))
| 'E'('0',f(suc(X0)))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_547) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X3),suc(X0))
| ~ iLEQ(suc(X1),suc(X4))
| ~ 'E'(s(s('0')),f(suc(X4)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X4))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ '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(X2))
| ~ 'E'(s(s('0')),f(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_563) ).
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/sandbox2/benchmark/theBenchmark.p',clause_539) ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p',clause_59) ).
fof(f14,axiom,
! [X0] :
( ~ 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_222) ).
fof(f15,axiom,
! [X0] :
( ~ 'LE'(f(X0),s(s('0')))
| 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_44) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X1),suc(X3))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X3),suc(X2))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_442) ).
fof(f17,axiom,
! [X0] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_89) ).
fof(f18,axiom,
! [X2,X3,X0,X1,X4] :
( ~ iLEQ(suc(X3),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X4),suc(X0))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X4))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X4)))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_151) ).
fof(f19,plain,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0)) ),
inference(resolution,[],[f12,f3]) ).
fof(f20,plain,
! [X0] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(resolution,[],[f8,f3]) ).
fof(f21,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0))
| 'E'(s(s(s('0'))),f(X0)) ),
inference(resolution,[],[f19,f7]) ).
fof(f22,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(resolution,[],[f19,f6]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f16]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ '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(X2)) ),
inference(duplicate_literal_removal,[],[f44]) ).
fof(f67,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(resolution,[],[f20,f7]) ).
fof(f68,plain,
! [X0] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(X0)))) ),
inference(resolution,[],[f20,f6]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X0),suc(X0))
| ~ '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(X0))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(factoring,[],[f18]) ).
fof(f91,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X2))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X2))) ),
inference(duplicate_literal_removal,[],[f90]) ).
fof(f113,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(X0))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f21,f15]) ).
fof(f114,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(suc(X0)))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f21,f14]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ '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)) ),
inference(factoring,[],[f11]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X0))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X2)) ),
inference(duplicate_literal_removal,[],[f136]) ).
fof(f159,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(suc(X0)))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(X0)) ),
inference(resolution,[],[f67,f15]) ).
fof(f160,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(suc(suc(X0))))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f67,f14]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(factoring,[],[f5]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ iLEQ(suc(X2),suc(X0))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X0),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2))) ),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f205,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(suc(X0)))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f22,f15]) ).
fof(f206,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(suc(suc(X0))))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0)))) ),
inference(resolution,[],[f22,f14]) ).
fof(f221,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(factoring,[],[f45]) ).
fof(f222,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f240,plain,
! [X0] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(resolution,[],[f222,f1]) ).
fof(f241,plain,
! [X0] :
( ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0)) ),
inference(duplicate_literal_removal,[],[f240]) ).
fof(f256,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(suc(suc(X0))))
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(suc(X0))) ),
inference(resolution,[],[f68,f15]) ).
fof(f257,plain,
! [X0] :
( 'LE'(f(X0),s('0'))
| 'E'(s(s(s('0'))),f(suc(suc(suc(X0)))))
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0)))) ),
inference(resolution,[],[f68,f14]) ).
fof(f262,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ iLEQ(suc(X0),suc(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(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(factoring,[],[f91]) ).
fof(f267,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f262]) ).
fof(f271,plain,
! [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,[],[f267,f2]) ).
fof(f273,plain,
! [X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literal_removal,[],[f271]) ).
fof(f288,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(X0))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(X0)) ),
inference(resolution,[],[f113,f17]) ).
fof(f289,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(resolution,[],[f113,f10]) ).
fof(f290,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(X0))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(resolution,[],[f159,f17]) ).
fof(f291,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(X0)))) ),
inference(resolution,[],[f159,f10]) ).
fof(f292,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(resolution,[],[f205,f17]) ).
fof(f293,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(X0)))) ),
inference(resolution,[],[f205,f10]) ).
fof(f294,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(resolution,[],[f114,f17]) ).
fof(f295,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(suc(X0))))
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(X0)))) ),
inference(resolution,[],[f114,f10]) ).
fof(f296,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(X0))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(suc(suc(X0)))) ),
inference(resolution,[],[f256,f17]) ).
fof(f297,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(X0))))) ),
inference(resolution,[],[f256,f10]) ).
fof(f303,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ iLEQ(suc(X0),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))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(factoring,[],[f137]) ).
fof(f306,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literal_removal,[],[f303]) ).
fof(f313,plain,
! [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,[],[f306,f4]) ).
fof(f316,plain,
! [X0] :
( ~ 'E'(s(s('0')),f(suc(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(duplicate_literal_removal,[],[f313]) ).
fof(f317,plain,
( 'E'(s('0'),f(z))
| 'E'(s(s('0')),f(z))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(z)) ),
inference(resolution,[],[f288,f9]) ).
fof(f319,definition,
( spl0_1
<=> 'E'(s(s(s('0'))),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f320,plain,
( 'E'(s(s(s('0'))),f(z))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f322,definition,
( spl0_2
<=> 'E'('0',f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f323,plain,
( 'E'('0',f(z))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f325,definition,
( spl0_3
<=> 'E'(s(s('0')),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f326,plain,
( 'E'(s(s('0')),f(z))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f328,definition,
( spl0_4
<=> 'E'(s('0'),f(z)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f329,plain,
( 'E'(s('0'),f(z))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f330,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f317,f328,f325,f322,f319]) ).
fof(f331,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(X0)))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(suc(suc(X0)))) ),
inference(resolution,[],[f160,f17]) ).
fof(f332,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(suc(X0))))
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(X0))))) ),
inference(resolution,[],[f160,f10]) ).
fof(f333,plain,
( 'E'(s('0'),f(z))
| 'E'(s(s('0')),f(z))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(suc(z))) ),
inference(resolution,[],[f290,f9]) ).
fof(f348,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(factoring,[],[f183]) ).
fof(f349,plain,
! [X0] :
( ~ iLEQ(suc(X0),suc(X0))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0))) ),
inference(duplicate_literal_removal,[],[f348]) ).
fof(f364,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(resolution,[],[f349,f13]) ).
fof(f368,plain,
! [X0] :
( ~ 'E'(s(s(s('0'))),f(suc(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(duplicate_literal_removal,[],[f364]) ).
fof(f369,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(suc(suc(X0)))) ),
inference(resolution,[],[f206,f17]) ).
fof(f370,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(suc(X0))))
| 'E'(s(s('0')),f(suc(suc(suc(X0)))))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(X0))))) ),
inference(resolution,[],[f206,f10]) ).
fof(f371,plain,
( 'E'(s('0'),f(z))
| 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(suc(z))) ),
inference(resolution,[],[f292,f9]) ).
fof(f372,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(X0)))
| 'E'(s(s('0')),f(suc(suc(X0))))
| 'E'('0',f(X0))
| 'E'(s(s(s('0'))),f(suc(suc(suc(X0))))) ),
inference(resolution,[],[f257,f17]) ).
fof(f373,plain,
! [X0] :
( 'LE'(f(X0),'0')
| 'E'(s('0'),f(suc(suc(X0))))
| 'E'(s(s('0')),f(suc(suc(suc(X0)))))
| 'E'('0',f(suc(X0)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(suc(X0)))))) ),
inference(resolution,[],[f257,f10]) ).
fof(f374,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(suc(z))) ),
inference(resolution,[],[f294,f9]) ).
fof(f375,plain,
( 'E'(s('0'),f(z))
| 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(suc(suc(z)))) ),
inference(resolution,[],[f296,f9]) ).
fof(f376,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(z))) ),
inference(resolution,[],[f289,f9]) ).
fof(f378,definition,
( spl0_5
<=> 'E'(s(s(s('0'))),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f379,plain,
( 'E'(s(s(s('0'))),f(suc(z)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f381,definition,
( spl0_6
<=> 'E'('0',f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f382,plain,
( 'E'('0',f(suc(z)))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f384,definition,
( spl0_7
<=> 'E'(s(s('0')),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f385,plain,
( 'E'(s(s('0')),f(suc(z)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,definition,
( spl0_8
<=> 'E'(s('0'),f(suc(z))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f388,plain,
( 'E'(s('0'),f(suc(z)))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f389,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f376,f387,f384,f381,f378]) ).
fof(f390,plain,
( ~ 'E'(s(s(s('0'))),f(z))
| ~ spl0_5 ),
inference(resolution,[],[f379,f368]) ).
fof(f391,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(suc(suc(z)))) ),
inference(resolution,[],[f331,f9]) ).
fof(f392,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(z)))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(suc(z)))) ),
inference(resolution,[],[f291,f9]) ).
fof(f394,definition,
( spl0_9
<=> 'E'(s(s(s('0'))),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f395,plain,
( 'E'(s(s(s('0'))),f(suc(suc(z))))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f396,plain,
( spl0_9
| spl0_6
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f392,f387,f384,f381,f394]) ).
fof(f397,plain,
( ~ 'E'('0',f(z))
| ~ spl0_6 ),
inference(resolution,[],[f382,f241]) ).
fof(f398,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(resolution,[],[f397,f323]) ).
fof(f399,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f400,plain,
( ~ 'E'(s(s('0')),f(z))
| ~ spl0_7 ),
inference(resolution,[],[f385,f316]) ).
fof(f401,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(suc(suc(z)))) ),
inference(resolution,[],[f369,f9]) ).
fof(f402,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(suc(z)))) ),
inference(resolution,[],[f293,f9]) ).
fof(f404,definition,
( spl0_10
<=> 'E'(s(s('0')),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f405,plain,
( 'E'(s(s('0')),f(suc(suc(z))))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f406,plain,
( spl0_9
| spl0_6
| spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f402,f387,f404,f381,f394]) ).
fof(f407,plain,
( ~ 'E'(s('0'),f(z))
| ~ spl0_8 ),
inference(resolution,[],[f388,f273]) ).
fof(f408,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(z))
| 'E'(s(s(s('0'))),f(suc(suc(suc(z))))) ),
inference(resolution,[],[f372,f9]) ).
fof(f409,plain,
( 'E'(s('0'),f(suc(suc(z))))
| 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(suc(z)))) ),
inference(resolution,[],[f295,f9]) ).
fof(f411,definition,
( spl0_11
<=> 'E'(s('0'),f(suc(suc(z)))) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f412,plain,
( 'E'(s('0'),f(suc(suc(z))))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f413,plain,
( spl0_9
| spl0_6
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f409,f411,f404,f381,f394]) ).
fof(f414,plain,
( ~ 'E'(s(s(s('0'))),f(suc(z)))
| ~ spl0_9 ),
inference(resolution,[],[f395,f368]) ).
fof(f415,plain,
( $false
| ~ spl0_5
| ~ spl0_9 ),
inference(resolution,[],[f414,f379]) ).
fof(f416,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f418,plain,
( $false
| ~ spl0_3
| ~ spl0_7 ),
inference(resolution,[],[f326,f400]) ).
fof(f419,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f418]) ).
fof(f420,plain,
( $false
| ~ spl0_4
| ~ spl0_8 ),
inference(resolution,[],[f329,f407]) ).
fof(f421,plain,
( ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f423,definition,
( spl0_12
<=> 'E'(s(s(s('0'))),f(suc(suc(suc(z))))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f424,plain,
( 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f425,plain,
( spl0_12
| spl0_2
| spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f408,f387,f404,f322,f423]) ).
fof(f426,plain,
( spl0_9
| spl0_2
| spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f401,f387,f404,f322,f394]) ).
fof(f427,plain,
( ~ 'E'(s(s('0')),f(suc(z)))
| ~ spl0_10 ),
inference(resolution,[],[f405,f316]) ).
fof(f428,plain,
( $false
| ~ spl0_7
| ~ spl0_10 ),
inference(resolution,[],[f427,f385]) ).
fof(f429,plain,
( ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f428]) ).
fof(f430,plain,
( spl0_9
| spl0_2
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f391,f387,f384,f322,f394]) ).
fof(f431,plain,
( spl0_5
| spl0_2
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f374,f387,f384,f322,f378]) ).
fof(f432,plain,
( spl0_5
| spl0_2
| spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f371,f328,f384,f322,f378]) ).
fof(f433,plain,
( spl0_9
| spl0_2
| spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f375,f328,f384,f322,f394]) ).
fof(f434,plain,
( spl0_5
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f333,f328,f325,f322,f378]) ).
fof(f436,plain,
( 'E'(s('0'),f(suc(z)))
| 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(z))))) ),
inference(resolution,[],[f297,f9]) ).
fof(f437,plain,
( 'E'(s('0'),f(suc(suc(z))))
| 'E'(s(s('0')),f(suc(suc(z))))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(z))))) ),
inference(resolution,[],[f332,f9]) ).
fof(f438,plain,
( 'E'(s('0'),f(suc(suc(z))))
| 'E'(s(s('0')),f(suc(suc(suc(z)))))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(z))))) ),
inference(resolution,[],[f370,f9]) ).
fof(f440,definition,
( spl0_13
<=> 'E'(s(s('0')),f(suc(suc(suc(z))))) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f441,plain,
( 'E'(s(s('0')),f(suc(suc(suc(z)))))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f442,plain,
( spl0_12
| spl0_6
| spl0_13
| spl0_11 ),
inference(avatar_split_clause,[],[f438,f411,f440,f381,f423]) ).
fof(f443,plain,
( ~ 'E'(s(s('0')),f(suc(suc(z))))
| ~ spl0_13 ),
inference(resolution,[],[f441,f316]) ).
fof(f444,plain,
( $false
| ~ spl0_10
| ~ spl0_13 ),
inference(resolution,[],[f443,f405]) ).
fof(f445,plain,
( ~ spl0_10
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f446,plain,
( ~ 'E'(s('0'),f(suc(z)))
| ~ spl0_11 ),
inference(resolution,[],[f412,f273]) ).
fof(f447,plain,
( $false
| ~ spl0_8
| ~ spl0_11 ),
inference(resolution,[],[f446,f388]) ).
fof(f448,plain,
( ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f447]) ).
fof(f449,plain,
( ~ 'E'(s(s(s('0'))),f(suc(suc(z))))
| ~ spl0_12 ),
inference(resolution,[],[f424,f368]) ).
fof(f450,plain,
( 'E'(s('0'),f(suc(suc(z))))
| 'E'(s(s('0')),f(suc(suc(suc(z)))))
| 'E'('0',f(suc(z)))
| 'E'(s(s(s('0'))),f(suc(suc(suc(suc(z)))))) ),
inference(resolution,[],[f373,f9]) ).
fof(f452,definition,
( spl0_14
<=> 'E'(s(s(s('0'))),f(suc(suc(suc(suc(z)))))) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f453,plain,
( 'E'(s(s(s('0'))),f(suc(suc(suc(suc(z))))))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f454,plain,
( spl0_14
| spl0_6
| spl0_13
| spl0_11 ),
inference(avatar_split_clause,[],[f450,f411,f440,f381,f452]) ).
fof(f455,plain,
( ~ 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))
| ~ spl0_14 ),
inference(resolution,[],[f453,f368]) ).
fof(f456,plain,
( $false
| ~ spl0_12
| ~ spl0_14 ),
inference(resolution,[],[f455,f424]) ).
fof(f457,plain,
( ~ spl0_12
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f458,plain,
( $false
| ~ spl0_9
| ~ spl0_12 ),
inference(resolution,[],[f395,f449]) ).
fof(f460,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f464,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f390,f320]) ).
fof(f465,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f464]) ).
fof(f466,plain,
( spl0_12
| spl0_6
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f437,f411,f404,f381,f423]) ).
fof(f467,plain,
( spl0_12
| spl0_6
| spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f436,f387,f404,f381,f423]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f330]) ).
cnf(s2,plain,
( spl0_5
| spl0_6
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f389]) ).
cnf(s3,plain,
( spl0_6
| spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f396]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(sat_conversion,[],[f399]) ).
cnf(s5,plain,
( spl0_6
| spl0_8
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f406]) ).
cnf(s6,plain,
( spl0_6
| spl0_9
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f413]) ).
cnf(s7,plain,
( ~ spl0_5
| ~ spl0_9 ),
inference(sat_conversion,[],[f416]) ).
cnf(s8,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(sat_conversion,[],[f419]) ).
cnf(s9,plain,
( ~ spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f421]) ).
cnf(s10,plain,
( spl0_2
| spl0_8
| spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f425]) ).
cnf(s11,plain,
( spl0_2
| spl0_8
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f426]) ).
cnf(s12,plain,
( ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f429]) ).
cnf(s13,plain,
( spl0_2
| spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f430]) ).
cnf(s14,plain,
( spl0_2
| spl0_5
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f431]) ).
cnf(s15,plain,
( spl0_2
| spl0_4
| spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f432]) ).
cnf(s16,plain,
( spl0_2
| spl0_4
| spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f433]) ).
cnf(s17,plain,
( spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f434]) ).
cnf(s18,plain,
( spl0_6
| spl0_11
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f442]) ).
cnf(s19,plain,
( ~ spl0_10
| ~ spl0_13 ),
inference(sat_conversion,[],[f445]) ).
cnf(s20,plain,
( ~ spl0_8
| ~ spl0_11 ),
inference(sat_conversion,[],[f448]) ).
cnf(s21,plain,
( spl0_6
| spl0_11
| spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f454]) ).
cnf(s22,plain,
( ~ spl0_12
| ~ spl0_14 ),
inference(sat_conversion,[],[f457]) ).
cnf(s23,plain,
( ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f460]) ).
cnf(s24,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f465]) ).
cnf(s25,plain,
( spl0_6
| spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f466]) ).
cnf(s26,plain,
( spl0_6
| spl0_8
| spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f467]) ).
cnf(s27,plain,
( spl0_10
| spl0_8
| spl0_2 ),
inference(rat,[],[s23,s11,s10]) ).
cnf(s28,plain,
( spl0_7
| spl0_8
| spl0_2 ),
inference(rat,[],[s7,s14,s13]) ).
cnf(s29,plain,
( spl0_8
| spl0_2 ),
inference(rat,[],[s28,s12,s27]) ).
cnf(s30,plain,
( spl0_7
| spl0_4
| spl0_2 ),
inference(rat,[],[s7,s15,s16]) ).
cnf(s31,plain,
( spl0_4
| spl0_2
| spl0_1 ),
inference(rat,[],[s30,s8,s1]) ).
cnf(s32,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s31,s9,s29]) ).
cnf(s33,plain,
( spl0_10
| spl0_8
| spl0_6 ),
inference(rat,[],[s23,s5,s26]) ).
cnf(s34,plain,
( spl0_7
| spl0_8
| spl0_6 ),
inference(rat,[],[s7,s3,s2]) ).
cnf(s35,plain,
( spl0_8
| spl0_6 ),
inference(rat,[],[s34,s12,s33]) ).
cnf(s36,plain,
( spl0_10
| spl0_11
| spl0_6 ),
inference(rat,[],[s23,s6,s25]) ).
cnf(s37,plain,
( spl0_13
| spl0_11
| spl0_6 ),
inference(rat,[],[s22,s18,s21]) ).
cnf(s38,plain,
( spl0_11
| spl0_6 ),
inference(rat,[],[s37,s19,s36]) ).
cnf(s39,plain,
spl0_6,
inference(rat,[],[s38,s20,s35]) ).
cnf(s40,plain,
~ spl0_2,
inference(rat,[],[s4,s39]) ).
cnf(s41,plain,
spl0_8,
inference(rat,[],[s29,s40]) ).
cnf(s42,plain,
spl0_1,
inference(rat,[],[s32,s40]) ).
cnf(s44,plain,
~ spl0_4,
inference(rat,[],[s9,s41]) ).
cnf(s45,plain,
~ spl0_5,
inference(rat,[],[s24,s42]) ).
cnf(s46,plain,
spl0_7,
inference(rat,[],[s30,s40,s44]) ).
cnf(s47,plain,
spl0_3,
inference(rat,[],[s17,s44,s40,s45]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s8,s46,s47]) ).
fof(f468,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO683-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 18:06:55 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.65/0.97 % (3629096)Input is clausal, will run a generic CNF schedule.
% 0.65/0.97 % (3629107)dis-21_1_sil=8000:lcm=predicate:random_seed=3362691531: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)
% 0.65/0.97 % (3629107)First to succeed.
% 0.65/0.97 % (3629107)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3629096"
% 0.65/0.97 % (3629104)lrs+10_1_sil=8000:sp=occurrence:random_seed=281598191:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.65/0.97 % (3629101)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=874480247:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.65/0.97 % (3629105)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2770990941:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.65/0.97 % (3629103)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3537863947:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.65/0.97 % (3629102)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2142443856:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.65/0.97 % (3629105)Refutation not found, incomplete strategy
% 0.65/0.97 % (3629105)------------------------------
% 0.65/0.97 % (3629105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.65/0.97 % (3629104)Refutation not found, incomplete strategy
% 0.65/0.97 % (3629104)------------------------------
% 0.65/0.97 % (3629104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.65/0.97 % (3629104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.97 % (3629105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.97 % (3629105)CaDiCaL version: 2.1.3
% 0.65/0.97 % (3629104)CaDiCaL version: 2.1.3
% 0.65/0.97 % (3629105)Termination reason: Refutation not found, incomplete strategy
% 0.65/0.97 % (3629105)Time elapsed: 0.001 s
% 0.65/0.97 % (3629104)Termination reason: Refutation not found, incomplete strategy
% 0.65/0.97 % (3629104)Time elapsed: 0.001 s
% 0.65/0.97 % (3629105)Peak memory usage: 86 MB
% 0.65/0.97 % (3629104)Peak memory usage: 86 MB
% 0.65/0.97 % (3629106)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1026013776:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.65/0.97 % (3629106)Also succeeded, but the first one will report.
% 0.65/0.97 % (3629107)Refutation found. Thanks to Tanya!
% 0.65/0.97 % SZS status Unsatisfiable for theBenchmark
% 0.65/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.16 % (3629107)------------------------------
% 2.75/1.16 % (3629107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.16 % (3629107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.16 % (3629107)CaDiCaL version: 2.1.3
% 2.75/1.16 % (3629107)Termination reason: Refutation
% 2.75/1.16 % (3629107)Time elapsed: 0.009 s
% 2.75/1.16 % (3629107)Peak memory usage: 89 MB
% 2.75/1.16 % (3629107)Instructions burned: 31 (million)
% 2.75/1.16 % (3629107)------------------------------
% 2.75/1.16 % (3629107)------------------------------
% 2.75/1.16 % (3629096)Success in time 0.3 s
% 2.75/1.16 % Vampire exiting
%------------------------------------------------------------------------------