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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SYO666-1 : 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 : n019.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 02:28:34 PM UTC 2026

% Result   : Unsatisfiable 2.87s 1.07s
% Output   : Refutation 3.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   50 (   7 unt;   0 def)
%            Number of atoms       :  339 (   0 equ)
%            Maximal formula atoms :   17 (   6 avg)
%            Number of connectives :  604 ( 315   ~; 289   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  10 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-1 aty)
%            Number of variables   :  115 ( 115   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ 'E'('0',f(suc(X0)))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(X2))
      | ~ 'E'('0',f(suc(X4)))
      | ~ 'E'('0',f(X1))
      | ~ iLEQ(suc(X5),suc(X0))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X4),suc(X5))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'('0',f(X4))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'('0',f(suc(X5)))
      | ~ 'E'('0',f(X3))
      | ~ 'E'('0',f(X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_102) ).

fof(f2,axiom,
    ! [X0] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | iLEQ(suc(X0),suc(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12) ).

fof(f3,axiom,
    ~ 'LE'(f(z),'0'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_98) ).

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_123) ).

fof(f5,axiom,
    ! [X0] :
      ( ~ 'LE'(f(X0),s('0'))
      | 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_42) ).

fof(f6,axiom,
    ! [X0] : 'LE'(f(X0),s(s('0'))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_83) ).

fof(f7,axiom,
    ! [X0] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X0))
      | iLEQ(suc(X0),suc(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_70) ).

fof(f8,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_29) ).

fof(f9,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_185) ).

fof(f10,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ 'E'(s('0'),f(suc(X5)))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'(s('0'),f(X3))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ iLEQ(suc(X4),suc(X1))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X0),suc(X4))
      | ~ 'E'(s('0'),f(suc(X0)))
      | ~ iLEQ(suc(X2),suc(X5))
      | ~ 'E'(s('0'),f(suc(X4)))
      | ~ 'E'(s('0'),f(X5))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X3),suc(X0))
      | ~ 'E'(s('0'),f(X4))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_179) ).

fof(f11,plain,
    ! [X0] :
      ( 'E'(s('0'),f(X0))
      | 'LE'(f(X0),s('0')) ),
    inference(forward_subsumption_resolution,[],[f9,f6]) ).

fof(f13,plain,
    ! [X0] :
      ( 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X0),s('0')) ),
    inference(forward_subsumption_resolution,[],[f8,f6]) ).

fof(f18,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X4),suc(X2))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X3),suc(X4))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'('0',f(suc(X4)))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X4)) ),
    inference(factoring,[],[f1]) ).

fof(f28,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X4),suc(X2))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X3),suc(X4))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'('0',f(suc(X4)))
      | ~ 'E'('0',f(X4)) ),
    inference(duplicate_literal_removal,[],[f18]) ).

fof(f31,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'('0',f(suc(X4)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X4),suc(X2))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X3),suc(X4))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X4)) ),
    inference(forward_subsumption_resolution,[],[f28,f2]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X3),suc(X1))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X4),suc(X3))
      | ~ 'E'(s('0'),f(suc(X4)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'(s('0'),f(X3))
      | ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(X4)) ),
    inference(factoring,[],[f10]) ).

fof(f44,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X3),suc(X1))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X4),suc(X3))
      | ~ 'E'(s('0'),f(suc(X4)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'(s('0'),f(X3))
      | ~ 'E'(s('0'),f(X4)) ),
    inference(duplicate_literal_removal,[],[f40]) ).

fof(f49,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X3),suc(X1))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X4),suc(X3))
      | ~ 'E'(s('0'),f(suc(X4)))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'(s('0'),f(X3))
      | ~ 'E'(s('0'),f(X4)) ),
    inference(forward_subsumption_resolution,[],[f44,f7]) ).

fof(f54,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X0),suc(X2))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(X0)) ),
    inference(factoring,[],[f31]) ).

fof(f60,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X0),suc(X2))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'('0',f(suc(X3))) ),
    inference(duplicate_literal_removal,[],[f54]) ).

fof(f63,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X0),suc(X2))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'('0',f(suc(X0))) ),
    inference(forward_subsumption_resolution,[],[f60,f2]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'('0',f(suc(X2))) ),
    inference(factoring,[],[f63]) ).

fof(f72,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'('0',f(suc(X2))) ),
    inference(duplicate_literal_removal,[],[f66]) ).

fof(f74,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'('0',f(suc(X2)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'('0',f(suc(X0))) ),
    inference(forward_subsumption_resolution,[],[f72,f2]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X1),suc(X0)) ),
    inference(factoring,[],[f74]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ iLEQ(suc(X1),suc(X0)) ),
    inference(duplicate_literal_removal,[],[f78]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X1),suc(X0)) ),
    inference(forward_subsumption_resolution,[],[f79,f2]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X0),suc(X0)) ),
    inference(factoring,[],[f81]) ).

fof(f85,plain,
    ! [X0] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | ~ iLEQ(suc(X0),suc(X0)) ),
    inference(duplicate_literal_removal,[],[f83]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0)) ),
    inference(forward_subsumption_resolution,[],[f85,f2]) ).

fof(f92,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X2))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(X3)) ),
    inference(factoring,[],[f49]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X2))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(X3)) ),
    inference(duplicate_literal_removal,[],[f92]) ).

fof(f101,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X2))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(X3)) ),
    inference(forward_subsumption_resolution,[],[f99,f7]) ).

fof(f108,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(X2)) ),
    inference(factoring,[],[f101]) ).

fof(f111,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'(s('0'),f(X2)) ),
    inference(duplicate_literal_removal,[],[f108]) ).

fof(f114,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'(s('0'),f(X2)) ),
    inference(forward_subsumption_resolution,[],[f111,f7]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'(s('0'),f(X0)) ),
    inference(factoring,[],[f114]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X0),suc(X0))
      | ~ iLEQ(suc(X1),suc(X0)) ),
    inference(duplicate_literal_removal,[],[f120]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X1),suc(X0)) ),
    inference(forward_subsumption_resolution,[],[f122,f7]) ).

fof(f129,plain,
    ! [X0] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X0),suc(X0)) ),
    inference(factoring,[],[f124]) ).

fof(f130,plain,
    ! [X0] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X0),suc(X0)) ),
    inference(duplicate_literal_removal,[],[f129]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X0)) ),
    inference(forward_subsumption_resolution,[],[f130,f7]) ).

fof(f133,plain,
    ! [X0] :
      ( ~ 'E'(s('0'),f(X0))
      | 'LE'(f(X0),s('0')) ),
    inference(resolution,[],[f131,f13]) ).

fof(f135,plain,
    ! [X0] : 'LE'(f(X0),s('0')),
    inference(forward_subsumption_resolution,[],[f133,f11]) ).

fof(f136,plain,
    ! [X0] :
      ( 'LE'(f(X0),'0')
      | 'E'('0',f(X0)) ),
    inference(resolution,[],[f135,f5]) ).

fof(f137,plain,
    ! [X0] :
      ( 'LE'(f(X0),'0')
      | 'E'('0',f(suc(X0))) ),
    inference(resolution,[],[f135,f4]) ).

fof(f138,plain,
    'E'('0',f(z)),
    inference(resolution,[],[f136,f3]) ).

fof(f139,plain,
    'E'('0',f(suc(z))),
    inference(resolution,[],[f137,f3]) ).

fof(f146,plain,
    ~ 'E'('0',f(z)),
    inference(resolution,[],[f139,f86]) ).

fof(f147,plain,
    $false,
    inference(forward_subsumption_resolution,[],[f146,f138]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SYO666-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18  % Computer : n019.cluster.edu
% 0.08/0.18  % Model    : x86_64 x86_64
% 0.08/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18  % Memory   : 8046.5625MB
% 0.08/0.18  % OS       : Linux 6.8.0-71-generic
% 0.08/0.18  % CPULimit : 300
% 0.08/0.18  % WCLimit  : 300
% 0.08/0.18  % DateTime : Mon Sep 28 18:02:04 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
% 2.87/1.07  % (54117)Input is clausal, will run a generic CNF schedule.
% 2.87/1.07  % (54126)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1346700994:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.87/1.07  % (54126)Refutation not found, incomplete strategy
% 2.87/1.07  % (54126)------------------------------
% 2.87/1.07  % (54126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.07  % (54126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.07  % (54126)CaDiCaL version: 2.1.3
% 2.87/1.07  % (54126)Termination reason: Refutation not found, incomplete strategy
% 2.87/1.07  % (54126)Time elapsed: 0.0000 s
% 2.87/1.07  % (54126)Peak memory usage: 86 MB
% 2.87/1.07  % (54124)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1622217627:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.87/1.07  % (54128)dis-21_1_sil=8000:lcm=predicate:random_seed=1375979890: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)
% 2.87/1.07  % (54122)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=3217010243:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.87/1.07  % (54125)lrs+10_1_sil=8000:sp=occurrence:random_seed=1613486631:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.87/1.07  % (54123)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1357889212:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.87/1.07  % (54127)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=772435471:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.87/1.07  % (54125)Refutation not found, incomplete strategy
% 2.87/1.07  % (54125)------------------------------
% 2.87/1.07  % (54125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.07  % (54125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.07  % (54125)CaDiCaL version: 2.1.3
% 2.87/1.07  % (54125)Termination reason: Refutation not found, incomplete strategy
% 2.87/1.07  % (54125)Time elapsed: 0.0000 s
% 2.87/1.07  % (54125)Peak memory usage: 86 MB
% 2.87/1.07  % (54127)First to succeed.
% 2.87/1.07  % (54127)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-54117"
% 2.87/1.07  % (54128)Also succeeded, but the first one will report.
% 2.87/1.07  % (54126)------------------------------
% 2.87/1.07  % (54126)------------------------------
% 2.87/1.07  % (54136)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=4265714861:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.87/1.07  % (54136)Refutation not found, incomplete strategy
% 2.87/1.07  % (54136)------------------------------
% 2.87/1.07  % (54136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.07  % (54136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.07  % (54136)CaDiCaL version: 2.1.3
% 2.87/1.07  % (54136)Termination reason: Refutation not found, incomplete strategy
% 2.87/1.07  % (54136)Time elapsed: 0.0000 s
% 2.87/1.07  % (54136)Peak memory usage: 86 MB
% 2.87/1.07  % (54125)------------------------------
% 2.87/1.07  % (54125)------------------------------
% 2.87/1.07  % (54127)Refutation found. Thanks to Tanya!
% 2.87/1.07  % SZS status Unsatisfiable for theBenchmark
% 2.87/1.07  % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.27  % (54127)------------------------------
% 3.60/1.27  % (54127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.27  % (54127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.27  % (54127)CaDiCaL version: 2.1.3
% 3.60/1.27  % (54127)Termination reason: Refutation
% 3.60/1.27  % (54127)Time elapsed: 0.013 s
% 3.60/1.27  % (54127)Peak memory usage: 88 MB
% 3.60/1.27  % (54127)Instructions burned: 24 (million)
% 3.60/1.27  % (54127)------------------------------
% 3.60/1.27  % (54127)------------------------------
% 3.60/1.27  % (54117)Success in time 0.427 s
% 3.60/1.27  % Vampire exiting
%------------------------------------------------------------------------------