↑ Up

Vampire-SAT---5.0.1.UNS-Ref.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SYO664-1 : 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 : n026.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 02:32:20 PM UTC 2026

% Result   : Unsatisfiable 0.19s 0.26s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   54 (   5 unt;   0 def)
%            Number of atoms       :  332 (   0 equ)
%            Maximal formula atoms :   14 (   6 avg)
%            Number of connectives :  489 ( 211   ~; 278   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   9 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   :  136 ( 136   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X4)))
      | ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ 'E'(s('0'),f(X3))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ iLEQ(suc(X3),suc(X2))
      | ~ 'E'(s('0'),f(X2))
      | ~ iLEQ(suc(X4),suc(X0))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(X4))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'(s('0'),f(suc(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_37) ).

fof(f2,axiom,
    ~ 'LE'(f(z),'0'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_70) ).

fof(f3,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_20) ).

fof(f4,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ iLEQ(suc(X3),suc(X0))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ iLEQ(suc(X2),suc(X1))
      | ~ iLEQ(suc(X1),suc(X3))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X2))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X4))
      | ~ iLEQ(suc(X0),suc(X4))
      | ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X4)))
      | ~ 'E'('0',f(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_66) ).

fof(f5,axiom,
    ! [X0] : 'LE'(f(X0),s(s('0'))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_58) ).

fof(f6,axiom,
    ! [X0] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | iLEQ(suc(X0),suc(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).

fof(f7,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_117) ).

fof(f8,axiom,
    ! [X0] :
      ( ~ 'LE'(f(X0),s('0'))
      | 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_94) ).

fof(f9,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_50) ).

fof(f10,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_83) ).

fof(f11,plain,
    ! [X0] :
      ( 'LE'(f(X0),s('0'))
      | 'E'(s('0'),f(X0)) ),
    inference(forward_subsumption_resolution,[],[f3,f5]) ).

fof(f15,plain,
    ! [X0] :
      ( 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X0),s('0')) ),
    inference(forward_subsumption_resolution,[],[f10,f5]) ).

fof(f16,plain,
    ! [X0] :
      ( 'LE'(f(X0),s('0'))
      | ~ 'E'(s('0'),f(X0))
      | iLEQ(suc(X0),suc(X0)) ),
    inference(resolution,[],[f15,f9]) ).

fof(f17,plain,
    ! [X0] :
      ( 'LE'(f(X0),s('0'))
      | iLEQ(suc(X0),suc(X0)) ),
    inference(forward_subsumption_resolution,[],[f16,f11]) ).

fof(f18,plain,
    ! [X0] :
      ( iLEQ(suc(X0),suc(X0))
      | 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    inference(resolution,[],[f17,f8]) ).

fof(f21,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ 'E'(s('0'),f(X3))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ iLEQ(suc(X3),suc(X2))
      | ~ 'E'(s('0'),f(X2))
      | ~ iLEQ(suc(X4),suc(X0))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(X4))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X4),s('0')) ),
    inference(resolution,[],[f1,f15]) ).

fof(f23,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ 'E'(s('0'),f(X3))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X2))
      | ~ 'E'(s('0'),f(X2))
      | ~ iLEQ(suc(X4),suc(X0))
      | ~ 'E'(s('0'),f(X1))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X4),s('0')) ),
    inference(forward_subsumption_resolution,[],[f21,f11]) ).

fof(f33,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(X3))
      | ~ iLEQ(suc(X2),suc(X1))
      | ~ 'E'(s('0'),f(X1))
      | ~ iLEQ(suc(X4),suc(X3))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X0))
      | ~ iLEQ(suc(X1),suc(X4))
      | ~ 'E'(s('0'),f(suc(X3)))
      | 'LE'(f(X4),s('0'))
      | 'LE'(f(X2),s('0')) ),
    inference(resolution,[],[f23,f15]) ).

fof(f35,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X3))
      | ~ iLEQ(suc(X2),suc(X1))
      | ~ 'E'(s('0'),f(X1))
      | ~ iLEQ(suc(X4),suc(X3))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X0))
      | ~ iLEQ(suc(X1),suc(X4))
      | ~ 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X4),s('0'))
      | 'LE'(f(X2),s('0')) ),
    inference(forward_subsumption_resolution,[],[f33,f11]) ).

fof(f48,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X1))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X1))
      | ~ 'E'(s('0'),f(X4))
      | ~ iLEQ(suc(X1),suc(X4))
      | ~ iLEQ(suc(X0),suc(X3))
      | ~ 'E'(s('0'),f(suc(X4)))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X1),s('0')) ),
    inference(resolution,[],[f35,f15]) ).

fof(f50,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X4)))
      | ~ iLEQ(suc(X2),suc(X0))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X1))
      | ~ 'E'(s('0'),f(X4))
      | ~ iLEQ(suc(X1),suc(X4))
      | ~ iLEQ(suc(X0),suc(X3))
      | ~ 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X1),s('0')) ),
    inference(forward_subsumption_resolution,[],[f48,f11]) ).

fof(f96,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'(s('0'),f(X1))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ 'E'(s('0'),f(X4))
      | ~ iLEQ(suc(X3),suc(X4))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'(s('0'),f(suc(X1)))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X4),s('0')) ),
    inference(resolution,[],[f50,f15]) ).

fof(f98,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X1))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ iLEQ(suc(X3),suc(X4))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ iLEQ(suc(X0),suc(X1))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X4),s('0')) ),
    inference(forward_subsumption_resolution,[],[f96,f11]) ).

fof(f100,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ iLEQ(suc(X4),suc(X0))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X4),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X0),s('0')) ),
    inference(resolution,[],[f98,f15]) ).

fof(f102,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ iLEQ(suc(X4),suc(X0))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ iLEQ(suc(X1),suc(X2))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X4),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X0),s('0')) ),
    inference(forward_subsumption_resolution,[],[f100,f11]) ).

fof(f108,plain,
    ! [X2,X3,X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ iLEQ(suc(X3),suc(X0))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X2),s('0')) ),
    inference(resolution,[],[f102,f17]) ).

fof(f115,plain,
    ! [X2,X3,X0,X1] :
      ( ~ iLEQ(suc(X3),suc(X0))
      | ~ iLEQ(suc(X2),suc(X3))
      | ~ iLEQ(suc(X0),suc(X1))
      | 'LE'(f(X3),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X1),s('0')) ),
    inference(duplicate_literal_removal,[],[f108]) ).

fof(f124,plain,
    ! [X2,X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | ~ iLEQ(suc(X1),suc(X2))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X2),s('0'))
      | 'LE'(f(X1),s('0')) ),
    inference(resolution,[],[f115,f17]) ).

fof(f131,plain,
    ! [X2,X0,X1] :
      ( ~ iLEQ(suc(X1),suc(X2))
      | ~ iLEQ(suc(X0),suc(X1))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X2),s('0')) ),
    inference(duplicate_literal_removal,[],[f124]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X1),s('0')) ),
    inference(resolution,[],[f131,f17]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | 'LE'(f(X1),s('0'))
      | 'LE'(f(X0),s('0')) ),
    inference(duplicate_literal_removal,[],[f140]) ).

fof(f154,plain,
    ! [X0] :
      ( 'LE'(f(X0),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    inference(resolution,[],[f147,f18]) ).

fof(f155,plain,
    ! [X0] :
      ( 'LE'(f(X0),s('0'))
      | 'LE'(f(X0),s('0'))
      | 'LE'(f(X0),s('0')) ),
    inference(resolution,[],[f147,f17]) ).

fof(f162,plain,
    ! [X0] : 'LE'(f(X0),s('0')),
    inference(duplicate_literal_removal,[],[f155]) ).

fof(f163,plain,
    ! [X0] :
      ( 'LE'(f(X0),s('0'))
      | 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    inference(duplicate_literal_removal,[],[f154]) ).

fof(f165,plain,
    ! [X0] :
      ( 'LE'(f(X0),'0')
      | 'E'('0',f(X0)) ),
    inference(forward_subsumption_resolution,[],[f163,f8]) ).

fof(f170,plain,
    ! [X0] :
      ( 'E'('0',f(suc(X0)))
      | 'LE'(f(X0),'0') ),
    inference(resolution,[],[f162,f7]) ).

fof(f173,plain,
    ! [X0] :
      ( 'LE'(f(X0),'0')
      | ~ 'E'('0',f(X0))
      | iLEQ(suc(X0),suc(X0)) ),
    inference(resolution,[],[f170,f6]) ).

fof(f174,plain,
    ! [X0] :
      ( iLEQ(suc(X0),suc(X0))
      | 'LE'(f(X0),'0') ),
    inference(forward_subsumption_resolution,[],[f173,f165]) ).

fof(f176,plain,
    ! [X2,X3,X0,X1] :
      ( 'LE'(f(X0),'0')
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ iLEQ(suc(X2),suc(X1))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X2))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X0),suc(X3))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(X0)) ),
    inference(resolution,[],[f174,f4]) ).

fof(f191,plain,
    ! [X2,X3,X0,X1] :
      ( 'LE'(f(X0),'0')
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ iLEQ(suc(X2),suc(X1))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X2))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X0),suc(X3))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X3))) ),
    inference(duplicate_literal_removal,[],[f176]) ).

fof(f195,plain,
    ! [X2,X3,X0,X1] :
      ( 'LE'(f(X0),'0')
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | ~ iLEQ(suc(X2),suc(X1))
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X2))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X0),suc(X3))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X3))) ),
    inference(forward_subsumption_resolution,[],[f191,f165]) ).

fof(f199,plain,
    ! [X2,X3,X0,X1] :
      ( ~ iLEQ(suc(X2),suc(X1))
      | ~ 'E'('0',f(suc(X1)))
      | ~ 'E'('0',f(suc(X2)))
      | 'LE'(f(X0),'0')
      | ~ iLEQ(suc(X1),suc(X0))
      | ~ 'E'('0',f(X2))
      | ~ 'E'('0',f(X3))
      | ~ iLEQ(suc(X0),suc(X3))
      | ~ 'E'('0',f(X1))
      | ~ 'E'('0',f(suc(X3))) ),
    inference(forward_subsumption_resolution,[],[f195,f170]) ).

fof(f200,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X0)))
      | 'LE'(f(X1),'0')
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(suc(X2)))
      | 'LE'(f(X0),'0') ),
    inference(resolution,[],[f199,f174]) ).

fof(f211,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | 'LE'(f(X1),'0')
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'('0',f(suc(X2)))
      | 'LE'(f(X0),'0') ),
    inference(duplicate_literal_removal,[],[f200]) ).

fof(f212,plain,
    ! [X2,X0,X1] :
      ( ~ 'E'('0',f(suc(X0)))
      | 'LE'(f(X1),'0')
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'('0',f(X2))
      | ~ iLEQ(suc(X1),suc(X2))
      | ~ 'E'('0',f(suc(X2)))
      | 'LE'(f(X0),'0') ),
    inference(forward_subsumption_resolution,[],[f211,f165]) ).

fof(f213,plain,
    ! [X2,X0,X1] :
      ( ~ iLEQ(suc(X1),suc(X2))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'('0',f(X2))
      | 'LE'(f(X1),'0')
      | ~ 'E'('0',f(suc(X2)))
      | 'LE'(f(X0),'0') ),
    inference(forward_subsumption_resolution,[],[f212,f170]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'('0',f(X1))
      | 'LE'(f(X1),'0')
      | ~ 'E'('0',f(suc(X1)))
      | 'LE'(f(X0),'0')
      | 'LE'(f(X1),'0') ),
    inference(resolution,[],[f213,f174]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'('0',f(X1))
      | 'LE'(f(X1),'0')
      | ~ 'E'('0',f(suc(X1)))
      | 'LE'(f(X0),'0') ),
    inference(duplicate_literal_removal,[],[f214]) ).

fof(f224,plain,
    ! [X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | 'LE'(f(X1),'0')
      | ~ 'E'('0',f(suc(X1)))
      | 'LE'(f(X0),'0') ),
    inference(forward_subsumption_resolution,[],[f222,f165]) ).

fof(f226,plain,
    ! [X0,X1] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | 'LE'(f(X1),'0')
      | 'LE'(f(X0),'0') ),
    inference(forward_subsumption_resolution,[],[f224,f170]) ).

fof(f227,plain,
    ! [X0] :
      ( 'LE'(f(X0),'0')
      | 'LE'(f(X0),'0')
      | 'LE'(f(X0),'0') ),
    inference(resolution,[],[f226,f174]) ).

fof(f238,plain,
    ! [X0] : 'LE'(f(X0),'0'),
    inference(duplicate_literal_removal,[],[f227]) ).

fof(f239,plain,
    $false,
    inference(resolution,[],[f238,f2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SYO664-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18  % Computer : n026.cluster.edu
% 0.09/0.18  % Model    : x86_64 x86_64
% 0.09/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18  % Memory   : 8046.5625MB
% 0.09/0.18  % OS       : Linux 6.8.0-71-generic
% 0.09/0.19  % CPULimit : 300
% 0.09/0.19  % WCLimit  : 300
% 0.09/0.19  % DateTime : Mon Sep 28 18:04:42 UTC 2026
% 0.09/0.19  % CPUTime  : 
% 0.09/0.19  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22  Running first-order model finding
% 0.09/0.22  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.26  % (4102568)Will run a generic schedule for satisfiability detection.
% 0.19/0.26  % (4102576)dis+10_1_sil=32000:sp=arity:random_seed=1550020137:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26  % (4102574)% WARNING: option uhcvi not known.
% 0.19/0.26  % (4102576) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4102568-4102576"...
% 0.19/0.26  % (4102574)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=915531803:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26  % (4102573)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3206426113_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26  % (4102578)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1842091238:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.26  % (4102575)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=136739257:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.26  % (4102576)...printing done.
% 0.19/0.26  % (4102577)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1493372583:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26  % (4102579)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3024815914:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.26  % (4102576)Refutation found. Thanks to Tanya!
% 0.19/0.26  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.26  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27  % (4102576)------------------------------
% 0.19/0.27  % (4102576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27  % (4102576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27  % (4102576)CaDiCaL version: 2.1.3
% 0.19/0.27  % (4102576)Termination reason: Refutation
% 0.19/0.27  % (4102576)Time elapsed: 0.007 s
% 0.19/0.27  % (4102576)Peak memory usage: 11 MB
% 0.19/0.27  % (4102576)Instructions burned: 25 (million)
% 0.19/0.27  % (4102568)Success in time 0.037 s
% 0.19/0.27  % Vampire exiting
%------------------------------------------------------------------------------