TSTP Solution File: SYO666-1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SYO666-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 20:54:42 EDT 2024

% Result   : Unsatisfiable 0.14s 0.36s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   42 (   8 unt;   0 def)
%            Number of atoms       :  209 (   0 equ)
%            Maximal formula atoms :   17 (   4 avg)
%            Number of connectives :  331 ( 164   ~; 167   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   8 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,
    ! [B_96,B_97,E,A_2,B_98,B_94,B_95] :
      ( ~ iLEQ(suc(B_96),suc(B_97))
      | ~ 'E'('0',f(suc(A_2)))
      | ~ 'E'('0',f(suc(B_96)))
      | ~ iLEQ(suc(B_97),suc(B_98))
      | ~ 'E'('0',f(suc(B_97)))
      | ~ 'E'('0',f(A_2))
      | ~ 'E'('0',f(suc(B_94)))
      | ~ 'E'('0',f(B_97))
      | ~ iLEQ(suc(B_95),suc(B_96))
      | ~ 'E'('0',f(B_96))
      | ~ iLEQ(suc(B_94),suc(B_95))
      | ~ 'E'('0',f(suc(B_98)))
      | ~ 'E'('0',f(B_94))
      | ~ iLEQ(suc(A_2),suc(B_94))
      | ~ 'E'('0',f(suc(B_95)))
      | ~ 'E'('0',f(B_98))
      | ~ 'E'('0',f(B_95)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [E,A_2] :
      ( ~ 'E'('0',f(A_2))
      | ~ 'E'('0',f(suc(A_2)))
      | iLEQ(suc(A_2),suc(A_2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f4,axiom,
    ! [LE,B_93,E] :
      ( ~ 'LE'(f(suc(B_93)),s('0'))
      | 'E'('0',f(suc(B_93)))
      | 'LE'(f(B_93),'0') ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [LE,B_93,E] :
      ( ~ 'LE'(f(B_93),s('0'))
      | 'E'('0',f(B_93))
      | 'LE'(f(B_93),'0') ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f7,axiom,
    ! [E,A_1] :
      ( ~ 'E'(s('0'),f(A_1))
      | ~ 'E'(s('0'),f(suc(A_1)))
      | iLEQ(suc(A_1),suc(A_1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [LE,B_68,E] :
      ( ~ 'LE'(f(suc(B_68)),s(s('0')))
      | 'E'(s('0'),f(suc(B_68)))
      | 'LE'(f(B_68),s('0')) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [LE,B_68,E] :
      ( ~ 'LE'(f(B_68),s(s('0')))
      | 'E'(s('0'),f(B_68))
      | 'LE'(f(B_68),s('0')) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [E,B_69,B_71,B_72,A_1,B_70,B_73] :
      ( ~ 'E'(s('0'),f(B_69))
      | ~ iLEQ(suc(B_71),suc(B_72))
      | ~ 'E'(s('0'),f(A_1))
      | ~ 'E'(s('0'),f(suc(A_1)))
      | ~ iLEQ(suc(B_70),suc(B_71))
      | ~ 'E'(s('0'),f(B_71))
      | ~ 'E'(s('0'),f(suc(B_71)))
      | ~ iLEQ(suc(B_69),suc(B_70))
      | ~ 'E'(s('0'),f(suc(B_69)))
      | ~ iLEQ(suc(B_72),suc(B_73))
      | ~ 'E'(s('0'),f(suc(B_70)))
      | ~ 'E'(s('0'),f(B_73))
      | ~ 'E'(s('0'),f(suc(B_72)))
      | ~ iLEQ(suc(A_1),suc(B_69))
      | ~ 'E'(s('0'),f(B_70))
      | ~ 'E'(s('0'),f(B_72))
      | ~ 'E'(s('0'),f(suc(B_73))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,plain,
    ! [B_95] :
      ( ! [B_98] :
          ( ! [A_2,B_94] :
              ( ! [B_96] :
                  ( ! [B_97] :
                      ( ~ iLEQ(suc(B_96),suc(B_97))
                      | ~ 'E'('0',f(suc(A_2)))
                      | ~ 'E'('0',f(suc(B_96)))
                      | ~ iLEQ(suc(B_97),suc(B_98))
                      | ~ 'E'('0',f(suc(B_97)))
                      | ~ 'E'('0',f(A_2))
                      | ~ 'E'('0',f(suc(B_94)))
                      | ~ 'E'('0',f(B_97)) )
                  | ~ iLEQ(suc(B_95),suc(B_96))
                  | ~ 'E'('0',f(B_96)) )
              | ~ iLEQ(suc(B_94),suc(B_95))
              | ~ 'E'('0',f(suc(B_98)))
              | ~ 'E'('0',f(B_94))
              | ~ iLEQ(suc(A_2),suc(B_94)) )
          | ~ 'E'('0',f(suc(B_95)))
          | ~ 'E'('0',f(B_98)) )
      | ~ 'E'('0',f(B_95)) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f12,plain,
    ! [X0,X1,E,X2,X3,X4,X5] :
      ( ~ iLEQ(suc(X0),suc(X1))
      | ~ '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))
      | ~ 'E'('0',f(suc(X3)))
      | ~ 'E'('0',f(X4))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'('0',f(suc(X5)))
      | ~ 'E'('0',f(X3))
      | ~ 'E'('0',f(X5)) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ! [A_2] :
      ( ~ 'E'('0',f(A_2))
      | ~ 'E'('0',f(suc(A_2)))
      | iLEQ(suc(A_2),suc(A_2)) ),
    inference(miniscoping,[status(esa)],[f2]) ).

fof(f14,plain,
    ! [E,X0] :
      ( ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(suc(X0)))
      | iLEQ(suc(X0),suc(X0)) ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [LE] : ~ 'LE'(f(z),'0'),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f16,plain,
    ! [B_93] :
      ( ~ 'LE'(f(suc(B_93)),s('0'))
      | 'E'('0',f(suc(B_93)))
      | 'LE'(f(B_93),'0') ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f17,plain,
    ! [LE,X0,E] :
      ( ~ 'LE'(f(suc(X0)),s('0'))
      | 'E'('0',f(suc(X0)))
      | 'LE'(f(X0),'0') ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [B_93] :
      ( ~ 'LE'(f(B_93),s('0'))
      | 'E'('0',f(B_93))
      | 'LE'(f(B_93),'0') ),
    inference(miniscoping,[status(esa)],[f5]) ).

fof(f19,plain,
    ! [LE,X0,E] :
      ( ~ 'LE'(f(X0),s('0'))
      | 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f20,plain,
    ! [A] : 'LE'(f(A),s(s('0'))),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f21,plain,
    ! [LE,X0] : 'LE'(f(X0),s(s('0'))),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [A_1] :
      ( ~ 'E'(s('0'),f(A_1))
      | ~ 'E'(s('0'),f(suc(A_1)))
      | iLEQ(suc(A_1),suc(A_1)) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f23,plain,
    ! [E,X0] :
      ( ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(suc(X0)))
      | iLEQ(suc(X0),suc(X0)) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [B_68] :
      ( ~ 'LE'(f(suc(B_68)),s(s('0')))
      | 'E'(s('0'),f(suc(B_68)))
      | 'LE'(f(B_68),s('0')) ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f25,plain,
    ! [LE,X0,E] :
      ( ~ 'LE'(f(suc(X0)),s(s('0')))
      | 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X0),s('0')) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [B_68] :
      ( ~ 'LE'(f(B_68),s(s('0')))
      | 'E'(s('0'),f(B_68))
      | 'LE'(f(B_68),s('0')) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f27,plain,
    ! [LE,X0,E] :
      ( ~ 'LE'(f(X0),s(s('0')))
      | 'E'(s('0'),f(X0))
      | 'LE'(f(X0),s('0')) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [B_73] :
      ( ! [B_72] :
          ( ! [B_70] :
              ( ! [B_69,A_1] :
                  ( ! [B_71] :
                      ( ~ 'E'(s('0'),f(B_69))
                      | ~ iLEQ(suc(B_71),suc(B_72))
                      | ~ 'E'(s('0'),f(A_1))
                      | ~ 'E'(s('0'),f(suc(A_1)))
                      | ~ iLEQ(suc(B_70),suc(B_71))
                      | ~ 'E'(s('0'),f(B_71))
                      | ~ 'E'(s('0'),f(suc(B_71))) )
                  | ~ iLEQ(suc(B_69),suc(B_70))
                  | ~ 'E'(s('0'),f(suc(B_69)))
                  | ~ iLEQ(suc(B_72),suc(B_73))
                  | ~ 'E'(s('0'),f(suc(B_70)))
                  | ~ 'E'(s('0'),f(B_73))
                  | ~ 'E'(s('0'),f(suc(B_72)))
                  | ~ iLEQ(suc(A_1),suc(B_69)) )
              | ~ 'E'(s('0'),f(B_70)) )
          | ~ 'E'(s('0'),f(B_72)) )
      | ~ 'E'(s('0'),f(suc(B_73))) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f29,plain,
    ! [E,X0,X1,X2,X3,X4,X5] :
      ( ~ 'E'(s('0'),f(X0))
      | ~ 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(suc(X5))) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
    ! [E,X0,LE] :
      ( 'E'(s('0'),f(suc(X0)))
      | 'LE'(f(X0),s('0')) ),
    inference(forward_subsumption_resolution,[status(thm)],[f25,f21]) ).

fof(f31,plain,
    ! [E,X0,LE] :
      ( 'E'(s('0'),f(X0))
      | 'LE'(f(X0),s('0')) ),
    inference(forward_subsumption_resolution,[status(thm)],[f27,f21]) ).

fof(f36,plain,
    ! [E,X0] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(X0))
      | ~ 'E'('0',f(suc(X0))) ),
    inference(resolution,[status(thm)],[f12,f14]) ).

fof(f37,plain,
    ! [E,X0] :
      ( ~ 'E'('0',f(suc(X0)))
      | ~ 'E'('0',f(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f36]) ).

fof(f68,plain,
    ! [E,X0] :
      ( ~ '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(suc(X0)))
      | ~ 'E'(s('0'),f(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)))
      | ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(suc(X0))) ),
    inference(resolution,[status(thm)],[f29,f23]) ).

fof(f69,plain,
    ! [E,X0] :
      ( ~ 'E'(s('0'),f(X0))
      | ~ 'E'(s('0'),f(suc(X0))) ),
    inference(duplicate_literals_removal,[status(esa)],[f68]) ).

fof(f95,plain,
    ! [E,X0,LE] :
      ( ~ 'E'('0',f(X0))
      | ~ 'LE'(f(suc(X0)),s('0'))
      | 'LE'(f(X0),'0') ),
    inference(resolution,[status(thm)],[f37,f17]) ).

fof(f96,plain,
    ! [E,X0,LE] :
      ( ~ 'E'(s('0'),f(X0))
      | 'LE'(f(X0),s('0')) ),
    inference(resolution,[status(thm)],[f69,f30]) ).

fof(f97,plain,
    ! [LE,X0] : 'LE'(f(X0),s('0')),
    inference(forward_subsumption_resolution,[status(thm)],[f96,f31]) ).

fof(f99,plain,
    ! [E,X0,LE] :
      ( 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    inference(backward_subsumption_resolution,[status(thm)],[f19,f97]) ).

fof(f102,plain,
    ! [E,X0,LE] :
      ( ~ 'E'('0',f(X0))
      | 'LE'(f(X0),'0') ),
    inference(backward_subsumption_resolution,[status(thm)],[f95,f97]) ).

fof(f103,plain,
    ! [LE,X0] : 'LE'(f(X0),'0'),
    inference(forward_subsumption_resolution,[status(thm)],[f102,f99]) ).

fof(f104,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f15,f103]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYO666-1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 21:27:48 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.14/0.36  % Refutation found
% 0.14/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.37  % Elapsed time: 0.015054 seconds
% 0.14/0.37  % CPU time: 0.038686 seconds
% 0.14/0.37  % Total memory used: 1.217 MB
% 0.14/0.37  % Net memory used: 1.134 MB
%------------------------------------------------------------------------------