TSTP Solution File: ALG226+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : ALG226+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:11:08 EDT 2024

% Result   : Theorem 64.20s 9.80s
% Output   : CNFRefutation 67.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   44 (  11 unt;   0 def)
%            Number of atoms       :  124 (  30 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  127 (  47   ~;  41   |;  23   &)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   33 (  30   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5405,axiom,
    ! [A,B,C] :
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16950,axiom,
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => B = k1_funct_4(k1_pboole(A),k7_relat_1(B,k1_closure3(A,B))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16951,conjecture,
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v2_relat_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,A) )
             => ( ( k1_closure3(A,B) = k1_closure3(A,C)
                  & k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C)) )
               => r6_pboole(A,B,C) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16952,negated_conjecture,
    ~ ! [A] :
        ( ~ v1_xboole_0(A)
       => ! [B] :
            ( ( v2_relat_1(B)
              & m1_pboole(B,A) )
           => ! [C] :
                ( ( v2_relat_1(C)
                  & m1_pboole(C,A) )
               => ( ( k1_closure3(A,B) = k1_closure3(A,C)
                    & k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C)) )
                 => r6_pboole(A,B,C) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f16951]) ).

fof(f33054,plain,
    ! [A,B,C] :
      ( ~ m1_pboole(B,A)
      | ~ m1_pboole(C,A)
      | ( r6_pboole(A,B,C)
      <=> B = C ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5405]) ).

fof(f33055,plain,
    ! [A,B,C] :
      ( ~ m1_pboole(B,A)
      | ~ m1_pboole(C,A)
      | ( ( ~ r6_pboole(A,B,C)
          | B = C )
        & ( r6_pboole(A,B,C)
          | B != C ) ) ),
    inference(NNF_transformation,[status(esa)],[f33054]) ).

fof(f33057,plain,
    ! [X0,X1,X2] :
      ( ~ m1_pboole(X0,X1)
      | ~ m1_pboole(X2,X1)
      | r6_pboole(X1,X0,X2)
      | X0 != X2 ),
    inference(cnf_transformation,[status(esa)],[f33055]) ).

fof(f75975,plain,
    ! [A] :
      ( v1_xboole_0(A)
      | ! [B] :
          ( ~ v2_relat_1(B)
          | ~ m1_pboole(B,A)
          | B = k1_funct_4(k1_pboole(A),k7_relat_1(B,k1_closure3(A,B))) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f16950]) ).

fof(f75976,plain,
    ! [X0,X1] :
      ( v1_xboole_0(X0)
      | ~ v2_relat_1(X1)
      | ~ m1_pboole(X1,X0)
      | X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) ),
    inference(cnf_transformation,[status(esa)],[f75975]) ).

fof(f75977,plain,
    ? [A] :
      ( ~ v1_xboole_0(A)
      & ? [B] :
          ( v2_relat_1(B)
          & m1_pboole(B,A)
          & ? [C] :
              ( v2_relat_1(C)
              & m1_pboole(C,A)
              & k1_closure3(A,B) = k1_closure3(A,C)
              & k7_relat_1(B,k1_closure3(A,B)) = k7_relat_1(C,k1_closure3(A,C))
              & ~ r6_pboole(A,B,C) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f16952]) ).

fof(f75978,plain,
    ( ~ v1_xboole_0(sk0_5437)
    & v2_relat_1(sk0_5438)
    & m1_pboole(sk0_5438,sk0_5437)
    & v2_relat_1(sk0_5439)
    & m1_pboole(sk0_5439,sk0_5437)
    & k1_closure3(sk0_5437,sk0_5438) = k1_closure3(sk0_5437,sk0_5439)
    & k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)) = k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439))
    & ~ r6_pboole(sk0_5437,sk0_5438,sk0_5439) ),
    inference(skolemization,[status(esa)],[f75977]) ).

fof(f75979,plain,
    ~ v1_xboole_0(sk0_5437),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f75980,plain,
    v2_relat_1(sk0_5438),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f75981,plain,
    m1_pboole(sk0_5438,sk0_5437),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f75982,plain,
    v2_relat_1(sk0_5439),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f75983,plain,
    m1_pboole(sk0_5439,sk0_5437),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f75984,plain,
    k1_closure3(sk0_5437,sk0_5438) = k1_closure3(sk0_5437,sk0_5439),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f75985,plain,
    k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)) = k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439)),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f75986,plain,
    ~ r6_pboole(sk0_5437,sk0_5438,sk0_5439),
    inference(cnf_transformation,[status(esa)],[f75978]) ).

fof(f85348,plain,
    ! [X2,X1] :
      ( ~ m1_pboole(X2,X1)
      | ~ m1_pboole(X2,X1)
      | r6_pboole(X1,X2,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f33057]) ).

fof(f85349,plain,
    ! [X0,X1] :
      ( ~ m1_pboole(X0,X1)
      | r6_pboole(X1,X0,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f85348]) ).

fof(f87967,plain,
    k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)) = k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5438)),
    inference(forward_demodulation,[status(thm)],[f75984,f75985]) ).

fof(f87971,plain,
    ! [X0] :
      ( v1_xboole_0(X0)
      | ~ m1_pboole(sk0_5439,X0)
      | sk0_5439 = k1_funct_4(k1_pboole(X0),k7_relat_1(sk0_5439,k1_closure3(X0,sk0_5439))) ),
    inference(resolution,[status(thm)],[f75976,f75982]) ).

fof(f87972,plain,
    ! [X0] :
      ( v1_xboole_0(X0)
      | ~ m1_pboole(sk0_5438,X0)
      | sk0_5438 = k1_funct_4(k1_pboole(X0),k7_relat_1(sk0_5438,k1_closure3(X0,sk0_5438))) ),
    inference(resolution,[status(thm)],[f75976,f75980]) ).

fof(f87974,plain,
    ( spl0_1356
  <=> v1_xboole_0(sk0_5437) ),
    introduced(split_symbol_definition) ).

fof(f87975,plain,
    ( v1_xboole_0(sk0_5437)
    | ~ spl0_1356 ),
    inference(component_clause,[status(thm)],[f87974]) ).

fof(f87977,plain,
    ( spl0_1357
  <=> sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439))) ),
    introduced(split_symbol_definition) ).

fof(f87978,plain,
    ( sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439)))
    | ~ spl0_1357 ),
    inference(component_clause,[status(thm)],[f87977]) ).

fof(f87980,plain,
    ( v1_xboole_0(sk0_5437)
    | sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5439))) ),
    inference(resolution,[status(thm)],[f87971,f75983]) ).

fof(f87981,plain,
    ( spl0_1356
    | spl0_1357 ),
    inference(split_clause,[status(thm)],[f87980,f87974,f87977]) ).

fof(f87996,plain,
    ( $false
    | ~ spl0_1356 ),
    inference(forward_subsumption_resolution,[status(thm)],[f87975,f75979]) ).

fof(f87997,plain,
    ~ spl0_1356,
    inference(contradiction_clause,[status(thm)],[f87996]) ).

fof(f87998,plain,
    ( sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5439,k1_closure3(sk0_5437,sk0_5438)))
    | ~ spl0_1357 ),
    inference(forward_demodulation,[status(thm)],[f75984,f87978]) ).

fof(f87999,plain,
    ( sk0_5439 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)))
    | ~ spl0_1357 ),
    inference(forward_demodulation,[status(thm)],[f87967,f87998]) ).

fof(f88007,plain,
    ( spl0_1362
  <=> sk0_5438 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438))) ),
    introduced(split_symbol_definition) ).

fof(f88008,plain,
    ( sk0_5438 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438)))
    | ~ spl0_1362 ),
    inference(component_clause,[status(thm)],[f88007]) ).

fof(f88010,plain,
    ( v1_xboole_0(sk0_5437)
    | sk0_5438 = k1_funct_4(k1_pboole(sk0_5437),k7_relat_1(sk0_5438,k1_closure3(sk0_5437,sk0_5438))) ),
    inference(resolution,[status(thm)],[f87972,f75981]) ).

fof(f88011,plain,
    ( spl0_1356
    | spl0_1362 ),
    inference(split_clause,[status(thm)],[f88010,f87974,f88007]) ).

fof(f88026,plain,
    ( sk0_5438 = sk0_5439
    | ~ spl0_1357
    | ~ spl0_1362 ),
    inference(forward_demodulation,[status(thm)],[f87999,f88008]) ).

fof(f88043,plain,
    ( ~ r6_pboole(sk0_5437,sk0_5438,sk0_5438)
    | ~ spl0_1357
    | ~ spl0_1362 ),
    inference(backward_demodulation,[status(thm)],[f88026,f75986]) ).

fof(f88046,plain,
    ( ~ m1_pboole(sk0_5438,sk0_5437)
    | ~ spl0_1357
    | ~ spl0_1362 ),
    inference(resolution,[status(thm)],[f88043,f85349]) ).

fof(f88047,plain,
    ( $false
    | ~ spl0_1357
    | ~ spl0_1362 ),
    inference(forward_subsumption_resolution,[status(thm)],[f88046,f75981]) ).

fof(f88048,plain,
    ( ~ spl0_1357
    | ~ spl0_1362 ),
    inference(contradiction_clause,[status(thm)],[f88047]) ).

fof(f88049,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f87981,f87997,f88011,f88048]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : ALG226+3 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Apr 29 23:23:52 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 1.60/1.80  % Drodi V3.6.0
% 64.20/9.80  % Refutation found
% 64.20/9.80  % SZS status Theorem for theBenchmark: Theorem is valid
% 64.20/9.80  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 68.00/10.21  % Elapsed time: 9.831143 seconds
% 68.00/10.21  % CPU time: 65.772336 seconds
% 68.00/10.21  % Total memory used: 4.495 GB
% 68.00/10.21  % Net memory used: 4.472 GB
%------------------------------------------------------------------------------