TSTP Solution File: KLE005+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 : Wed May 31 12:15:25 EDT 2023

% Result   : Theorem 0.08s 0.29s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   44 (  16 unt;   0 def)
%            Number of atoms       :  104 (  58 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  103 (  43   ~;  42   |;  10   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   40 (;  40   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : addition(A,B) = addition(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A] : addition(A,zero) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A] : multiplication(A,zero) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [A] : multiplication(zero,A) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( multiplication(X0,X1) = zero
        & multiplication(X1,X0) = zero
        & addition(X0,X1) = one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X0,X1] :
      ( test(X0)
     => ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X0] :
      ( ~ test(X0)
     => c(X0) = zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    c(one) = zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    c(one) != zero,
    inference(negated_conjecture,[status(cth)],[f17]) ).

fof(f19,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f21,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f28,plain,
    ! [X0] : multiplication(X0,zero) = zero,
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f29,plain,
    ! [X0] : multiplication(zero,X0) = zero,
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( ~ complement(X1,X0)
        | ( multiplication(X0,X1) = zero
          & multiplication(X1,X0) = zero
          & addition(X0,X1) = one ) )
      & ( complement(X1,X0)
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero
        | addition(X0,X1) != one ) ),
    inference(NNF_transformation,[status(esa)],[f14]) ).

fof(f40,plain,
    ( ! [X0,X1] :
        ( ~ complement(X1,X0)
        | ( multiplication(X0,X1) = zero
          & multiplication(X1,X0) = zero
          & addition(X0,X1) = one ) )
    & ! [X0,X1] :
        ( complement(X1,X0)
        | multiplication(X0,X1) != zero
        | multiplication(X1,X0) != zero
        | addition(X0,X1) != one ) ),
    inference(miniscoping,[status(esa)],[f39]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | multiplication(X1,X0) != zero
      | multiplication(X0,X1) != zero
      | addition(X1,X0) != one ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | ( ( c(X0) != X1
          | complement(X0,X1) )
        & ( c(X0) = X1
          | ~ complement(X0,X1) ) ) ),
    inference(NNF_transformation,[status(esa)],[f45]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ test(X0)
      | ( ! [X1] :
            ( c(X0) != X1
            | complement(X0,X1) )
        & ! [X1] :
            ( c(X0) = X1
            | ~ complement(X0,X1) ) ) ),
    inference(miniscoping,[status(esa)],[f46]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | c(X0) = X1
      | ~ complement(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    ! [X0] :
      ( test(X0)
      | c(X0) = zero ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f51,plain,
    ! [X0] :
      ( test(X0)
      | c(X0) = zero ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,plain,
    c(one) != zero,
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f55,plain,
    ( spl0_0
  <=> zero = zero ),
    introduced(split_symbol_definition) ).

fof(f57,plain,
    ( zero != zero
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f55]) ).

fof(f58,plain,
    ( spl0_1
  <=> test(one) ),
    introduced(split_symbol_definition) ).

fof(f61,plain,
    ( zero != zero
    | test(one) ),
    inference(paramodulation,[status(thm)],[f51,f52]) ).

fof(f62,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f61,f55,f58]) ).

fof(f63,plain,
    ( $false
    | spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f57]) ).

fof(f64,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f63]) ).

fof(f113,plain,
    ! [X0] : X0 = addition(zero,X0),
    inference(paramodulation,[status(thm)],[f21,f19]) ).

fof(f130,plain,
    ! [X0] :
      ( complement(X0,zero)
      | multiplication(zero,X0) != zero
      | multiplication(X0,zero) != zero
      | X0 != one ),
    inference(paramodulation,[status(thm)],[f113,f44]) ).

fof(f131,plain,
    ! [X0] :
      ( complement(X0,zero)
      | zero != zero
      | multiplication(X0,zero) != zero
      | X0 != one ),
    inference(forward_demodulation,[status(thm)],[f29,f130]) ).

fof(f132,plain,
    ! [X0] :
      ( complement(X0,zero)
      | zero != zero
      | zero != zero
      | X0 != one ),
    inference(forward_demodulation,[status(thm)],[f28,f131]) ).

fof(f133,plain,
    ! [X0] :
      ( complement(X0,zero)
      | zero != zero
      | X0 != one ),
    inference(duplicate_literals_removal,[status(esa)],[f132]) ).

fof(f134,plain,
    ! [X0] :
      ( complement(X0,zero)
      | X0 != one ),
    inference(trivial_equality_resolution,[status(esa)],[f133]) ).

fof(f135,plain,
    complement(one,zero),
    inference(destructive_equality_resolution,[status(esa)],[f134]) ).

fof(f137,plain,
    ( spl0_10
  <=> c(one) = zero ),
    introduced(split_symbol_definition) ).

fof(f138,plain,
    ( c(one) = zero
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f137]) ).

fof(f140,plain,
    ( ~ test(one)
    | c(one) = zero ),
    inference(resolution,[status(thm)],[f135,f49]) ).

fof(f141,plain,
    ( ~ spl0_1
    | spl0_10 ),
    inference(split_clause,[status(thm)],[f140,f58,f137]) ).

fof(f142,plain,
    ( $false
    | ~ spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f138,f52]) ).

fof(f143,plain,
    ~ spl0_10,
    inference(contradiction_clause,[status(thm)],[f142]) ).

fof(f144,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f62,f64,f141,f143]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Tue May 30 11:47:46 EDT 2023
% 0.08/0.28  % CPUTime  : 
% 0.08/0.28  % Drodi V3.5.1
% 0.08/0.29  % Refutation found
% 0.08/0.29  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.29  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.30  % Elapsed time: 0.015802 seconds
% 0.12/0.30  % CPU time: 0.024543 seconds
% 0.12/0.30  % Memory used: 14.377 MB
%------------------------------------------------------------------------------