TSTP Solution File: KLE025+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 12:15:33 EDT 2023

% Result   : Theorem 3.08s 0.75s
% Output   : CNFRefutation 3.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   34 (  18 unt;   0 def)
%            Number of atoms       :   83 (  50 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   74 (  25   ~;  20   |;  21   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   52 (;  46   !;   6   ?)

% 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(f6,axiom,
    ! [A] : multiplication(A,one) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    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(f19,conjecture,
    ! [X0,X1,X2] :
      ( ( test(X1)
        & test(X2) )
     => ( multiplication(multiplication(X1,X0),c(X2)) = zero
       => multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( test(X1)
          & test(X2) )
       => ( multiplication(multiplication(X1,X0),c(X2)) = zero
         => multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
    inference(negated_conjecture,[status(cth)],[f19]) ).

fof(f21,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f23,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f26,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f28,plain,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f41,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(f42,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)],[f41]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ complement(X0,X1)
      | addition(X1,X0) = one ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | ( ( c(X0) != X1
          | complement(X0,X1) )
        & ( c(X0) = X1
          | ~ complement(X0,X1) ) ) ),
    inference(NNF_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    ! [X0] :
      ( ~ test(X0)
      | ( ! [X1] :
            ( c(X0) != X1
            | complement(X0,X1) )
        & ! [X1] :
            ( c(X0) = X1
            | ~ complement(X0,X1) ) ) ),
    inference(miniscoping,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ test(X0)
      | c(X0) != X1
      | complement(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f58,plain,
    ? [X0,X1,X2] :
      ( test(X1)
      & test(X2)
      & multiplication(multiplication(X1,X0),c(X2)) = zero
      & multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f59,plain,
    ? [X1,X2] :
      ( test(X1)
      & test(X2)
      & ? [X0] :
          ( multiplication(multiplication(X1,X0),c(X2)) = zero
          & multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ) ),
    inference(miniscoping,[status(esa)],[f58]) ).

fof(f60,plain,
    ( test(sk0_1)
    & test(sk0_2)
    & multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) = zero
    & multiplication(sk0_1,sk0_3) != multiplication(multiplication(sk0_1,sk0_3),sk0_2) ),
    inference(skolemization,[status(esa)],[f59]) ).

fof(f62,plain,
    test(sk0_2),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f63,plain,
    multiplication(multiplication(sk0_1,sk0_3),c(sk0_2)) = zero,
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f64,plain,
    multiplication(sk0_1,sk0_3) != multiplication(multiplication(sk0_1,sk0_3),sk0_2),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(X0,c(X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f50]) ).

fof(f201,plain,
    ! [X0] : X0 = addition(zero,X0),
    inference(paramodulation,[status(thm)],[f23,f21]) ).

fof(f277,plain,
    ! [X0] : multiplication(multiplication(sk0_1,sk0_3),addition(c(sk0_2),X0)) = addition(zero,multiplication(multiplication(sk0_1,sk0_3),X0)),
    inference(paramodulation,[status(thm)],[f63,f28]) ).

fof(f1258,plain,
    ! [X0] :
      ( addition(c(X0),X0) = one
      | ~ test(X0) ),
    inference(resolution,[status(thm)],[f45,f65]) ).

fof(f2551,plain,
    ! [X0] : multiplication(multiplication(sk0_1,sk0_3),addition(c(sk0_2),X0)) = multiplication(multiplication(sk0_1,sk0_3),X0),
    inference(forward_demodulation,[status(thm)],[f201,f277]) ).

fof(f4871,plain,
    addition(c(sk0_2),sk0_2) = one,
    inference(resolution,[status(thm)],[f1258,f62]) ).

fof(f4891,plain,
    multiplication(multiplication(sk0_1,sk0_3),one) = multiplication(multiplication(sk0_1,sk0_3),sk0_2),
    inference(paramodulation,[status(thm)],[f4871,f2551]) ).

fof(f4892,plain,
    multiplication(sk0_1,sk0_3) = multiplication(multiplication(sk0_1,sk0_3),sk0_2),
    inference(forward_demodulation,[status(thm)],[f26,f4891]) ).

fof(f4893,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f4892,f64]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29  % Computer : n004.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Tue May 30 11:41:52 EDT 2023
% 0.09/0.29  % CPUTime  : 
% 0.14/0.30  % Drodi V3.5.1
% 3.08/0.75  % Refutation found
% 3.08/0.75  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.08/0.75  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.54/0.78  % Elapsed time: 0.477482 seconds
% 3.54/0.78  % CPU time: 3.648532 seconds
% 3.54/0.78  % Memory used: 118.711 MB
%------------------------------------------------------------------------------