TSTP Solution File: KLE007+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE007+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 12:15:26 EDT 2023

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   33 (  18 unt;   0 def)
%            Number of atoms       :   75 (  43 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   72 (  30   ~;  20   |;  16   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   41 (;  39   !;   2   ?)

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

fof(f7,axiom,
    ! [A] : multiplication(one,A) = 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] :
      ( ( test(X1)
        & test(X0) )
     => one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f27,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f7]) ).

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] :
      ( test(X1)
      & test(X0)
      & one != addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f59,plain,
    ( test(sk0_2)
    & test(sk0_1)
    & one != addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))) ),
    inference(skolemization,[status(esa)],[f58]) ).

fof(f60,plain,
    test(sk0_2),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f61,plain,
    test(sk0_1),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f62,plain,
    one != addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f63,plain,
    ! [X0] :
      ( ~ test(X0)
      | complement(X0,c(X0)) ),
    inference(destructive_equality_resolution,[status(esa)],[f50]) ).

fof(f144,plain,
    one != multiplication(addition(sk0_1,c(sk0_1)),addition(sk0_2,c(sk0_2))),
    inference(backward_demodulation,[status(thm)],[f28,f62]) ).

fof(f145,plain,
    one != multiplication(addition(c(sk0_1),sk0_1),addition(sk0_2,c(sk0_2))),
    inference(forward_demodulation,[status(thm)],[f21,f144]) ).

fof(f146,plain,
    one != multiplication(addition(c(sk0_1),sk0_1),addition(c(sk0_2),sk0_2)),
    inference(forward_demodulation,[status(thm)],[f21,f145]) ).

fof(f181,plain,
    ! [X0] :
      ( ~ test(X0)
      | addition(c(X0),X0) = one ),
    inference(resolution,[status(thm)],[f63,f45]) ).

fof(f190,plain,
    addition(c(sk0_1),sk0_1) = one,
    inference(resolution,[status(thm)],[f181,f61]) ).

fof(f191,plain,
    addition(c(sk0_2),sk0_2) = one,
    inference(resolution,[status(thm)],[f181,f60]) ).

fof(f339,plain,
    one != multiplication(one,addition(c(sk0_2),sk0_2)),
    inference(forward_demodulation,[status(thm)],[f190,f146]) ).

fof(f340,plain,
    one != addition(c(sk0_2),sk0_2),
    inference(forward_demodulation,[status(thm)],[f27,f339]) ).

fof(f341,plain,
    one != one,
    inference(forward_demodulation,[status(thm)],[f191,f340]) ).

fof(f342,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f341]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE007+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n018.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue May 30 11:55:40 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  % Drodi V3.5.1
% 0.14/0.38  % Refutation found
% 0.14/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40  % Elapsed time: 0.047948 seconds
% 0.14/0.40  % CPU time: 0.233434 seconds
% 0.14/0.40  % Memory used: 24.099 MB
%------------------------------------------------------------------------------