TSTP Solution File: KLE052+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE052+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 12:15:40 EDT 2023

% Result   : Theorem 1.44s 0.58s
% Output   : CNFRefutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   36 (  31 unt;   0 def)
%            Number of atoms       :   45 (  32 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (  11   ~;   6   |;   2   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   58 (;  57   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : addition(A,B) = addition(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] : addition(A,A) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A] : multiplication(one,A) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> addition(A,B) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [X0] : addition(domain(X0),one) = one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,conjecture,
    ! [X0] : multiplication(domain(X0),X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,negated_conjecture,
    ~ ! [X0] : multiplication(domain(X0),X0) = X0,
    inference(negated_conjecture,[status(cth)],[f18]) ).

fof(f20,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f21,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f23,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f26,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f28,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f31,plain,
    ! [A,B] :
      ( ( ~ leq(A,B)
        | addition(A,B) = B )
      & ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(NNF_transformation,[status(esa)],[f12]) ).

fof(f32,plain,
    ( ! [A,B] :
        ( ~ leq(A,B)
        | addition(A,B) = B )
    & ! [A,B] :
        ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(miniscoping,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f32]) ).

fof(f35,plain,
    ! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f37,plain,
    ! [X0] : addition(domain(X0),one) = one,
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f40,plain,
    ? [X0] : multiplication(domain(X0),X0) != X0,
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f41,plain,
    multiplication(domain(sk0_0),sk0_0) != sk0_0,
    inference(skolemization,[status(esa)],[f40]) ).

fof(f42,plain,
    multiplication(domain(sk0_0),sk0_0) != sk0_0,
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f771,plain,
    ! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f23,f21]) ).

fof(f1328,plain,
    ! [X0] : addition(one,domain(X0)) = one,
    inference(forward_demodulation,[status(thm)],[f20,f37]) ).

fof(f2607,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(resolution,[status(thm)],[f771,f34]) ).

fof(f2714,plain,
    ! [X0,X1] : leq(X0,addition(X1,X0)),
    inference(paramodulation,[status(thm)],[f20,f2607]) ).

fof(f2722,plain,
    ! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
    inference(paramodulation,[status(thm)],[f28,f2714]) ).

fof(f9183,plain,
    ! [X0,X1] : leq(multiplication(domain(X0),X1),multiplication(one,X1)),
    inference(paramodulation,[status(thm)],[f1328,f2722]) ).

fof(f9184,plain,
    ! [X0,X1] : leq(multiplication(domain(X0),X1),X1),
    inference(forward_demodulation,[status(thm)],[f26,f9183]) ).

fof(f9229,plain,
    ! [X0,X1] : addition(multiplication(domain(X0),X1),X1) = X1,
    inference(resolution,[status(thm)],[f9184,f33]) ).

fof(f9230,plain,
    ! [X0,X1] : addition(X0,multiplication(domain(X1),X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f20,f9229]) ).

fof(f9272,plain,
    ! [X0] : X0 = multiplication(domain(X0),X0),
    inference(backward_demodulation,[status(thm)],[f9230,f35]) ).

fof(f9465,plain,
    sk0_0 != sk0_0,
    inference(backward_demodulation,[status(thm)],[f9272,f42]) ).

fof(f9466,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f9465]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem  : KLE052+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33  % Computer : n032.cluster.edu
% 0.09/0.33  % Model    : x86_64 x86_64
% 0.09/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33  % Memory   : 8042.1875MB
% 0.09/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33  % CPULimit : 300
% 0.09/0.33  % WCLimit  : 300
% 0.09/0.33  % DateTime : Tue May 30 11:48:31 EDT 2023
% 0.09/0.33  % CPUTime  : 
% 0.09/0.33  % Drodi V3.5.1
% 1.44/0.58  % Refutation found
% 1.44/0.58  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.44/0.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.62  % Elapsed time: 0.274508 seconds
% 1.44/0.62  % CPU time: 1.791390 seconds
% 1.44/0.62  % Memory used: 74.599 MB
%------------------------------------------------------------------------------