TSTP Solution File: KLE040+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 12:15:37 EDT 2023

% Result   : Theorem 9.19s 1.62s
% Output   : CNFRefutation 9.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   75 (  64 unt;   0 def)
%            Number of atoms       :   90 (  62 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   31 (  16   ~;  11   |;   2   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 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   :  135 (; 134   !;   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(f5,axiom,
    ! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] : multiplication(A,one) = A,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f8,axiom,
    ! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    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,
    ! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [A,B,C] :
      ( leq(addition(multiplication(A,B),C),B)
     => leq(multiplication(star(A),C),B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,conjecture,
    ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
    inference(negated_conjecture,[status(cth)],[f17]) ).

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

fof(f20,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f22,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f23,plain,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f24,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f25,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f26,plain,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f27,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f30,plain,
    ! [A,B] :
      ( ( ~ leq(A,B)
        | addition(A,B) = B )
      & ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(NNF_transformation,[status(esa)],[f12]) ).

fof(f31,plain,
    ( ! [A,B] :
        ( ~ leq(A,B)
        | addition(A,B) = B )
    & ! [A,B] :
        ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f34,plain,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f36,plain,
    ! [A,B,C] :
      ( ~ leq(addition(multiplication(A,B),C),B)
      | leq(multiplication(star(A),C),B) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ~ leq(addition(multiplication(X0,X1),X2),X1)
      | leq(multiplication(star(X0),X2),X1) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f40,plain,
    ? [X0] : multiplication(star(X0),star(X0)) != star(X0),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

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

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

fof(f100,plain,
    ! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f22,f20]) ).

fof(f142,plain,
    ! [X0] : leq(X0,X0),
    inference(resolution,[status(thm)],[f33,f22]) ).

fof(f169,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(resolution,[status(thm)],[f100,f33]) ).

fof(f181,plain,
    ! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f19,f100]) ).

fof(f237,plain,
    ! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
    inference(paramodulation,[status(thm)],[f23,f27]) ).

fof(f245,plain,
    ! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f25,f27]) ).

fof(f246,plain,
    ! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f19,f245]) ).

fof(f247,plain,
    ! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
    inference(paramodulation,[status(thm)],[f23,f27]) ).

fof(f269,plain,
    ! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f34,f32]) ).

fof(f270,plain,
    ! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f20,f269]) ).

fof(f271,plain,
    ! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f19,f270]) ).

fof(f282,plain,
    ! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
    inference(paramodulation,[status(thm)],[f26,f237]) ).

fof(f283,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
    inference(forward_demodulation,[status(thm)],[f19,f282]) ).

fof(f284,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
    inference(forward_demodulation,[status(thm)],[f19,f283]) ).

fof(f285,plain,
    ! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
    inference(paramodulation,[status(thm)],[f19,f237]) ).

fof(f619,plain,
    ! [X0,X1] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,multiplication(X1,one))),
    inference(paramodulation,[status(thm)],[f24,f284]) ).

fof(f620,plain,
    ! [X0,X1] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
    inference(forward_demodulation,[status(thm)],[f24,f619]) ).

fof(f884,plain,
    ! [X0,X1,X2] :
      ( ~ leq(multiplication(addition(X0,X1),X2),X2)
      | leq(multiplication(star(X0),multiplication(X1,X2)),X2) ),
    inference(paramodulation,[status(thm)],[f27,f37]) ).

fof(f1197,plain,
    ! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
    inference(paramodulation,[status(thm)],[f620,f169]) ).

fof(f2348,plain,
    ! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = multiplication(addition(X2,multiplication(X0,X1)),X3),
    inference(forward_demodulation,[status(thm)],[f247,f285]) ).

fof(f2386,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,multiplication(one,X0)),X2),
    inference(paramodulation,[status(thm)],[f25,f2348]) ).

fof(f2387,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
    inference(forward_demodulation,[status(thm)],[f25,f2386]) ).

fof(f7524,plain,
    ! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f246,f271]) ).

fof(f7556,plain,
    ! [X0,X1] : leq(X0,multiplication(X0,star(X1))),
    inference(paramodulation,[status(thm)],[f7524,f1197]) ).

fof(f7628,plain,
    ! [X0] : addition(multiplication(addition(X0,one),star(X0)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
    inference(paramodulation,[status(thm)],[f7524,f181]) ).

fof(f7629,plain,
    ! [X0] : addition(star(X0),multiplication(addition(X0,one),star(X0))) = addition(multiplication(addition(X0,one),star(X0)),one),
    inference(forward_demodulation,[status(thm)],[f19,f7628]) ).

fof(f7630,plain,
    ! [X0] : multiplication(addition(addition(X0,one),one),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
    inference(forward_demodulation,[status(thm)],[f246,f7629]) ).

fof(f7631,plain,
    ! [X0] : multiplication(addition(one,addition(X0,one)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
    inference(forward_demodulation,[status(thm)],[f2387,f7630]) ).

fof(f7632,plain,
    ! [X0] : multiplication(addition(one,X0),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
    inference(forward_demodulation,[status(thm)],[f181,f7631]) ).

fof(f7633,plain,
    ! [X0] : multiplication(addition(one,X0),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
    inference(forward_demodulation,[status(thm)],[f19,f7632]) ).

fof(f7634,plain,
    ! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f7524,f7633]) ).

fof(f7871,plain,
    ! [X0] : leq(one,star(X0)),
    inference(paramodulation,[status(thm)],[f25,f7556]) ).

fof(f7877,plain,
    ! [X0] : addition(one,star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f7871,f32]) ).

fof(f11183,plain,
    ! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
    inference(paramodulation,[status(thm)],[f2387,f7634]) ).

fof(f13258,plain,
    ! [X0] :
      ( ~ leq(star(X0),star(X0))
      | leq(multiplication(star(X0),multiplication(one,star(X0))),star(X0)) ),
    inference(paramodulation,[status(thm)],[f11183,f884]) ).

fof(f13259,plain,
    ! [X0] :
      ( ~ leq(star(X0),star(X0))
      | leq(multiplication(star(X0),star(X0)),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f25,f13258]) ).

fof(f13260,plain,
    ! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f13259,f142]) ).

fof(f15685,plain,
    ! [X0] : addition(multiplication(star(X0),star(X0)),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f13260,f32]) ).

fof(f15686,plain,
    ! [X0] : addition(star(X0),multiplication(star(X0),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f19,f15685]) ).

fof(f15687,plain,
    ! [X0] : multiplication(addition(star(X0),one),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f246,f15686]) ).

fof(f15688,plain,
    ! [X0] : multiplication(addition(one,star(X0)),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f2387,f15687]) ).

fof(f15689,plain,
    ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f7877,f15688]) ).

fof(f15835,plain,
    star(sk0_0) != star(sk0_0),
    inference(backward_demodulation,[status(thm)],[f15689,f42]) ).

fof(f15836,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f15835]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.32  % Computer : n007.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Tue May 30 11:34:47 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  % Drodi V3.5.1
% 9.19/1.62  % Refutation found
% 9.19/1.62  % SZS status Theorem for theBenchmark: Theorem is valid
% 9.19/1.62  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.82/1.67  % Elapsed time: 1.328694 seconds
% 9.82/1.67  % CPU time: 9.980261 seconds
% 9.82/1.67  % Memory used: 161.498 MB
%------------------------------------------------------------------------------