TSTP Solution File: KLE140+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE140+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 12:15:52 EDT 2023

% Result   : Theorem 119.03s 15.42s
% Output   : CNFRefutation 120.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   49 (  35 unt;   0 def)
%            Number of atoms       :   67 (  38 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   37 (  19   ~;  10   |;   4   &)
%                                         (   1 <=>;   3  =>;   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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   76 (;  74   !;   2   ?)

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

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

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

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

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

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

fof(f15,axiom,
    ! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [A,B,C] :
      ( leq(C,addition(multiplication(A,C),B))
     => leq(C,multiplication(strong_iteration(A),B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [A,B] :
      ( leq(A,B)
    <=> addition(A,B) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,conjecture,
    ! [X0,X1] :
      ( leq(X0,X1)
     => leq(strong_iteration(X0),strong_iteration(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,negated_conjecture,
    ~ ! [X0,X1] :
        ( leq(X0,X1)
       => leq(strong_iteration(X0),strong_iteration(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(f22,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f24,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

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

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

fof(f29,plain,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

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

fof(f38,plain,
    ! [A,B,C] :
      ( ~ leq(C,addition(multiplication(A,C),B))
      | leq(C,multiplication(strong_iteration(A),B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ~ leq(X0,addition(multiplication(X1,X0),X2))
      | leq(X0,multiplication(strong_iteration(X1),X2)) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f41,plain,
    ! [A,B] :
      ( ( ~ leq(A,B)
        | addition(A,B) = B )
      & ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(NNF_transformation,[status(esa)],[f18]) ).

fof(f42,plain,
    ( ! [A,B] :
        ( ~ leq(A,B)
        | addition(A,B) = B )
    & ! [A,B] :
        ( leq(A,B)
        | addition(A,B) != B ) ),
    inference(miniscoping,[status(esa)],[f41]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f45,plain,
    ? [X0,X1] :
      ( leq(X0,X1)
      & ~ leq(strong_iteration(X0),strong_iteration(X1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f46,plain,
    ( leq(sk0_0,sk0_1)
    & ~ leq(strong_iteration(sk0_0),strong_iteration(sk0_1)) ),
    inference(skolemization,[status(esa)],[f45]) ).

fof(f47,plain,
    leq(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ~ leq(strong_iteration(sk0_0),strong_iteration(sk0_1)),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f49,plain,
    addition(sk0_0,sk0_1) = sk0_1,
    inference(resolution,[status(thm)],[f43,f47]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ leq(X0,addition(multiplication(X1,X0),one))
      | leq(X0,strong_iteration(X1)) ),
    inference(paramodulation,[status(thm)],[f26,f39]) ).

fof(f159,plain,
    ! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
    inference(forward_demodulation,[status(thm)],[f21,f37]) ).

fof(f177,plain,
    ! [X0,X1] : addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)) = addition(strong_iteration(X0),X1),
    inference(paramodulation,[status(thm)],[f159,f22]) ).

fof(f181,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
    inference(paramodulation,[status(thm)],[f21,f22]) ).

fof(f182,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f22,f181]) ).

fof(f185,plain,
    ! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f24,f22]) ).

fof(f208,plain,
    ! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
    inference(paramodulation,[status(thm)],[f159,f185]) ).

fof(f209,plain,
    ! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
    inference(forward_demodulation,[status(thm)],[f159,f208]) ).

fof(f225,plain,
    ! [X0,X1] : addition(one,addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
    inference(paramodulation,[status(thm)],[f209,f22]) ).

fof(f353,plain,
    ! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
    inference(paramodulation,[status(thm)],[f27,f29]) ).

fof(f2967,plain,
    ! [X0,X1] :
      ( ~ leq(X0,addition(one,multiplication(X1,X0)))
      | leq(X0,strong_iteration(X1)) ),
    inference(forward_demodulation,[status(thm)],[f21,f67]) ).

fof(f2968,plain,
    ~ leq(strong_iteration(sk0_0),addition(one,multiplication(sk0_1,strong_iteration(sk0_0)))),
    inference(resolution,[status(thm)],[f2967,f48]) ).

fof(f7632,plain,
    ! [X0,X1] : addition(one,multiplication(addition(X0,X1),strong_iteration(X0))) = addition(strong_iteration(X0),multiplication(X1,strong_iteration(X0))),
    inference(paramodulation,[status(thm)],[f29,f177]) ).

fof(f9305,plain,
    addition(strong_iteration(sk0_0),addition(one,multiplication(sk0_1,strong_iteration(sk0_0)))) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
    inference(resolution,[status(thm)],[f2968,f44]) ).

fof(f9306,plain,
    addition(one,addition(strong_iteration(sk0_0),multiplication(sk0_1,strong_iteration(sk0_0)))) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
    inference(forward_demodulation,[status(thm)],[f182,f9305]) ).

fof(f19290,plain,
    addition(strong_iteration(sk0_0),multiplication(sk0_1,strong_iteration(sk0_0))) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
    inference(forward_demodulation,[status(thm)],[f225,f9306]) ).

fof(f19291,plain,
    multiplication(addition(one,sk0_1),strong_iteration(sk0_0)) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
    inference(forward_demodulation,[status(thm)],[f353,f19290]) ).

fof(f79774,plain,
    ! [X0,X1] : addition(one,multiplication(addition(X0,X1),strong_iteration(X0))) = multiplication(addition(one,X1),strong_iteration(X0)),
    inference(forward_demodulation,[status(thm)],[f353,f7632]) ).

fof(f80114,plain,
    addition(one,multiplication(sk0_1,strong_iteration(sk0_0))) = multiplication(addition(one,sk0_1),strong_iteration(sk0_0)),
    inference(paramodulation,[status(thm)],[f49,f79774]) ).

fof(f80115,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f80114,f19291]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE140+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n010.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 11:37:22 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 119.03/15.42  % Refutation found
% 119.03/15.42  % SZS status Theorem for theBenchmark: Theorem is valid
% 119.03/15.42  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 122.14/15.77  % Elapsed time: 15.401806 seconds
% 122.14/15.77  % CPU time: 121.130658 seconds
% 122.14/15.77  % Memory used: 946.774 MB
%------------------------------------------------------------------------------