TSTP Solution File: NUM925+6 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM925+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 : Tue Apr 30 20:36:07 EDT 2024

% Result   : Theorem 2.99s 0.85s
% Output   : CNFRefutation 3.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   38 (  26 unt;   0 def)
%            Number of atoms       :   58 (  45 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   42 (  22   ~;  15   |;   2   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-4 aty)
%            Number of variables   :   41 (  41   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f39,axiom,
    ! [X_a,B_1_1,B_2] : hAPP(X_a,X_a,B_1_1,ti(X_a,B_2)) = hAPP(X_a,X_a,B_1_1,B_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f46,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f78,axiom,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f89,axiom,
    ! [K_2,L_1] :
      ( hAPP(int,int,bit0,K_2) = hAPP(int,int,bit0,L_1)
    <=> K_2 = L_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f119,axiom,
    pls = zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f121,axiom,
    ! [K] : hAPP(int,int,plus_plus(int,K),pls) = K,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f138,axiom,
    ! [K] : hAPP(int,int,bit1,K) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),K)),K),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f210,axiom,
    ! [X_a] :
      ( ring_11004092258visors(X_a)
     => ! [N,A_1] :
          ( ti(X_a,A_1) != zero_zero(X_a)
         => hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f554,axiom,
    ring_11004092258visors(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f660,conjecture,
    hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f661,negated_conjecture,
    ~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
    inference(negated_conjecture,[status(cth)],[f660]) ).

fof(f738,plain,
    ! [X0,X1,X2] : hAPP(X0,X0,X1,ti(X0,X2)) = hAPP(X0,X0,X1,X2),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f748,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f816,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    inference(cnf_transformation,[status(esa)],[f78]) ).

fof(f850,plain,
    ! [K_2,L_1] :
      ( ( hAPP(int,int,bit0,K_2) != hAPP(int,int,bit0,L_1)
        | K_2 = L_1 )
      & ( hAPP(int,int,bit0,K_2) = hAPP(int,int,bit0,L_1)
        | K_2 != L_1 ) ),
    inference(NNF_transformation,[status(esa)],[f89]) ).

fof(f851,plain,
    ( ! [K_2,L_1] :
        ( hAPP(int,int,bit0,K_2) != hAPP(int,int,bit0,L_1)
        | K_2 = L_1 )
    & ! [K_2,L_1] :
        ( hAPP(int,int,bit0,K_2) = hAPP(int,int,bit0,L_1)
        | K_2 != L_1 ) ),
    inference(miniscoping,[status(esa)],[f850]) ).

fof(f852,plain,
    ! [X0,X1] :
      ( hAPP(int,int,bit0,X0) != hAPP(int,int,bit0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f851]) ).

fof(f944,plain,
    pls = zero_zero(int),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f946,plain,
    ! [X0] : hAPP(int,int,plus_plus(int,X0),pls) = X0,
    inference(cnf_transformation,[status(esa)],[f121]) ).

fof(f976,plain,
    ! [X0] : hAPP(int,int,bit1,X0) = hAPP(int,int,plus_plus(int,hAPP(int,int,plus_plus(int,one_one(int)),X0)),X0),
    inference(cnf_transformation,[status(esa)],[f138]) ).

fof(f1181,plain,
    ! [X_a] :
      ( ~ ring_11004092258visors(X_a)
      | ! [N,A_1] :
          ( ti(X_a,A_1) = zero_zero(X_a)
          | hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f210]) ).

fof(f1182,plain,
    ! [X_a] :
      ( ~ ring_11004092258visors(X_a)
      | ! [A_1] :
          ( ti(X_a,A_1) = zero_zero(X_a)
          | ! [N] : hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ),
    inference(miniscoping,[status(esa)],[f1181]) ).

fof(f1183,plain,
    ! [X0,X1,X2] :
      ( ~ ring_11004092258visors(X0)
      | ti(X0,X1) = zero_zero(X0)
      | hAPP(nat,X0,power_power(X0,X1),X2) != zero_zero(X0) ),
    inference(cnf_transformation,[status(esa)],[f1182]) ).

fof(f2255,plain,
    ring_11004092258visors(int),
    inference(cnf_transformation,[status(esa)],[f554]) ).

fof(f2361,plain,
    hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
    inference(cnf_transformation,[status(esa)],[f661]) ).

fof(f2418,plain,
    hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = pls,
    inference(backward_demodulation,[status(thm)],[f944,f2361]) ).

fof(f2427,plain,
    hAPP(int,int,bit1,pls) = hAPP(int,int,plus_plus(int,one_one(int)),pls),
    inference(paramodulation,[status(thm)],[f976,f946]) ).

fof(f2428,plain,
    hAPP(int,int,bit1,pls) = one_one(int),
    inference(forward_demodulation,[status(thm)],[f946,f2427]) ).

fof(f2437,plain,
    hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
    inference(backward_demodulation,[status(thm)],[f2428,f2418]) ).

fof(f2441,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    inference(forward_demodulation,[status(thm)],[f944,f748]) ).

fof(f2823,plain,
    ! [X0] : ti(int,X0) = X0,
    inference(resolution,[status(thm)],[f738,f852]) ).

fof(f2920,plain,
    ! [X0,X1] :
      ( ti(int,X0) = zero_zero(int)
      | hAPP(nat,int,power_power(int,X0),X1) != zero_zero(int) ),
    inference(resolution,[status(thm)],[f2255,f1183]) ).

fof(f2921,plain,
    ! [X0,X1] :
      ( ti(int,X0) = pls
      | hAPP(nat,int,power_power(int,X0),X1) != zero_zero(int) ),
    inference(forward_demodulation,[status(thm)],[f944,f2920]) ).

fof(f2922,plain,
    ! [X0,X1] :
      ( ti(int,X0) = pls
      | hAPP(nat,int,power_power(int,X0),X1) != pls ),
    inference(forward_demodulation,[status(thm)],[f944,f2921]) ).

fof(f3138,plain,
    ! [X0,X1] :
      ( X0 = pls
      | hAPP(nat,int,power_power(int,X0),X1) != pls ),
    inference(forward_demodulation,[status(thm)],[f2823,f2922]) ).

fof(f3139,plain,
    hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) = pls,
    inference(resolution,[status(thm)],[f3138,f2437]) ).

fof(f3779,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    inference(backward_demodulation,[status(thm)],[f3139,f2441]) ).

fof(f3780,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f3779,f816]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM925+6 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 20:54:29 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.42  % Drodi V3.6.0
% 2.99/0.85  % Refutation found
% 2.99/0.85  % SZS status Theorem for theBenchmark: Theorem is valid
% 2.99/0.85  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.48/0.88  % Elapsed time: 0.528820 seconds
% 3.48/0.88  % CPU time: 3.608536 seconds
% 3.48/0.88  % Total memory used: 168.905 MB
% 3.48/0.88  % Net memory used: 167.203 MB
%------------------------------------------------------------------------------