TSTP Solution File: NUM925+7 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% 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 : Tue Apr 30 20:36:07 EDT 2024

% Result   : Theorem 4.41s 0.98s
% Output   : CNFRefutation 4.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   58 (  29 unt;   0 def)
%            Number of atoms       :   95 (  38 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   71 (  34   ~;  29   |;   0   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   5 con; 0-4 aty)
%            Number of variables   :   28 (  28   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f18,axiom,
    ! [B_1_1,B_2_1,X_a] :
      ( cancel_semigroup_add(X_a)
     => ti(X_a,plus_plus(X_a,B_1_1,B_2_1)) = plus_plus(X_a,B_1_1,B_2_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f50,hypothesis,
    ! [B_1_1] : ti(int,bit1(B_1_1)) = bit1(B_1_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f98,axiom,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f130,axiom,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f135,axiom,
    one_one(int) = number_number_of(int,bit1(pls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f171,axiom,
    pls = zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f218,axiom,
    ! [K_1] : number_number_of(int,K_1) = ti(int,K_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f263,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(f1104,axiom,
    ring_11004092258visors(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1111,axiom,
    cancel_semigroup_add(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1251,conjecture,
    hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1252,negated_conjecture,
    ~ ( hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ),
    inference(negated_conjecture,[status(cth)],[f1251]) ).

fof(f1297,plain,
    ! [B_1_1,B_2_1,X_a] :
      ( ~ cancel_semigroup_add(X_a)
      | ti(X_a,plus_plus(X_a,B_1_1,B_2_1)) = plus_plus(X_a,B_1_1,B_2_1) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f1298,plain,
    ! [X_a] :
      ( ~ cancel_semigroup_add(X_a)
      | ! [B_1_1,B_2_1] : ti(X_a,plus_plus(X_a,B_1_1,B_2_1)) = plus_plus(X_a,B_1_1,B_2_1) ),
    inference(miniscoping,[status(esa)],[f1297]) ).

fof(f1299,plain,
    ! [X0,X1,X2] :
      ( ~ cancel_semigroup_add(X0)
      | ti(X0,plus_plus(X0,X1,X2)) = plus_plus(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f1298]) ).

fof(f1368,plain,
    ! [X0] : ti(int,bit1(X0)) = bit1(X0),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f1461,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    inference(cnf_transformation,[status(esa)],[f98]) ).

fof(f1529,plain,
    ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f1546,plain,
    one_one(int) = number_number_of(int,bit1(pls)),
    inference(cnf_transformation,[status(esa)],[f135]) ).

fof(f1657,plain,
    pls = zero_zero(int),
    inference(cnf_transformation,[status(esa)],[f171]) ).

fof(f1754,plain,
    ! [X0] : number_number_of(int,X0) = ti(int,X0),
    inference(cnf_transformation,[status(esa)],[f218]) ).

fof(f1895,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)],[f263]) ).

fof(f1896,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)],[f1895]) ).

fof(f1897,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)],[f1896]) ).

fof(f4388,plain,
    ring_11004092258visors(int),
    inference(cnf_transformation,[status(esa)],[f1104]) ).

fof(f4395,plain,
    cancel_semigroup_add(int),
    inference(cnf_transformation,[status(esa)],[f1111]) ).

fof(f4535,plain,
    hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
    inference(cnf_transformation,[status(esa)],[f1252]) ).

fof(f4602,plain,
    hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) = pls,
    inference(backward_demodulation,[status(thm)],[f1657,f4535]) ).

fof(f4654,plain,
    hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)))),
    inference(forward_demodulation,[status(thm)],[f1657,f1461]) ).

fof(f5044,plain,
    ( spl0_13
  <=> pls = zero_zero(int) ),
    introduced(split_symbol_definition) ).

fof(f5046,plain,
    ( pls != zero_zero(int)
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f5044]) ).

fof(f5082,plain,
    one_one(int) = ti(int,bit1(pls)),
    inference(paramodulation,[status(thm)],[f1546,f1754]) ).

fof(f5125,plain,
    one_one(int) = bit1(pls),
    inference(paramodulation,[status(thm)],[f1368,f5082]) ).

fof(f5158,plain,
    hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(one_one(int)))) = pls,
    inference(backward_demodulation,[status(thm)],[f5125,f4602]) ).

fof(f5684,plain,
    ( spl0_95
  <=> cancel_semigroup_add(int) ),
    introduced(split_symbol_definition) ).

fof(f5686,plain,
    ( ~ cancel_semigroup_add(int)
    | spl0_95 ),
    inference(component_clause,[status(thm)],[f5684]) ).

fof(f6165,plain,
    ( spl0_159
  <=> ring_11004092258visors(int) ),
    introduced(split_symbol_definition) ).

fof(f6167,plain,
    ( ~ ring_11004092258visors(int)
    | spl0_159 ),
    inference(component_clause,[status(thm)],[f6165]) ).

fof(f6632,plain,
    ( spl0_235
  <=> ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) ),
    introduced(split_symbol_definition) ).

fof(f6633,plain,
    ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int)
    | ~ spl0_235 ),
    inference(component_clause,[status(thm)],[f6632]) ).

fof(f6635,plain,
    ( ~ ring_11004092258visors(int)
    | ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int)
    | pls != zero_zero(int) ),
    inference(paramodulation,[status(thm)],[f5158,f1897]) ).

fof(f6636,plain,
    ( ~ spl0_159
    | spl0_235
    | ~ spl0_13 ),
    inference(split_clause,[status(thm)],[f6635,f6165,f6632,f5044]) ).

fof(f8163,plain,
    ( pls != pls
    | spl0_13 ),
    inference(forward_demodulation,[status(thm)],[f1657,f5046]) ).

fof(f8164,plain,
    ( $false
    | spl0_13 ),
    inference(trivial_equality_resolution,[status(esa)],[f8163]) ).

fof(f8165,plain,
    spl0_13,
    inference(contradiction_clause,[status(thm)],[f8164]) ).

fof(f8218,plain,
    ( $false
    | spl0_159 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4388,f6167]) ).

fof(f8219,plain,
    spl0_159,
    inference(contradiction_clause,[status(thm)],[f8218]) ).

fof(f8221,plain,
    ( ti(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))) = pls
    | ~ spl0_235 ),
    inference(forward_demodulation,[status(thm)],[f1657,f6633]) ).

fof(f8230,plain,
    ( $false
    | spl0_95 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4395,f5686]) ).

fof(f8231,plain,
    spl0_95,
    inference(contradiction_clause,[status(thm)],[f8230]) ).

fof(f8719,plain,
    ( spl0_407
  <=> pls = plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n)) ),
    introduced(split_symbol_definition) ).

fof(f8720,plain,
    ( pls = plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))
    | ~ spl0_407 ),
    inference(component_clause,[status(thm)],[f8719]) ).

fof(f8722,plain,
    ( ~ cancel_semigroup_add(int)
    | pls = plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))
    | ~ spl0_235 ),
    inference(paramodulation,[status(thm)],[f8221,f1299]) ).

fof(f8723,plain,
    ( ~ spl0_95
    | spl0_407
    | ~ spl0_235 ),
    inference(split_clause,[status(thm)],[f8722,f5684,f8719,f6632]) ).

fof(f8790,plain,
    ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls))
    | ~ spl0_407 ),
    inference(backward_demodulation,[status(thm)],[f8720,f4654]) ).

fof(f8791,plain,
    ( $false
    | ~ spl0_407 ),
    inference(forward_subsumption_resolution,[status(thm)],[f8790,f1529]) ).

fof(f8792,plain,
    ~ spl0_407,
    inference(contradiction_clause,[status(thm)],[f8791]) ).

fof(f8793,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f6636,f8165,f8219,f8231,f8723,f8792]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : NUM925+7 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Mon Apr 29 20:58:50 EDT 2024
% 0.09/0.28  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 4.41/0.98  % Refutation found
% 4.41/0.98  % SZS status Theorem for theBenchmark: Theorem is valid
% 4.41/0.98  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.95/1.02  % Elapsed time: 0.741093 seconds
% 4.95/1.02  % CPU time: 5.099512 seconds
% 4.95/1.02  % Total memory used: 253.052 MB
% 4.95/1.02  % Net memory used: 250.518 MB
%------------------------------------------------------------------------------