TSTP Solution File: NUM453+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 12:29:12 EDT 2023

% Result   : Theorem 0.20s 0.52s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   85 (  16 unt;   0 def)
%            Number of atoms       :  186 (  59 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  180 (  79   ~;  77   |;  12   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   7 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   44 (;  44   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => aInteger0(smndt0(W0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => aInteger0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [W0,W1,W2] :
      ( ( aInteger0(W0)
        & aInteger0(W1)
        & aInteger0(W2) )
     => sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f46,hypothesis,
    ( aInteger0(xp)
    & xp != sz00
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f48,conjecture,
    ( sdtpldt0(sz10,xp) != sz10
    & sdtpldt0(sz10,smndt0(xp)) != sz10 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f49,negated_conjecture,
    ~ ( sdtpldt0(sz10,xp) != sz10
      & sdtpldt0(sz10,smndt0(xp)) != sz10 ),
    inference(negated_conjecture,[status(cth)],[f48]) ).

fof(f53,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f54,plain,
    aInteger0(sz10),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f55,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | aInteger0(smndt0(W0)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | aInteger0(smndt0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f57,plain,
    ! [W0,W1] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | aInteger0(sdtpldt0(W0,W1)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | aInteger0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f57]) ).

fof(f61,plain,
    ! [W0,W1,W2] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | ~ aInteger0(W2)
      | sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | ~ aInteger0(X2)
      | sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f63,plain,
    ! [W0,W1] :
      ( ~ aInteger0(W0)
      | ~ aInteger0(W1)
      | sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f63]) ).

fof(f65,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f66,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | X0 = sdtpldt0(sz00,X0) ),
    inference(cnf_transformation,[status(esa)],[f65]) ).

fof(f68,plain,
    ! [W0] :
      ( ~ aInteger0(W0)
      | ( sdtpldt0(W0,smndt0(W0)) = sz00
        & sz00 = sdtpldt0(smndt0(W0),W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,smndt0(X0)) = sz00 ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sz00 = sdtpldt0(smndt0(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f229,plain,
    aInteger0(xp),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f230,plain,
    xp != sz00,
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f234,plain,
    ( sdtpldt0(sz10,xp) = sz10
    | sdtpldt0(sz10,smndt0(xp)) = sz10 ),
    inference(pre_NNF_transformation,[status(esa)],[f49]) ).

fof(f235,plain,
    ( sdtpldt0(sz10,xp) = sz10
    | sdtpldt0(sz10,smndt0(xp)) = sz10 ),
    inference(cnf_transformation,[status(esa)],[f234]) ).

fof(f245,plain,
    ( spl0_0
  <=> sdtpldt0(sz10,xp) = sz10 ),
    introduced(split_symbol_definition) ).

fof(f246,plain,
    ( sdtpldt0(sz10,xp) = sz10
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f245]) ).

fof(f248,plain,
    ( spl0_1
  <=> sdtpldt0(sz10,smndt0(xp)) = sz10 ),
    introduced(split_symbol_definition) ).

fof(f249,plain,
    ( sdtpldt0(sz10,smndt0(xp)) = sz10
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f248]) ).

fof(f251,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f235,f245,f248]) ).

fof(f289,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,xp) = sdtpldt0(xp,X0) ),
    inference(resolution,[status(thm)],[f64,f229]) ).

fof(f290,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0) ),
    inference(resolution,[status(thm)],[f64,f54]) ).

fof(f292,plain,
    sdtpldt0(xp,sz10) = sdtpldt0(sz10,xp),
    inference(resolution,[status(thm)],[f290,f229]) ).

fof(f306,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | sdtpldt0(X0,sdtpldt0(X1,xp)) = sdtpldt0(sdtpldt0(X0,X1),xp) ),
    inference(resolution,[status(thm)],[f62,f229]) ).

fof(f307,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | ~ aInteger0(X1)
      | sdtpldt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtpldt0(X0,X1),sz10) ),
    inference(resolution,[status(thm)],[f62,f54]) ).

fof(f314,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sdtpldt0(sz10,xp)) = sdtpldt0(sdtpldt0(X0,sz10),xp) ),
    inference(resolution,[status(thm)],[f306,f54]) ).

fof(f315,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),xp)
      | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f246,f314]) ).

fof(f316,plain,
    ! [X0] :
      ( sdtpldt0(smndt0(X0),sz10) = sdtpldt0(sdtpldt0(smndt0(X0),sz10),xp)
      | ~ aInteger0(X0)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f315,f56]) ).

fof(f323,plain,
    ( sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f316,f54]) ).

fof(f345,plain,
    sdtpldt0(xp,sz00) = xp,
    inference(resolution,[status(thm)],[f66,f229]) ).

fof(f347,plain,
    ( spl0_6
  <=> aInteger0(sz00) ),
    introduced(split_symbol_definition) ).

fof(f349,plain,
    ( ~ aInteger0(sz00)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f347]) ).

fof(f350,plain,
    ( spl0_7
  <=> sdtpldt0(sz00,xp) = xp ),
    introduced(split_symbol_definition) ).

fof(f351,plain,
    ( sdtpldt0(sz00,xp) = xp
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f350]) ).

fof(f353,plain,
    ( ~ aInteger0(sz00)
    | sdtpldt0(sz00,xp) = xp ),
    inference(paramodulation,[status(thm)],[f345,f289]) ).

fof(f354,plain,
    ( ~ spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f353,f347,f350]) ).

fof(f355,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f349,f53]) ).

fof(f356,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f355]) ).

fof(f358,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | aInteger0(sdtpldt0(X0,xp)) ),
    inference(resolution,[status(thm)],[f58,f229]) ).

fof(f362,plain,
    sz10 = sdtpldt0(sz00,sz10),
    inference(resolution,[status(thm)],[f67,f54]) ).

fof(f364,plain,
    sdtpldt0(xp,smndt0(xp)) = sz00,
    inference(resolution,[status(thm)],[f69,f229]) ).

fof(f368,plain,
    aInteger0(sdtpldt0(sz10,xp)),
    inference(resolution,[status(thm)],[f358,f54]) ).

fof(f437,plain,
    sz00 = sdtpldt0(smndt0(sz10),sz10),
    inference(resolution,[status(thm)],[f70,f54]) ).

fof(f477,plain,
    ( spl0_8
  <=> aInteger0(smndt0(xp)) ),
    introduced(split_symbol_definition) ).

fof(f478,plain,
    ( aInteger0(smndt0(xp))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f477]) ).

fof(f479,plain,
    ( ~ aInteger0(smndt0(xp))
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f477]) ).

fof(f485,plain,
    ( ~ aInteger0(xp)
    | spl0_8 ),
    inference(resolution,[status(thm)],[f479,f56]) ).

fof(f486,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f485,f229]) ).

fof(f487,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f486]) ).

fof(f509,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sdtpldt0(smndt0(xp),sz10)) = sdtpldt0(sdtpldt0(X0,smndt0(xp)),sz10)
      | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f478,f307]) ).

fof(f517,plain,
    ( sdtpldt0(smndt0(xp),sz10) = sdtpldt0(sz10,smndt0(xp))
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f478,f290]) ).

fof(f518,plain,
    ( sdtpldt0(smndt0(xp),sz10) = sz10
    | ~ spl0_1
    | ~ spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f249,f517]) ).

fof(f522,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,smndt0(xp)),sz10)
      | ~ spl0_1
      | ~ spl0_8 ),
    inference(backward_demodulation,[status(thm)],[f518,f509]) ).

fof(f538,plain,
    ( sdtpldt0(xp,sz10) = sdtpldt0(sdtpldt0(xp,smndt0(xp)),sz10)
    | ~ spl0_1
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f522,f229]) ).

fof(f539,plain,
    ( sdtpldt0(sz10,xp) = sdtpldt0(sdtpldt0(xp,smndt0(xp)),sz10)
    | ~ spl0_1
    | ~ spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f292,f538]) ).

fof(f540,plain,
    ( sdtpldt0(sz10,xp) = sdtpldt0(sz00,sz10)
    | ~ spl0_1
    | ~ spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f364,f539]) ).

fof(f541,plain,
    ( sdtpldt0(sz10,xp) = sz10
    | ~ spl0_1
    | ~ spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f362,f540]) ).

fof(f617,plain,
    ( spl0_12
  <=> aInteger0(sdtpldt0(xp,sz10)) ),
    introduced(split_symbol_definition) ).

fof(f619,plain,
    ( ~ aInteger0(sdtpldt0(xp,sz10))
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f617]) ).

fof(f625,plain,
    ( sz00 = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f437,f323]) ).

fof(f626,plain,
    ( sz00 = sdtpldt0(sz00,xp)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f437,f625]) ).

fof(f627,plain,
    ( sz00 = xp
    | ~ spl0_7
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f351,f626]) ).

fof(f628,plain,
    ( $false
    | ~ spl0_7
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f627,f230]) ).

fof(f629,plain,
    ( ~ spl0_7
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f628]) ).

fof(f630,plain,
    ( ~ aInteger0(sdtpldt0(sz10,xp))
    | spl0_12 ),
    inference(forward_demodulation,[status(thm)],[f292,f619]) ).

fof(f631,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f630,f368]) ).

fof(f632,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f631]) ).

fof(f634,plain,
    ( spl0_0
    | ~ spl0_1
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f541,f245,f248,f477]) ).

fof(f651,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f251,f354,f356,f487,f629,f632,f634]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 09:57:42 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.20/0.52  % Refutation found
% 0.20/0.52  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.52  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.53  % Elapsed time: 0.180789 seconds
% 0.20/0.53  % CPU time: 1.310189 seconds
% 0.20/0.53  % Memory used: 73.468 MB
%------------------------------------------------------------------------------