TSTP Solution File: GRP774+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 12:12:40 EDT 2023

% Result   : Theorem 8.99s 1.62s
% Output   : CNFRefutation 8.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   83 (  59 unt;   0 def)
%            Number of atoms       :  121 (  79 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   64 (  26   ~;  22   |;  11   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  118 (; 114   !;   4   ?)

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

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

fof(f3,axiom,
    ! [X0,X1] :
      ( d(X0,X1)
    <=> ( product(X0,product(X1,X0)) = X0
        & product(X1,product(X0,X1)) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,conjecture,
    ! [X2,X3,X4,X5] :
      ( ( d(X2,X3)
        & d(X4,X5) )
     => d(product(X2,X4),product(X3,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,negated_conjecture,
    ~ ! [X2,X3,X4,X5] :
        ( ( d(X2,X3)
          & d(X4,X5) )
       => d(product(X2,X4),product(X3,X5)) ),
    inference(negated_conjecture,[status(cth)],[f4]) ).

fof(f6,plain,
    ! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f7,plain,
    ! [X0] : product(X0,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ( ~ d(X0,X1)
        | ( product(X0,product(X1,X0)) = X0
          & product(X1,product(X0,X1)) = X1 ) )
      & ( d(X0,X1)
        | product(X0,product(X1,X0)) != X0
        | product(X1,product(X0,X1)) != X1 ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f9,plain,
    ( ! [X0,X1] :
        ( ~ d(X0,X1)
        | ( product(X0,product(X1,X0)) = X0
          & product(X1,product(X0,X1)) = X1 ) )
    & ! [X0,X1] :
        ( d(X0,X1)
        | product(X0,product(X1,X0)) != X0
        | product(X1,product(X0,X1)) != X1 ) ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ d(X0,X1)
      | product(X0,product(X1,X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ~ d(X0,X1)
      | product(X1,product(X0,X1)) = X1 ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( d(X0,X1)
      | product(X0,product(X1,X0)) != X0
      | product(X1,product(X0,X1)) != X1 ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f13,plain,
    ? [X2,X3,X4,X5] :
      ( d(X2,X3)
      & d(X4,X5)
      & ~ d(product(X2,X4),product(X3,X5)) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f14,plain,
    ( d(sk0_0,sk0_1)
    & d(sk0_2,sk0_3)
    & ~ d(product(sk0_0,sk0_2),product(sk0_1,sk0_3)) ),
    inference(skolemization,[status(esa)],[f13]) ).

fof(f15,plain,
    d(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    d(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f17,plain,
    ~ d(product(sk0_0,sk0_2),product(sk0_1,sk0_3)),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f18,plain,
    product(sk0_2,product(sk0_3,sk0_2)) = sk0_2,
    inference(resolution,[status(thm)],[f10,f16]) ).

fof(f19,plain,
    product(sk0_0,product(sk0_1,sk0_0)) = sk0_0,
    inference(resolution,[status(thm)],[f10,f15]) ).

fof(f20,plain,
    product(sk0_3,product(sk0_2,sk0_3)) = sk0_3,
    inference(resolution,[status(thm)],[f11,f16]) ).

fof(f21,plain,
    product(sk0_1,product(sk0_0,sk0_1)) = sk0_1,
    inference(resolution,[status(thm)],[f11,f15]) ).

fof(f22,plain,
    ! [X0,X1] : product(X0,X1) = product(X0,product(X1,product(X0,X1))),
    inference(paramodulation,[status(thm)],[f7,f6]) ).

fof(f26,plain,
    ! [X0] : product(sk0_2,X0) = product(sk0_2,product(product(sk0_3,sk0_2),X0)),
    inference(paramodulation,[status(thm)],[f18,f6]) ).

fof(f27,plain,
    ! [X0] : product(sk0_2,X0) = product(sk0_2,product(sk0_3,product(sk0_2,X0))),
    inference(forward_demodulation,[status(thm)],[f6,f26]) ).

fof(f28,plain,
    ! [X0,X1] : product(X0,X1) = product(X0,product(X0,X1)),
    inference(paramodulation,[status(thm)],[f7,f6]) ).

fof(f30,plain,
    ! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,product(product(X0,X1),X2))),
    inference(paramodulation,[status(thm)],[f6,f28]) ).

fof(f31,plain,
    ! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(product(X0,X1),X2))),
    inference(forward_demodulation,[status(thm)],[f6,f30]) ).

fof(f32,plain,
    ! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X0,product(X1,X2)))),
    inference(forward_demodulation,[status(thm)],[f6,f31]) ).

fof(f44,plain,
    ! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,product(X2,product(product(X0,X1),X2)))),
    inference(paramodulation,[status(thm)],[f6,f22]) ).

fof(f45,plain,
    ! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X2,product(product(X0,X1),X2)))),
    inference(forward_demodulation,[status(thm)],[f6,f44]) ).

fof(f46,plain,
    ! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X2,product(X0,product(X1,X2))))),
    inference(forward_demodulation,[status(thm)],[f6,f45]) ).

fof(f100,plain,
    ( spl0_0
  <=> product(product(sk0_0,sk0_2),product(product(sk0_1,sk0_3),product(sk0_0,sk0_2))) = product(sk0_0,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f102,plain,
    ( product(product(sk0_0,sk0_2),product(product(sk0_1,sk0_3),product(sk0_0,sk0_2))) != product(sk0_0,sk0_2)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f100]) ).

fof(f103,plain,
    ( spl0_1
  <=> product(product(sk0_1,sk0_3),product(product(sk0_0,sk0_2),product(sk0_1,sk0_3))) = product(sk0_1,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f105,plain,
    ( product(product(sk0_1,sk0_3),product(product(sk0_0,sk0_2),product(sk0_1,sk0_3))) != product(sk0_1,sk0_3)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f103]) ).

fof(f106,plain,
    ( product(product(sk0_0,sk0_2),product(product(sk0_1,sk0_3),product(sk0_0,sk0_2))) != product(sk0_0,sk0_2)
    | product(product(sk0_1,sk0_3),product(product(sk0_0,sk0_2),product(sk0_1,sk0_3))) != product(sk0_1,sk0_3) ),
    inference(resolution,[status(thm)],[f12,f17]) ).

fof(f107,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f106,f100,f103]) ).

fof(f108,plain,
    ( product(sk0_0,product(sk0_2,product(product(sk0_1,sk0_3),product(sk0_0,sk0_2)))) != product(sk0_0,sk0_2)
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f6,f102]) ).

fof(f109,plain,
    ( product(sk0_0,product(sk0_2,product(sk0_1,product(sk0_3,product(sk0_0,sk0_2))))) != product(sk0_0,sk0_2)
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f6,f108]) ).

fof(f116,plain,
    ! [X0] : product(sk0_0,X0) = product(sk0_0,product(product(sk0_1,sk0_0),X0)),
    inference(paramodulation,[status(thm)],[f19,f6]) ).

fof(f117,plain,
    ! [X0] : product(sk0_0,X0) = product(sk0_0,product(sk0_1,product(sk0_0,X0))),
    inference(forward_demodulation,[status(thm)],[f6,f116]) ).

fof(f141,plain,
    ! [X0] : product(sk0_3,X0) = product(sk0_3,product(product(sk0_2,sk0_3),X0)),
    inference(paramodulation,[status(thm)],[f20,f6]) ).

fof(f142,plain,
    ! [X0] : product(sk0_3,X0) = product(sk0_3,product(sk0_2,product(sk0_3,X0))),
    inference(forward_demodulation,[status(thm)],[f6,f141]) ).

fof(f166,plain,
    ! [X0] : product(sk0_1,X0) = product(sk0_1,product(product(sk0_0,sk0_1),X0)),
    inference(paramodulation,[status(thm)],[f21,f6]) ).

fof(f167,plain,
    ! [X0] : product(sk0_1,X0) = product(sk0_1,product(sk0_0,product(sk0_1,X0))),
    inference(forward_demodulation,[status(thm)],[f6,f166]) ).

fof(f168,plain,
    ! [X0,X1,X2,X3] : product(product(X0,X1),product(X2,X3)) = product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))),
    inference(paramodulation,[status(thm)],[f6,f32]) ).

fof(f169,plain,
    ! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))),
    inference(forward_demodulation,[status(thm)],[f6,f168]) ).

fof(f170,plain,
    ! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(X0,product(X1,product(X2,X3)))))),
    inference(forward_demodulation,[status(thm)],[f6,f169]) ).

fof(f269,plain,
    ! [X0,X1,X2,X3] : product(product(X0,X1),product(X2,X3)) = product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,X3)))))),
    inference(paramodulation,[status(thm)],[f6,f46]) ).

fof(f270,plain,
    ! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,X3)))))),
    inference(forward_demodulation,[status(thm)],[f6,f269]) ).

fof(f271,plain,
    ! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(X3,product(X0,product(X1,product(X2,X3))))))),
    inference(forward_demodulation,[status(thm)],[f6,f270]) ).

fof(f465,plain,
    ! [X0] : product(sk0_1,product(X0,product(sk0_0,product(sk0_1,X0)))) = product(sk0_1,product(sk0_0,product(sk0_1,X0))),
    inference(paramodulation,[status(thm)],[f46,f167]) ).

fof(f466,plain,
    ! [X0] : product(sk0_1,product(X0,product(sk0_0,product(sk0_1,X0)))) = product(sk0_1,X0),
    inference(forward_demodulation,[status(thm)],[f167,f465]) ).

fof(f1433,plain,
    ! [X0,X1] : product(X0,product(sk0_1,product(sk0_0,product(sk0_1,X1)))) = product(X0,product(sk0_1,product(sk0_0,product(X0,product(sk0_1,X1))))),
    inference(paramodulation,[status(thm)],[f167,f170]) ).

fof(f1434,plain,
    ! [X0,X1] : product(X0,product(sk0_1,X1)) = product(X0,product(sk0_1,product(sk0_0,product(X0,product(sk0_1,X1))))),
    inference(forward_demodulation,[status(thm)],[f167,f1433]) ).

fof(f1441,plain,
    ! [X0,X1] : product(X0,product(sk0_3,product(sk0_2,product(sk0_3,X1)))) = product(X0,product(sk0_3,product(sk0_2,product(X0,product(sk0_3,X1))))),
    inference(paramodulation,[status(thm)],[f142,f170]) ).

fof(f1442,plain,
    ! [X0,X1] : product(X0,product(sk0_3,X1)) = product(X0,product(sk0_3,product(sk0_2,product(X0,product(sk0_3,X1))))),
    inference(forward_demodulation,[status(thm)],[f142,f1441]) ).

fof(f1443,plain,
    ! [X0] : product(X0,product(sk0_3,product(sk0_2,sk0_3))) = product(X0,product(sk0_3,product(sk0_2,product(X0,sk0_3)))),
    inference(paramodulation,[status(thm)],[f20,f170]) ).

fof(f1444,plain,
    ! [X0] : product(X0,sk0_3) = product(X0,product(sk0_3,product(sk0_2,product(X0,sk0_3)))),
    inference(forward_demodulation,[status(thm)],[f20,f1443]) ).

fof(f1449,plain,
    ! [X0,X1] : product(X0,product(sk0_0,product(sk0_1,product(sk0_0,X1)))) = product(X0,product(sk0_0,product(sk0_1,product(X0,product(sk0_0,X1))))),
    inference(paramodulation,[status(thm)],[f117,f170]) ).

fof(f1450,plain,
    ! [X0,X1] : product(X0,product(sk0_0,X1)) = product(X0,product(sk0_0,product(sk0_1,product(X0,product(sk0_0,X1))))),
    inference(forward_demodulation,[status(thm)],[f117,f1449]) ).

fof(f1460,plain,
    ! [X0,X1] : product(X0,product(sk0_2,product(sk0_3,product(sk0_2,X1)))) = product(X0,product(sk0_2,product(sk0_3,product(X0,product(sk0_2,X1))))),
    inference(paramodulation,[status(thm)],[f27,f170]) ).

fof(f1461,plain,
    ! [X0,X1] : product(X0,product(sk0_2,X1)) = product(X0,product(sk0_2,product(sk0_3,product(X0,product(sk0_2,X1))))),
    inference(forward_demodulation,[status(thm)],[f27,f1460]) ).

fof(f1462,plain,
    ! [X0] : product(X0,product(sk0_2,product(sk0_3,sk0_2))) = product(X0,product(sk0_2,product(sk0_3,product(X0,sk0_2)))),
    inference(paramodulation,[status(thm)],[f18,f170]) ).

fof(f1463,plain,
    ! [X0] : product(X0,sk0_2) = product(X0,product(sk0_2,product(sk0_3,product(X0,sk0_2)))),
    inference(forward_demodulation,[status(thm)],[f18,f1462]) ).

fof(f3601,plain,
    ! [X0,X1] : product(X0,product(sk0_1,product(X1,product(sk0_0,product(X0,product(sk0_1,X1)))))) = product(X0,product(sk0_1,product(sk0_0,product(X0,product(sk0_1,X1))))),
    inference(paramodulation,[status(thm)],[f271,f1434]) ).

fof(f3602,plain,
    ! [X0,X1] : product(X0,product(sk0_1,product(X1,product(sk0_0,product(X0,product(sk0_1,X1)))))) = product(X0,product(sk0_1,X1)),
    inference(forward_demodulation,[status(thm)],[f1434,f3601]) ).

fof(f4134,plain,
    ! [X0,X1] : product(X0,product(sk0_0,product(X1,product(sk0_1,product(X0,product(sk0_0,X1)))))) = product(X0,product(sk0_0,product(sk0_1,product(X0,product(sk0_0,X1))))),
    inference(paramodulation,[status(thm)],[f271,f1450]) ).

fof(f4135,plain,
    ! [X0,X1] : product(X0,product(sk0_0,product(X1,product(sk0_1,product(X0,product(sk0_0,X1)))))) = product(X0,product(sk0_0,X1)),
    inference(forward_demodulation,[status(thm)],[f1450,f4134]) ).

fof(f9303,plain,
    product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3))))) = product(sk0_1,product(sk0_3,product(sk0_2,product(sk0_1,sk0_3)))),
    inference(paramodulation,[status(thm)],[f3602,f1442]) ).

fof(f9304,plain,
    product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3))))) = product(sk0_1,sk0_3),
    inference(forward_demodulation,[status(thm)],[f1444,f9303]) ).

fof(f10928,plain,
    product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3)))) = product(sk0_3,product(sk0_0,product(sk0_1,sk0_3))),
    inference(paramodulation,[status(thm)],[f9304,f1450]) ).

fof(f18601,plain,
    product(sk0_0,product(sk0_2,product(sk0_1,product(sk0_3,product(sk0_0,sk0_2))))) = product(sk0_0,product(sk0_2,product(sk0_3,product(sk0_0,sk0_2)))),
    inference(paramodulation,[status(thm)],[f4135,f1461]) ).

fof(f18602,plain,
    product(sk0_0,product(sk0_2,product(sk0_1,product(sk0_3,product(sk0_0,sk0_2))))) = product(sk0_0,sk0_2),
    inference(forward_demodulation,[status(thm)],[f1463,f18601]) ).

fof(f18603,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f18602,f109]) ).

fof(f18604,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f18603]) ).

fof(f18952,plain,
    ( product(sk0_1,product(sk0_3,product(product(sk0_0,sk0_2),product(sk0_1,sk0_3)))) != product(sk0_1,sk0_3)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f6,f105]) ).

fof(f18953,plain,
    ( product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3))))) != product(sk0_1,sk0_3)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f6,f18952]) ).

fof(f18954,plain,
    ( product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_1,sk0_3)))) != product(sk0_1,sk0_3)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f10928,f18953]) ).

fof(f18955,plain,
    ( product(sk0_1,sk0_3) != product(sk0_1,sk0_3)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f466,f18954]) ).

fof(f18956,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f18955]) ).

fof(f18957,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f18956]) ).

fof(f18958,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f107,f18604,f18957]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n003.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 11:28:23 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.5.1
% 8.99/1.62  % Refutation found
% 8.99/1.62  % SZS status Theorem for theBenchmark: Theorem is valid
% 8.99/1.62  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.66/1.68  % Elapsed time: 1.355093 seconds
% 9.66/1.68  % CPU time: 9.703402 seconds
% 9.66/1.68  % Memory used: 193.868 MB
%------------------------------------------------------------------------------