TSTP Solution File: ALG210+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:11:01 EDT 2024

% Result   : Theorem 3.21s 0.77s
% Output   : CNFRefutation 3.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   72 (  59 unt;   0 def)
%            Number of atoms       :  109 (  79 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   57 (  20   ~;  14   |;  20   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   74 (  65   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B,C] : times(times(A,B),C) = times(B,times(C,A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B] :
      ( element(B)
    <=> ? [C] :
          ( times(B,C) = B
          & times(B,B) = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,conjecture,
    ! [A,B,C] :
      ( ( element(A)
        & element(B)
        & C = times(A,B) )
     => element(C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( element(A)
          & element(B)
          & C = times(A,B) )
       => element(C) ),
    inference(negated_conjecture,[status(cth)],[f3]) ).

fof(f5,plain,
    ! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f6,plain,
    ! [B] :
      ( ( ~ element(B)
        | ? [C] :
            ( times(B,C) = B
            & times(B,B) = C ) )
      & ( element(B)
        | ! [C] :
            ( times(B,C) != B
            | times(B,B) != C ) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f7,plain,
    ( ! [B] :
        ( ~ element(B)
        | ? [C] :
            ( times(B,C) = B
            & times(B,B) = C ) )
    & ! [B] :
        ( element(B)
        | ! [C] :
            ( times(B,C) != B
            | times(B,B) != C ) ) ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f8,plain,
    ( ! [B] :
        ( ~ element(B)
        | ( times(B,sk0_0(B)) = B
          & times(B,B) = sk0_0(B) ) )
    & ! [B] :
        ( element(B)
        | ! [C] :
            ( times(B,C) != B
            | times(B,B) != C ) ) ),
    inference(skolemization,[status(esa)],[f7]) ).

fof(f9,plain,
    ! [X0] :
      ( ~ element(X0)
      | times(X0,sk0_0(X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f10,plain,
    ! [X0] :
      ( ~ element(X0)
      | times(X0,X0) = sk0_0(X0) ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( element(X0)
      | times(X0,X1) != X0
      | times(X0,X0) != X1 ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f12,plain,
    ? [A,B,C] :
      ( element(A)
      & element(B)
      & C = times(A,B)
      & ~ element(C) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f13,plain,
    ? [C] :
      ( ? [A,B] :
          ( element(A)
          & element(B)
          & C = times(A,B) )
      & ~ element(C) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f14,plain,
    ( element(sk0_2)
    & element(sk0_3)
    & sk0_1 = times(sk0_2,sk0_3)
    & ~ element(sk0_1) ),
    inference(skolemization,[status(esa)],[f13]) ).

fof(f15,plain,
    element(sk0_2),
    inference(cnf_transformation,[status(esa)],[f14]) ).

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

fof(f17,plain,
    sk0_1 = times(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f18,plain,
    ~ element(sk0_1),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f19,plain,
    ! [X0] :
      ( element(X0)
      | times(X0,times(X0,X0)) != X0 ),
    inference(destructive_equality_resolution,[status(esa)],[f11]) ).

fof(f20,plain,
    times(sk0_1,times(sk0_1,sk0_1)) != sk0_1,
    inference(resolution,[status(thm)],[f19,f18]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] : times(times(X0,times(X1,X2)),X3) = times(X1,times(X3,times(X2,X0))),
    inference(paramodulation,[status(thm)],[f5,f5]) ).

fof(f22,plain,
    ! [X0,X1,X2,X3] : times(times(X0,X1),times(X2,X3)) = times(X0,times(X2,times(X1,X3))),
    inference(forward_demodulation,[status(thm)],[f5,f21]) ).

fof(f23,plain,
    ! [X0,X1,X2,X3] : times(X0,times(times(X1,X2),X3)) = times(X3,times(X1,times(X0,X2))),
    inference(forward_demodulation,[status(thm)],[f5,f22]) ).

fof(f24,plain,
    ! [X0,X1,X2,X3] : times(X0,times(X1,times(X2,X3))) = times(X2,times(X3,times(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f5,f23]) ).

fof(f25,plain,
    ! [X0] : times(sk0_1,X0) = times(sk0_3,times(X0,sk0_2)),
    inference(paramodulation,[status(thm)],[f17,f5]) ).

fof(f26,plain,
    ! [X0,X1] : times(sk0_1,times(X0,X1)) = times(sk0_3,times(X1,times(sk0_2,X0))),
    inference(paramodulation,[status(thm)],[f5,f25]) ).

fof(f27,plain,
    ! [X0,X1] : times(times(sk0_1,X0),X1) = times(times(X0,sk0_2),times(X1,sk0_3)),
    inference(paramodulation,[status(thm)],[f25,f5]) ).

fof(f28,plain,
    ! [X0,X1] : times(X0,times(X1,sk0_1)) = times(times(X0,sk0_2),times(X1,sk0_3)),
    inference(forward_demodulation,[status(thm)],[f5,f27]) ).

fof(f29,plain,
    ! [X0,X1] : times(X0,times(X1,sk0_1)) = times(sk0_2,times(times(X1,sk0_3),X0)),
    inference(forward_demodulation,[status(thm)],[f5,f28]) ).

fof(f30,plain,
    ! [X0,X1] : times(X0,times(X1,sk0_1)) = times(sk0_2,times(sk0_3,times(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f5,f29]) ).

fof(f36,plain,
    ! [X0,X1] : times(X0,times(sk0_1,X1)) = times(X1,times(sk0_2,times(X0,sk0_3))),
    inference(paramodulation,[status(thm)],[f25,f24]) ).

fof(f119,plain,
    ! [X0,X1] : times(sk0_1,times(X0,X1)) = times(sk0_2,times(X0,times(sk0_3,X1))),
    inference(forward_demodulation,[status(thm)],[f24,f26]) ).

fof(f154,plain,
    ! [X0] : times(sk0_3,times(X0,sk0_1)) = times(sk0_1,times(sk0_3,X0)),
    inference(paramodulation,[status(thm)],[f119,f30]) ).

fof(f157,plain,
    ! [X0] : times(X0,times(sk0_2,sk0_1)) = times(sk0_2,times(sk0_1,X0)),
    inference(paramodulation,[status(thm)],[f25,f30]) ).

fof(f1247,plain,
    times(sk0_3,sk0_0(sk0_3)) = sk0_3,
    inference(resolution,[status(thm)],[f9,f16]) ).

fof(f1248,plain,
    times(sk0_2,sk0_0(sk0_2)) = sk0_2,
    inference(resolution,[status(thm)],[f9,f15]) ).

fof(f1250,plain,
    times(sk0_3,sk0_3) = sk0_0(sk0_3),
    inference(resolution,[status(thm)],[f10,f16]) ).

fof(f1251,plain,
    times(sk0_2,sk0_2) = sk0_0(sk0_2),
    inference(resolution,[status(thm)],[f10,f15]) ).

fof(f1265,plain,
    ! [X0] : times(sk0_3,X0) = times(sk0_0(sk0_3),times(X0,sk0_3)),
    inference(paramodulation,[status(thm)],[f1247,f5]) ).

fof(f1282,plain,
    times(sk0_3,times(sk0_3,sk0_1)) = times(sk0_2,times(sk0_3,sk0_0(sk0_3))),
    inference(paramodulation,[status(thm)],[f1250,f30]) ).

fof(f1283,plain,
    times(sk0_1,times(sk0_3,sk0_3)) = times(sk0_2,times(sk0_3,sk0_0(sk0_3))),
    inference(forward_demodulation,[status(thm)],[f154,f1282]) ).

fof(f1284,plain,
    times(sk0_1,sk0_0(sk0_3)) = times(sk0_2,times(sk0_3,sk0_0(sk0_3))),
    inference(forward_demodulation,[status(thm)],[f1250,f1283]) ).

fof(f1285,plain,
    times(sk0_1,sk0_0(sk0_3)) = times(sk0_2,sk0_3),
    inference(forward_demodulation,[status(thm)],[f1247,f1284]) ).

fof(f1286,plain,
    times(sk0_1,sk0_0(sk0_3)) = sk0_1,
    inference(forward_demodulation,[status(thm)],[f17,f1285]) ).

fof(f1289,plain,
    ! [X0] : times(sk0_0(sk0_3),X0) = times(sk0_3,times(X0,sk0_3)),
    inference(paramodulation,[status(thm)],[f1250,f5]) ).

fof(f1298,plain,
    ! [X0] : times(sk0_0(sk0_2),X0) = times(sk0_2,times(X0,sk0_2)),
    inference(paramodulation,[status(thm)],[f1251,f5]) ).

fof(f1308,plain,
    ! [X0] : times(sk0_1,X0) = times(sk0_0(sk0_3),times(X0,sk0_1)),
    inference(paramodulation,[status(thm)],[f1286,f5]) ).

fof(f1530,plain,
    times(sk0_3,sk0_2) = times(sk0_0(sk0_3),sk0_1),
    inference(paramodulation,[status(thm)],[f17,f1265]) ).

fof(f3116,plain,
    times(sk0_0(sk0_3),sk0_3) = times(sk0_3,sk0_0(sk0_3)),
    inference(paramodulation,[status(thm)],[f1250,f1289]) ).

fof(f3117,plain,
    times(sk0_0(sk0_3),sk0_3) = sk0_3,
    inference(forward_demodulation,[status(thm)],[f1247,f3116]) ).

fof(f3119,plain,
    times(sk0_0(sk0_3),sk0_2) = times(sk0_3,sk0_1),
    inference(paramodulation,[status(thm)],[f17,f1289]) ).

fof(f3189,plain,
    ! [X0] : times(sk0_0(sk0_3),times(sk0_1,X0)) = times(X0,times(sk0_2,sk0_3)),
    inference(paramodulation,[status(thm)],[f3117,f36]) ).

fof(f3190,plain,
    ! [X0] : times(sk0_0(sk0_3),times(sk0_1,X0)) = times(X0,sk0_1),
    inference(forward_demodulation,[status(thm)],[f17,f3189]) ).

fof(f3224,plain,
    times(sk0_0(sk0_3),times(sk0_2,sk0_1)) = times(sk0_2,times(sk0_3,times(sk0_3,sk0_1))),
    inference(paramodulation,[status(thm)],[f3119,f30]) ).

fof(f3225,plain,
    times(sk0_2,times(sk0_1,sk0_0(sk0_3))) = times(sk0_2,times(sk0_3,times(sk0_3,sk0_1))),
    inference(forward_demodulation,[status(thm)],[f157,f3224]) ).

fof(f3226,plain,
    times(sk0_2,sk0_1) = times(sk0_2,times(sk0_3,times(sk0_3,sk0_1))),
    inference(forward_demodulation,[status(thm)],[f1286,f3225]) ).

fof(f3227,plain,
    times(sk0_2,sk0_1) = times(sk0_3,times(sk0_1,sk0_1)),
    inference(forward_demodulation,[status(thm)],[f30,f3226]) ).

fof(f3228,plain,
    times(sk0_2,sk0_1) = times(sk0_1,times(sk0_3,sk0_1)),
    inference(forward_demodulation,[status(thm)],[f154,f3227]) ).

fof(f3236,plain,
    times(sk0_0(sk0_2),sk0_2) = times(sk0_2,sk0_0(sk0_2)),
    inference(paramodulation,[status(thm)],[f1251,f1298]) ).

fof(f3237,plain,
    times(sk0_0(sk0_2),sk0_2) = sk0_2,
    inference(forward_demodulation,[status(thm)],[f1248,f3236]) ).

fof(f3305,plain,
    times(sk0_1,sk0_0(sk0_2)) = times(sk0_3,sk0_2),
    inference(paramodulation,[status(thm)],[f3237,f25]) ).

fof(f3344,plain,
    times(sk0_1,sk0_2) = times(sk0_2,times(sk0_1,sk0_0(sk0_3))),
    inference(paramodulation,[status(thm)],[f157,f1308]) ).

fof(f3345,plain,
    times(sk0_1,sk0_2) = times(sk0_2,sk0_1),
    inference(forward_demodulation,[status(thm)],[f1286,f3344]) ).

fof(f3346,plain,
    times(sk0_1,sk0_0(sk0_3)) = times(sk0_0(sk0_3),times(sk0_3,sk0_2)),
    inference(paramodulation,[status(thm)],[f1530,f1308]) ).

fof(f3347,plain,
    sk0_1 = times(sk0_0(sk0_3),times(sk0_3,sk0_2)),
    inference(forward_demodulation,[status(thm)],[f1286,f3346]) ).

fof(f3621,plain,
    times(sk0_0(sk0_3),times(sk0_3,sk0_2)) = times(sk0_0(sk0_2),sk0_1),
    inference(paramodulation,[status(thm)],[f3305,f3190]) ).

fof(f3622,plain,
    sk0_1 = times(sk0_0(sk0_2),sk0_1),
    inference(forward_demodulation,[status(thm)],[f3347,f3621]) ).

fof(f3891,plain,
    times(sk0_1,sk0_2) = times(sk0_1,times(sk0_3,sk0_1)),
    inference(forward_demodulation,[status(thm)],[f3345,f3228]) ).

fof(f3896,plain,
    times(sk0_1,times(sk0_1,sk0_1)) = times(sk0_2,times(sk0_1,sk0_2)),
    inference(paramodulation,[status(thm)],[f3891,f119]) ).

fof(f3897,plain,
    times(sk0_1,times(sk0_1,sk0_1)) = times(sk0_0(sk0_2),sk0_1),
    inference(forward_demodulation,[status(thm)],[f1298,f3896]) ).

fof(f3898,plain,
    times(sk0_1,times(sk0_1,sk0_1)) = sk0_1,
    inference(forward_demodulation,[status(thm)],[f3622,f3897]) ).

fof(f3899,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f3898,f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n005.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 : Mon Apr 29 23:31:41 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 3.21/0.77  % Refutation found
% 3.21/0.77  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.21/0.77  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.21/0.80  % Elapsed time: 0.441432 seconds
% 3.21/0.80  % CPU time: 3.295274 seconds
% 3.21/0.80  % Total memory used: 68.422 MB
% 3.21/0.80  % Net memory used: 68.167 MB
%------------------------------------------------------------------------------