TSTP Solution File: GRP659+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP659+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 20:21:18 EDT 2024

% Result   : Theorem 37.63s 5.17s
% Output   : CNFRefutation 39.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   53 (  47 unt;   0 def)
%            Number of atoms       :   59 (  58 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   17 (  11   ~;   4   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   0 con; 1-2 aty)
%            Number of variables   :   98 (  93   !;   5   ?)

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

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

fof(f3,axiom,
    ! [B,A] : mult(rd(A,B),B) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [B,A] : rd(mult(A,B),B) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [C,B,A] : mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,conjecture,
    ? [X0] :
    ! [X1] :
      ( mult(X1,X0) = X1
      & mult(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,negated_conjecture,
    ~ ? [X0] :
      ! [X1] :
        ( mult(X1,X0) = X1
        & mult(X0,X1) = X1 ),
    inference(negated_conjecture,[status(cth)],[f6]) ).

fof(f8,plain,
    ! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f9,plain,
    ! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f10,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f11,plain,
    ! [X0,X1] : rd(mult(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f12,plain,
    ! [X0,X1,X2] : mult(mult(X0,mult(X1,X2)),X1) = mult(mult(X0,X1),mult(X2,X1)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f13,plain,
    ! [X0] :
    ? [X1] :
      ( mult(X1,X0) != X1
      | mult(X0,X1) != X1 ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] : mult(X1,X0) != X1
      | ? [X1] : mult(X0,X1) != X1 ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [X0] :
      ( mult(sk0_0(X0),X0) != sk0_0(X0)
      | mult(X0,sk0_1(X0)) != sk0_1(X0) ),
    inference(skolemization,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0] :
      ( mult(sk0_0(X0),X0) != sk0_0(X0)
      | mult(X0,sk0_1(X0)) != sk0_1(X0) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f3099,plain,
    ! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(ld(X2,X1),X2)),
    inference(paramodulation,[status(thm)],[f8,f12]) ).

fof(f3146,plain,
    ! [X0,X1] : ld(rd(X0,X1),X0) = X1,
    inference(paramodulation,[status(thm)],[f10,f9]) ).

fof(f3293,plain,
    ! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
    inference(paramodulation,[status(thm)],[f8,f11]) ).

fof(f3486,plain,
    ! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),mult(ld(X2,X1),X2)) = mult(X0,X2),
    inference(paramodulation,[status(thm)],[f3099,f11]) ).

fof(f3487,plain,
    ! [X0,X1,X2] : ld(mult(X0,X1),mult(mult(X0,X2),X1)) = mult(ld(X1,X2),X1),
    inference(paramodulation,[status(thm)],[f3099,f9]) ).

fof(f3719,plain,
    ! [X0,X1,X2] : rd(mult(X0,X1),mult(ld(X1,X2),X1)) = mult(rd(X0,X2),X1),
    inference(paramodulation,[status(thm)],[f10,f3486]) ).

fof(f3742,plain,
    ! [X0] : X0 = mult(ld(X0,X0),X0),
    inference(paramodulation,[status(thm)],[f9,f3487]) ).

fof(f3805,plain,
    ! [X0,X1,X2] : ld(mult(X0,X1),mult(X2,X1)) = mult(ld(X1,ld(X0,X2)),X1),
    inference(paramodulation,[status(thm)],[f8,f3487]) ).

fof(f3864,plain,
    ! [X0,X1] : ld(mult(ld(X0,X0),X1),mult(X0,X1)) = mult(ld(X1,X0),X1),
    inference(paramodulation,[status(thm)],[f3742,f3487]) ).

fof(f3868,plain,
    ! [X0] : rd(X0,X0) = ld(X0,X0),
    inference(paramodulation,[status(thm)],[f3742,f11]) ).

fof(f4181,plain,
    ! [X0,X1,X2] : rd(mult(X0,X1),mult(X2,X1)) = mult(rd(X0,mult(X1,X2)),X1),
    inference(paramodulation,[status(thm)],[f9,f3719]) ).

fof(f5485,plain,
    ! [X0,X1,X2] : rd(ld(mult(X0,X1),mult(X2,X1)),X1) = ld(X1,ld(X0,X2)),
    inference(paramodulation,[status(thm)],[f3805,f11]) ).

fof(f5756,plain,
    ! [X0,X1] : ld(mult(X0,X1),mult(X0,X1)) = mult(rd(X0,mult(X1,X0)),X1),
    inference(paramodulation,[status(thm)],[f3868,f4181]) ).

fof(f5759,plain,
    ! [X0,X1] : rd(X0,mult(X1,X0)) = mult(rd(ld(X0,X0),mult(X0,X1)),X0),
    inference(paramodulation,[status(thm)],[f3742,f4181]) ).

fof(f7952,plain,
    ! [X0] : ld(mult(X0,ld(X0,X0)),mult(X0,ld(X0,X0))) = mult(rd(X0,X0),ld(X0,X0)),
    inference(paramodulation,[status(thm)],[f3742,f5756]) ).

fof(f7953,plain,
    ! [X0] : ld(X0,mult(X0,ld(X0,X0))) = mult(rd(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f8,f7952]) ).

fof(f7954,plain,
    ! [X0] : ld(X0,X0) = mult(rd(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f9,f7953]) ).

fof(f7955,plain,
    ! [X0] : ld(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f3868,f7954]) ).

fof(f8087,plain,
    ! [X0,X1] : rd(ld(mult(X0,X1),mult(X0,X1)),X1) = rd(X0,mult(X1,X0)),
    inference(paramodulation,[status(thm)],[f5756,f11]) ).

fof(f8088,plain,
    ! [X0,X1] : ld(X0,ld(X1,X1)) = rd(X1,mult(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f5485,f8087]) ).

fof(f8296,plain,
    ! [X0] : ld(mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),ld(X0,X0)) = mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),
    inference(paramodulation,[status(thm)],[f7955,f3864]) ).

fof(f8297,plain,
    ! [X0] : ld(ld(mult(X0,ld(X0,X0)),mult(X0,ld(X0,X0))),ld(X0,X0)) = mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f3805,f8296]) ).

fof(f8298,plain,
    ! [X0] : ld(ld(X0,mult(X0,ld(X0,X0))),ld(X0,X0)) = mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f8,f8297]) ).

fof(f8299,plain,
    ! [X0] : ld(ld(X0,X0),ld(X0,X0)) = mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f9,f8298]) ).

fof(f8300,plain,
    ! [X0] : ld(ld(X0,X0),ld(X0,X0)) = ld(mult(X0,ld(X0,X0)),mult(X0,ld(X0,X0))),
    inference(forward_demodulation,[status(thm)],[f3805,f8299]) ).

fof(f8301,plain,
    ! [X0] : ld(ld(X0,X0),ld(X0,X0)) = ld(X0,mult(X0,ld(X0,X0))),
    inference(forward_demodulation,[status(thm)],[f8,f8300]) ).

fof(f8302,plain,
    ! [X0] : ld(ld(X0,X0),ld(X0,X0)) = ld(X0,X0),
    inference(forward_demodulation,[status(thm)],[f9,f8301]) ).

fof(f13053,plain,
    ! [X0,X1] : ld(X0,ld(X1,X1)) = mult(rd(ld(X1,X1),mult(X1,X0)),X1),
    inference(forward_demodulation,[status(thm)],[f8088,f5759]) ).

fof(f13210,plain,
    ! [X0,X1] : ld(rd(ld(X0,X0),mult(X0,X1)),ld(X0,X0)) = rd(X0,ld(X1,ld(X0,X0))),
    inference(paramodulation,[status(thm)],[f13053,f8088]) ).

fof(f13211,plain,
    ! [X0,X1] : mult(X0,X1) = rd(X0,ld(X1,ld(X0,X0))),
    inference(forward_demodulation,[status(thm)],[f3146,f13210]) ).

fof(f13677,plain,
    ! [X0,X1] : mult(ld(X0,X0),X1) = rd(ld(X0,X0),ld(X1,ld(X0,X0))),
    inference(paramodulation,[status(thm)],[f8302,f13211]) ).

fof(f13678,plain,
    ! [X0,X1] : mult(ld(X0,X0),X1) = X1,
    inference(forward_demodulation,[status(thm)],[f3293,f13677]) ).

fof(f13700,plain,
    ! [X0] : mult(sk0_0(ld(X0,X0)),ld(X0,X0)) != sk0_0(ld(X0,X0)),
    inference(resolution,[status(thm)],[f13678,f16]) ).

fof(f13923,plain,
    ! [X0,X1] : rd(X0,X0) = ld(X1,X1),
    inference(paramodulation,[status(thm)],[f13678,f11]) ).

fof(f13924,plain,
    ! [X0,X1] : ld(X0,X0) = ld(X1,X1),
    inference(forward_demodulation,[status(thm)],[f3868,f13923]) ).

fof(f18856,plain,
    ! [X0,X1] : mult(sk0_0(ld(X0,X0)),ld(X1,X1)) != sk0_0(ld(X0,X0)),
    inference(paramodulation,[status(thm)],[f13924,f13700]) ).

fof(f18866,plain,
    $false,
    inference(resolution,[status(thm)],[f18856,f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP659+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Apr 29 23:50:18 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.6.0
% 37.63/5.17  % Refutation found
% 37.63/5.17  % SZS status Theorem for theBenchmark: Theorem is valid
% 37.63/5.17  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 39.42/5.33  % Elapsed time: 4.982921 seconds
% 39.42/5.33  % CPU time: 39.092882 seconds
% 39.42/5.33  % Total memory used: 926.382 MB
% 39.42/5.33  % Net memory used: 923.130 MB
%------------------------------------------------------------------------------