TSTP Solution File: GRP683-11 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP683-11 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 20:21:24 EDT 2024

% Result   : Unsatisfiable 2.23s 0.63s
% Output   : CNFRefutation 2.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   50 (  50 unt;   0 def)
%            Number of atoms       :   50 (  49 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  135 ( 135   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A] : rd(mult(A,A),A) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f6,axiom,
    ! [A,B,C,D] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    mult(rd(mult(x3,x4),x4),x5) != mult(x3,x5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,plain,
    ! [X0] : rd(mult(X0,X0),X0) = X0,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f12,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f14,plain,
    ! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f16,plain,
    mult(rd(mult(x3,x4),x4),x5) != mult(x3,x5),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f17,plain,
    mult(mult(rd(x3,x4),x4),x5) != mult(x3,x5),
    inference(backward_demodulation,[status(thm)],[f12,f16]) ).

fof(f18,plain,
    ! [X0] : mult(rd(X0,X0),X0) = X0,
    inference(backward_demodulation,[status(thm)],[f12,f10]) ).

fof(f20,plain,
    ! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
    inference(forward_demodulation,[status(thm)],[f12,f14]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
    inference(forward_demodulation,[status(thm)],[f12,f20]) ).

fof(f22,plain,
    ! [X0,X1,X2] : mult(mult(rd(X0,rd(X1,X2)),rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(rd(X1,X2),X2),X2)),
    inference(paramodulation,[status(thm)],[f12,f21]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),mult(rd(X2,X3),X3)),rd(mult(X2,X3),X3)) = mult(X0,mult(rd(X1,X3),X3)),
    inference(paramodulation,[status(thm)],[f12,f21]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3)) = mult(X0,mult(rd(X1,X3),X3)),
    inference(forward_demodulation,[status(thm)],[f12,f26]) ).

fof(f58,plain,
    ! [X0,X1,X2] : mult(rd(mult(X0,X1),X2),mult(rd(X2,X2),X2)) = mult(X0,mult(rd(X1,X2),X2)),
    inference(paramodulation,[status(thm)],[f18,f27]) ).

fof(f59,plain,
    ! [X0,X1,X2] : mult(rd(mult(X0,X1),X2),X2) = mult(X0,mult(rd(X1,X2),X2)),
    inference(forward_demodulation,[status(thm)],[f18,f58]) ).

fof(f81,plain,
    ! [X0,X1,X2,X3] : mult(X0,mult(rd(X1,rd(X2,X3)),rd(X2,X3))) = mult(X0,mult(rd(X1,X3),X3)),
    inference(backward_demodulation,[status(thm)],[f59,f21]) ).

fof(f83,plain,
    ! [X0,X1] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,mult(rd(X1,X1),X1)),
    inference(paramodulation,[status(thm)],[f12,f59]) ).

fof(f84,plain,
    ! [X0,X1] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,X1),
    inference(forward_demodulation,[status(thm)],[f18,f83]) ).

fof(f91,plain,
    ! [X0,X1] : mult(rd(X0,X1),X1) = mult(rd(X0,X0),mult(rd(X0,X1),X1)),
    inference(paramodulation,[status(thm)],[f18,f59]) ).

fof(f93,plain,
    ! [X0,X1,X2] : mult(rd(rd(mult(X0,X1),X2),X2),X2) = rd(mult(X0,mult(rd(X1,X2),X2)),X2),
    inference(paramodulation,[status(thm)],[f59,f12]) ).

fof(f96,plain,
    ! [X0,X1,X2] : mult(rd(mult(X0,X1),X2),X2) = mult(mult(rd(X0,X1),X1),mult(rd(X1,X2),X2)),
    inference(paramodulation,[status(thm)],[f84,f59]) ).

fof(f97,plain,
    ! [X0,X1,X2] : mult(X0,mult(rd(X1,X2),X2)) = mult(mult(rd(X0,X1),X1),mult(rd(X1,X2),X2)),
    inference(forward_demodulation,[status(thm)],[f59,f96]) ).

fof(f168,plain,
    ! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,X0),mult(rd(X0,X2),X2)),
    inference(paramodulation,[status(thm)],[f91,f81]) ).

fof(f169,plain,
    ! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,X2),X2),
    inference(forward_demodulation,[status(thm)],[f91,f168]) ).

fof(f217,plain,
    ! [X0,X1,X2] : mult(X0,rd(X1,X2)) = mult(X0,mult(rd(rd(X1,X2),X2),X2)),
    inference(forward_demodulation,[status(thm)],[f84,f22]) ).

fof(f231,plain,
    ! [X0,X1] : mult(rd(rd(X0,X1),rd(X0,X1)),rd(X0,X1)) = mult(rd(rd(X0,X1),X1),X1),
    inference(paramodulation,[status(thm)],[f91,f217]) ).

fof(f232,plain,
    ! [X0,X1] : rd(X0,X1) = mult(rd(rd(X0,X1),X1),X1),
    inference(forward_demodulation,[status(thm)],[f18,f231]) ).

fof(f303,plain,
    ! [X0,X1,X2] : mult(rd(rd(X0,X1),X2),X2) = mult(rd(rd(X0,X1),X1),mult(rd(X1,X2),X2)),
    inference(paramodulation,[status(thm)],[f232,f59]) ).

fof(f312,plain,
    ! [X0,X1,X2] : mult(rd(X0,mult(rd(X1,X2),X2)),rd(mult(X1,X2),X2)) = mult(rd(X0,X2),X2),
    inference(paramodulation,[status(thm)],[f12,f169]) ).

fof(f313,plain,
    ! [X0,X1,X2] : mult(rd(X0,mult(rd(X1,X2),X2)),mult(rd(X1,X2),X2)) = mult(rd(X0,X2),X2),
    inference(forward_demodulation,[status(thm)],[f12,f312]) ).

fof(f586,plain,
    ! [X0,X1,X2] : rd(mult(X0,X1),X2) = rd(mult(X0,mult(rd(X1,X2),X2)),X2),
    inference(forward_demodulation,[status(thm)],[f232,f93]) ).

fof(f885,plain,
    ! [X0,X1,X2] : mult(rd(rd(X0,mult(X1,X2)),X2),X2) = mult(rd(rd(X0,mult(X1,X2)),mult(X1,X2)),mult(mult(rd(X1,X2),X2),X2)),
    inference(paramodulation,[status(thm)],[f12,f303]) ).

fof(f886,plain,
    ! [X0,X1,X2] : mult(rd(rd(X0,mult(X1,X2)),X2),X2) = mult(rd(rd(X0,mult(X1,X2)),mult(X1,X2)),mult(X1,X2)),
    inference(forward_demodulation,[status(thm)],[f84,f885]) ).

fof(f887,plain,
    ! [X0,X1,X2] : mult(rd(rd(X0,mult(X1,X2)),X2),X2) = rd(X0,mult(X1,X2)),
    inference(forward_demodulation,[status(thm)],[f232,f886]) ).

fof(f998,plain,
    ! [X0,X1,X2,X3] : mult(rd(X0,rd(X1,mult(X2,X3))),mult(rd(rd(X1,mult(X2,X3)),X3),X3)) = mult(rd(X0,X3),X3),
    inference(paramodulation,[status(thm)],[f887,f313]) ).

fof(f999,plain,
    ! [X0,X1,X2,X3] : mult(rd(X0,rd(X1,mult(X2,X3))),rd(X1,mult(X2,X3))) = mult(rd(X0,X3),X3),
    inference(forward_demodulation,[status(thm)],[f887,f998]) ).

fof(f1000,plain,
    ! [X0,X1,X2] : mult(rd(X0,mult(X1,X2)),mult(X1,X2)) = mult(rd(X0,X2),X2),
    inference(forward_demodulation,[status(thm)],[f169,f999]) ).

fof(f1103,plain,
    ! [X0,X1,X2] : rd(mult(rd(X0,mult(rd(X1,X2),X2)),X1),X2) = rd(mult(rd(X0,X2),X2),X2),
    inference(paramodulation,[status(thm)],[f313,f586]) ).

fof(f1104,plain,
    ! [X0,X1,X2] : rd(mult(rd(X0,mult(rd(X1,X2),X2)),X1),X2) = mult(rd(rd(X0,X2),X2),X2),
    inference(forward_demodulation,[status(thm)],[f12,f1103]) ).

fof(f1105,plain,
    ! [X0,X1,X2] : rd(mult(rd(X0,mult(rd(X1,X2),X2)),X1),X2) = rd(X0,X2),
    inference(forward_demodulation,[status(thm)],[f232,f1104]) ).

fof(f1368,plain,
    ! [X0,X1,X2,X3] : mult(X0,mult(rd(mult(rd(X1,mult(rd(X2,X3),X3)),X2),X3),X3)) = mult(mult(rd(X0,mult(rd(X1,mult(rd(X2,X3),X3)),X2)),mult(rd(X1,mult(rd(X2,X3),X3)),X2)),mult(rd(X1,X3),X3)),
    inference(paramodulation,[status(thm)],[f1105,f97]) ).

fof(f1369,plain,
    ! [X0,X1,X2,X3] : mult(X0,mult(rd(X1,mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3))) = mult(mult(rd(X0,mult(rd(X1,mult(rd(X2,X3),X3)),X2)),mult(rd(X1,mult(rd(X2,X3),X3)),X2)),mult(rd(X1,X3),X3)),
    inference(forward_demodulation,[status(thm)],[f59,f1368]) ).

fof(f1370,plain,
    ! [X0,X1,X2,X3] : mult(X0,mult(rd(X1,X2),X2)) = mult(mult(rd(X0,mult(rd(X1,mult(rd(X3,X2),X2)),X3)),mult(rd(X1,mult(rd(X3,X2),X2)),X3)),mult(rd(X1,X2),X2)),
    inference(forward_demodulation,[status(thm)],[f1000,f1369]) ).

fof(f1371,plain,
    ! [X0,X1,X2,X3] : mult(X0,mult(rd(X1,X2),X2)) = mult(mult(rd(X0,X3),X3),mult(rd(X1,X2),X2)),
    inference(forward_demodulation,[status(thm)],[f1000,f1370]) ).

fof(f2770,plain,
    ! [X0,X1,X2] : mult(X0,mult(rd(X1,X1),X1)) = mult(mult(rd(X0,X2),X2),X1),
    inference(paramodulation,[status(thm)],[f18,f1371]) ).

fof(f2771,plain,
    ! [X0,X1,X2] : mult(X0,X1) = mult(mult(rd(X0,X2),X2),X1),
    inference(forward_demodulation,[status(thm)],[f18,f2770]) ).

fof(f2866,plain,
    mult(x3,x5) != mult(x3,x5),
    inference(backward_demodulation,[status(thm)],[f2771,f17]) ).

fof(f2867,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f2866]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP683-11 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n027.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 Apr 30 00:55:17 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 2.23/0.63  % Refutation found
% 2.23/0.63  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.23/0.63  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.23/0.64  % Elapsed time: 0.297314 seconds
% 2.23/0.64  % CPU time: 2.264335 seconds
% 2.23/0.64  % Total memory used: 60.946 MB
% 2.23/0.64  % Net memory used: 58.462 MB
%------------------------------------------------------------------------------