TSTP Solution File: GRP748+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP748+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 20:21:32 EDT 2024

% Result   : Theorem 15.23s 2.33s
% Output   : CNFRefutation 15.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   40 (  28 unt;   0 def)
%            Number of atoms       :   62 (  61 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   34 (  12   ~;  16   |;   6   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;  13 con; 0-2 aty)
%            Number of variables   :   94 (  82   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [B,A] : ld(A,mult(A,B)) = B,
    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(f6,axiom,
    ! [A] : mult(unit,A) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [B,A] : mult(mult(A,B),i(B)) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A] : mult(A,i(A)) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A] : mult(i(A),A) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [B,A] :
      ( mult(A,B) = mult(B,A)
      | mult(i(A),mult(A,B)) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ( ! [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)
    | ! [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)
    | ! [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)
    | ! [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ( ! [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)
      | ! [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)
      | ! [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)
      | ! [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f15,plain,
    ! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f17,plain,
    ! [X0,X1] : rd(mult(X0,X1),X1) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f19,plain,
    ! [X0] : mult(unit,X0) = X0,
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f20,plain,
    ! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(mult(X1,X2),X1)),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f21,plain,
    ! [X0,X1] : mult(mult(X0,X1),i(X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f22,plain,
    ! [X0] : mult(X0,i(X0)) = unit,
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f23,plain,
    ! [X0] : mult(i(X0),X0) = unit,
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( mult(X0,X1) = mult(X1,X0)
      | mult(i(X0),mult(X0,X1)) = X1 ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f25,plain,
    ( ? [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) != mult(mult(mult(X2,X0),X2),X1)
    & ? [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) != mult(mult(mult(X3,X5),X4),X5)
    & ? [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) != mult(mult(X8,mult(X6,X7)),X8)
    & ? [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) != mult(X11,mult(mult(X9,X10),X11)) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f26,plain,
    ( mult(sk0_2,mult(sk0_0,mult(sk0_2,sk0_1))) != mult(mult(mult(sk0_2,sk0_0),sk0_2),sk0_1)
    & mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(mult(mult(sk0_3,sk0_5),sk0_4),sk0_5)
    & mult(mult(sk0_8,sk0_6),mult(sk0_7,sk0_8)) != mult(mult(sk0_8,mult(sk0_6,sk0_7)),sk0_8)
    & mult(mult(sk0_11,sk0_9),mult(sk0_10,sk0_11)) != mult(sk0_11,mult(mult(sk0_9,sk0_10),sk0_11)) ),
    inference(skolemization,[status(esa)],[f25]) ).

fof(f28,plain,
    mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(mult(mult(sk0_3,sk0_5),sk0_4),sk0_5),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f31,plain,
    mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(sk0_3,mult(mult(sk0_5,sk0_4),sk0_5)),
    inference(backward_demodulation,[status(thm)],[f20,f28]) ).

fof(f1043,plain,
    ! [X0,X1] : mult(mult(unit,X0),X1) = mult(i(X1),mult(mult(X1,X0),X1)),
    inference(paramodulation,[status(thm)],[f23,f20]) ).

fof(f1044,plain,
    ! [X0,X1] : mult(X0,X1) = mult(i(X1),mult(mult(X1,X0),X1)),
    inference(forward_demodulation,[status(thm)],[f19,f1043]) ).

fof(f1058,plain,
    ! [X0,X1] : mult(X0,i(i(X1))) = mult(X0,X1),
    inference(paramodulation,[status(thm)],[f21,f21]) ).

fof(f1059,plain,
    ! [X0] : mult(unit,i(i(X0))) = X0,
    inference(paramodulation,[status(thm)],[f22,f21]) ).

fof(f1060,plain,
    ! [X0] : i(i(X0)) = X0,
    inference(forward_demodulation,[status(thm)],[f19,f1059]) ).

fof(f1136,plain,
    ! [X0,X1] : mult(mult(X0,i(X1)),X1) = X0,
    inference(paramodulation,[status(thm)],[f1060,f21]) ).

fof(f1210,plain,
    ! [X0,X1] : rd(X0,X1) = mult(X0,i(X1)),
    inference(paramodulation,[status(thm)],[f1136,f17]) ).

fof(f1385,plain,
    ! [X0,X1] : rd(X0,i(X1)) = mult(X0,X1),
    inference(forward_demodulation,[status(thm)],[f1210,f1058]) ).

fof(f1870,plain,
    ! [X0,X1] :
      ( rd(mult(X0,X1),X0) = X1
      | mult(i(X0),mult(X0,X1)) = X1 ),
    inference(paramodulation,[status(thm)],[f24,f17]) ).

fof(f1907,plain,
    ! [X0,X1] :
      ( ld(i(X0),X1) = mult(X0,X1)
      | mult(X0,X1) = mult(X1,X0) ),
    inference(paramodulation,[status(thm)],[f24,f15]) ).

fof(f4566,plain,
    ! [X0,X1] :
      ( mult(mult(i(X0),X1),X0) = X1
      | mult(i(i(X0)),mult(i(X0),X1)) = X1 ),
    inference(paramodulation,[status(thm)],[f1385,f1870]) ).

fof(f4567,plain,
    ! [X0,X1] :
      ( mult(mult(i(X0),X1),X0) = X1
      | mult(X0,mult(i(X0),X1)) = X1 ),
    inference(forward_demodulation,[status(thm)],[f1060,f4566]) ).

fof(f13057,plain,
    ! [X0,X1] :
      ( mult(X0,mult(i(X0),X1)) = X1
      | mult(X0,mult(i(X0),X1)) = X1
      | ld(i(X0),mult(i(X0),X1)) = mult(X0,mult(i(X0),X1)) ),
    inference(paramodulation,[status(thm)],[f1907,f4567]) ).

fof(f13058,plain,
    ! [X0,X1] :
      ( mult(X0,mult(i(X0),X1)) = X1
      | mult(X0,mult(i(X0),X1)) = X1
      | X1 = mult(X0,mult(i(X0),X1)) ),
    inference(forward_demodulation,[status(thm)],[f15,f13057]) ).

fof(f13059,plain,
    ! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
    inference(duplicate_literals_removal,[status(esa)],[f13058]) ).

fof(f13406,plain,
    ! [X0,X1] : mult(X0,mult(X1,X0)) = mult(mult(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f1044,f13059]) ).

fof(f15069,plain,
    mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))),
    inference(forward_demodulation,[status(thm)],[f13406,f31]) ).

fof(f15070,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f15069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP748+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Apr 30 00:29:55 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 15.23/2.33  % Refutation found
% 15.23/2.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 15.23/2.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.86/2.41  % Elapsed time: 2.046759 seconds
% 15.86/2.41  % CPU time: 15.865140 seconds
% 15.86/2.41  % Total memory used: 344.500 MB
% 15.86/2.41  % Net memory used: 342.772 MB
%------------------------------------------------------------------------------