TSTP Solution File: GRP123-1.003 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP123-1.003 : TPTP v3.4.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory   : 1003MB
% OS       : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May  6 12:23:48 EDT 2009

% Result   : Unsatisfiable 31.6s
% Output   : Refutation 31.6s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   35 (  22 unt;   0 def)
%            Number of atoms       :   65 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   68 (  38   ~;  30   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   42 (   0 sgn  17   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_2,plain,
    group_element(e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169530264,plain,
    group_element(e_2),
    inference(rewrite,[status(thm)],[element_2]),
    [] ).

fof(element_3,plain,
    group_element(e_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169534040,plain,
    group_element(e_3),
    inference(rewrite,[status(thm)],[element_3]),
    [] ).

fof(product_total_function1,plain,
    ! [A,B] :
      ( ~ group_element(A)
      | ~ group_element(B)
      | product(A,B,e_1)
      | product(A,B,e_2)
      | product(A,B,e_3) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169572880,plain,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product(A,B,e_1)
    | product(A,B,e_2)
    | product(A,B,e_3) ),
    inference(rewrite,[status(thm)],[product_total_function1]),
    [] ).

fof(product_right_cancellation,plain,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(A,D,C)
      | equalish(B,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169589304,plain,
    ( ~ product(A,B,C)
    | ~ product(A,D,C)
    | equalish(B,D) ),
    inference(rewrite,[status(thm)],[product_right_cancellation]),
    [] ).

fof(product_idempotence,plain,
    ! [A] : product(A,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169597280,plain,
    product(A,A,A),
    inference(rewrite,[status(thm)],[product_idempotence]),
    [] ).

cnf(180482408,plain,
    ( ~ product(A,B,A)
    | equalish(A,B) ),
    inference(resolution,[status(thm)],[169589304,169597280]),
    [] ).

fof(e_3_is_not_e_2,plain,
    ~ equalish(e_3,e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169561384,plain,
    ~ equalish(e_3,e_2),
    inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
    [] ).

cnf(180559480,plain,
    ~ product(e_3,e_2,e_3),
    inference(resolution,[status(thm)],[180482408,169561384]),
    [] ).

cnf(180864776,plain,
    ( product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[169530264,169534040,169572880,180559480]),
    [] ).

fof(product_left_cancellation,plain,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(D,B,C)
      | equalish(A,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169592936,plain,
    ( ~ product(A,B,C)
    | ~ product(D,B,C)
    | equalish(A,D) ),
    inference(rewrite,[status(thm)],[product_left_cancellation]),
    [] ).

cnf(180615408,plain,
    ( ~ product(B,A,A)
    | equalish(A,B) ),
    inference(resolution,[status(thm)],[169592936,169597280]),
    [] ).

fof(e_2_is_not_e_3,plain,
    ~ equalish(e_2,e_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169549840,plain,
    ~ equalish(e_2,e_3),
    inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
    [] ).

cnf(180662528,plain,
    ~ product(e_3,e_2,e_2),
    inference(resolution,[status(thm)],[180615408,169549840]),
    [] ).

cnf(182383504,plain,
    product(e_3,e_2,e_1),
    inference(resolution,[status(thm)],[180864776,180662528]),
    [] ).

fof(e_2_is_not_e_1,plain,
    ~ equalish(e_2,e_1),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169546272,plain,
    ~ equalish(e_2,e_1),
    inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
    [] ).

cnf(180649184,plain,
    ~ product(e_1,e_2,e_2),
    inference(resolution,[status(thm)],[180615408,169546272]),
    [] ).

fof(e_1_is_not_e_2,plain,
    ~ equalish(e_1,e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169538560,plain,
    ~ equalish(e_1,e_2),
    inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
    [] ).

cnf(180494440,plain,
    ~ product(e_1,e_2,e_1),
    inference(resolution,[status(thm)],[180482408,169538560]),
    [] ).

fof(element_1,plain,
    group_element(e_1),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169526312,plain,
    group_element(e_1),
    inference(rewrite,[status(thm)],[element_1]),
    [] ).

fof(qg1_2,plain,
    ! [A,B,C,D,E,F] :
      ( ~ product(A,B,C)
      | ~ product(D,E,C)
      | ~ product(F,B,A)
      | ~ product(F,E,D)
      | equalish(B,E) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
    [] ).

cnf(169614200,plain,
    ( ~ product(A,B,C)
    | ~ product(D,E,C)
    | ~ product(F,B,A)
    | ~ product(F,E,D)
    | equalish(B,E) ),
    inference(rewrite,[status(thm)],[qg1_2]),
    [] ).

cnf(185622280,plain,
    ( ~ product(B,C,A)
    | ~ product(A,C,B)
    | equalish(A,C) ),
    inference(resolution,[status(thm)],[169614200,169597280]),
    [] ).

cnf(185638488,plain,
    ( ~ product(A,e_2,e_1)
    | ~ product(e_1,e_2,A) ),
    inference(resolution,[status(thm)],[185622280,169538560]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[182383504,180649184,180494440,169526312,169530264,185638488,169572880]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 31 seconds
% START OF PROOF SEQUENCE
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169530264,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
% 
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169534040,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
% 
% fof(product_total_function1,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169572880,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
% 
% fof(product_right_cancellation,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169589304,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
% 
% fof(product_idempotence,plain,(product(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169597280,plain,(product(A,A,A)),inference(rewrite,[status(thm)],[product_idempotence]),[]).
% 
% cnf(180482408,plain,(~product(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[169589304,169597280]),[]).
% 
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169561384,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
% 
% cnf(180559480,plain,(~product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[180482408,169561384]),[]).
% 
% cnf(180864776,plain,(product(e_3,e_2,e_1)|product(e_3,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169530264,169534040,169572880,180559480]),[]).
% 
% fof(product_left_cancellation,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169592936,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
% 
% cnf(180615408,plain,(~product(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[169592936,169597280]),[]).
% 
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169549840,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
% 
% cnf(180662528,plain,(~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[180615408,169549840]),[]).
% 
% cnf(182383504,plain,(product(e_3,e_2,e_1)),inference(resolution,[status(thm)],[180864776,180662528]),[]).
% 
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169546272,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
% 
% cnf(180649184,plain,(~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[180615408,169546272]),[]).
% 
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169538560,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
% 
% cnf(180494440,plain,(~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[180482408,169538560]),[]).
% 
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169526312,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
% 
% fof(qg1_2,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
% 
% cnf(169614200,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),inference(rewrite,[status(thm)],[qg1_2]),[]).
% 
% cnf(185622280,plain,(~product(B,C,A)|~product(A,C,B)|equalish(A,C)),inference(resolution,[status(thm)],[169614200,169597280]),[]).
% 
% cnf(185638488,plain,(~product(A,e_2,e_1)|~product(e_1,e_2,A)),inference(resolution,[status(thm)],[185622280,169538560]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182383504,180649184,180494440,169526312,169530264,185638488,169572880]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------