TSTP Solution File: GRP123-7.003 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP123-7.003 : TPTP v3.4.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art08.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 12:24:06 EDT 2009

% Result   : Unsatisfiable 0.5s
% Output   : Refutation 0.5s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   49 (  26 unt;   0 def)
%            Number of atoms       :   90 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   94 (  53   ~;  41   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   68 (   0 sgn  28   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_1,plain,
    group_element(e_1),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168050560,plain,
    group_element(e_1),
    inference(rewrite,[status(thm)],[element_1]),
    [] ).

fof(element_2,plain,
    group_element(e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168054656,plain,
    group_element(e_2),
    inference(rewrite,[status(thm)],[element_2]),
    [] ).

fof(product1_right_cancellation,plain,
    ! [A,B,C,D] :
      ( ~ product1(A,B,C)
      | ~ product1(A,D,C)
      | equalish(B,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(167997824,plain,
    ( ~ product1(A,B,C)
    | ~ product1(A,D,C)
    | equalish(B,D) ),
    inference(rewrite,[status(thm)],[product1_right_cancellation]),
    [] ).

fof(product1_idempotence,plain,
    ! [A] : product1(A,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168125488,plain,
    product1(A,A,A),
    inference(rewrite,[status(thm)],[product1_idempotence]),
    [] ).

cnf(176952192,plain,
    ( ~ product1(A,B,A)
    | equalish(A,B) ),
    inference(resolution,[status(thm)],[167997824,168125488]),
    [] ).

fof(e_3_is_not_e_2,plain,
    ~ equalish(e_3,e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168085912,plain,
    ~ equalish(e_3,e_2),
    inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
    [] ).

cnf(177029264,plain,
    ~ product1(e_3,e_2,e_3),
    inference(resolution,[status(thm)],[176952192,168085912]),
    [] ).

fof(product1_left_cancellation,plain,
    ! [A,B,C,D] :
      ( ~ product1(A,B,C)
      | ~ product1(D,B,C)
      | equalish(A,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168121136,plain,
    ( ~ product1(A,B,C)
    | ~ product1(D,B,C)
    | equalish(A,D) ),
    inference(rewrite,[status(thm)],[product1_left_cancellation]),
    [] ).

cnf(177060192,plain,
    ( ~ product1(B,A,A)
    | equalish(A,B) ),
    inference(resolution,[status(thm)],[168121136,168125488]),
    [] ).

fof(e_2_is_not_e_3,plain,
    ~ equalish(e_2,e_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168078456,plain,
    ~ equalish(e_2,e_3),
    inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
    [] ).

cnf(177099640,plain,
    ~ product1(e_3,e_2,e_2),
    inference(resolution,[status(thm)],[177060192,168078456]),
    [] ).

fof(element_3,plain,
    group_element(e_3),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168058352,plain,
    group_element(e_3),
    inference(rewrite,[status(thm)],[element_3]),
    [] ).

fof(product1_total_function1,plain,
    ! [A,B] :
      ( ~ group_element(A)
      | ~ group_element(B)
      | product1(A,B,e_1)
      | product1(A,B,e_2)
      | product1(A,B,e_3) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168097376,plain,
    ( ~ group_element(A)
    | ~ group_element(B)
    | product1(A,B,e_1)
    | product1(A,B,e_2)
    | product1(A,B,e_3) ),
    inference(rewrite,[status(thm)],[product1_total_function1]),
    [] ).

fof(qg1a,plain,
    ! [A,B,C,D] :
      ( ~ product1(A,B,C)
      | ~ product1(C,B,D)
      | product2(D,A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168163480,plain,
    ( ~ product1(A,B,C)
    | ~ product1(C,B,D)
    | product2(D,A,B) ),
    inference(rewrite,[status(thm)],[qg1a]),
    [] ).

fof(product2_total_function2,plain,
    ! [A,B,C,D] :
      ( ~ product2(A,B,C)
      | ~ product2(A,B,D)
      | equalish(C,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168142088,plain,
    ( ~ product2(A,B,C)
    | ~ product2(A,B,D)
    | equalish(C,D) ),
    inference(rewrite,[status(thm)],[product2_total_function2]),
    [] ).

fof(product2_idempotence,plain,
    ! [A] : product2(A,A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168158448,plain,
    product2(A,A,A),
    inference(rewrite,[status(thm)],[product2_idempotence]),
    [] ).

cnf(176564712,plain,
    ( ~ product2(A,A,B)
    | equalish(A,B) ),
    inference(resolution,[status(thm)],[168142088,168158448]),
    [] ).

cnf(177200944,plain,
    ~ product2(e_3,e_3,e_2),
    inference(resolution,[status(thm)],[176564712,168085912]),
    [] ).

cnf(177510792,plain,
    ( ~ product1(e_3,e_2,A)
    | ~ product1(A,e_2,e_3) ),
    inference(resolution,[status(thm)],[168163480,177200944]),
    [] ).

cnf(179320928,plain,
    ~ product1(e_1,e_2,e_3),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[177029264,177099640,168054656,168058352,168097376,177510792]),
    [] ).

cnf(183186552,plain,
    ( product1(e_1,e_2,e_1)
    | product1(e_1,e_2,e_2) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[168050560,168054656,179320928,168097376]),
    [] ).

fof(e_1_is_not_e_2,plain,
    ~ equalish(e_1,e_2),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(167998136,plain,
    ~ equalish(e_1,e_2),
    inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
    [] ).

cnf(176964256,plain,
    ~ product1(e_1,e_2,e_1),
    inference(resolution,[status(thm)],[176952192,167998136]),
    [] ).

fof(product2_right_cancellation,plain,
    ! [A,B,C,D] :
      ( ~ product2(A,B,C)
      | ~ product2(A,D,C)
      | equalish(B,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168150472,plain,
    ( ~ product2(A,B,C)
    | ~ product2(A,D,C)
    | equalish(B,D) ),
    inference(rewrite,[status(thm)],[product2_right_cancellation]),
    [] ).

cnf(176617928,plain,
    ( ~ product2(A,B,A)
    | equalish(A,B) ),
    inference(resolution,[status(thm)],[168150472,168158448]),
    [] ).

fof(e_2_is_not_e_1,plain,
    ~ equalish(e_2,e_1),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168074888,plain,
    ~ equalish(e_2,e_1),
    inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
    [] ).

cnf(176629808,plain,
    ~ product2(e_2,e_1,e_2),
    inference(resolution,[status(thm)],[176617928,168074888]),
    [] ).

cnf(176711768,plain,
    ( ~ product1(e_1,e_2,A)
    | ~ product1(A,e_2,e_2) ),
    inference(resolution,[status(thm)],[168163480,176629808]),
    [] ).

cnf(176720488,plain,
    ~ product1(e_1,e_2,e_2),
    inference(resolution,[status(thm)],[176711768,168125488]),
    [] ).

cnf(176765640,plain,
    ( product1(e_1,e_2,e_1)
    | product1(e_1,e_2,e_3) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[168050560,168054656,168097376,176720488]),
    [] ).

fof(product1_total_function2,plain,
    ! [A,B,C,D] :
      ( ~ product1(A,B,C)
      | ~ product1(A,B,D)
      | equalish(C,D) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),
    [] ).

cnf(168108928,plain,
    ( ~ product1(A,B,C)
    | ~ product1(A,B,D)
    | equalish(C,D) ),
    inference(rewrite,[status(thm)],[product1_total_function2]),
    [] ).

cnf(176823192,plain,
    ( ~ product1(A,B,e_2)
    | ~ product1(A,B,e_3) ),
    inference(resolution,[status(thm)],[168108928,168078456]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[183186552,176964256,176765640,176823192]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168050560,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
% 
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168054656,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
% 
% fof(product1_right_cancellation,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(167997824,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product1_right_cancellation]),[]).
% 
% fof(product1_idempotence,plain,(product1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168125488,plain,(product1(A,A,A)),inference(rewrite,[status(thm)],[product1_idempotence]),[]).
% 
% cnf(176952192,plain,(~product1(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[167997824,168125488]),[]).
% 
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168085912,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
% 
% cnf(177029264,plain,(~product1(e_3,e_2,e_3)),inference(resolution,[status(thm)],[176952192,168085912]),[]).
% 
% fof(product1_left_cancellation,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168121136,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product1_left_cancellation]),[]).
% 
% cnf(177060192,plain,(~product1(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[168121136,168125488]),[]).
% 
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168078456,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
% 
% cnf(177099640,plain,(~product1(e_3,e_2,e_2)),inference(resolution,[status(thm)],[177060192,168078456]),[]).
% 
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168058352,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
% 
% fof(product1_total_function1,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168097376,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)),inference(rewrite,[status(thm)],[product1_total_function1]),[]).
% 
% fof(qg1a,plain,(~product1(A,B,C)|~product1(C,B,D)|product2(D,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168163480,plain,(~product1(A,B,C)|~product1(C,B,D)|product2(D,A,B)),inference(rewrite,[status(thm)],[qg1a]),[]).
% 
% fof(product2_total_function2,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168142088,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product2_total_function2]),[]).
% 
% fof(product2_idempotence,plain,(product2(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168158448,plain,(product2(A,A,A)),inference(rewrite,[status(thm)],[product2_idempotence]),[]).
% 
% cnf(176564712,plain,(~product2(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[168142088,168158448]),[]).
% 
% cnf(177200944,plain,(~product2(e_3,e_3,e_2)),inference(resolution,[status(thm)],[176564712,168085912]),[]).
% 
% cnf(177510792,plain,(~product1(e_3,e_2,A)|~product1(A,e_2,e_3)),inference(resolution,[status(thm)],[168163480,177200944]),[]).
% 
% cnf(179320928,plain,(~product1(e_1,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177029264,177099640,168054656,168058352,168097376,177510792]),[]).
% 
% cnf(183186552,plain,(product1(e_1,e_2,e_1)|product1(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168050560,168054656,179320928,168097376]),[]).
% 
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(167998136,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
% 
% cnf(176964256,plain,(~product1(e_1,e_2,e_1)),inference(resolution,[status(thm)],[176952192,167998136]),[]).
% 
% fof(product2_right_cancellation,plain,(~product2(A,B,C)|~product2(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168150472,plain,(~product2(A,B,C)|~product2(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product2_right_cancellation]),[]).
% 
% cnf(176617928,plain,(~product2(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[168150472,168158448]),[]).
% 
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168074888,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
% 
% cnf(176629808,plain,(~product2(e_2,e_1,e_2)),inference(resolution,[status(thm)],[176617928,168074888]),[]).
% 
% cnf(176711768,plain,(~product1(e_1,e_2,A)|~product1(A,e_2,e_2)),inference(resolution,[status(thm)],[168163480,176629808]),[]).
% 
% cnf(176720488,plain,(~product1(e_1,e_2,e_2)),inference(resolution,[status(thm)],[176711768,168125488]),[]).
% 
% cnf(176765640,plain,(product1(e_1,e_2,e_1)|product1(e_1,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168050560,168054656,168097376,176720488]),[]).
% 
% fof(product1_total_function2,plain,(~product1(A,B,C)|~product1(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-7.003.tptp',unknown),[]).
% 
% cnf(168108928,plain,(~product1(A,B,C)|~product1(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product1_total_function2]),[]).
% 
% cnf(176823192,plain,(~product1(A,B,e_2)|~product1(A,B,e_3)),inference(resolution,[status(thm)],[168108928,168078456]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[183186552,176964256,176765640,176823192]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------