## TSTP Solution File: GRP125-1.003 by Faust---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : GRP125-1.003 : TPTP v3.4.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.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 12:25:50 EDT 2009

% Result   : Unsatisfiable 0.2s
% Output   : Refutation 0.2s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   39 (  21 unt;   0 def)
%            Number of atoms       :   71 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   73 (  41   ~;  32   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   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   :   47 (   0 sgn  19   !;   0   ?)

%------------------------------------------------------------------------------
%----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/GRP125-1.003.tptp',unknown),
[] ).

cnf(142453752,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/GRP125-1.003.tptp',unknown),
[] ).

cnf(142457704,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).

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/GRP125-1.003.tptp',unknown),
[] ).

cnf(142524464,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).

fof(product_idempotence,plain,
! [A] : product(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),
[] ).

cnf(142528808,plain,
product(A,A,A),
inference(rewrite,[status(thm)],[product_idempotence]),
[] ).

cnf(150886400,plain,
( ~ product(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[142524464,142528808]),
[] ).

fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),
[] ).

cnf(142473712,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).

cnf(150915176,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[150886400,142473712]),
[] ).

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/GRP125-1.003.tptp',unknown),
[] ).

cnf(142504408,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/GRP125-1.003.tptp',unknown),
[] ).

cnf(142520832,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).

cnf(150790176,plain,
( ~ product(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[142520832,142528808]),
[] ).

fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),
[] ).

cnf(142466000,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).

cnf(150802072,plain,
~ product(e_1,e_2,e_1),
inference(resolution,[status(thm)],[150790176,142466000]),
[] ).

cnf(152839088,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[142453752,142457704,142504408,150802072]),
[] ).

fof(qg3,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),
[] ).

cnf(142537760,plain,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
inference(rewrite,[status(thm)],[qg3]),
[] ).

fof(product_total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),
[] ).

cnf(142516600,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).

cnf(150652728,plain,
( ~ product(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[142516600,142528808]),
[] ).

fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),
[] ).

cnf(142481088,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).

cnf(150750048,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[150652728,142481088]),
[] ).

cnf(151082400,plain,
( ~ product(e_1,A,e_3)
| ~ product(A,e_1,e_3) ),
inference(resolution,[status(thm)],[142537760,150750048]),
[] ).

cnf(154747032,plain,
~ product(e_2,e_1,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[150915176,152839088,151082400]),
[] ).

cnf(154958088,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[142453752,142457704,154747032,142504408]),
[] ).

cnf(150898312,plain,
~ product(e_2,e_1,e_1),
inference(resolution,[status(thm)],[150886400,142466000]),
[] ).

cnf(150818936,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[150790176,142473712]),
[] ).

cnf(152849752,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[142453752,142457704,142504408,150818936]),
[] ).

fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),
[] ).

cnf(142488824,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).

cnf(150596232,plain,
( ~ product(A,B,e_3)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[142516600,142488824]),
[] ).

\$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[154958088,150898312,152849752,150596232]),
[] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142453752,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/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142457704,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% 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/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142524464,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% fof(product_idempotence,plain,(product(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142528808,plain,(product(A,A,A)),inference(rewrite,[status(thm)],[product_idempotence]),[]).
%
% cnf(150886400,plain,(~product(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[142524464,142528808]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142473712,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(150915176,plain,(~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[150886400,142473712]),[]).
%
% 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/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142504408,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/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142520832,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(150790176,plain,(~product(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[142520832,142528808]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142466000,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(150802072,plain,(~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[150790176,142466000]),[]).
%
% cnf(152839088,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[142453752,142457704,142504408,150802072]),[]).
%
% fof(qg3,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142537760,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,A)),inference(rewrite,[status(thm)],[qg3]),[]).
%
% fof(product_total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142516600,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(150652728,plain,(~product(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[142516600,142528808]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142481088,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(150750048,plain,(~product(e_3,e_3,e_1)),inference(resolution,[status(thm)],[150652728,142481088]),[]).
%
% cnf(151082400,plain,(~product(e_1,A,e_3)|~product(A,e_1,e_3)),inference(resolution,[status(thm)],[142537760,150750048]),[]).
%
% cnf(154747032,plain,(~product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[150915176,152839088,151082400]),[]).
%
% cnf(154958088,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[142453752,142457704,154747032,142504408]),[]).
%
% cnf(150898312,plain,(~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[150886400,142466000]),[]).
%
% cnf(150818936,plain,(~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[150790176,142473712]),[]).
%
% cnf(152849752,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[142453752,142457704,142504408,150818936]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-1.003.tptp',unknown),[]).
%
% cnf(142488824,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(150596232,plain,(~product(A,B,e_3)|~product(A,B,e_2)),inference(resolution,[status(thm)],[142516600,142488824]),[]).
%