%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP123-8.003 : 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 12:24:09 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 46 ( 27 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 83 ( 48 ~; 35 |; 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 : 58 ( 0 sgn 24 !; 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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168237240,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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168096992,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168286608,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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168349856,plain,
( ~ product1(A,B,C)
| ~ product1(C,B,D)
| product2(D,A,B) ),
inference(rewrite,[status(thm)],[qg1a]),
[] ).
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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168332472,plain,
( ~ product2(A,B,C)
| ~ product2(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product2_right_cancellation]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),
[] ).
cnf(168253640,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(177304184,plain,
( ~ product2(A,e_1,B)
| ~ product2(A,e_2,B) ),
inference(resolution,[status(thm)],[168332472,168253640]),
[] ).
fof(product2_idempotence,plain,
! [A] : product2(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),
[] ).
cnf(168340616,plain,
product2(A,A,A),
inference(rewrite,[status(thm)],[product2_idempotence]),
[] ).
cnf(177429568,plain,
~ product2(e_1,e_2,e_1),
inference(resolution,[status(thm)],[177304184,168340616]),
[] ).
cnf(177479112,plain,
( ~ product1(e_2,e_1,A)
| ~ product1(A,e_1,e_1) ),
inference(resolution,[status(thm)],[168349856,177429568]),
[] ).
fof(product1_idempotence,plain,
! [A] : product1(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),
[] ).
cnf(168307296,plain,
product1(A,A,A),
inference(rewrite,[status(thm)],[product1_idempotence]),
[] ).
cnf(177487816,plain,
~ product1(e_2,e_1,e_1),
inference(resolution,[status(thm)],[177479112,168307296]),
[] ).
cnf(185018648,plain,
( product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168237240,168096992,168286608,177487816]),
[] ).
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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168299320,plain,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product1_right_cancellation]),
[] ).
cnf(178293000,plain,
( ~ product1(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[168299320,168307296]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),
[] ).
cnf(168261672,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(178321864,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[178293000,168261672]),
[] ).
cnf(186008640,plain,
product1(e_2,e_1,e_3),
inference(resolution,[status(thm)],[185018648,178321864]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),
[] ).
cnf(168269048,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(178344472,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[178293000,168269048]),
[] ).
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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168302952,plain,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product1_left_cancellation]),
[] ).
cnf(178403024,plain,
( ~ product1(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[168302952,168307296]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),
[] ).
cnf(168257896,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(178411048,plain,
~ product1(e_3,e_1,e_1),
inference(resolution,[status(thm)],[178403024,168257896]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),
[] ).
cnf(168249184,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
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/GRP123-8.003.tptp',unknown),
[] ).
cnf(168328112,plain,
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product2_total_function2]),
[] ).
cnf(178510496,plain,
( ~ product2(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[168328112,168340616]),
[] ).
cnf(178548952,plain,
~ product2(e_3,e_3,e_1),
inference(resolution,[status(thm)],[178510496,168269048]),
[] ).
cnf(179071184,plain,
( ~ product1(e_3,e_1,A)
| ~ product1(A,e_1,e_3) ),
inference(resolution,[status(thm)],[168349856,178548952]),
[] ).
cnf(185366760,plain,
~ product1(e_2,e_1,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[178344472,178411048,168237240,168249184,168286608,179071184]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[186008640,185366760]),
[] ).
%------------------------------------------------------------------------------
%----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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168237240,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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168096992,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% 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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168286608,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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168349856,plain,(~product1(A,B,C)|~product1(C,B,D)|product2(D,A,B)),inference(rewrite,[status(thm)],[qg1a]),[]).
%
% 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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168332472,plain,(~product2(A,B,C)|~product2(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product2_right_cancellation]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168253640,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(177304184,plain,(~product2(A,e_1,B)|~product2(A,e_2,B)),inference(resolution,[status(thm)],[168332472,168253640]),[]).
%
% fof(product2_idempotence,plain,(product2(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168340616,plain,(product2(A,A,A)),inference(rewrite,[status(thm)],[product2_idempotence]),[]).
%
% cnf(177429568,plain,(~product2(e_1,e_2,e_1)),inference(resolution,[status(thm)],[177304184,168340616]),[]).
%
% cnf(177479112,plain,(~product1(e_2,e_1,A)|~product1(A,e_1,e_1)),inference(resolution,[status(thm)],[168349856,177429568]),[]).
%
% fof(product1_idempotence,plain,(product1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168307296,plain,(product1(A,A,A)),inference(rewrite,[status(thm)],[product1_idempotence]),[]).
%
% cnf(177487816,plain,(~product1(e_2,e_1,e_1)),inference(resolution,[status(thm)],[177479112,168307296]),[]).
%
% cnf(185018648,plain,(product1(e_2,e_1,e_2)|product1(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168237240,168096992,168286608,177487816]),[]).
%
% 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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168299320,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product1_right_cancellation]),[]).
%
% cnf(178293000,plain,(~product1(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[168299320,168307296]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168261672,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(178321864,plain,(~product1(e_2,e_1,e_2)),inference(resolution,[status(thm)],[178293000,168261672]),[]).
%
% cnf(186008640,plain,(product1(e_2,e_1,e_3)),inference(resolution,[status(thm)],[185018648,178321864]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168269048,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(178344472,plain,(~product1(e_3,e_1,e_3)),inference(resolution,[status(thm)],[178293000,168269048]),[]).
%
% 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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168302952,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product1_left_cancellation]),[]).
%
% cnf(178403024,plain,(~product1(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[168302952,168307296]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168257896,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(178411048,plain,(~product1(e_3,e_1,e_1)),inference(resolution,[status(thm)],[178403024,168257896]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168249184,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% 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/GRP123-8.003.tptp',unknown),[]).
%
% cnf(168328112,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product2_total_function2]),[]).
%
% cnf(178510496,plain,(~product2(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[168328112,168340616]),[]).
%
% cnf(178548952,plain,(~product2(e_3,e_3,e_1)),inference(resolution,[status(thm)],[178510496,168269048]),[]).
%
% cnf(179071184,plain,(~product1(e_3,e_1,A)|~product1(A,e_1,e_3)),inference(resolution,[status(thm)],[168349856,178548952]),[]).
%
% cnf(185366760,plain,(~product1(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[178344472,178411048,168237240,168249184,168286608,179071184]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[186008640,185366760]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------