TSTP Solution File: GRP123-6.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP123-6.003 : 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 12:24:03 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 45 ( 25 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 82 ( 46 ~; 36 |; 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 : 59 ( 0 sgn 24 !; 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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167057648,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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167061424,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167120512,plain,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product1_left_cancellation]),
[] ).
fof(product1_idempotence,plain,
! [A] : product1(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),
[] ).
cnf(167128944,plain,
product1(A,A,A),
inference(rewrite,[status(thm)],[product1_idempotence]),
[] ).
cnf(175871944,plain,
( ~ product1(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[167120512,167128944]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),
[] ).
cnf(167085184,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(176105824,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[175871944,167085184]),
[] ).
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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167116880,plain,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product1_right_cancellation]),
[] ).
cnf(175830624,plain,
( ~ product1(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[167116880,167128944]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),
[] ).
cnf(167069928,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(176018464,plain,
~ product1(e_1,e_3,e_1),
inference(resolution,[status(thm)],[175830624,167069928]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),
[] ).
cnf(167053632,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167100328,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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167162520,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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167145320,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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167157608,plain,
product2(A,A,A),
inference(rewrite,[status(thm)],[product2_idempotence]),
[] ).
cnf(176138808,plain,
( ~ product2(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[167145320,167157608]),
[] ).
cnf(176159608,plain,
~ product2(e_1,e_1,e_3),
inference(resolution,[status(thm)],[176138808,167069928]),
[] ).
cnf(176438288,plain,
( ~ product1(e_1,e_3,A)
| ~ product1(A,e_3,e_1) ),
inference(resolution,[status(thm)],[167162520,176159608]),
[] ).
cnf(178058096,plain,
~ product1(e_2,e_3,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[176105824,176018464,167053632,167061424,167100328,176438288]),
[] ).
cnf(178290864,plain,
( product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167057648,167061424,178058096,167100328]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),
[] ).
cnf(167088832,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(175883880,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[175871944,167088832]),
[] ).
cnf(175838352,plain,
( ~ product1(A,B,A)
| equalish(B,A) ),
inference(resolution,[status(thm)],[167116880,167128944]),
[] ).
cnf(175846712,plain,
~ product1(e_2,e_3,e_2),
inference(resolution,[status(thm)],[175838352,167088832]),
[] ).
cnf(177624496,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167057648,167061424,167100328,175846712]),
[] ).
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/GRP123-6.003.tptp',unknown),
[] ).
cnf(167112584,plain,
( ~ product1(A,B,C)
| ~ product1(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product1_total_function2]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),
[] ).
cnf(167065944,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(175518720,plain,
( ~ product1(A,B,e_1)
| ~ product1(A,B,e_2) ),
inference(resolution,[status(thm)],[167112584,167065944]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[178290864,175883880,177624496,175518720]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167057648,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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167061424,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% 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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167120512,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product1_left_cancellation]),[]).
%
% fof(product1_idempotence,plain,(product1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167128944,plain,(product1(A,A,A)),inference(rewrite,[status(thm)],[product1_idempotence]),[]).
%
% cnf(175871944,plain,(~product1(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[167120512,167128944]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167085184,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(176105824,plain,(~product1(e_1,e_3,e_3)),inference(resolution,[status(thm)],[175871944,167085184]),[]).
%
% 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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167116880,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product1_right_cancellation]),[]).
%
% cnf(175830624,plain,(~product1(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[167116880,167128944]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167069928,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(176018464,plain,(~product1(e_1,e_3,e_1)),inference(resolution,[status(thm)],[175830624,167069928]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167053632,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% 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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167100328,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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167162520,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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167145320,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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167157608,plain,(product2(A,A,A)),inference(rewrite,[status(thm)],[product2_idempotence]),[]).
%
% cnf(176138808,plain,(~product2(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[167145320,167157608]),[]).
%
% cnf(176159608,plain,(~product2(e_1,e_1,e_3)),inference(resolution,[status(thm)],[176138808,167069928]),[]).
%
% cnf(176438288,plain,(~product1(e_1,e_3,A)|~product1(A,e_3,e_1)),inference(resolution,[status(thm)],[167162520,176159608]),[]).
%
% cnf(178058096,plain,(~product1(e_2,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[176105824,176018464,167053632,167061424,167100328,176438288]),[]).
%
% cnf(178290864,plain,(product1(e_2,e_3,e_2)|product1(e_2,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167057648,167061424,178058096,167100328]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167088832,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(175883880,plain,(~product1(e_2,e_3,e_3)),inference(resolution,[status(thm)],[175871944,167088832]),[]).
%
% cnf(175838352,plain,(~product1(A,B,A)|equalish(B,A)),inference(resolution,[status(thm)],[167116880,167128944]),[]).
%
% cnf(175846712,plain,(~product1(e_2,e_3,e_2)),inference(resolution,[status(thm)],[175838352,167088832]),[]).
%
% cnf(177624496,plain,(product1(e_2,e_3,e_1)|product1(e_2,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167057648,167061424,167100328,175846712]),[]).
%
% 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/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167112584,plain,(~product1(A,B,C)|~product1(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product1_total_function2]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-6.003.tptp',unknown),[]).
%
% cnf(167065944,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(175518720,plain,(~product1(A,B,e_1)|~product1(A,B,e_2)),inference(resolution,[status(thm)],[167112584,167065944]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[178290864,175883880,177624496,175518720]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------