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
%
%------------------------------------------------------------------------------