TSTP Solution File: ALG011-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ALG011-1 : TPTP v3.4.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 10:57:22 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(conjecture_1,plain,
! [A,B] :
( d(f(A,B))
| ~ c(A)
| ~ c(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),
[] ).
cnf(160557568,plain,
( d(f(A,B))
| ~ c(A)
| ~ c(B) ),
inference(rewrite,[status(thm)],[conjecture_1]),
[] ).
fof(partition_c_not_empty,plain,
c(a1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),
[] ).
cnf(160541408,plain,
c(a1),
inference(rewrite,[status(thm)],[partition_c_not_empty]),
[] ).
cnf(170974144,plain,
( d(f(a1,A))
| ~ c(A) ),
inference(resolution,[status(thm)],[160557568,160541408]),
[] ).
fof(conjecture_2,plain,
! [A,B] :
( c(f(A,B))
| ~ d(A)
| ~ d(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),
[] ).
cnf(160564840,plain,
( c(f(A,B))
| ~ d(A)
| ~ d(B) ),
inference(rewrite,[status(thm)],[conjecture_2]),
[] ).
fof(partition_d_not_empty,plain,
d(a2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),
[] ).
cnf(160546040,plain,
d(a2),
inference(rewrite,[status(thm)],[partition_d_not_empty]),
[] ).
cnf(171034832,plain,
c(f(a2,a2)),
inference(resolution,[status(thm)],[160564840,160546040]),
[] ).
cnf(171156960,plain,
d(f(a1,f(a2,a2))),
inference(resolution,[status(thm)],[170974144,171034832]),
[] ).
fof(f_is_associative,plain,
! [A,B,C] : $equal(f(f(A,B),C),f(A,f(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),
[] ).
cnf(160524536,plain,
$equal(f(f(A,B),C),f(A,f(B,C))),
inference(rewrite,[status(thm)],[f_is_associative]),
[] ).
cnf(172323720,plain,
d(f(f(a1,a2),a2)),
inference(paramodulation,[status(thm)],[171156960,160524536,theory(equality)]),
[] ).
fof(partitions_union,plain,
! [A] :
( c(A)
| d(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),
[] ).
cnf(160531088,plain,
( c(A)
| d(A) ),
inference(rewrite,[status(thm)],[partitions_union]),
[] ).
cnf(171723040,plain,
( d(f(a1,A))
| d(A) ),
inference(resolution,[status(thm)],[170974144,160531088]),
[] ).
fof(partitions_exclusive,plain,
! [A] :
( ~ c(A)
| ~ d(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),
[] ).
cnf(160537648,plain,
( ~ c(A)
| ~ d(A) ),
inference(rewrite,[status(thm)],[partitions_exclusive]),
[] ).
cnf(171858176,plain,
( d(A)
| ~ c(f(a1,A)) ),
inference(resolution,[status(thm)],[171723040,160537648]),
[] ).
cnf(170986856,plain,
d(f(a1,a1)),
inference(resolution,[status(thm)],[160557568,160541408]),
[] ).
cnf(171081248,plain,
( c(f(f(a1,a1),A))
| ~ d(A) ),
inference(resolution,[status(thm)],[160564840,170986856]),
[] ).
cnf(171129928,plain,
c(f(f(a1,a1),a2)),
inference(resolution,[status(thm)],[171081248,160546040]),
[] ).
cnf(172922496,plain,
c(f(a1,f(a1,a2))),
inference(paramodulation,[status(thm)],[171129928,160524536,theory(equality)]),
[] ).
cnf(174534120,plain,
d(f(a1,a2)),
inference(resolution,[status(thm)],[171858176,172922496]),
[] ).
cnf(171049296,plain,
( c(f(A,a2))
| ~ d(A) ),
inference(resolution,[status(thm)],[160564840,160546040]),
[] ).
cnf(174573472,plain,
c(f(f(a1,a2),a2)),
inference(resolution,[status(thm)],[174534120,171049296]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[172323720,174573472,160537648]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(conjecture_1,plain,(d(f(A,B))|~c(A)|~c(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),[]).
%
% cnf(160557568,plain,(d(f(A,B))|~c(A)|~c(B)),inference(rewrite,[status(thm)],[conjecture_1]),[]).
%
% fof(partition_c_not_empty,plain,(c(a1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),[]).
%
% cnf(160541408,plain,(c(a1)),inference(rewrite,[status(thm)],[partition_c_not_empty]),[]).
%
% cnf(170974144,plain,(d(f(a1,A))|~c(A)),inference(resolution,[status(thm)],[160557568,160541408]),[]).
%
% fof(conjecture_2,plain,(c(f(A,B))|~d(A)|~d(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),[]).
%
% cnf(160564840,plain,(c(f(A,B))|~d(A)|~d(B)),inference(rewrite,[status(thm)],[conjecture_2]),[]).
%
% fof(partition_d_not_empty,plain,(d(a2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),[]).
%
% cnf(160546040,plain,(d(a2)),inference(rewrite,[status(thm)],[partition_d_not_empty]),[]).
%
% cnf(171034832,plain,(c(f(a2,a2))),inference(resolution,[status(thm)],[160564840,160546040]),[]).
%
% cnf(171156960,plain,(d(f(a1,f(a2,a2)))),inference(resolution,[status(thm)],[170974144,171034832]),[]).
%
% fof(f_is_associative,plain,($equal(f(f(A,B),C),f(A,f(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),[]).
%
% cnf(160524536,plain,($equal(f(f(A,B),C),f(A,f(B,C)))),inference(rewrite,[status(thm)],[f_is_associative]),[]).
%
% cnf(172323720,plain,(d(f(f(a1,a2),a2))),inference(paramodulation,[status(thm)],[171156960,160524536,theory(equality)]),[]).
%
% fof(partitions_union,plain,(c(A)|d(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),[]).
%
% cnf(160531088,plain,(c(A)|d(A)),inference(rewrite,[status(thm)],[partitions_union]),[]).
%
% cnf(171723040,plain,(d(f(a1,A))|d(A)),inference(resolution,[status(thm)],[170974144,160531088]),[]).
%
% fof(partitions_exclusive,plain,(~c(A)|~d(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ALG/ALG011-1.tptp',unknown),[]).
%
% cnf(160537648,plain,(~c(A)|~d(A)),inference(rewrite,[status(thm)],[partitions_exclusive]),[]).
%
% cnf(171858176,plain,(d(A)|~c(f(a1,A))),inference(resolution,[status(thm)],[171723040,160537648]),[]).
%
% cnf(170986856,plain,(d(f(a1,a1))),inference(resolution,[status(thm)],[160557568,160541408]),[]).
%
% cnf(171081248,plain,(c(f(f(a1,a1),A))|~d(A)),inference(resolution,[status(thm)],[160564840,170986856]),[]).
%
% cnf(171129928,plain,(c(f(f(a1,a1),a2))),inference(resolution,[status(thm)],[171081248,160546040]),[]).
%
% cnf(172922496,plain,(c(f(a1,f(a1,a2)))),inference(paramodulation,[status(thm)],[171129928,160524536,theory(equality)]),[]).
%
% cnf(174534120,plain,(d(f(a1,a2))),inference(resolution,[status(thm)],[171858176,172922496]),[]).
%
% cnf(171049296,plain,(c(f(A,a2))|~d(A)),inference(resolution,[status(thm)],[160564840,160546040]),[]).
%
% cnf(174573472,plain,(c(f(f(a1,a2),a2))),inference(resolution,[status(thm)],[174534120,171049296]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[172323720,174573472,160537648]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------