%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LDA007-3 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:58:26 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 : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(a1,plain,
! [A,B,C] : $equal(f(f(A,B),f(A,C)),f(A,f(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),
[] ).
cnf(147345552,plain,
$equal(f(f(A,B),f(A,C)),f(A,f(B,C))),
inference(rewrite,[status(thm)],[a1]),
[] ).
fof(prove_equation,plain,
~ $equal(f(tt_ts,tk),f(t,tsk)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),
[] ).
cnf(147374304,plain,
~ $equal(f(tt_ts,tk),f(t,tsk)),
inference(rewrite,[status(thm)],[prove_equation]),
[] ).
fof(clause_3,plain,
$equal(f(tt,ts),tt_ts),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),
[] ).
cnf(147357688,plain,
$equal(f(tt,ts),tt_ts),
inference(rewrite,[status(thm)],[clause_3]),
[] ).
cnf(155182008,plain,
~ $equal(f(f(tt,ts),tk),f(t,tsk)),
inference(paramodulation,[status(thm)],[147374304,147357688,theory(equality)]),
[] ).
fof(clause_1,plain,
$equal(f(t,t),tt),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),
[] ).
cnf(147349736,plain,
$equal(f(t,t),tt),
inference(rewrite,[status(thm)],[clause_1]),
[] ).
cnf(155254984,plain,
~ $equal(f(f(f(t,t),ts),tk),f(t,tsk)),
inference(paramodulation,[status(thm)],[155182008,147349736,theory(equality)]),
[] ).
fof(clause_2,plain,
$equal(f(t,s),ts),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),
[] ).
cnf(147353776,plain,
$equal(f(t,s),ts),
inference(rewrite,[status(thm)],[clause_2]),
[] ).
cnf(155464360,plain,
~ $equal(f(f(f(t,t),f(t,s)),tk),f(t,tsk)),
inference(paramodulation,[status(thm)],[155254984,147353776,theory(equality)]),
[] ).
cnf(156156720,plain,
~ $equal(f(f(t,f(t,s)),tk),f(t,tsk)),
inference(paramodulation,[status(thm)],[155464360,147345552,theory(equality)]),
[] ).
cnf(156307256,plain,
~ $equal(f(f(t,ts),tk),f(t,tsk)),
inference(paramodulation,[status(thm)],[156156720,147353776,theory(equality)]),
[] ).
fof(clause_4,plain,
$equal(f(t,k),tk),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),
[] ).
cnf(147365656,plain,
$equal(f(t,k),tk),
inference(rewrite,[status(thm)],[clause_4]),
[] ).
cnf(156362656,plain,
~ $equal(f(f(t,ts),f(t,k)),f(t,tsk)),
inference(paramodulation,[status(thm)],[156307256,147365656,theory(equality)]),
[] ).
fof(clause_5,plain,
$equal(f(ts,k),tsk),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),
[] ).
cnf(147369632,plain,
$equal(f(ts,k),tsk),
inference(rewrite,[status(thm)],[clause_5]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[147345552,156362656,147369632,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(a1,plain,($equal(f(f(A,B),f(A,C)),f(A,f(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),[]).
%
% cnf(147345552,plain,($equal(f(f(A,B),f(A,C)),f(A,f(B,C)))),inference(rewrite,[status(thm)],[a1]),[]).
%
% fof(prove_equation,plain,(~$equal(f(tt_ts,tk),f(t,tsk))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),[]).
%
% cnf(147374304,plain,(~$equal(f(tt_ts,tk),f(t,tsk))),inference(rewrite,[status(thm)],[prove_equation]),[]).
%
% fof(clause_3,plain,($equal(f(tt,ts),tt_ts)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),[]).
%
% cnf(147357688,plain,($equal(f(tt,ts),tt_ts)),inference(rewrite,[status(thm)],[clause_3]),[]).
%
% cnf(155182008,plain,(~$equal(f(f(tt,ts),tk),f(t,tsk))),inference(paramodulation,[status(thm)],[147374304,147357688,theory(equality)]),[]).
%
% fof(clause_1,plain,($equal(f(t,t),tt)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),[]).
%
% cnf(147349736,plain,($equal(f(t,t),tt)),inference(rewrite,[status(thm)],[clause_1]),[]).
%
% cnf(155254984,plain,(~$equal(f(f(f(t,t),ts),tk),f(t,tsk))),inference(paramodulation,[status(thm)],[155182008,147349736,theory(equality)]),[]).
%
% fof(clause_2,plain,($equal(f(t,s),ts)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),[]).
%
% cnf(147353776,plain,($equal(f(t,s),ts)),inference(rewrite,[status(thm)],[clause_2]),[]).
%
% cnf(155464360,plain,(~$equal(f(f(f(t,t),f(t,s)),tk),f(t,tsk))),inference(paramodulation,[status(thm)],[155254984,147353776,theory(equality)]),[]).
%
% cnf(156156720,plain,(~$equal(f(f(t,f(t,s)),tk),f(t,tsk))),inference(paramodulation,[status(thm)],[155464360,147345552,theory(equality)]),[]).
%
% cnf(156307256,plain,(~$equal(f(f(t,ts),tk),f(t,tsk))),inference(paramodulation,[status(thm)],[156156720,147353776,theory(equality)]),[]).
%
% fof(clause_4,plain,($equal(f(t,k),tk)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),[]).
%
% cnf(147365656,plain,($equal(f(t,k),tk)),inference(rewrite,[status(thm)],[clause_4]),[]).
%
% cnf(156362656,plain,(~$equal(f(f(t,ts),f(t,k)),f(t,tsk))),inference(paramodulation,[status(thm)],[156307256,147365656,theory(equality)]),[]).
%
% fof(clause_5,plain,($equal(f(ts,k),tsk)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LDA/LDA007-3.tptp',unknown),[]).
%
% cnf(147369632,plain,($equal(f(ts,k),tsk)),inference(rewrite,[status(thm)],[clause_5]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[147345552,156362656,147369632,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------