TSTP Solution File: LCL212-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL212-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 13:46:28 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 11 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_2,plain,
! [A,B] :
( theorem(A)
| ~ theorem(implies(B,A))
| ~ theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
[] ).
cnf(160369648,plain,
( theorem(A)
| ~ theorem(implies(B,A))
| ~ theorem(B) ),
inference(rewrite,[status(thm)],[rule_2]),
[] ).
fof(rule_1,plain,
! [A] :
( theorem(A)
| ~ axiom(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
[] ).
cnf(160350800,plain,
( theorem(A)
| ~ axiom(A) ),
inference(rewrite,[status(thm)],[rule_1]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
[] ).
cnf(160327600,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(168276328,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[160350800,160327600]),
[] ).
cnf(168629072,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[160369648,168276328]),
[] ).
fof(axiom_1_3,plain,
! [A,B] : axiom(implies(A,or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
[] ).
cnf(160323872,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(168175328,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[160350800,160323872]),
[] ).
cnf(168507000,plain,
( theorem(or(B,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[160369648,168175328]),
[] ).
cnf(170158184,plain,
( theorem(or(B,A))
| ~ theorem(B) ),
inference(resolution,[status(thm)],[168629072,168507000]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
[] ).
cnf(160344312,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(168338544,plain,
theorem(implies(A,implies(B,A))),
inference(paramodulation,[status(thm)],[168175328,160344312,theory(equality)]),
[] ).
cnf(168530640,plain,
( theorem(implies(B,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[160369648,168338544]),
[] ).
cnf(169081264,plain,
theorem(implies(A,implies(B,implies(C,B)))),
inference(resolution,[status(thm)],[168530640,168338544]),
[] ).
cnf(170753584,plain,
theorem(or(implies(B,implies(C,implies(D,C))),A)),
inference(resolution,[status(thm)],[170158184,169081264]),
[] ).
fof(prove_this,plain,
~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
[] ).
cnf(160378560,plain,
~ theorem(implies(not(p),implies(q,implies(implies(p,q),q)))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),
[] ).
cnf(160319648,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(168167408,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[160350800,160319648]),
[] ).
cnf(168188728,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[160369648,168167408]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[170753584,160378560,168188728]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
%
% cnf(160369648,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
%
% cnf(160350800,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
%
% cnf(160327600,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(168276328,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[160350800,160327600]),[]).
%
% cnf(168629072,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[160369648,168276328]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
%
% cnf(160323872,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(168175328,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[160350800,160323872]),[]).
%
% cnf(168507000,plain,(theorem(or(B,A))|~theorem(A)),inference(resolution,[status(thm)],[160369648,168175328]),[]).
%
% cnf(170158184,plain,(theorem(or(B,A))|~theorem(B)),inference(resolution,[status(thm)],[168629072,168507000]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
%
% cnf(160344312,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(168338544,plain,(theorem(implies(A,implies(B,A)))),inference(paramodulation,[status(thm)],[168175328,160344312,theory(equality)]),[]).
%
% cnf(168530640,plain,(theorem(implies(B,A))|~theorem(A)),inference(resolution,[status(thm)],[160369648,168338544]),[]).
%
% cnf(169081264,plain,(theorem(implies(A,implies(B,implies(C,B))))),inference(resolution,[status(thm)],[168530640,168338544]),[]).
%
% cnf(170753584,plain,(theorem(or(implies(B,implies(C,implies(D,C))),A))),inference(resolution,[status(thm)],[170158184,169081264]),[]).
%
% fof(prove_this,plain,(~theorem(implies(not(p),implies(q,implies(implies(p,q),q))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
%
% cnf(160378560,plain,(~theorem(implies(not(p),implies(q,implies(implies(p,q),q))))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL212-3.tptp',unknown),[]).
%
% cnf(160319648,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(168167408,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[160350800,160319648]),[]).
%
% cnf(168188728,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[160369648,168167408]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[170753584,160378560,168188728]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------