TSTP Solution File: LCL176-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL176-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 13:44:53 EDT 2009
% Result : Unsatisfiable 2.2s
% Output : Refutation 2.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 21 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 8 sgn 13 !; 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/LCL176-3.tptp',unknown),
[] ).
cnf(167319312,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/LCL176-3.tptp',unknown),
[] ).
cnf(167300496,plain,
( theorem(A)
| ~ axiom(A) ),
inference(rewrite,[status(thm)],[rule_1]),
[] ).
fof(axiom_1_3,plain,
! [A,B] : axiom(implies(A,or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),
[] ).
cnf(167273696,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(175153824,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[167300496,167273696]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),
[] ).
cnf(167294040,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(175491600,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[175153824,167294040,theory(equality)]),
[] ).
cnf(175775656,plain,
( theorem(A)
| ~ theorem(implies(or(not(B),or(C,B)),A)) ),
inference(resolution,[status(thm)],[167319312,175491600]),
[] ).
fof(axiom_1_5,plain,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),
[] ).
cnf(167281408,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(175322296,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[167300496,167281408]),
[] ).
cnf(213827608,plain,
theorem(or(B,or(not(A),A))),
inference(resolution,[status(thm)],[175775656,175322296]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),
[] ).
cnf(167277424,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(175379760,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[167300496,167277424]),
[] ).
cnf(175802808,plain,
( theorem(or(B,A))
| ~ theorem(or(A,B)) ),
inference(resolution,[status(thm)],[167319312,175379760]),
[] ).
cnf(175666416,plain,
( theorem(or(B,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[167319312,175153824]),
[] ).
cnf(179538768,plain,
( theorem(or(B,A))
| ~ theorem(B) ),
inference(resolution,[status(thm)],[175802808,175666416]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),
[] ).
cnf(167269504,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(175144328,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[167300496,167269504]),
[] ).
cnf(175168016,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[167319312,175144328]),
[] ).
cnf(180192440,plain,
( theorem(or(B,A))
| ~ theorem(or(B,B)) ),
inference(resolution,[status(thm)],[179538768,175168016]),
[] ).
fof(prove_this,plain,
~ theorem(implies(p,p)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),
[] ).
cnf(167328104,plain,
~ theorem(implies(p,p)),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(175410520,plain,
~ theorem(or(not(p),p)),
inference(paramodulation,[status(thm)],[167328104,167294040,theory(equality)]),
[] ).
cnf(175952552,plain,
~ theorem(or(or(not(p),p),or(not(p),p))),
inference(resolution,[status(thm)],[175168016,175410520]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[213827608,180192440,175952552]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167319312,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167300496,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167273696,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(175153824,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[167300496,167273696]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167294040,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(175491600,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[175153824,167294040,theory(equality)]),[]).
%
% cnf(175775656,plain,(theorem(A)|~theorem(implies(or(not(B),or(C,B)),A))),inference(resolution,[status(thm)],[167319312,175491600]),[]).
%
% fof(axiom_1_5,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167281408,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(175322296,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[167300496,167281408]),[]).
%
% cnf(213827608,plain,(theorem(or(B,or(not(A),A)))),inference(resolution,[status(thm)],[175775656,175322296]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167277424,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(175379760,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[167300496,167277424]),[]).
%
% cnf(175802808,plain,(theorem(or(B,A))|~theorem(or(A,B))),inference(resolution,[status(thm)],[167319312,175379760]),[]).
%
% cnf(175666416,plain,(theorem(or(B,A))|~theorem(A)),inference(resolution,[status(thm)],[167319312,175153824]),[]).
%
% cnf(179538768,plain,(theorem(or(B,A))|~theorem(B)),inference(resolution,[status(thm)],[175802808,175666416]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167269504,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(175144328,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[167300496,167269504]),[]).
%
% cnf(175168016,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[167319312,175144328]),[]).
%
% cnf(180192440,plain,(theorem(or(B,A))|~theorem(or(B,B))),inference(resolution,[status(thm)],[179538768,175168016]),[]).
%
% fof(prove_this,plain,(~theorem(implies(p,p))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL176-3.tptp',unknown),[]).
%
% cnf(167328104,plain,(~theorem(implies(p,p))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(175410520,plain,(~theorem(or(not(p),p))),inference(paramodulation,[status(thm)],[167328104,167294040,theory(equality)]),[]).
%
% cnf(175952552,plain,(~theorem(or(or(not(p),p),or(not(p),p)))),inference(resolution,[status(thm)],[175168016,175410520]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[213827608,180192440,175952552]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------