TSTP Solution File: HEN008-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN008-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:15:48 EDT 2009
% Result : Unsatisfiable 42.4s
% Output : Refutation 42.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 41 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(closure,plain,
! [A,B] : quotient(A,B,divide(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163625728,plain,
quotient(A,B,divide(A,B)),
inference(rewrite,[status(thm)],[closure]),
[] ).
fof(quotient_less_equal,plain,
! [A,B] :
( ~ less_equal(A,B)
| quotient(A,B,zero) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163570464,plain,
( ~ less_equal(A,B)
| quotient(A,B,zero) ),
inference(rewrite,[status(thm)],[quotient_less_equal]),
[] ).
fof(zero_is_smallest,plain,
! [A] : less_equal(zero,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163603216,plain,
less_equal(zero,A),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(171443976,plain,
quotient(zero,A,zero),
inference(resolution,[status(thm)],[163570464,163603216]),
[] ).
fof(less_equal_and_equal,plain,
! [A,B] :
( ~ less_equal(A,B)
| ~ less_equal(B,A)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163617168,plain,
( ~ less_equal(A,B)
| ~ less_equal(B,A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[less_equal_and_equal]),
[] ).
fof(quotient_property,plain,
! [A,B,C,D,E,F,G,H] :
( ~ quotient(A,B,C)
| ~ quotient(B,D,E)
| ~ quotient(A,D,F)
| ~ quotient(F,E,G)
| ~ quotient(C,D,H)
| less_equal(G,H) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163598712,plain,
( ~ quotient(A,B,C)
| ~ quotient(B,D,E)
| ~ quotient(A,D,F)
| ~ quotient(F,E,G)
| ~ quotient(C,D,H)
| less_equal(G,H) ),
inference(rewrite,[status(thm)],[quotient_property]),
[] ).
cnf(179643968,plain,
( ~ less_equal(B,A)
| $equal(B,A)
| ~ quotient(C,D,E)
| ~ quotient(D,F,G)
| ~ quotient(C,F,H)
| ~ quotient(H,G,A)
| ~ quotient(E,F,B) ),
inference(resolution,[status(thm)],[163617168,163598712]),
[] ).
fof(aQc,plain,
quotient(a,c,aqc),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163642720,plain,
quotient(a,c,aqc),
inference(rewrite,[status(thm)],[aQc]),
[] ).
cnf(192888520,plain,
( ~ less_equal(B,A)
| $equal(B,A)
| ~ quotient(a,C,D)
| ~ quotient(C,c,E)
| ~ quotient(aqc,E,A)
| ~ quotient(D,c,B) ),
inference(resolution,[status(thm)],[179643968,163642720]),
[] ).
fof(bQc,plain,
quotient(b,c,bqc),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163646640,plain,
quotient(b,c,bqc),
inference(rewrite,[status(thm)],[bQc]),
[] ).
cnf(209834496,plain,
( ~ less_equal(B,A)
| $equal(B,A)
| ~ quotient(a,b,C)
| ~ quotient(aqc,bqc,A)
| ~ quotient(C,c,B) ),
inference(resolution,[status(thm)],[192888520,163646640]),
[] ).
fof(aLEb,plain,
less_equal(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163634712,plain,
less_equal(a,b),
inference(rewrite,[status(thm)],[aLEb]),
[] ).
cnf(172864272,plain,
quotient(a,b,zero),
inference(resolution,[status(thm)],[163570464,163634712]),
[] ).
cnf(210243912,plain,
( ~ less_equal(B,A)
| $equal(B,A)
| ~ quotient(aqc,bqc,A)
| ~ quotient(zero,c,B) ),
inference(resolution,[status(thm)],[209834496,172864272]),
[] ).
cnf(210455768,plain,
( ~ less_equal(A,divide(aqc,bqc))
| $equal(A,divide(aqc,bqc))
| ~ quotient(zero,c,A) ),
inference(resolution,[status(thm)],[210243912,163625728]),
[] ).
cnf(210495280,plain,
$equal(zero,divide(aqc,bqc)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[171443976,210455768,163603216]),
[] ).
fof(less_equal_quotient,plain,
! [A,B] :
( ~ quotient(A,B,zero)
| less_equal(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163577200,plain,
( ~ quotient(A,B,zero)
| less_equal(A,B) ),
inference(rewrite,[status(thm)],[less_equal_quotient]),
[] ).
fof(prove_aQcLEbQc,plain,
~ less_equal(aqc,bqc),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),
[] ).
cnf(163650464,plain,
~ less_equal(aqc,bqc),
inference(rewrite,[status(thm)],[prove_aQcLEbQc]),
[] ).
cnf(172881064,plain,
~ quotient(aqc,bqc,zero),
inference(resolution,[status(thm)],[163577200,163650464]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[163625728,210495280,172881064,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 42 seconds
% START OF PROOF SEQUENCE
% fof(closure,plain,(quotient(A,B,divide(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163625728,plain,(quotient(A,B,divide(A,B))),inference(rewrite,[status(thm)],[closure]),[]).
%
% fof(quotient_less_equal,plain,(~less_equal(A,B)|quotient(A,B,zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163570464,plain,(~less_equal(A,B)|quotient(A,B,zero)),inference(rewrite,[status(thm)],[quotient_less_equal]),[]).
%
% fof(zero_is_smallest,plain,(less_equal(zero,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163603216,plain,(less_equal(zero,A)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(171443976,plain,(quotient(zero,A,zero)),inference(resolution,[status(thm)],[163570464,163603216]),[]).
%
% fof(less_equal_and_equal,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163617168,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[less_equal_and_equal]),[]).
%
% fof(quotient_property,plain,(~quotient(A,B,C)|~quotient(B,D,E)|~quotient(A,D,F)|~quotient(F,E,G)|~quotient(C,D,H)|less_equal(G,H)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163598712,plain,(~quotient(A,B,C)|~quotient(B,D,E)|~quotient(A,D,F)|~quotient(F,E,G)|~quotient(C,D,H)|less_equal(G,H)),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(179643968,plain,(~less_equal(B,A)|$equal(B,A)|~quotient(C,D,E)|~quotient(D,F,G)|~quotient(C,F,H)|~quotient(H,G,A)|~quotient(E,F,B)),inference(resolution,[status(thm)],[163617168,163598712]),[]).
%
% fof(aQc,plain,(quotient(a,c,aqc)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163642720,plain,(quotient(a,c,aqc)),inference(rewrite,[status(thm)],[aQc]),[]).
%
% cnf(192888520,plain,(~less_equal(B,A)|$equal(B,A)|~quotient(a,C,D)|~quotient(C,c,E)|~quotient(aqc,E,A)|~quotient(D,c,B)),inference(resolution,[status(thm)],[179643968,163642720]),[]).
%
% fof(bQc,plain,(quotient(b,c,bqc)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163646640,plain,(quotient(b,c,bqc)),inference(rewrite,[status(thm)],[bQc]),[]).
%
% cnf(209834496,plain,(~less_equal(B,A)|$equal(B,A)|~quotient(a,b,C)|~quotient(aqc,bqc,A)|~quotient(C,c,B)),inference(resolution,[status(thm)],[192888520,163646640]),[]).
%
% fof(aLEb,plain,(less_equal(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163634712,plain,(less_equal(a,b)),inference(rewrite,[status(thm)],[aLEb]),[]).
%
% cnf(172864272,plain,(quotient(a,b,zero)),inference(resolution,[status(thm)],[163570464,163634712]),[]).
%
% cnf(210243912,plain,(~less_equal(B,A)|$equal(B,A)|~quotient(aqc,bqc,A)|~quotient(zero,c,B)),inference(resolution,[status(thm)],[209834496,172864272]),[]).
%
% cnf(210455768,plain,(~less_equal(A,divide(aqc,bqc))|$equal(A,divide(aqc,bqc))|~quotient(zero,c,A)),inference(resolution,[status(thm)],[210243912,163625728]),[]).
%
% cnf(210495280,plain,($equal(zero,divide(aqc,bqc))),inference(forward_subsumption_resolution__resolution,[status(thm)],[171443976,210455768,163603216]),[]).
%
% fof(less_equal_quotient,plain,(~quotient(A,B,zero)|less_equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163577200,plain,(~quotient(A,B,zero)|less_equal(A,B)),inference(rewrite,[status(thm)],[less_equal_quotient]),[]).
%
% fof(prove_aQcLEbQc,plain,(~less_equal(aqc,bqc)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN008-1.tptp',unknown),[]).
%
% cnf(163650464,plain,(~less_equal(aqc,bqc)),inference(rewrite,[status(thm)],[prove_aQcLEbQc]),[]).
%
% cnf(172881064,plain,(~quotient(aqc,bqc,zero)),inference(resolution,[status(thm)],[163577200,163650464]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[163625728,210495280,172881064,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------