TSTP Solution File: HEN012-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : HEN012-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 13:16:28 EDT 2009
% Result : Unsatisfiable 184.4s
% Output : Refutation 184.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 91 ( 47 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 5 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(quotient_less_equal,plain,
! [A,B] :
( ~ less_equal(A,B)
| quotient(A,B,zero) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),
[] ).
cnf(143233600,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/HEN012-1.tptp',unknown),
[] ).
cnf(143261880,plain,
less_equal(zero,A),
inference(rewrite,[status(thm)],[zero_is_smallest]),
[] ).
cnf(151071144,plain,
quotient(zero,A,zero),
inference(resolution,[status(thm)],[143233600,143261880]),
[] ).
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/HEN012-1.tptp',unknown),
[] ).
cnf(143271616,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/HEN012-1.tptp',unknown),
[] ).
cnf(143257504,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(158026496,plain,
( ~ less_equal(A,B)
| $equal(B,A)
| ~ quotient(C,D,E)
| ~ quotient(D,F,G)
| ~ quotient(C,F,H)
| ~ quotient(H,G,B)
| ~ quotient(E,F,A) ),
inference(resolution,[status(thm)],[143271616,143257504]),
[] ).
cnf(174221896,plain,
( ~ less_equal(A,B)
| $equal(B,A)
| ~ quotient(C,zero,D)
| ~ quotient(C,E,F)
| ~ quotient(F,zero,B)
| ~ quotient(D,E,A) ),
inference(resolution,[status(thm)],[158026496,151071144]),
[] ).
fof(closure,plain,
! [A,B] : quotient(A,B,divide(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),
[] ).
cnf(143284168,plain,
quotient(A,B,divide(A,B)),
inference(rewrite,[status(thm)],[closure]),
[] ).
cnf(176030104,plain,
( ~ less_equal(A,B)
| $equal(B,A)
| ~ quotient(C,D,E)
| ~ quotient(E,zero,B)
| ~ quotient(divide(C,zero),D,A) ),
inference(resolution,[status(thm)],[174221896,143284168]),
[] ).
cnf(176321080,plain,
( ~ less_equal(A,B)
| $equal(B,A)
| ~ quotient(divide(C,D),zero,B)
| ~ quotient(divide(C,zero),D,A) ),
inference(resolution,[status(thm)],[176030104,143284168]),
[] ).
cnf(176367048,plain,
( ~ less_equal(A,divide(divide(B,C),zero))
| $equal(divide(divide(B,C),zero),A)
| ~ quotient(divide(B,zero),C,A) ),
inference(resolution,[status(thm)],[176321080,143284168]),
[] ).
fof(divisor_existence,plain,
! [A,B,C] :
( ~ quotient(A,B,C)
| less_equal(C,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),
[] ).
cnf(143245832,plain,
( ~ quotient(A,B,C)
| less_equal(C,A) ),
inference(rewrite,[status(thm)],[divisor_existence]),
[] ).
cnf(151481232,plain,
less_equal(divide(A,B),A),
inference(resolution,[status(thm)],[143245832,143284168]),
[] ).
cnf(152285472,plain,
quotient(divide(A,B),A,zero),
inference(resolution,[status(thm)],[151481232,143233600]),
[] ).
cnf(176513600,plain,
$equal(divide(divide(A,A),zero),zero),
inference(forward_subsumption_resolution__resolution,[status(thm)],[143261880,176367048,152285472]),
[] ).
cnf(379503048,plain,
quotient(divide(A,A),zero,zero),
inference(paramodulation,[status(thm)],[176513600,143284168,theory(equality)]),
[] ).
fof(less_equal_quotient,plain,
! [A,B] :
( ~ quotient(A,B,zero)
| less_equal(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),
[] ).
cnf(143240208,plain,
( ~ quotient(A,B,zero)
| less_equal(A,B) ),
inference(rewrite,[status(thm)],[less_equal_quotient]),
[] ).
cnf(152321896,plain,
( ~ less_equal(B,A)
| $equal(B,A)
| ~ quotient(A,B,zero) ),
inference(resolution,[status(thm)],[143271616,143240208]),
[] ).
cnf(157667376,plain,
( $equal(B,A)
| ~ quotient(A,B,zero)
| ~ quotient(B,A,zero) ),
inference(resolution,[status(thm)],[152321896,143240208]),
[] ).
cnf(384001584,plain,
$equal(zero,divide(A,A)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[151071144,379503048,157667376]),
[] ).
cnf(385245400,plain,
quotient(A,A,zero),
inference(paramodulation,[status(thm)],[384001584,143284168,theory(equality)]),
[] ).
fof(prove_X_less_than_or_equal_to_X,plain,
~ less_equal(x,x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),
[] ).
cnf(143292896,plain,
~ less_equal(x,x),
inference(rewrite,[status(thm)],[prove_X_less_than_or_equal_to_X]),
[] ).
cnf(151156408,plain,
~ quotient(x,x,zero),
inference(resolution,[status(thm)],[143240208,143292896]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[385245400,151156408]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 184 seconds
% START OF PROOF SEQUENCE
% fof(quotient_less_equal,plain,(~less_equal(A,B)|quotient(A,B,zero)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143233600,plain,(~less_equal(A,B)|quotient(A,B,zero)),inference(rewrite,[status(thm)],[quotient_less_equal]),[]).
%
% fof(zero_is_smallest,plain,(less_equal(zero,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143261880,plain,(less_equal(zero,A)),inference(rewrite,[status(thm)],[zero_is_smallest]),[]).
%
% cnf(151071144,plain,(quotient(zero,A,zero)),inference(resolution,[status(thm)],[143233600,143261880]),[]).
%
% fof(less_equal_and_equal,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143271616,plain,(~less_equal(A,B)|~less_equal(B,A)|$equal(B,A)),inference(rewrite,[status(thm)],[less_equal_and_equal]),[]).
%
% fof(quotient_property,plain,(~quotient(A,B,C)|~quotient(B,D,E)|~quotient(A,D,F)|~quotient(F,E,G)|~quotient(C,D,H)|less_equal(G,H)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143257504,plain,(~quotient(A,B,C)|~quotient(B,D,E)|~quotient(A,D,F)|~quotient(F,E,G)|~quotient(C,D,H)|less_equal(G,H)),inference(rewrite,[status(thm)],[quotient_property]),[]).
%
% cnf(158026496,plain,(~less_equal(A,B)|$equal(B,A)|~quotient(C,D,E)|~quotient(D,F,G)|~quotient(C,F,H)|~quotient(H,G,B)|~quotient(E,F,A)),inference(resolution,[status(thm)],[143271616,143257504]),[]).
%
% cnf(174221896,plain,(~less_equal(A,B)|$equal(B,A)|~quotient(C,zero,D)|~quotient(C,E,F)|~quotient(F,zero,B)|~quotient(D,E,A)),inference(resolution,[status(thm)],[158026496,151071144]),[]).
%
% fof(closure,plain,(quotient(A,B,divide(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143284168,plain,(quotient(A,B,divide(A,B))),inference(rewrite,[status(thm)],[closure]),[]).
%
% cnf(176030104,plain,(~less_equal(A,B)|$equal(B,A)|~quotient(C,D,E)|~quotient(E,zero,B)|~quotient(divide(C,zero),D,A)),inference(resolution,[status(thm)],[174221896,143284168]),[]).
%
% cnf(176321080,plain,(~less_equal(A,B)|$equal(B,A)|~quotient(divide(C,D),zero,B)|~quotient(divide(C,zero),D,A)),inference(resolution,[status(thm)],[176030104,143284168]),[]).
%
% cnf(176367048,plain,(~less_equal(A,divide(divide(B,C),zero))|$equal(divide(divide(B,C),zero),A)|~quotient(divide(B,zero),C,A)),inference(resolution,[status(thm)],[176321080,143284168]),[]).
%
% fof(divisor_existence,plain,(~quotient(A,B,C)|less_equal(C,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143245832,plain,(~quotient(A,B,C)|less_equal(C,A)),inference(rewrite,[status(thm)],[divisor_existence]),[]).
%
% cnf(151481232,plain,(less_equal(divide(A,B),A)),inference(resolution,[status(thm)],[143245832,143284168]),[]).
%
% cnf(152285472,plain,(quotient(divide(A,B),A,zero)),inference(resolution,[status(thm)],[151481232,143233600]),[]).
%
% cnf(176513600,plain,($equal(divide(divide(A,A),zero),zero)),inference(forward_subsumption_resolution__resolution,[status(thm)],[143261880,176367048,152285472]),[]).
%
% cnf(379503048,plain,(quotient(divide(A,A),zero,zero)),inference(paramodulation,[status(thm)],[176513600,143284168,theory(equality)]),[]).
%
% fof(less_equal_quotient,plain,(~quotient(A,B,zero)|less_equal(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143240208,plain,(~quotient(A,B,zero)|less_equal(A,B)),inference(rewrite,[status(thm)],[less_equal_quotient]),[]).
%
% cnf(152321896,plain,(~less_equal(B,A)|$equal(B,A)|~quotient(A,B,zero)),inference(resolution,[status(thm)],[143271616,143240208]),[]).
%
% cnf(157667376,plain,($equal(B,A)|~quotient(A,B,zero)|~quotient(B,A,zero)),inference(resolution,[status(thm)],[152321896,143240208]),[]).
%
% cnf(384001584,plain,($equal(zero,divide(A,A))),inference(forward_subsumption_resolution__resolution,[status(thm)],[151071144,379503048,157667376]),[]).
%
% cnf(385245400,plain,(quotient(A,A,zero)),inference(paramodulation,[status(thm)],[384001584,143284168,theory(equality)]),[]).
%
% fof(prove_X_less_than_or_equal_to_X,plain,(~less_equal(x,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/HEN/HEN012-1.tptp',unknown),[]).
%
% cnf(143292896,plain,(~less_equal(x,x)),inference(rewrite,[status(thm)],[prove_X_less_than_or_equal_to_X]),[]).
%
% cnf(151156408,plain,(~quotient(x,x,zero)),inference(resolution,[status(thm)],[143240208,143292896]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[385245400,151156408]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------