%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM022-1 : 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 14:50:46 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 3 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(transitivity,plain,
! [A,B,C] :
( ~ equalish(A,B)
| ~ equalish(C,A)
| equalish(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142913120,plain,
( ~ equalish(A,B)
| ~ equalish(C,A)
| equalish(C,B) ),
inference(rewrite,[status(thm)],[transitivity]),
[] ).
fof(transitivity_of_less,plain,
! [A,B,C] :
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142853376,plain,
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ),
inference(rewrite,[status(thm)],[transitivity_of_less]),
[] ).
fof(a_less_than_b,plain,
less(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142917752,plain,
less(a,b),
inference(rewrite,[status(thm)],[a_less_than_b]),
[] ).
cnf(150764000,plain,
( ~ less(b,A)
| less(a,A) ),
inference(resolution,[status(thm)],[142853376,142917752]),
[] ).
fof(prove_a_less_than_d,plain,
~ less(a,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142847384,plain,
~ less(a,d),
inference(rewrite,[status(thm)],[prove_a_less_than_d]),
[] ).
cnf(150837392,plain,
~ less(b,d),
inference(resolution,[status(thm)],[150764000,142847384]),
[] ).
fof(divides_only_less_or_equal,plain,
! [A,B] :
( ~ divides(A,B)
| less(A,B)
| equalish(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142896088,plain,
( ~ divides(A,B)
| less(A,B)
| equalish(A,B) ),
inference(rewrite,[status(thm)],[divides_only_less_or_equal]),
[] ).
fof(b_divides_d,plain,
divides(b,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142926624,plain,
divides(b,d),
inference(rewrite,[status(thm)],[b_divides_d]),
[] ).
cnf(150802624,plain,
( less(b,d)
| equalish(b,d) ),
inference(resolution,[status(thm)],[142896088,142926624]),
[] ).
cnf(151199952,plain,
equalish(b,d),
inference(resolution,[status(thm)],[150837392,150802624]),
[] ).
cnf(151421648,plain,
( ~ equalish(A,b)
| equalish(A,d) ),
inference(resolution,[status(thm)],[142913120,151199952]),
[] ).
fof(smaller_number,plain,
! [A,B,C] :
( ~ equalish(add(successor(A),B),C)
| less(B,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142860000,plain,
( ~ equalish(add(successor(A),B),C)
| less(B,C) ),
inference(rewrite,[status(thm)],[smaller_number]),
[] ).
cnf(150827792,plain,
~ equalish(add(successor(A),a),d),
inference(resolution,[status(thm)],[142860000,142847384]),
[] ).
cnf(151687432,plain,
~ equalish(add(successor(A),a),b),
inference(resolution,[status(thm)],[151421648,150827792]),
[] ).
fof(less_lemma,plain,
! [A,B] :
( ~ less(A,B)
| equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),
[] ).
cnf(142883848,plain,
( ~ less(A,B)
| equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ),
inference(rewrite,[status(thm)],[less_lemma]),
[] ).
cnf(150789656,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b),
inference(resolution,[status(thm)],[142883848,142917752]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[151687432,150789656]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(transitivity,plain,(~equalish(A,B)|~equalish(C,A)|equalish(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142913120,plain,(~equalish(A,B)|~equalish(C,A)|equalish(C,B)),inference(rewrite,[status(thm)],[transitivity]),[]).
%
% fof(transitivity_of_less,plain,(~less(A,B)|~less(C,A)|less(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142853376,plain,(~less(A,B)|~less(C,A)|less(C,B)),inference(rewrite,[status(thm)],[transitivity_of_less]),[]).
%
% fof(a_less_than_b,plain,(less(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142917752,plain,(less(a,b)),inference(rewrite,[status(thm)],[a_less_than_b]),[]).
%
% cnf(150764000,plain,(~less(b,A)|less(a,A)),inference(resolution,[status(thm)],[142853376,142917752]),[]).
%
% fof(prove_a_less_than_d,plain,(~less(a,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142847384,plain,(~less(a,d)),inference(rewrite,[status(thm)],[prove_a_less_than_d]),[]).
%
% cnf(150837392,plain,(~less(b,d)),inference(resolution,[status(thm)],[150764000,142847384]),[]).
%
% fof(divides_only_less_or_equal,plain,(~divides(A,B)|less(A,B)|equalish(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142896088,plain,(~divides(A,B)|less(A,B)|equalish(A,B)),inference(rewrite,[status(thm)],[divides_only_less_or_equal]),[]).
%
% fof(b_divides_d,plain,(divides(b,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142926624,plain,(divides(b,d)),inference(rewrite,[status(thm)],[b_divides_d]),[]).
%
% cnf(150802624,plain,(less(b,d)|equalish(b,d)),inference(resolution,[status(thm)],[142896088,142926624]),[]).
%
% cnf(151199952,plain,(equalish(b,d)),inference(resolution,[status(thm)],[150837392,150802624]),[]).
%
% cnf(151421648,plain,(~equalish(A,b)|equalish(A,d)),inference(resolution,[status(thm)],[142913120,151199952]),[]).
%
% fof(smaller_number,plain,(~equalish(add(successor(A),B),C)|less(B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142860000,plain,(~equalish(add(successor(A),B),C)|less(B,C)),inference(rewrite,[status(thm)],[smaller_number]),[]).
%
% cnf(150827792,plain,(~equalish(add(successor(A),a),d)),inference(resolution,[status(thm)],[142860000,142847384]),[]).
%
% cnf(151687432,plain,(~equalish(add(successor(A),a),b)),inference(resolution,[status(thm)],[151421648,150827792]),[]).
%
% fof(less_lemma,plain,(~less(A,B)|equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM022-1.tptp',unknown),[]).
%
% cnf(142883848,plain,(~less(A,B)|equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)),inference(rewrite,[status(thm)],[less_lemma]),[]).
%
% cnf(150789656,plain,(equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b)),inference(resolution,[status(thm)],[142883848,142917752]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[151687432,150789656]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------