TSTP Solution File: GEO002-4 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO002-4 : TPTP v3.4.2. Released v1.1.0.
% 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 11:51:49 EDT 2009
% Result : Unsatisfiable 2.0s
% Output : Refutation 2.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 28 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 84 ( 9 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(outer_pasch1,plain,
! [A,B,C,D,E] :
( ~ between(A,B,C)
| ~ between(D,C,E)
| between(A,outer_pasch(B,A,D,E,C),D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144614576,plain,
( ~ between(A,B,C)
| ~ between(D,C,E)
| between(A,outer_pasch(B,A,D,E,C),D) ),
inference(rewrite,[status(thm)],[outer_pasch1]),
[] ).
fof(transitivity_for_betweeness,plain,
! [A,B,C,D] :
( ~ between(A,B,C)
| ~ between(B,D,C)
| between(A,B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144592088,plain,
( ~ between(A,B,C)
| ~ between(B,D,C)
| between(A,B,D) ),
inference(rewrite,[status(thm)],[transitivity_for_betweeness]),
[] ).
fof(segment_construction1,plain,
! [A,B,C,D] : between(A,B,extension(A,B,C,D)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144641640,plain,
between(A,B,extension(A,B,C,D)),
inference(rewrite,[status(thm)],[segment_construction1]),
[] ).
cnf(152497152,plain,
( ~ between(B,C,extension(A,B,D,E))
| between(A,B,C) ),
inference(resolution,[status(thm)],[144592088,144641640]),
[] ).
fof(between_substitution3,plain,
! [A,B,C,D] :
( ~ equalish(A,B)
| ~ between(C,D,A)
| between(C,D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144654632,plain,
( ~ equalish(A,B)
| ~ between(C,D,A)
| between(C,D,B) ),
inference(rewrite,[status(thm)],[between_substitution3]),
[] ).
cnf(152511640,plain,
between(A,A,A),
inference(resolution,[status(thm)],[144592088,144641640]),
[] ).
cnf(153393960,plain,
( ~ equalish(A,B)
| between(A,A,B) ),
inference(resolution,[status(thm)],[144654632,152511640]),
[] ).
fof(identity_for_equidistance,plain,
! [A,B,C] :
( ~ equidistant(A,B,C,C)
| equalish(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144598632,plain,
( ~ equidistant(A,B,C,C)
| equalish(A,B) ),
inference(rewrite,[status(thm)],[identity_for_equidistance]),
[] ).
fof(segment_construction2,plain,
! [A,B,C,D] : equidistant(A,extension(B,A,C,D),C,D),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144646472,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(rewrite,[status(thm)],[segment_construction2]),
[] ).
cnf(152810008,plain,
equalish(A,extension(C,A,B,B)),
inference(resolution,[status(thm)],[144598632,144646472]),
[] ).
cnf(153609568,plain,
between(A,A,extension(C,A,B,B)),
inference(resolution,[status(thm)],[153393960,152810008]),
[] ).
cnf(154265824,plain,
between(A,B,B),
inference(resolution,[status(thm)],[152497152,153609568]),
[] ).
cnf(159017608,plain,
between(A,outer_pasch(B,A,A,B,B),A),
inference(resolution,[status(thm)],[144614576,154265824]),
[] ).
cnf(154435672,plain,
( ~ between(B,C,B)
| between(A,B,C) ),
inference(resolution,[status(thm)],[154265824,144592088]),
[] ).
fof(prove_a_between_a_and_b,plain,
~ between(a,a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144662568,plain,
~ between(a,a,b),
inference(rewrite,[status(thm)],[prove_a_between_a_and_b]),
[] ).
cnf(152456456,plain,
( ~ between(a,a,A)
| ~ between(a,b,A) ),
inference(resolution,[status(thm)],[144592088,144662568]),
[] ).
cnf(155457352,plain,
( ~ between(b,A,b)
| ~ between(a,a,A) ),
inference(resolution,[status(thm)],[154435672,152456456]),
[] ).
cnf(165380168,plain,
~ between(a,a,outer_pasch(A,b,b,A,A)),
inference(resolution,[status(thm)],[159017608,155457352]),
[] ).
fof(outer_pasch2,plain,
! [A,B,C,D,E] :
( ~ between(A,B,C)
| ~ between(D,C,E)
| between(E,B,outer_pasch(B,A,D,E,C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),
[] ).
cnf(144633344,plain,
( ~ between(A,B,C)
| ~ between(D,C,E)
| between(E,B,outer_pasch(B,A,D,E,C)) ),
inference(rewrite,[status(thm)],[outer_pasch2]),
[] ).
cnf(160852512,plain,
between(B,B,outer_pasch(B,A,A,B,B)),
inference(resolution,[status(thm)],[144633344,154265824]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[165380168,160852512]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(outer_pasch1,plain,(~between(A,B,C)|~between(D,C,E)|between(A,outer_pasch(B,A,D,E,C),D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144614576,plain,(~between(A,B,C)|~between(D,C,E)|between(A,outer_pasch(B,A,D,E,C),D)),inference(rewrite,[status(thm)],[outer_pasch1]),[]).
%
% fof(transitivity_for_betweeness,plain,(~between(A,B,C)|~between(B,D,C)|between(A,B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144592088,plain,(~between(A,B,C)|~between(B,D,C)|between(A,B,D)),inference(rewrite,[status(thm)],[transitivity_for_betweeness]),[]).
%
% fof(segment_construction1,plain,(between(A,B,extension(A,B,C,D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144641640,plain,(between(A,B,extension(A,B,C,D))),inference(rewrite,[status(thm)],[segment_construction1]),[]).
%
% cnf(152497152,plain,(~between(B,C,extension(A,B,D,E))|between(A,B,C)),inference(resolution,[status(thm)],[144592088,144641640]),[]).
%
% fof(between_substitution3,plain,(~equalish(A,B)|~between(C,D,A)|between(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144654632,plain,(~equalish(A,B)|~between(C,D,A)|between(C,D,B)),inference(rewrite,[status(thm)],[between_substitution3]),[]).
%
% cnf(152511640,plain,(between(A,A,A)),inference(resolution,[status(thm)],[144592088,144641640]),[]).
%
% cnf(153393960,plain,(~equalish(A,B)|between(A,A,B)),inference(resolution,[status(thm)],[144654632,152511640]),[]).
%
% fof(identity_for_equidistance,plain,(~equidistant(A,B,C,C)|equalish(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144598632,plain,(~equidistant(A,B,C,C)|equalish(A,B)),inference(rewrite,[status(thm)],[identity_for_equidistance]),[]).
%
% fof(segment_construction2,plain,(equidistant(A,extension(B,A,C,D),C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144646472,plain,(equidistant(A,extension(B,A,C,D),C,D)),inference(rewrite,[status(thm)],[segment_construction2]),[]).
%
% cnf(152810008,plain,(equalish(A,extension(C,A,B,B))),inference(resolution,[status(thm)],[144598632,144646472]),[]).
%
% cnf(153609568,plain,(between(A,A,extension(C,A,B,B))),inference(resolution,[status(thm)],[153393960,152810008]),[]).
%
% cnf(154265824,plain,(between(A,B,B)),inference(resolution,[status(thm)],[152497152,153609568]),[]).
%
% cnf(159017608,plain,(between(A,outer_pasch(B,A,A,B,B),A)),inference(resolution,[status(thm)],[144614576,154265824]),[]).
%
% cnf(154435672,plain,(~between(B,C,B)|between(A,B,C)),inference(resolution,[status(thm)],[154265824,144592088]),[]).
%
% fof(prove_a_between_a_and_b,plain,(~between(a,a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144662568,plain,(~between(a,a,b)),inference(rewrite,[status(thm)],[prove_a_between_a_and_b]),[]).
%
% cnf(152456456,plain,(~between(a,a,A)|~between(a,b,A)),inference(resolution,[status(thm)],[144592088,144662568]),[]).
%
% cnf(155457352,plain,(~between(b,A,b)|~between(a,a,A)),inference(resolution,[status(thm)],[154435672,152456456]),[]).
%
% cnf(165380168,plain,(~between(a,a,outer_pasch(A,b,b,A,A))),inference(resolution,[status(thm)],[159017608,155457352]),[]).
%
% fof(outer_pasch2,plain,(~between(A,B,C)|~between(D,C,E)|between(E,B,outer_pasch(B,A,D,E,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO002-4.tptp',unknown),[]).
%
% cnf(144633344,plain,(~between(A,B,C)|~between(D,C,E)|between(E,B,outer_pasch(B,A,D,E,C))),inference(rewrite,[status(thm)],[outer_pasch2]),[]).
%
% cnf(160852512,plain,(between(B,B,outer_pasch(B,A,A,B,B))),inference(resolution,[status(thm)],[144633344,154265824]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[165380168,160852512]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------