TSTP Solution File: GEO032-3 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO032-3 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 11:53:14 EDT 2009
% Result : Unsatisfiable 2.1s
% Output : Refutation 2.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 31 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 40 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(u_to_w_equals_u1_to_w1,plain,
equidistant(u,w,u1,w1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163636568,plain,
equidistant(u,w,u1,w1),
inference(rewrite,[status(thm)],[u_to_w_equals_u1_to_w1]),
[] ).
fof(v_to_w_equals_v1_to_w1,plain,
~ equidistant(v,w,v1,w1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163907864,plain,
~ equidistant(v,w,v1,w1),
inference(rewrite,[status(thm)],[v_to_w_equals_v1_to_w1]),
[] ).
fof(u_to_v_equals_u1_to_v1,plain,
equidistant(u,v,u1,v1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163895936,plain,
equidistant(u,v,u1,v1),
inference(rewrite,[status(thm)],[u_to_v_equals_u1_to_v1]),
[] ).
fof(d12,plain,
! [A,B,C,D,E,F,G,H] :
( ~ equidistant(A,B,C,D)
| ~ equidistant(A,E,C,F)
| ~ equidistant(A,G,C,H)
| ~ equidistant(E,G,F,H)
| ~ between(A,B,E)
| ~ between(C,D,F)
| equidistant(B,G,D,H) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163884672,plain,
( ~ equidistant(A,B,C,D)
| ~ equidistant(A,E,C,F)
| ~ equidistant(A,G,C,H)
| ~ equidistant(E,G,F,H)
| ~ between(A,B,E)
| ~ between(C,D,F)
| equidistant(B,G,D,H) ),
inference(rewrite,[status(thm)],[d12]),
[] ).
fof(v1_between_u1_and_w1,plain,
between(u1,v1,w1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163892024,plain,
between(u1,v1,w1),
inference(rewrite,[status(thm)],[v1_between_u1_and_w1]),
[] ).
cnf(178548048,plain,
( ~ equidistant(A,B,u1,v1)
| ~ equidistant(A,C,u1,w1)
| ~ equidistant(A,D,u1,E)
| ~ equidistant(C,D,w1,E)
| ~ between(A,B,C)
| equidistant(B,D,v1,E) ),
inference(resolution,[status(thm)],[163884672,163892024]),
[] ).
fof(v_between_u_and_w,plain,
between(u,v,w),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163883536,plain,
between(u,v,w),
inference(rewrite,[status(thm)],[v_between_u_and_w]),
[] ).
cnf(180882968,plain,
( ~ equidistant(u,A,u1,B)
| ~ equidistant(w,A,w1,B)
| equidistant(v,A,v1,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[163895936,163636568,178548048,163883536]),
[] ).
cnf(190907224,plain,
~ equidistant(w,w,w1,w1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[163907864,180882968,163636568]),
[] ).
fof(d7,plain,
! [A,B] : equidistant(A,A,B,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163654368,plain,
equidistant(A,A,B,B),
inference(rewrite,[status(thm)],[d7]),
[] ).
cnf(177153144,plain,
( ~ equidistant(A,B,C,D)
| ~ equidistant(A,E,C,F)
| ~ between(A,B,E)
| ~ between(C,D,F)
| equidistant(B,E,D,F) ),
inference(resolution,[status(thm)],[163884672,163654368]),
[] ).
cnf(196077352,plain,
( ~ equidistant(u,A,u1,B)
| ~ between(u,w,A)
| ~ between(u1,w1,B)
| equidistant(w,A,w1,B) ),
inference(resolution,[status(thm)],[177153144,163636568]),
[] ).
fof(t3,plain,
! [A,B] : between(A,B,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),
[] ).
cnf(163718960,plain,
between(A,B,B),
inference(rewrite,[status(thm)],[t3]),
[] ).
cnf(196246960,plain,
( ~ equidistant(u,w,u1,A)
| ~ between(u1,w1,A)
| equidistant(w,w,w1,A) ),
inference(resolution,[status(thm)],[196077352,163718960]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[163636568,190907224,196246960,163718960]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(u_to_w_equals_u1_to_w1,plain,(equidistant(u,w,u1,w1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163636568,plain,(equidistant(u,w,u1,w1)),inference(rewrite,[status(thm)],[u_to_w_equals_u1_to_w1]),[]).
%
% fof(v_to_w_equals_v1_to_w1,plain,(~equidistant(v,w,v1,w1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163907864,plain,(~equidistant(v,w,v1,w1)),inference(rewrite,[status(thm)],[v_to_w_equals_v1_to_w1]),[]).
%
% fof(u_to_v_equals_u1_to_v1,plain,(equidistant(u,v,u1,v1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163895936,plain,(equidistant(u,v,u1,v1)),inference(rewrite,[status(thm)],[u_to_v_equals_u1_to_v1]),[]).
%
% fof(d12,plain,(~equidistant(A,B,C,D)|~equidistant(A,E,C,F)|~equidistant(A,G,C,H)|~equidistant(E,G,F,H)|~between(A,B,E)|~between(C,D,F)|equidistant(B,G,D,H)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163884672,plain,(~equidistant(A,B,C,D)|~equidistant(A,E,C,F)|~equidistant(A,G,C,H)|~equidistant(E,G,F,H)|~between(A,B,E)|~between(C,D,F)|equidistant(B,G,D,H)),inference(rewrite,[status(thm)],[d12]),[]).
%
% fof(v1_between_u1_and_w1,plain,(between(u1,v1,w1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163892024,plain,(between(u1,v1,w1)),inference(rewrite,[status(thm)],[v1_between_u1_and_w1]),[]).
%
% cnf(178548048,plain,(~equidistant(A,B,u1,v1)|~equidistant(A,C,u1,w1)|~equidistant(A,D,u1,E)|~equidistant(C,D,w1,E)|~between(A,B,C)|equidistant(B,D,v1,E)),inference(resolution,[status(thm)],[163884672,163892024]),[]).
%
% fof(v_between_u_and_w,plain,(between(u,v,w)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163883536,plain,(between(u,v,w)),inference(rewrite,[status(thm)],[v_between_u_and_w]),[]).
%
% cnf(180882968,plain,(~equidistant(u,A,u1,B)|~equidistant(w,A,w1,B)|equidistant(v,A,v1,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[163895936,163636568,178548048,163883536]),[]).
%
% cnf(190907224,plain,(~equidistant(w,w,w1,w1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[163907864,180882968,163636568]),[]).
%
% fof(d7,plain,(equidistant(A,A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163654368,plain,(equidistant(A,A,B,B)),inference(rewrite,[status(thm)],[d7]),[]).
%
% cnf(177153144,plain,(~equidistant(A,B,C,D)|~equidistant(A,E,C,F)|~between(A,B,E)|~between(C,D,F)|equidistant(B,E,D,F)),inference(resolution,[status(thm)],[163884672,163654368]),[]).
%
% cnf(196077352,plain,(~equidistant(u,A,u1,B)|~between(u,w,A)|~between(u1,w1,B)|equidistant(w,A,w1,B)),inference(resolution,[status(thm)],[177153144,163636568]),[]).
%
% fof(t3,plain,(between(A,B,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO032-3.tptp',unknown),[]).
%
% cnf(163718960,plain,(between(A,B,B)),inference(rewrite,[status(thm)],[t3]),[]).
%
% cnf(196246960,plain,(~equidistant(u,w,u1,A)|~between(u1,w1,A)|equidistant(w,w,w1,A)),inference(resolution,[status(thm)],[196077352,163718960]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[163636568,190907224,196246960,163718960]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------