TSTP Solution File: GEO126-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GEO126-1 : TPTP v3.4.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 11:56:48 EDT 2009
% Result : Unsatisfiable 19.6s
% Output : Refutation 19.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 21 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 43 ( 1 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(start_point_defn_8,plain,
! [A,B,C] :
( ~ start_point(A,B)
| $equal(C,A)
| ~ incident_o(C,B)
| ordered_by(B,A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163778464,plain,
( ~ start_point(A,B)
| $equal(C,A)
| ~ incident_o(C,B)
| ordered_by(B,A,C) ),
inference(rewrite,[status(thm)],[start_point_defn_8]),
[] ).
fof(o4_29,plain,
! [A] : start_point(ax2_sk6(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(164049744,plain,
start_point(ax2_sk6(A),A),
inference(rewrite,[status(thm)],[o4_29]),
[] ).
cnf(172391088,plain,
( $equal(B,ax2_sk6(A))
| ~ incident_o(B,A)
| ordered_by(A,ax2_sk6(A),B) ),
inference(resolution,[status(thm)],[163778464,164049744]),
[] ).
fof(theorem_4_11_133,plain,
! [A,B] :
( ~ ordered_by(sk25,A,B)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(164184912,plain,
( ~ ordered_by(sk25,A,B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[theorem_4_11_133]),
[] ).
cnf(426360224,plain,
( $equal(A,ax2_sk6(sk25))
| ~ incident_o(A,sk25) ),
inference(resolution,[status(thm)],[172391088,164184912]),
[] ).
fof(o2_21,plain,
! [A,B] :
( ~ incident_c(A,ax2_sk3(B))
| incident_o(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163957744,plain,
( ~ incident_c(A,ax2_sk3(B))
| incident_o(A,B) ),
inference(rewrite,[status(thm)],[o2_21]),
[] ).
fof(inner_point_defn_21,plain,
! [A,B] :
( ~ inner_point(A,B)
| incident_c(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163099424,plain,
( ~ inner_point(A,B)
| incident_c(A,B) ),
inference(rewrite,[status(thm)],[inner_point_defn_21]),
[] ).
fof(c3_37,plain,
! [A] : inner_point(ax0_sk8(A),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163513432,plain,
inner_point(ax0_sk8(A),A),
inference(rewrite,[status(thm)],[c3_37]),
[] ).
cnf(172275040,plain,
incident_c(ax0_sk8(A),A),
inference(resolution,[status(thm)],[163099424,163513432]),
[] ).
cnf(172409912,plain,
incident_o(ax0_sk8(ax2_sk3(A)),A),
inference(resolution,[status(thm)],[163957744,172275040]),
[] ).
cnf(427464344,plain,
$equal(ax0_sk8(ax2_sk3(sk25)),ax2_sk6(sk25)),
inference(resolution,[status(thm)],[426360224,172409912]),
[] ).
cnf(428939600,plain,
inner_point(ax2_sk6(sk25),ax2_sk3(sk25)),
inference(paramodulation,[status(thm)],[427464344,163513432,theory(equality)]),
[] ).
fof(end_point_defn_13,plain,
! [A,B] :
( ~ end_point(A,B)
| incident_c(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163208440,plain,
( ~ end_point(A,B)
| incident_c(A,B) ),
inference(rewrite,[status(thm)],[end_point_defn_13]),
[] ).
fof(open_defn_33,plain,
! [A] :
( ~ open(A)
| end_point(ax0_sk7(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163462752,plain,
( ~ open(A)
| end_point(ax0_sk7(A),A) ),
inference(rewrite,[status(thm)],[open_defn_33]),
[] ).
fof(o2_19,plain,
! [A] : open(ax2_sk3(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163936640,plain,
open(ax2_sk3(A)),
inference(rewrite,[status(thm)],[o2_19]),
[] ).
cnf(172196720,plain,
end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),
inference(resolution,[status(thm)],[163462752,163936640]),
[] ).
cnf(173902192,plain,
incident_c(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),
inference(resolution,[status(thm)],[163208440,172196720]),
[] ).
cnf(179174056,plain,
incident_o(ax0_sk7(ax2_sk3(A)),A),
inference(resolution,[status(thm)],[163957744,173902192]),
[] ).
cnf(427478288,plain,
$equal(ax0_sk7(ax2_sk3(sk25)),ax2_sk6(sk25)),
inference(resolution,[status(thm)],[426360224,179174056]),
[] ).
fof(inner_point_defn_22,plain,
! [A,B] :
( ~ inner_point(A,B)
| ~ end_point(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),
[] ).
cnf(163334176,plain,
( ~ inner_point(A,B)
| ~ end_point(A,B) ),
inference(rewrite,[status(thm)],[inner_point_defn_22]),
[] ).
cnf(179009600,plain,
~ inner_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),
inference(resolution,[status(thm)],[163334176,172196720]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[428939600,427478288,179009600,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 18 seconds
% START OF PROOF SEQUENCE
% fof(start_point_defn_8,plain,(~start_point(A,B)|$equal(C,A)|~incident_o(C,B)|ordered_by(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163778464,plain,(~start_point(A,B)|$equal(C,A)|~incident_o(C,B)|ordered_by(B,A,C)),inference(rewrite,[status(thm)],[start_point_defn_8]),[]).
%
% fof(o4_29,plain,(start_point(ax2_sk6(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(164049744,plain,(start_point(ax2_sk6(A),A)),inference(rewrite,[status(thm)],[o4_29]),[]).
%
% cnf(172391088,plain,($equal(B,ax2_sk6(A))|~incident_o(B,A)|ordered_by(A,ax2_sk6(A),B)),inference(resolution,[status(thm)],[163778464,164049744]),[]).
%
% fof(theorem_4_11_133,plain,(~ordered_by(sk25,A,B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(164184912,plain,(~ordered_by(sk25,A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[theorem_4_11_133]),[]).
%
% cnf(426360224,plain,($equal(A,ax2_sk6(sk25))|~incident_o(A,sk25)),inference(resolution,[status(thm)],[172391088,164184912]),[]).
%
% fof(o2_21,plain,(~incident_c(A,ax2_sk3(B))|incident_o(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163957744,plain,(~incident_c(A,ax2_sk3(B))|incident_o(A,B)),inference(rewrite,[status(thm)],[o2_21]),[]).
%
% fof(inner_point_defn_21,plain,(~inner_point(A,B)|incident_c(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163099424,plain,(~inner_point(A,B)|incident_c(A,B)),inference(rewrite,[status(thm)],[inner_point_defn_21]),[]).
%
% fof(c3_37,plain,(inner_point(ax0_sk8(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163513432,plain,(inner_point(ax0_sk8(A),A)),inference(rewrite,[status(thm)],[c3_37]),[]).
%
% cnf(172275040,plain,(incident_c(ax0_sk8(A),A)),inference(resolution,[status(thm)],[163099424,163513432]),[]).
%
% cnf(172409912,plain,(incident_o(ax0_sk8(ax2_sk3(A)),A)),inference(resolution,[status(thm)],[163957744,172275040]),[]).
%
% cnf(427464344,plain,($equal(ax0_sk8(ax2_sk3(sk25)),ax2_sk6(sk25))),inference(resolution,[status(thm)],[426360224,172409912]),[]).
%
% cnf(428939600,plain,(inner_point(ax2_sk6(sk25),ax2_sk3(sk25))),inference(paramodulation,[status(thm)],[427464344,163513432,theory(equality)]),[]).
%
% fof(end_point_defn_13,plain,(~end_point(A,B)|incident_c(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163208440,plain,(~end_point(A,B)|incident_c(A,B)),inference(rewrite,[status(thm)],[end_point_defn_13]),[]).
%
% fof(open_defn_33,plain,(~open(A)|end_point(ax0_sk7(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163462752,plain,(~open(A)|end_point(ax0_sk7(A),A)),inference(rewrite,[status(thm)],[open_defn_33]),[]).
%
% fof(o2_19,plain,(open(ax2_sk3(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163936640,plain,(open(ax2_sk3(A))),inference(rewrite,[status(thm)],[o2_19]),[]).
%
% cnf(172196720,plain,(end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A))),inference(resolution,[status(thm)],[163462752,163936640]),[]).
%
% cnf(173902192,plain,(incident_c(ax0_sk7(ax2_sk3(A)),ax2_sk3(A))),inference(resolution,[status(thm)],[163208440,172196720]),[]).
%
% cnf(179174056,plain,(incident_o(ax0_sk7(ax2_sk3(A)),A)),inference(resolution,[status(thm)],[163957744,173902192]),[]).
%
% cnf(427478288,plain,($equal(ax0_sk7(ax2_sk3(sk25)),ax2_sk6(sk25))),inference(resolution,[status(thm)],[426360224,179174056]),[]).
%
% fof(inner_point_defn_22,plain,(~inner_point(A,B)|~end_point(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GEO/GEO126-1.tptp',unknown),[]).
%
% cnf(163334176,plain,(~inner_point(A,B)|~end_point(A,B)),inference(rewrite,[status(thm)],[inner_point_defn_22]),[]).
%
% cnf(179009600,plain,(~inner_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A))),inference(resolution,[status(thm)],[163334176,172196720]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[428939600,427478288,179009600,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------