TSTP Solution File: ANA021-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ANA021-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 11:24:26 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_NatBin_OSuc__pred_H_0,plain,
! [A] :
( ~ c_less(c_0,A,tc_nat)
| $equal(c_suc(c_minus(A,c_1,tc_nat)),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),
[] ).
cnf(144212192,plain,
( ~ c_less(c_0,A,tc_nat)
| $equal(c_suc(c_minus(A,c_1,tc_nat)),A) ),
inference(rewrite,[status(thm)],[cls_NatBin_OSuc__pred_H_0]),
[] ).
fof(cls_Nat_Onot__gr0_0,plain,
! [A] :
( c_less(c_0,A,tc_nat)
| $equal(c_0,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),
[] ).
cnf(144219096,plain,
( c_less(c_0,A,tc_nat)
| $equal(c_0,A) ),
inference(rewrite,[status(thm)],[cls_Nat_Onot__gr0_0]),
[] ).
fof(cls_conjecture_3,plain,
~ $equal(c_0,v_x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),
[] ).
cnf(144233360,plain,
~ $equal(c_0,v_x),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(157327240,plain,
c_less(c_0,v_x,tc_nat),
inference(resolution,[status(thm)],[144219096,144233360]),
[] ).
cnf(157351016,plain,
$equal(c_suc(c_minus(v_x,c_1,tc_nat)),v_x),
inference(resolution,[status(thm)],[144212192,157327240]),
[] ).
fof(cls_conjecture_2,plain,
! [A] : c_lessequals(c_hol_oabs(v_f(c_suc(A)),t_a),c_times(v_c,c_hol_oabs(v_h(c_suc(A)),t_a),t_a),t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),
[] ).
cnf(144224072,plain,
c_lessequals(c_hol_oabs(v_f(c_suc(A)),t_a),c_times(v_c,c_hol_oabs(v_h(c_suc(A)),t_a),t_a),t_a),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(157447832,plain,
c_lessequals(c_hol_oabs(v_f(c_suc(c_minus(v_x,c_1,tc_nat))),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a),
inference(paramodulation,[status(thm)],[157351016,144224072,theory(equality)]),
[] ).
fof(cls_conjecture_4,plain,
~ c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),
[] ).
cnf(144238512,plain,
~ c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157447832,144238512,157351016,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_NatBin_OSuc__pred_H_0,plain,(~c_less(c_0,A,tc_nat)|$equal(c_suc(c_minus(A,c_1,tc_nat)),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),[]).
%
% cnf(144212192,plain,(~c_less(c_0,A,tc_nat)|$equal(c_suc(c_minus(A,c_1,tc_nat)),A)),inference(rewrite,[status(thm)],[cls_NatBin_OSuc__pred_H_0]),[]).
%
% fof(cls_Nat_Onot__gr0_0,plain,(c_less(c_0,A,tc_nat)|$equal(c_0,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),[]).
%
% cnf(144219096,plain,(c_less(c_0,A,tc_nat)|$equal(c_0,A)),inference(rewrite,[status(thm)],[cls_Nat_Onot__gr0_0]),[]).
%
% fof(cls_conjecture_3,plain,(~$equal(c_0,v_x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),[]).
%
% cnf(144233360,plain,(~$equal(c_0,v_x)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(157327240,plain,(c_less(c_0,v_x,tc_nat)),inference(resolution,[status(thm)],[144219096,144233360]),[]).
%
% cnf(157351016,plain,($equal(c_suc(c_minus(v_x,c_1,tc_nat)),v_x)),inference(resolution,[status(thm)],[144212192,157327240]),[]).
%
% fof(cls_conjecture_2,plain,(c_lessequals(c_hol_oabs(v_f(c_suc(A)),t_a),c_times(v_c,c_hol_oabs(v_h(c_suc(A)),t_a),t_a),t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),[]).
%
% cnf(144224072,plain,(c_lessequals(c_hol_oabs(v_f(c_suc(A)),t_a),c_times(v_c,c_hol_oabs(v_h(c_suc(A)),t_a),t_a),t_a)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(157447832,plain,(c_lessequals(c_hol_oabs(v_f(c_suc(c_minus(v_x,c_1,tc_nat))),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a)),inference(paramodulation,[status(thm)],[157351016,144224072,theory(equality)]),[]).
%
% fof(cls_conjecture_4,plain,(~c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ANA/ANA021-2.tptp',unknown),[]).
%
% cnf(144238512,plain,(~c_lessequals(c_hol_oabs(v_f(v_x),t_a),c_times(v_c,c_hol_oabs(v_h(v_x),t_a),t_a),t_a)),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157447832,144238512,157351016,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------