TSTP Solution File: SWV254-2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SWV254-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 16:28:48 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 20 ( 5 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(clsarity_nat_3,plain,
class_orderings_oorder(tc_nat),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),
[] ).
cnf(167121136,plain,
class_orderings_oorder(tc_nat),
inference(rewrite,[status(thm)],[clsarity_nat_3]),
[] ).
fof(cls_SetInterval_OatLeastLessThan__empty_0,plain,
! [A,B,C] :
( ~ class_orderings_oorder(A)
| ~ c_lessequals(B,C,A)
| $equal(c_emptyset,c_setinterval_oatleastlessthan(C,B,A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),
[] ).
cnf(167093448,plain,
( ~ class_orderings_oorder(A)
| ~ c_lessequals(B,C,A)
| $equal(c_emptyset,c_setinterval_oatleastlessthan(C,B,A)) ),
inference(rewrite,[status(thm)],[cls_SetInterval_OatLeastLessThan__empty_0]),
[] ).
fof(cls_conjecture_0,plain,
! [A] : c_lessequals(A,v_x(A),tc_nat),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),
[] ).
cnf(167112424,plain,
c_lessequals(A,v_x(A),tc_nat),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(177580248,plain,
$equal(c_emptyset,c_setinterval_oatleastlessthan(v_x(A),A,tc_nat)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167121136,167093448,167112424]),
[] ).
fof(cls_conjecture_1,plain,
! [A] : $equal(v_nat,v_x(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),
[] ).
cnf(167116488,plain,
$equal(v_nat,v_x(A)),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(177708656,plain,
$equal(c_emptyset,c_setinterval_oatleastlessthan(v_nat,A,tc_nat)),
inference(paramodulation,[status(thm)],[177580248,167116488,theory(equality)]),
[] ).
fof(cls_SetInterval_OatLeastLessThan__singleton_0,plain,
! [A] : $equal(c_insert(A,c_emptyset,tc_nat),c_setinterval_oatleastlessthan(A,c_suc(A),tc_nat)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),
[] ).
cnf(167098600,plain,
$equal(c_insert(A,c_emptyset,tc_nat),c_setinterval_oatleastlessthan(A,c_suc(A),tc_nat)),
inference(rewrite,[status(thm)],[cls_SetInterval_OatLeastLessThan__singleton_0]),
[] ).
cnf(177912896,plain,
$equal(c_insert(v_nat,c_emptyset,tc_nat),c_emptyset),
inference(paramodulation,[status(thm)],[177708656,167098600,theory(equality)]),
[] ).
fof(cls_Set_Oempty__not__insert_0,plain,
! [A,B,C] : ~ $equal(c_insert(A,B,C),c_emptyset),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),
[] ).
cnf(167103536,plain,
~ $equal(c_insert(A,B,C),c_emptyset),
inference(rewrite,[status(thm)],[cls_Set_Oempty__not__insert_0]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[177912896,167103536]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(clsarity_nat_3,plain,(class_orderings_oorder(tc_nat)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),[]).
%
% cnf(167121136,plain,(class_orderings_oorder(tc_nat)),inference(rewrite,[status(thm)],[clsarity_nat_3]),[]).
%
% fof(cls_SetInterval_OatLeastLessThan__empty_0,plain,(~class_orderings_oorder(A)|~c_lessequals(B,C,A)|$equal(c_emptyset,c_setinterval_oatleastlessthan(C,B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),[]).
%
% cnf(167093448,plain,(~class_orderings_oorder(A)|~c_lessequals(B,C,A)|$equal(c_emptyset,c_setinterval_oatleastlessthan(C,B,A))),inference(rewrite,[status(thm)],[cls_SetInterval_OatLeastLessThan__empty_0]),[]).
%
% fof(cls_conjecture_0,plain,(c_lessequals(A,v_x(A),tc_nat)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),[]).
%
% cnf(167112424,plain,(c_lessequals(A,v_x(A),tc_nat)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(177580248,plain,($equal(c_emptyset,c_setinterval_oatleastlessthan(v_x(A),A,tc_nat))),inference(forward_subsumption_resolution__resolution,[status(thm)],[167121136,167093448,167112424]),[]).
%
% fof(cls_conjecture_1,plain,($equal(v_nat,v_x(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),[]).
%
% cnf(167116488,plain,($equal(v_nat,v_x(A))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(177708656,plain,($equal(c_emptyset,c_setinterval_oatleastlessthan(v_nat,A,tc_nat))),inference(paramodulation,[status(thm)],[177580248,167116488,theory(equality)]),[]).
%
% fof(cls_SetInterval_OatLeastLessThan__singleton_0,plain,($equal(c_insert(A,c_emptyset,tc_nat),c_setinterval_oatleastlessthan(A,c_suc(A),tc_nat))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),[]).
%
% cnf(167098600,plain,($equal(c_insert(A,c_emptyset,tc_nat),c_setinterval_oatleastlessthan(A,c_suc(A),tc_nat))),inference(rewrite,[status(thm)],[cls_SetInterval_OatLeastLessThan__singleton_0]),[]).
%
% cnf(177912896,plain,($equal(c_insert(v_nat,c_emptyset,tc_nat),c_emptyset)),inference(paramodulation,[status(thm)],[177708656,167098600,theory(equality)]),[]).
%
% fof(cls_Set_Oempty__not__insert_0,plain,(~$equal(c_insert(A,B,C),c_emptyset)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SWV/SWV254-2.tptp',unknown),[]).
%
% cnf(167103536,plain,(~$equal(c_insert(A,B,C),c_emptyset)),inference(rewrite,[status(thm)],[cls_Set_Oempty__not__insert_0]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[177912896,167103536]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------