TSTP Solution File: SET825-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET825-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 15:38:21 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 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_0,plain,
v_q(v_n),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),
[] ).
cnf(168381712,plain,
v_q(v_n),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
fof(cls_Relation_Opair__in__Id__conv__iff1_0,plain,
! [A,B,C] :
( ~ c_in(c_pair(A,B,C,C),c_relation_oid,tc_prod(C,C))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),
[] ).
cnf(168376752,plain,
( ~ c_in(c_pair(A,B,C,C),c_relation_oid,tc_prod(C,C))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[cls_Relation_Opair__in__Id__conv__iff1_0]),
[] ).
fof(cls_Relation_OIdI_0,plain,
! [A,B] : c_in(c_pair(A,A,B,B),c_relation_oid,tc_prod(B,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),
[] ).
cnf(168365728,plain,
c_in(c_pair(A,A,B,B),c_relation_oid,tc_prod(B,B)),
inference(rewrite,[status(thm)],[cls_Relation_OIdI_0]),
[] ).
fof(cls_conjecture_3,plain,
! [A] :
( c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_pair(c_suc(v_x(A)),c_suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),
[] ).
cnf(168414296,plain,
( c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_pair(c_suc(v_x(A)),c_suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
fof(cls_conjecture_2,plain,
! [A] :
( c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| c_in(c_pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),
[] ).
cnf(168398616,plain,
( c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| c_in(c_pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat)) ),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(184210376,plain,
( c_in(c_pair(v_x(c_relation_oid),v_xa(c_relation_oid),tc_nat,tc_nat),c_relation_oid,tc_prod(tc_nat,tc_nat))
| $equal(v_m,v_n) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168365728,168398616,168376752]),
[] ).
cnf(184229112,plain,
( $equal(v_m,v_n)
| $equal(v_xa(c_relation_oid),v_x(c_relation_oid)) ),
inference(resolution,[status(thm)],[184210376,168376752]),
[] ).
cnf(184294072,plain,
$equal(v_m,v_n),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168376752,168365728,168414296,184229112,theory(equality)]),
[] ).
fof(cls_conjecture_1,plain,
~ v_q(v_m),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),
[] ).
cnf(168390728,plain,
~ v_q(v_m),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168381712,184294072,168390728,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_0,plain,(v_q(v_n)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),[]).
%
% cnf(168381712,plain,(v_q(v_n)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% fof(cls_Relation_Opair__in__Id__conv__iff1_0,plain,(~c_in(c_pair(A,B,C,C),c_relation_oid,tc_prod(C,C))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),[]).
%
% cnf(168376752,plain,(~c_in(c_pair(A,B,C,C),c_relation_oid,tc_prod(C,C))|$equal(B,A)),inference(rewrite,[status(thm)],[cls_Relation_Opair__in__Id__conv__iff1_0]),[]).
%
% fof(cls_Relation_OIdI_0,plain,(c_in(c_pair(A,A,B,B),c_relation_oid,tc_prod(B,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),[]).
%
% cnf(168365728,plain,(c_in(c_pair(A,A,B,B),c_relation_oid,tc_prod(B,B))),inference(rewrite,[status(thm)],[cls_Relation_OIdI_0]),[]).
%
% fof(cls_conjecture_3,plain,(c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|~c_in(c_pair(c_suc(v_x(A)),c_suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|~c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),[]).
%
% cnf(168414296,plain,(c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|~c_in(c_pair(c_suc(v_x(A)),c_suc(v_xa(A)),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|~c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% fof(cls_conjecture_2,plain,(c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|c_in(c_pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|~c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),[]).
%
% cnf(168398616,plain,(c_in(c_pair(v_n,v_m,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|c_in(c_pair(v_x(A),v_xa(A),tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))|~c_in(c_pair(c_0,c_0,tc_nat,tc_nat),A,tc_prod(tc_nat,tc_nat))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(184210376,plain,(c_in(c_pair(v_x(c_relation_oid),v_xa(c_relation_oid),tc_nat,tc_nat),c_relation_oid,tc_prod(tc_nat,tc_nat))|$equal(v_m,v_n)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168365728,168398616,168376752]),[]).
%
% cnf(184229112,plain,($equal(v_m,v_n)|$equal(v_xa(c_relation_oid),v_x(c_relation_oid))),inference(resolution,[status(thm)],[184210376,168376752]),[]).
%
% cnf(184294072,plain,($equal(v_m,v_n)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168376752,168365728,168414296,184229112,theory(equality)]),[]).
%
% fof(cls_conjecture_1,plain,(~v_q(v_m)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET825-2.tptp',unknown),[]).
%
% cnf(168390728,plain,(~v_q(v_m)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168381712,184294072,168390728,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------