TSTP Solution File: SWV413+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SWV413+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 16:35:09 EDT 2009
% Result : Theorem 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 52 ( 15 ~; 22 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l49_co,plain,
! [E] :
( ( pair_in_list(u,v,w)
| ~ less_than(x,E) )
& ( strictly_less_than(v,x)
| ~ less_than(x,E) )
& ( less_than(x,w)
| ~ less_than(x,E) )
& ( ~ pair_in_list(update_slb(u,x),v,E)
| ~ less_than(x,E) )
& ( pair_in_list(u,v,w)
| pair_in_list(u,v,w) )
& ( strictly_less_than(v,x)
| pair_in_list(u,v,w) )
& ( less_than(x,w)
| pair_in_list(u,v,w) )
& ( ~ pair_in_list(update_slb(u,x),v,E)
| pair_in_list(u,v,w) )
& ( pair_in_list(u,v,w)
| strictly_less_than(v,x) )
& ( strictly_less_than(v,x)
| strictly_less_than(v,x) )
& ( less_than(x,w)
| strictly_less_than(v,x) )
& ( ~ pair_in_list(update_slb(u,x),v,E)
| strictly_less_than(v,x) )
& ( pair_in_list(u,v,w)
| less_than(x,w) )
& ( strictly_less_than(v,x)
| less_than(x,w) )
& ( less_than(x,w)
| less_than(x,w) )
& ( ~ pair_in_list(update_slb(u,x),v,E)
| less_than(x,w) ) ),
file('/tmp/SystemOnTPTP13104/SWV413+1.p',unknown),
[] ).
cnf(169880640,plain,
less_than(x,w),
inference(rewrite,[status(thm)],[l49_co]),
[] ).
cnf(169917032,plain,
( ~ pair_in_list(update_slb(u,x),v,E)
| ~ less_than(x,E) ),
inference(rewrite,[status(thm)],[l49_co]),
[] ).
fof(l49_li3637,plain,
! [A,B,C,D] :
( ~ pair_in_list(A,B,C)
| ~ less_than(D,C)
| pair_in_list(update_slb(A,D),B,C) ),
file('/tmp/SystemOnTPTP13104/SWV413+1.p',unknown),
[] ).
cnf(169687248,plain,
( ~ pair_in_list(A,B,C)
| ~ less_than(D,C)
| pair_in_list(update_slb(A,D),B,C) ),
inference(rewrite,[status(thm)],[l49_li3637]),
[] ).
cnf(201245576,plain,
( ~ pair_in_list(A,B,w)
| pair_in_list(update_slb(A,x),B,w) ),
inference(resolution,[status(thm)],[169687248,169880640]),
[] ).
cnf(169903072,plain,
pair_in_list(u,v,w),
inference(rewrite,[status(thm)],[l49_co]),
[] ).
cnf(201322088,plain,
pair_in_list(update_slb(u,x),v,w),
inference(resolution,[status(thm)],[201245576,169903072]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[169880640,169917032,201322088]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l49_co,plain,(((pair_in_list(u,v,w)|~less_than(x,E))&(strictly_less_than(v,x)|~less_than(x,E))&(less_than(x,w)|~less_than(x,E))&(~pair_in_list(update_slb(u,x),v,E)|~less_than(x,E))&(pair_in_list(u,v,w)|pair_in_list(u,v,w))&(strictly_less_than(v,x)|pair_in_list(u,v,w))&(less_than(x,w)|pair_in_list(u,v,w))&(~pair_in_list(update_slb(u,x),v,E)|pair_in_list(u,v,w))&(pair_in_list(u,v,w)|strictly_less_than(v,x))&(strictly_less_than(v,x)|strictly_less_than(v,x))&(less_than(x,w)|strictly_less_than(v,x))&(~pair_in_list(update_slb(u,x),v,E)|strictly_less_than(v,x))&(pair_in_list(u,v,w)|less_than(x,w))&(strictly_less_than(v,x)|less_than(x,w))&(less_than(x,w)|less_than(x,w))&(~pair_in_list(update_slb(u,x),v,E)|less_than(x,w)))),file('/tmp/SystemOnTPTP13104/SWV413+1.p',unknown),[]).
%
% cnf(169880640,plain,(less_than(x,w)),inference(rewrite,[status(thm)],[l49_co]),[]).
%
% cnf(169917032,plain,(~pair_in_list(update_slb(u,x),v,E)|~less_than(x,E)),inference(rewrite,[status(thm)],[l49_co]),[]).
%
% fof(l49_li3637,plain,(~pair_in_list(A,B,C)|~less_than(D,C)|pair_in_list(update_slb(A,D),B,C)),file('/tmp/SystemOnTPTP13104/SWV413+1.p',unknown),[]).
%
% cnf(169687248,plain,(~pair_in_list(A,B,C)|~less_than(D,C)|pair_in_list(update_slb(A,D),B,C)),inference(rewrite,[status(thm)],[l49_li3637]),[]).
%
% cnf(201245576,plain,(~pair_in_list(A,B,w)|pair_in_list(update_slb(A,x),B,w)),inference(resolution,[status(thm)],[169687248,169880640]),[]).
%
% cnf(169903072,plain,(pair_in_list(u,v,w)),inference(rewrite,[status(thm)],[l49_co]),[]).
%
% cnf(201322088,plain,(pair_in_list(update_slb(u,x),v,w)),inference(resolution,[status(thm)],[201245576,169903072]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[169880640,169917032,201322088]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------