TSTP Solution File: SET834-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET834-2 : TPTP v3.4.2. Released v3.2.0.
% 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 15:38:46 EDT 2009
% Result : Unsatisfiable 1.6s
% Output : Refutation 1.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 26 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 65 ( 6 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_4,plain,
~ c_in(v_x,v_y,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162592200,plain,
~ c_in(v_x,v_y,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_4]),
[] ).
fof(cls_conjecture_3,plain,
~ c_in(v_x,v_z,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162584120,plain,
~ c_in(v_x,v_z,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
fof(cls_Set_OUnE_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_union(B,C,D),D)
| c_in(A,C,D)
| c_in(A,B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162549008,plain,
( ~ c_in(A,c_union(B,C,D),D)
| c_in(A,C,D)
| c_in(A,B,D) ),
inference(rewrite,[status(thm)],[cls_Set_OUnE_0]),
[] ).
fof(cls_conjecture_5,plain,
! [A] :
( c_lessequals(v_x,A,tc_set(t_a))
| ~ c_lessequals(v_z,A,tc_set(t_a))
| ~ c_lessequals(v_y,A,tc_set(t_a)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162600320,plain,
( c_lessequals(v_x,A,tc_set(t_a))
| ~ c_lessequals(v_z,A,tc_set(t_a))
| ~ c_lessequals(v_y,A,tc_set(t_a)) ),
inference(rewrite,[status(thm)],[cls_conjecture_5]),
[] ).
fof(cls_Set_OsubsetD_0,plain,
! [A,B,C,D] :
( ~ c_in(A,B,C)
| ~ c_lessequals(B,D,tc_set(C))
| c_in(A,D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162559664,plain,
( ~ c_in(A,B,C)
| ~ c_lessequals(B,D,tc_set(C))
| c_in(A,D,C) ),
inference(rewrite,[status(thm)],[cls_Set_OsubsetD_0]),
[] ).
cnf(183928872,plain,
( ~ c_lessequals(v_z,A,tc_set(t_a))
| ~ c_lessequals(v_y,A,tc_set(t_a))
| ~ c_in(B,v_x,t_a)
| c_in(B,A,t_a) ),
inference(resolution,[status(thm)],[162600320,162559664]),
[] ).
fof(cls_Set_OsubsetI_1,plain,
! [A,B,C] :
( ~ c_in(c_main_osubseti__1(A,B,C),B,C)
| c_lessequals(A,B,tc_set(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162576208,plain,
( ~ c_in(c_main_osubseti__1(A,B,C),B,C)
| c_lessequals(A,B,tc_set(C)) ),
inference(rewrite,[status(thm)],[cls_Set_OsubsetI_1]),
[] ).
fof(cls_Set_OUnCI_0,plain,
! [A,B,C,D] :
( ~ c_in(A,B,C)
| c_in(A,c_union(D,B,C),C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162537536,plain,
( ~ c_in(A,B,C)
| c_in(A,c_union(D,B,C),C) ),
inference(rewrite,[status(thm)],[cls_Set_OUnCI_0]),
[] ).
fof(cls_Set_OsubsetI_0,plain,
! [A,B,C] :
( c_in(c_main_osubseti__1(A,B,C),A,C)
| c_lessequals(A,B,tc_set(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162570288,plain,
( c_in(c_main_osubseti__1(A,B,C),A,C)
| c_lessequals(A,B,tc_set(C)) ),
inference(rewrite,[status(thm)],[cls_Set_OsubsetI_0]),
[] ).
cnf(178762976,plain,
( c_in(c_main_osubseti__1(A,D,B),c_union(C,A,B),B)
| c_lessequals(A,D,tc_set(B)) ),
inference(resolution,[status(thm)],[162537536,162570288]),
[] ).
cnf(192269984,plain,
c_lessequals(A,c_union(C,A,B),tc_set(B)),
inference(resolution,[status(thm)],[162576208,178762976]),
[] ).
cnf(193711120,plain,
( ~ c_lessequals(v_y,c_union(B,v_z,t_a),tc_set(t_a))
| ~ c_in(A,v_x,t_a)
| c_in(A,c_union(B,v_z,t_a),t_a) ),
inference(resolution,[status(thm)],[183928872,192269984]),
[] ).
fof(cls_Set_OUnCI_1,plain,
! [A,B,C,D] :
( ~ c_in(A,B,C)
| c_in(A,c_union(B,D,C),C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162542024,plain,
( ~ c_in(A,B,C)
| c_in(A,c_union(B,D,C),C) ),
inference(rewrite,[status(thm)],[cls_Set_OUnCI_1]),
[] ).
cnf(178851472,plain,
( c_in(c_main_osubseti__1(A,D,B),c_union(A,C,B),B)
| c_lessequals(A,D,tc_set(B)) ),
inference(resolution,[status(thm)],[162542024,162570288]),
[] ).
cnf(203357160,plain,
c_lessequals(A,c_union(A,C,B),tc_set(B)),
inference(resolution,[status(thm)],[178851472,162576208]),
[] ).
cnf(216551320,plain,
( ~ c_in(A,v_x,t_a)
| c_in(A,c_union(v_y,v_z,t_a),t_a) ),
inference(resolution,[status(thm)],[193711120,203357160]),
[] ).
fof(cls_conjecture_2,plain,
c_in(v_x,v_x,t_a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),
[] ).
cnf(162580048,plain,
c_in(v_x,v_x,t_a),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(216559104,plain,
c_in(v_x,c_union(v_y,v_z,t_a),t_a),
inference(resolution,[status(thm)],[216551320,162580048]),
[] ).
cnf(217342832,plain,
( c_in(v_x,v_z,t_a)
| c_in(v_x,v_y,t_a) ),
inference(resolution,[status(thm)],[162549008,216559104]),
[] ).
cnf(218242928,plain,
c_in(v_x,v_y,t_a),
inference(resolution,[status(thm)],[162584120,217342832]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[162592200,218242928]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_4,plain,(~c_in(v_x,v_y,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162592200,plain,(~c_in(v_x,v_y,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_4]),[]).
%
% fof(cls_conjecture_3,plain,(~c_in(v_x,v_z,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162584120,plain,(~c_in(v_x,v_z,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% fof(cls_Set_OUnE_0,plain,(~c_in(A,c_union(B,C,D),D)|c_in(A,C,D)|c_in(A,B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162549008,plain,(~c_in(A,c_union(B,C,D),D)|c_in(A,C,D)|c_in(A,B,D)),inference(rewrite,[status(thm)],[cls_Set_OUnE_0]),[]).
%
% fof(cls_conjecture_5,plain,(c_lessequals(v_x,A,tc_set(t_a))|~c_lessequals(v_z,A,tc_set(t_a))|~c_lessequals(v_y,A,tc_set(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162600320,plain,(c_lessequals(v_x,A,tc_set(t_a))|~c_lessequals(v_z,A,tc_set(t_a))|~c_lessequals(v_y,A,tc_set(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_5]),[]).
%
% fof(cls_Set_OsubsetD_0,plain,(~c_in(A,B,C)|~c_lessequals(B,D,tc_set(C))|c_in(A,D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162559664,plain,(~c_in(A,B,C)|~c_lessequals(B,D,tc_set(C))|c_in(A,D,C)),inference(rewrite,[status(thm)],[cls_Set_OsubsetD_0]),[]).
%
% cnf(183928872,plain,(~c_lessequals(v_z,A,tc_set(t_a))|~c_lessequals(v_y,A,tc_set(t_a))|~c_in(B,v_x,t_a)|c_in(B,A,t_a)),inference(resolution,[status(thm)],[162600320,162559664]),[]).
%
% fof(cls_Set_OsubsetI_1,plain,(~c_in(c_main_osubseti__1(A,B,C),B,C)|c_lessequals(A,B,tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162576208,plain,(~c_in(c_main_osubseti__1(A,B,C),B,C)|c_lessequals(A,B,tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_OsubsetI_1]),[]).
%
% fof(cls_Set_OUnCI_0,plain,(~c_in(A,B,C)|c_in(A,c_union(D,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162537536,plain,(~c_in(A,B,C)|c_in(A,c_union(D,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OUnCI_0]),[]).
%
% fof(cls_Set_OsubsetI_0,plain,(c_in(c_main_osubseti__1(A,B,C),A,C)|c_lessequals(A,B,tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162570288,plain,(c_in(c_main_osubseti__1(A,B,C),A,C)|c_lessequals(A,B,tc_set(C))),inference(rewrite,[status(thm)],[cls_Set_OsubsetI_0]),[]).
%
% cnf(178762976,plain,(c_in(c_main_osubseti__1(A,D,B),c_union(C,A,B),B)|c_lessequals(A,D,tc_set(B))),inference(resolution,[status(thm)],[162537536,162570288]),[]).
%
% cnf(192269984,plain,(c_lessequals(A,c_union(C,A,B),tc_set(B))),inference(resolution,[status(thm)],[162576208,178762976]),[]).
%
% cnf(193711120,plain,(~c_lessequals(v_y,c_union(B,v_z,t_a),tc_set(t_a))|~c_in(A,v_x,t_a)|c_in(A,c_union(B,v_z,t_a),t_a)),inference(resolution,[status(thm)],[183928872,192269984]),[]).
%
% fof(cls_Set_OUnCI_1,plain,(~c_in(A,B,C)|c_in(A,c_union(B,D,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162542024,plain,(~c_in(A,B,C)|c_in(A,c_union(B,D,C),C)),inference(rewrite,[status(thm)],[cls_Set_OUnCI_1]),[]).
%
% cnf(178851472,plain,(c_in(c_main_osubseti__1(A,D,B),c_union(A,C,B),B)|c_lessequals(A,D,tc_set(B))),inference(resolution,[status(thm)],[162542024,162570288]),[]).
%
% cnf(203357160,plain,(c_lessequals(A,c_union(A,C,B),tc_set(B))),inference(resolution,[status(thm)],[178851472,162576208]),[]).
%
% cnf(216551320,plain,(~c_in(A,v_x,t_a)|c_in(A,c_union(v_y,v_z,t_a),t_a)),inference(resolution,[status(thm)],[193711120,203357160]),[]).
%
% fof(cls_conjecture_2,plain,(c_in(v_x,v_x,t_a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET834-2.tptp',unknown),[]).
%
% cnf(162580048,plain,(c_in(v_x,v_x,t_a)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(216559104,plain,(c_in(v_x,c_union(v_y,v_z,t_a),t_a)),inference(resolution,[status(thm)],[216551320,162580048]),[]).
%
% cnf(217342832,plain,(c_in(v_x,v_z,t_a)|c_in(v_x,v_y,t_a)),inference(resolution,[status(thm)],[162549008,216559104]),[]).
%
% cnf(218242928,plain,(c_in(v_x,v_y,t_a)),inference(resolution,[status(thm)],[162584120,217342832]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162592200,218242928]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------