TSTP Solution File: COM011-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COM011-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 11:36:46 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 24 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 65 ( 5 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_UNITY_Oconstrains__weaken__L_0,plain,
! [A,B,C,D,E] :
( ~ c_in(A,c_unity_oconstrains(B,C,D),tc_unity_oprogram(D))
| ~ c_lessequals(E,B,tc_set(D))
| c_in(A,c_unity_oconstrains(E,C,D),tc_unity_oprogram(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165762032,plain,
( ~ c_in(A,c_unity_oconstrains(B,C,D),tc_unity_oprogram(D))
| ~ c_lessequals(E,B,tc_set(D))
| c_in(A,c_unity_oconstrains(E,C,D),tc_unity_oprogram(D)) ),
inference(rewrite,[status(thm)],[cls_UNITY_Oconstrains__weaken__L_0]),
[] ).
fof(cls_conjecture_0,plain,
c_in(v_f,c_unity_oconstrains(v_a,c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165711440,plain,
c_in(v_f,c_unity_oconstrains(v_a,c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(180351664,plain,
( ~ c_lessequals(A,v_a,tc_set(t_a))
| c_in(v_f,c_unity_oconstrains(A,c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a)) ),
inference(resolution,[status(thm)],[165762032,165711440]),
[] ).
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/COM/COM011-2.tptp',unknown),
[] ).
cnf(165750296,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_ODiffE_1,plain,
! [A,B,C,D] :
( ~ c_in(A,c_minus(B,C,tc_set(D)),D)
| c_in(A,B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165733952,plain,
( ~ c_in(A,c_minus(B,C,tc_set(D)),D)
| c_in(A,B,D) ),
inference(rewrite,[status(thm)],[cls_Set_ODiffE_1]),
[] ).
cnf(179045192,plain,
( c_lessequals(A,B,tc_set(C))
| ~ c_in(c_main_osubseti__1(A,B,C),c_minus(B,D,tc_set(C)),C) ),
inference(resolution,[status(thm)],[165750296,165733952]),
[] ).
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/COM/COM011-2.tptp',unknown),
[] ).
cnf(165740120,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(179462416,plain,
c_lessequals(c_minus(A,C,tc_set(B)),A,tc_set(B)),
inference(resolution,[status(thm)],[179045192,165740120]),
[] ).
cnf(180612456,plain,
c_in(v_f,c_unity_oconstrains(c_minus(v_a,A,tc_set(t_a)),c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a)),
inference(resolution,[status(thm)],[180351664,179462416]),
[] ).
fof(cls_WFair_Otransient__strengthen_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_wfair_otransient(B,C),tc_unity_oprogram(C))
| ~ c_lessequals(D,B,tc_set(C))
| c_in(A,c_wfair_otransient(D,C),tc_unity_oprogram(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165791720,plain,
( ~ c_in(A,c_wfair_otransient(B,C),tc_unity_oprogram(C))
| ~ c_lessequals(D,B,tc_set(C))
| c_in(A,c_wfair_otransient(D,C),tc_unity_oprogram(C)) ),
inference(rewrite,[status(thm)],[cls_WFair_Otransient__strengthen_0]),
[] ).
fof(cls_conjecture_1,plain,
c_in(v_f,c_wfair_otransient(v_a,t_a),tc_unity_oprogram(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165715816,plain,
c_in(v_f,c_wfair_otransient(v_a,t_a),tc_unity_oprogram(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(178896672,plain,
( ~ c_lessequals(A,v_a,tc_set(t_a))
| c_in(v_f,c_wfair_otransient(A,t_a),tc_unity_oprogram(t_a)) ),
inference(resolution,[status(thm)],[165791720,165715816]),
[] ).
cnf(179856368,plain,
c_in(v_f,c_wfair_otransient(c_minus(v_a,A,tc_set(t_a)),t_a),tc_unity_oprogram(t_a)),
inference(resolution,[status(thm)],[178896672,179462416]),
[] ).
fof(cls_WFair_OensuresI_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_unity_oconstrains(c_minus(B,C,tc_set(D)),c_union(B,C,D),D),tc_unity_oprogram(D))
| ~ c_in(A,c_wfair_otransient(c_minus(B,C,tc_set(D)),D),tc_unity_oprogram(D))
| c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165774216,plain,
( ~ c_in(A,c_unity_oconstrains(c_minus(B,C,tc_set(D)),c_union(B,C,D),D),tc_unity_oprogram(D))
| ~ c_in(A,c_wfair_otransient(c_minus(B,C,tc_set(D)),D),tc_unity_oprogram(D))
| c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D)) ),
inference(rewrite,[status(thm)],[cls_WFair_OensuresI_0]),
[] ).
fof(cls_WFair_OleadsTo__Basis_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D))
| c_in(A,c_wfair_oleadsto(B,C,D),tc_unity_oprogram(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165784208,plain,
( ~ c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D))
| c_in(A,c_wfair_oleadsto(B,C,D),tc_unity_oprogram(D)) ),
inference(rewrite,[status(thm)],[cls_WFair_OleadsTo__Basis_0]),
[] ).
fof(cls_conjecture_2,plain,
~ c_in(v_f,c_wfair_oleadsto(v_a,v_b,t_a),tc_unity_oprogram(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),
[] ).
cnf(165720664,plain,
~ c_in(v_f,c_wfair_oleadsto(v_a,v_b,t_a),tc_unity_oprogram(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(179096240,plain,
~ c_in(v_f,c_wfair_oensures(v_a,v_b,t_a),tc_unity_oprogram(t_a)),
inference(resolution,[status(thm)],[165784208,165720664]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[180612456,179856368,165774216,179096240]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_UNITY_Oconstrains__weaken__L_0,plain,(~c_in(A,c_unity_oconstrains(B,C,D),tc_unity_oprogram(D))|~c_lessequals(E,B,tc_set(D))|c_in(A,c_unity_oconstrains(E,C,D),tc_unity_oprogram(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165762032,plain,(~c_in(A,c_unity_oconstrains(B,C,D),tc_unity_oprogram(D))|~c_lessequals(E,B,tc_set(D))|c_in(A,c_unity_oconstrains(E,C,D),tc_unity_oprogram(D))),inference(rewrite,[status(thm)],[cls_UNITY_Oconstrains__weaken__L_0]),[]).
%
% fof(cls_conjecture_0,plain,(c_in(v_f,c_unity_oconstrains(v_a,c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165711440,plain,(c_in(v_f,c_unity_oconstrains(v_a,c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(180351664,plain,(~c_lessequals(A,v_a,tc_set(t_a))|c_in(v_f,c_unity_oconstrains(A,c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a))),inference(resolution,[status(thm)],[165762032,165711440]),[]).
%
% 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/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165750296,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_ODiffE_1,plain,(~c_in(A,c_minus(B,C,tc_set(D)),D)|c_in(A,B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165733952,plain,(~c_in(A,c_minus(B,C,tc_set(D)),D)|c_in(A,B,D)),inference(rewrite,[status(thm)],[cls_Set_ODiffE_1]),[]).
%
% cnf(179045192,plain,(c_lessequals(A,B,tc_set(C))|~c_in(c_main_osubseti__1(A,B,C),c_minus(B,D,tc_set(C)),C)),inference(resolution,[status(thm)],[165750296,165733952]),[]).
%
% 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/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165740120,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(179462416,plain,(c_lessequals(c_minus(A,C,tc_set(B)),A,tc_set(B))),inference(resolution,[status(thm)],[179045192,165740120]),[]).
%
% cnf(180612456,plain,(c_in(v_f,c_unity_oconstrains(c_minus(v_a,A,tc_set(t_a)),c_union(v_a,v_b,t_a),t_a),tc_unity_oprogram(t_a))),inference(resolution,[status(thm)],[180351664,179462416]),[]).
%
% fof(cls_WFair_Otransient__strengthen_0,plain,(~c_in(A,c_wfair_otransient(B,C),tc_unity_oprogram(C))|~c_lessequals(D,B,tc_set(C))|c_in(A,c_wfair_otransient(D,C),tc_unity_oprogram(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165791720,plain,(~c_in(A,c_wfair_otransient(B,C),tc_unity_oprogram(C))|~c_lessequals(D,B,tc_set(C))|c_in(A,c_wfair_otransient(D,C),tc_unity_oprogram(C))),inference(rewrite,[status(thm)],[cls_WFair_Otransient__strengthen_0]),[]).
%
% fof(cls_conjecture_1,plain,(c_in(v_f,c_wfair_otransient(v_a,t_a),tc_unity_oprogram(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165715816,plain,(c_in(v_f,c_wfair_otransient(v_a,t_a),tc_unity_oprogram(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(178896672,plain,(~c_lessequals(A,v_a,tc_set(t_a))|c_in(v_f,c_wfair_otransient(A,t_a),tc_unity_oprogram(t_a))),inference(resolution,[status(thm)],[165791720,165715816]),[]).
%
% cnf(179856368,plain,(c_in(v_f,c_wfair_otransient(c_minus(v_a,A,tc_set(t_a)),t_a),tc_unity_oprogram(t_a))),inference(resolution,[status(thm)],[178896672,179462416]),[]).
%
% fof(cls_WFair_OensuresI_0,plain,(~c_in(A,c_unity_oconstrains(c_minus(B,C,tc_set(D)),c_union(B,C,D),D),tc_unity_oprogram(D))|~c_in(A,c_wfair_otransient(c_minus(B,C,tc_set(D)),D),tc_unity_oprogram(D))|c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165774216,plain,(~c_in(A,c_unity_oconstrains(c_minus(B,C,tc_set(D)),c_union(B,C,D),D),tc_unity_oprogram(D))|~c_in(A,c_wfair_otransient(c_minus(B,C,tc_set(D)),D),tc_unity_oprogram(D))|c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D))),inference(rewrite,[status(thm)],[cls_WFair_OensuresI_0]),[]).
%
% fof(cls_WFair_OleadsTo__Basis_0,plain,(~c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D))|c_in(A,c_wfair_oleadsto(B,C,D),tc_unity_oprogram(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165784208,plain,(~c_in(A,c_wfair_oensures(B,C,D),tc_unity_oprogram(D))|c_in(A,c_wfair_oleadsto(B,C,D),tc_unity_oprogram(D))),inference(rewrite,[status(thm)],[cls_WFair_OleadsTo__Basis_0]),[]).
%
% fof(cls_conjecture_2,plain,(~c_in(v_f,c_wfair_oleadsto(v_a,v_b,t_a),tc_unity_oprogram(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM011-2.tptp',unknown),[]).
%
% cnf(165720664,plain,(~c_in(v_f,c_wfair_oleadsto(v_a,v_b,t_a),tc_unity_oprogram(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(179096240,plain,(~c_in(v_f,c_wfair_oensures(v_a,v_b,t_a),tc_unity_oprogram(t_a))),inference(resolution,[status(thm)],[165784208,165720664]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[180612456,179856368,165774216,179096240]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------