TSTP Solution File: LCL429-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL429-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 13:49:43 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 75 ( 9 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_5,plain,
~ c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,v_t,t_a),c_insert(c_proplog_opl_ovar(v_v,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165593816,plain,
~ c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,v_t,t_a),c_insert(c_proplog_opl_ovar(v_v,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_5]),
[] ).
fof(cls_PropLog_ODiff__weaken__left_0,plain,
! [A,B,C,D,E] :
( ~ c_in(A,c_proplog_othms(c_minus(B,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D))
| ~ c_lessequals(B,E,tc_set(tc_proplog_opl(D)))
| c_in(A,c_proplog_othms(c_minus(E,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165501112,plain,
( ~ c_in(A,c_proplog_othms(c_minus(B,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D))
| ~ c_lessequals(B,E,tc_set(tc_proplog_opl(D)))
| c_in(A,c_proplog_othms(c_minus(E,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D)) ),
inference(rewrite,[status(thm)],[cls_PropLog_ODiff__weaken__left_0]),
[] ).
fof(cls_conjecture_3,plain,
! [A] : c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),v_f,tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165584832,plain,
c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),v_f,tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a)),
inference(rewrite,[status(thm)],[cls_conjecture_3]),
[] ).
cnf(176119200,plain,
( ~ c_lessequals(c_proplog_ohyps(v_p,B,t_a),A,tc_set(tc_proplog_opl(t_a)))
| c_in(v_p,c_proplog_othms(c_minus(A,v_f,tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a)) ),
inference(resolution,[status(thm)],[165501112,165584832]),
[] ).
fof(cls_PropLog_Oweaken__left_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_proplog_othms(B,C),tc_proplog_opl(C))
| ~ c_lessequals(B,D,tc_set(tc_proplog_opl(C)))
| c_in(A,c_proplog_othms(D,C),tc_proplog_opl(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165580352,plain,
( ~ c_in(A,c_proplog_othms(B,C),tc_proplog_opl(C))
| ~ c_lessequals(B,D,tc_set(tc_proplog_opl(C)))
| c_in(A,c_proplog_othms(D,C),tc_proplog_opl(C)) ),
inference(rewrite,[status(thm)],[cls_PropLog_Oweaken__left_0]),
[] ).
cnf(176950696,plain,
( ~ c_lessequals(c_proplog_ohyps(v_p,B,t_a),A,tc_set(tc_proplog_opl(t_a)))
| ~ c_lessequals(c_minus(A,v_f,tc_set(tc_proplog_opl(t_a))),C,tc_set(tc_proplog_opl(t_a)))
| c_in(v_p,c_proplog_othms(C,t_a),tc_proplog_opl(t_a)) ),
inference(resolution,[status(thm)],[176119200,165580352]),
[] ).
fof(cls_PropLog_Othms__excluded__middle__rule_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_proplog_othms(c_insert(B,C,tc_proplog_opl(D)),D),tc_proplog_opl(D))
| ~ c_in(A,c_proplog_othms(c_insert(c_proplog_opl_oop_a_n_62(B,c_proplog_opl_ofalse,D),C,tc_proplog_opl(D)),D),tc_proplog_opl(D))
| c_in(A,c_proplog_othms(C,D),tc_proplog_opl(D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165568136,plain,
( ~ c_in(A,c_proplog_othms(c_insert(B,C,tc_proplog_opl(D)),D),tc_proplog_opl(D))
| ~ c_in(A,c_proplog_othms(c_insert(c_proplog_opl_oop_a_n_62(B,c_proplog_opl_ofalse,D),C,tc_proplog_opl(D)),D),tc_proplog_opl(D))
| c_in(A,c_proplog_othms(C,D),tc_proplog_opl(D)) ),
inference(rewrite,[status(thm)],[cls_PropLog_Othms__excluded__middle__rule_0]),
[] ).
cnf(178523592,plain,
( ~ c_lessequals(c_proplog_ohyps(v_p,B,t_a),A,tc_set(tc_proplog_opl(t_a)))
| ~ c_lessequals(c_minus(A,v_f,tc_set(tc_proplog_opl(t_a))),c_insert(c_proplog_opl_oop_a_n_62(C,c_proplog_opl_ofalse,t_a),D,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a)))
| ~ c_in(v_p,c_proplog_othms(c_insert(C,D,tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a))
| c_in(v_p,c_proplog_othms(D,t_a),tc_proplog_opl(t_a)) ),
inference(resolution,[status(thm)],[176950696,165568136]),
[] ).
fof(cls_PropLog_Ohyps__Diff_0,plain,
! [A,B,C,D] : c_lessequals(c_proplog_ohyps(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),c_insert(c_proplog_opl_oop_a_n_62(c_proplog_opl_ovar(C,D),c_proplog_opl_ofalse,D),c_minus(c_proplog_ohyps(A,B,D),c_insert(c_proplog_opl_ovar(C,D),c_emptyset,tc_proplog_opl(D)),tc_set(tc_proplog_opl(D))),tc_proplog_opl(D)),tc_set(tc_proplog_opl(D))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165511208,plain,
c_lessequals(c_proplog_ohyps(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),c_insert(c_proplog_opl_oop_a_n_62(c_proplog_opl_ovar(C,D),c_proplog_opl_ofalse,D),c_minus(c_proplog_ohyps(A,B,D),c_insert(c_proplog_opl_ovar(C,D),c_emptyset,tc_proplog_opl(D)),tc_set(tc_proplog_opl(D))),tc_proplog_opl(D)),tc_set(tc_proplog_opl(D))),
inference(rewrite,[status(thm)],[cls_PropLog_Ohyps__Diff_0]),
[] ).
cnf(184131640,plain,
( ~ c_lessequals(c_minus(c_insert(c_proplog_opl_oop_a_n_62(c_proplog_opl_ovar(D,t_a),c_proplog_opl_ofalse,t_a),c_minus(c_proplog_ohyps(v_p,C,t_a),c_insert(c_proplog_opl_ovar(D,t_a),c_emptyset,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),tc_proplog_opl(t_a)),v_f,tc_set(tc_proplog_opl(t_a))),c_insert(c_proplog_opl_oop_a_n_62(A,c_proplog_opl_ofalse,t_a),B,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a)))
| ~ c_in(v_p,c_proplog_othms(c_insert(A,B,tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a))
| c_in(v_p,c_proplog_othms(B,t_a),tc_proplog_opl(t_a)) ),
inference(resolution,[status(thm)],[178523592,165511208]),
[] ).
fof(cls_PropLog_Oinsert__Diff__subset2_0,plain,
! [A,B,C,D,E] : c_lessequals(c_minus(c_insert(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),E,tc_set(D)),c_insert(A,c_minus(B,c_insert(C,E,D),tc_set(D)),D),tc_set(D)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165524464,plain,
c_lessequals(c_minus(c_insert(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),E,tc_set(D)),c_insert(A,c_minus(B,c_insert(C,E,D),tc_set(D)),D),tc_set(D)),
inference(rewrite,[status(thm)],[cls_PropLog_Oinsert__Diff__subset2_0]),
[] ).
cnf(184592248,plain,
( ~ c_in(v_p,c_proplog_othms(c_insert(c_proplog_opl_ovar(B,t_a),c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(c_proplog_opl_ovar(B,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a))
| c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(c_proplog_opl_ovar(B,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a)) ),
inference(resolution,[status(thm)],[184131640,165524464]),
[] ).
cnf(176083608,plain,
( ~ c_lessequals(c_minus(c_proplog_ohyps(v_p,B,t_a),v_f,tc_set(tc_proplog_opl(t_a))),A,tc_set(tc_proplog_opl(t_a)))
| c_in(v_p,c_proplog_othms(A,t_a),tc_proplog_opl(t_a)) ),
inference(resolution,[status(thm)],[165580352,165584832]),
[] ).
fof(cls_PropLog_Oinsert__Diff__same_0,plain,
! [A,B,C,D] : c_lessequals(c_minus(A,B,tc_set(C)),c_insert(D,c_minus(A,c_insert(D,B,C),tc_set(C)),C),tc_set(C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),
[] ).
cnf(165520016,plain,
c_lessequals(c_minus(A,B,tc_set(C)),c_insert(D,c_minus(A,c_insert(D,B,C),tc_set(C)),C),tc_set(C)),
inference(rewrite,[status(thm)],[cls_PropLog_Oinsert__Diff__same_0]),
[] ).
cnf(176164560,plain,
c_in(v_p,c_proplog_othms(c_insert(B,c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(B,v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a)),
inference(resolution,[status(thm)],[176083608,165520016]),
[] ).
cnf(184670144,plain,
c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(c_proplog_opl_ovar(B,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a)),
inference(resolution,[status(thm)],[184592248,176164560]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[165593816,184670144]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_5,plain,(~c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,v_t,t_a),c_insert(c_proplog_opl_ovar(v_v,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165593816,plain,(~c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,v_t,t_a),c_insert(c_proplog_opl_ovar(v_v,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_5]),[]).
%
% fof(cls_PropLog_ODiff__weaken__left_0,plain,(~c_in(A,c_proplog_othms(c_minus(B,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D))|~c_lessequals(B,E,tc_set(tc_proplog_opl(D)))|c_in(A,c_proplog_othms(c_minus(E,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165501112,plain,(~c_in(A,c_proplog_othms(c_minus(B,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D))|~c_lessequals(B,E,tc_set(tc_proplog_opl(D)))|c_in(A,c_proplog_othms(c_minus(E,C,tc_set(tc_proplog_opl(D))),D),tc_proplog_opl(D))),inference(rewrite,[status(thm)],[cls_PropLog_ODiff__weaken__left_0]),[]).
%
% fof(cls_conjecture_3,plain,(c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),v_f,tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165584832,plain,(c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),v_f,tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a))),inference(rewrite,[status(thm)],[cls_conjecture_3]),[]).
%
% cnf(176119200,plain,(~c_lessequals(c_proplog_ohyps(v_p,B,t_a),A,tc_set(tc_proplog_opl(t_a)))|c_in(v_p,c_proplog_othms(c_minus(A,v_f,tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[165501112,165584832]),[]).
%
% fof(cls_PropLog_Oweaken__left_0,plain,(~c_in(A,c_proplog_othms(B,C),tc_proplog_opl(C))|~c_lessequals(B,D,tc_set(tc_proplog_opl(C)))|c_in(A,c_proplog_othms(D,C),tc_proplog_opl(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165580352,plain,(~c_in(A,c_proplog_othms(B,C),tc_proplog_opl(C))|~c_lessequals(B,D,tc_set(tc_proplog_opl(C)))|c_in(A,c_proplog_othms(D,C),tc_proplog_opl(C))),inference(rewrite,[status(thm)],[cls_PropLog_Oweaken__left_0]),[]).
%
% cnf(176950696,plain,(~c_lessequals(c_proplog_ohyps(v_p,B,t_a),A,tc_set(tc_proplog_opl(t_a)))|~c_lessequals(c_minus(A,v_f,tc_set(tc_proplog_opl(t_a))),C,tc_set(tc_proplog_opl(t_a)))|c_in(v_p,c_proplog_othms(C,t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[176119200,165580352]),[]).
%
% fof(cls_PropLog_Othms__excluded__middle__rule_0,plain,(~c_in(A,c_proplog_othms(c_insert(B,C,tc_proplog_opl(D)),D),tc_proplog_opl(D))|~c_in(A,c_proplog_othms(c_insert(c_proplog_opl_oop_a_n_62(B,c_proplog_opl_ofalse,D),C,tc_proplog_opl(D)),D),tc_proplog_opl(D))|c_in(A,c_proplog_othms(C,D),tc_proplog_opl(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165568136,plain,(~c_in(A,c_proplog_othms(c_insert(B,C,tc_proplog_opl(D)),D),tc_proplog_opl(D))|~c_in(A,c_proplog_othms(c_insert(c_proplog_opl_oop_a_n_62(B,c_proplog_opl_ofalse,D),C,tc_proplog_opl(D)),D),tc_proplog_opl(D))|c_in(A,c_proplog_othms(C,D),tc_proplog_opl(D))),inference(rewrite,[status(thm)],[cls_PropLog_Othms__excluded__middle__rule_0]),[]).
%
% cnf(178523592,plain,(~c_lessequals(c_proplog_ohyps(v_p,B,t_a),A,tc_set(tc_proplog_opl(t_a)))|~c_lessequals(c_minus(A,v_f,tc_set(tc_proplog_opl(t_a))),c_insert(c_proplog_opl_oop_a_n_62(C,c_proplog_opl_ofalse,t_a),D,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a)))|~c_in(v_p,c_proplog_othms(c_insert(C,D,tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a))|c_in(v_p,c_proplog_othms(D,t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[176950696,165568136]),[]).
%
% fof(cls_PropLog_Ohyps__Diff_0,plain,(c_lessequals(c_proplog_ohyps(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),c_insert(c_proplog_opl_oop_a_n_62(c_proplog_opl_ovar(C,D),c_proplog_opl_ofalse,D),c_minus(c_proplog_ohyps(A,B,D),c_insert(c_proplog_opl_ovar(C,D),c_emptyset,tc_proplog_opl(D)),tc_set(tc_proplog_opl(D))),tc_proplog_opl(D)),tc_set(tc_proplog_opl(D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165511208,plain,(c_lessequals(c_proplog_ohyps(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),c_insert(c_proplog_opl_oop_a_n_62(c_proplog_opl_ovar(C,D),c_proplog_opl_ofalse,D),c_minus(c_proplog_ohyps(A,B,D),c_insert(c_proplog_opl_ovar(C,D),c_emptyset,tc_proplog_opl(D)),tc_set(tc_proplog_opl(D))),tc_proplog_opl(D)),tc_set(tc_proplog_opl(D)))),inference(rewrite,[status(thm)],[cls_PropLog_Ohyps__Diff_0]),[]).
%
% cnf(184131640,plain,(~c_lessequals(c_minus(c_insert(c_proplog_opl_oop_a_n_62(c_proplog_opl_ovar(D,t_a),c_proplog_opl_ofalse,t_a),c_minus(c_proplog_ohyps(v_p,C,t_a),c_insert(c_proplog_opl_ovar(D,t_a),c_emptyset,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),tc_proplog_opl(t_a)),v_f,tc_set(tc_proplog_opl(t_a))),c_insert(c_proplog_opl_oop_a_n_62(A,c_proplog_opl_ofalse,t_a),B,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a)))|~c_in(v_p,c_proplog_othms(c_insert(A,B,tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a))|c_in(v_p,c_proplog_othms(B,t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[178523592,165511208]),[]).
%
% fof(cls_PropLog_Oinsert__Diff__subset2_0,plain,(c_lessequals(c_minus(c_insert(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),E,tc_set(D)),c_insert(A,c_minus(B,c_insert(C,E,D),tc_set(D)),D),tc_set(D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165524464,plain,(c_lessequals(c_minus(c_insert(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),E,tc_set(D)),c_insert(A,c_minus(B,c_insert(C,E,D),tc_set(D)),D),tc_set(D))),inference(rewrite,[status(thm)],[cls_PropLog_Oinsert__Diff__subset2_0]),[]).
%
% cnf(184592248,plain,(~c_in(v_p,c_proplog_othms(c_insert(c_proplog_opl_ovar(B,t_a),c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(c_proplog_opl_ovar(B,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a))|c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(c_proplog_opl_ovar(B,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[184131640,165524464]),[]).
%
% cnf(176083608,plain,(~c_lessequals(c_minus(c_proplog_ohyps(v_p,B,t_a),v_f,tc_set(tc_proplog_opl(t_a))),A,tc_set(tc_proplog_opl(t_a)))|c_in(v_p,c_proplog_othms(A,t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[165580352,165584832]),[]).
%
% fof(cls_PropLog_Oinsert__Diff__same_0,plain,(c_lessequals(c_minus(A,B,tc_set(C)),c_insert(D,c_minus(A,c_insert(D,B,C),tc_set(C)),C),tc_set(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL429-2.tptp',unknown),[]).
%
% cnf(165520016,plain,(c_lessequals(c_minus(A,B,tc_set(C)),c_insert(D,c_minus(A,c_insert(D,B,C),tc_set(C)),C),tc_set(C))),inference(rewrite,[status(thm)],[cls_PropLog_Oinsert__Diff__same_0]),[]).
%
% cnf(176164560,plain,(c_in(v_p,c_proplog_othms(c_insert(B,c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(B,v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),tc_proplog_opl(t_a)),t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[176083608,165520016]),[]).
%
% cnf(184670144,plain,(c_in(v_p,c_proplog_othms(c_minus(c_proplog_ohyps(v_p,A,t_a),c_insert(c_proplog_opl_ovar(B,t_a),v_f,tc_proplog_opl(t_a)),tc_set(tc_proplog_opl(t_a))),t_a),tc_proplog_opl(t_a))),inference(resolution,[status(thm)],[184592248,176164560]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[165593816,184670144]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------