TSTP Solution File: SET821-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET821-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:38:03 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 17 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 8 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_2,plain,
! [A] :
( c_in(v_c,A,tc_intdef_oint)
| ~ c_in(v_b,A,tc_intdef_oint)
| c_in(v_a,A,tc_intdef_oint) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171062560,plain,
( c_in(v_c,A,tc_intdef_oint)
| ~ c_in(v_b,A,tc_intdef_oint)
| c_in(v_a,A,tc_intdef_oint) ),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
fof(cls_Set_OinsertCI_1,plain,
! [A,B,C] : c_in(A,c_insert(A,B,C),C),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171026592,plain,
c_in(A,c_insert(A,B,C),C),
inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),
[] ).
cnf(184216336,plain,
( c_in(v_c,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
| c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint) ),
inference(resolution,[status(thm)],[171062560,171026592]),
[] ).
fof(cls_Set_OinsertE_0,plain,
! [A,B,C,D] :
( ~ c_in(A,c_insert(B,C,D),D)
| c_in(A,C,D)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171042392,plain,
( ~ c_in(A,c_insert(B,C,D),D)
| c_in(A,C,D)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[cls_Set_OinsertE_0]),
[] ).
cnf(184988720,plain,
( c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
| c_in(v_c,A,tc_intdef_oint)
| $equal(v_b,v_c) ),
inference(resolution,[status(thm)],[184216336,171042392]),
[] ).
fof(cls_conjecture_1,plain,
c_less(v_b,v_c,tc_intdef_oint),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171055344,plain,
c_less(v_b,v_c,tc_intdef_oint),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
cnf(186668152,plain,
( c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
| c_in(v_c,A,tc_intdef_oint)
| c_less(v_c,v_c,tc_intdef_oint) ),
inference(paramodulation,[status(thm)],[184988720,171055344,theory(equality)]),
[] ).
fof(cls_Orderings_Oorder__less__irrefl__iff1_0,plain,
! [A,B] :
( ~ class_orderings_oorder(A)
| ~ c_less(B,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(170999880,plain,
( ~ class_orderings_oorder(A)
| ~ c_less(B,B,A) ),
inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__irrefl__iff1_0]),
[] ).
fof(clsarity_IntDef__Oint_31,plain,
class_orderings_oorder(tc_intdef_oint),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171067416,plain,
class_orderings_oorder(tc_intdef_oint),
inference(rewrite,[status(thm)],[clsarity_IntDef__Oint_31]),
[] ).
cnf(184144672,plain,
~ c_less(A,A,tc_intdef_oint),
inference(resolution,[status(thm)],[170999880,171067416]),
[] ).
cnf(190718808,plain,
( c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)
| c_in(v_c,A,tc_intdef_oint) ),
inference(resolution,[status(thm)],[186668152,184144672]),
[] ).
cnf(190887128,plain,
( c_in(v_c,A,tc_intdef_oint)
| c_in(v_a,A,tc_intdef_oint)
| $equal(v_b,v_a) ),
inference(resolution,[status(thm)],[190718808,171042392]),
[] ).
fof(cls_conjecture_0,plain,
c_less(v_a,v_b,tc_intdef_oint),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171047136,plain,
c_less(v_a,v_b,tc_intdef_oint),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(191111784,plain,
( c_in(v_c,A,tc_intdef_oint)
| c_in(v_a,A,tc_intdef_oint)
| c_less(v_b,v_b,tc_intdef_oint) ),
inference(paramodulation,[status(thm)],[190887128,171047136,theory(equality)]),
[] ).
cnf(191130656,plain,
( c_in(v_c,A,tc_intdef_oint)
| c_in(v_a,A,tc_intdef_oint) ),
inference(resolution,[status(thm)],[191111784,184144672]),
[] ).
fof(cls_Set_OComplD__dest_0,plain,
! [A,B,C] :
( ~ c_in(A,B,C)
| ~ c_in(A,c_uminus(B,tc_set(C)),C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171006728,plain,
( ~ c_in(A,B,C)
| ~ c_in(A,c_uminus(B,tc_set(C)),C) ),
inference(rewrite,[status(thm)],[cls_Set_OComplD__dest_0]),
[] ).
cnf(184189344,plain,
~ c_in(A,c_uminus(c_insert(A,C,B),tc_set(B)),B),
inference(resolution,[status(thm)],[171006728,171026592]),
[] ).
cnf(191288904,plain,
c_in(v_a,c_uminus(c_insert(v_c,A,tc_intdef_oint),tc_set(tc_intdef_oint)),tc_intdef_oint),
inference(resolution,[status(thm)],[191130656,184189344]),
[] ).
fof(cls_Set_OinsertCI_0,plain,
! [A,B,C,D] :
( ~ c_in(A,B,C)
| c_in(A,c_insert(D,B,C),C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),
[] ).
cnf(171022496,plain,
( ~ c_in(A,B,C)
| c_in(A,c_insert(D,B,C),C) ),
inference(rewrite,[status(thm)],[cls_Set_OinsertCI_0]),
[] ).
cnf(184168272,plain,
c_in(A,c_insert(C,c_insert(A,D,B),B),B),
inference(resolution,[status(thm)],[171022496,171026592]),
[] ).
cnf(184353696,plain,
~ c_in(A,c_uminus(c_insert(C,c_insert(A,D,B),B),tc_set(B)),B),
inference(resolution,[status(thm)],[171006728,184168272]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[191288904,184353696]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_2,plain,(c_in(v_c,A,tc_intdef_oint)|~c_in(v_b,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171062560,plain,(c_in(v_c,A,tc_intdef_oint)|~c_in(v_b,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% fof(cls_Set_OinsertCI_1,plain,(c_in(A,c_insert(A,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171026592,plain,(c_in(A,c_insert(A,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),[]).
%
% cnf(184216336,plain,(c_in(v_c,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)),inference(resolution,[status(thm)],[171062560,171026592]),[]).
%
% fof(cls_Set_OinsertE_0,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171042392,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),inference(rewrite,[status(thm)],[cls_Set_OinsertE_0]),[]).
%
% cnf(184988720,plain,(c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_c,A,tc_intdef_oint)|$equal(v_b,v_c)),inference(resolution,[status(thm)],[184216336,171042392]),[]).
%
% fof(cls_conjecture_1,plain,(c_less(v_b,v_c,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171055344,plain,(c_less(v_b,v_c,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% cnf(186668152,plain,(c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_c,A,tc_intdef_oint)|c_less(v_c,v_c,tc_intdef_oint)),inference(paramodulation,[status(thm)],[184988720,171055344,theory(equality)]),[]).
%
% fof(cls_Orderings_Oorder__less__irrefl__iff1_0,plain,(~class_orderings_oorder(A)|~c_less(B,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(170999880,plain,(~class_orderings_oorder(A)|~c_less(B,B,A)),inference(rewrite,[status(thm)],[cls_Orderings_Oorder__less__irrefl__iff1_0]),[]).
%
% fof(clsarity_IntDef__Oint_31,plain,(class_orderings_oorder(tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171067416,plain,(class_orderings_oorder(tc_intdef_oint)),inference(rewrite,[status(thm)],[clsarity_IntDef__Oint_31]),[]).
%
% cnf(184144672,plain,(~c_less(A,A,tc_intdef_oint)),inference(resolution,[status(thm)],[170999880,171067416]),[]).
%
% cnf(190718808,plain,(c_in(v_a,c_insert(v_b,A,tc_intdef_oint),tc_intdef_oint)|c_in(v_c,A,tc_intdef_oint)),inference(resolution,[status(thm)],[186668152,184144672]),[]).
%
% cnf(190887128,plain,(c_in(v_c,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)|$equal(v_b,v_a)),inference(resolution,[status(thm)],[190718808,171042392]),[]).
%
% fof(cls_conjecture_0,plain,(c_less(v_a,v_b,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171047136,plain,(c_less(v_a,v_b,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(191111784,plain,(c_in(v_c,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)|c_less(v_b,v_b,tc_intdef_oint)),inference(paramodulation,[status(thm)],[190887128,171047136,theory(equality)]),[]).
%
% cnf(191130656,plain,(c_in(v_c,A,tc_intdef_oint)|c_in(v_a,A,tc_intdef_oint)),inference(resolution,[status(thm)],[191111784,184144672]),[]).
%
% fof(cls_Set_OComplD__dest_0,plain,(~c_in(A,B,C)|~c_in(A,c_uminus(B,tc_set(C)),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171006728,plain,(~c_in(A,B,C)|~c_in(A,c_uminus(B,tc_set(C)),C)),inference(rewrite,[status(thm)],[cls_Set_OComplD__dest_0]),[]).
%
% cnf(184189344,plain,(~c_in(A,c_uminus(c_insert(A,C,B),tc_set(B)),B)),inference(resolution,[status(thm)],[171006728,171026592]),[]).
%
% cnf(191288904,plain,(c_in(v_a,c_uminus(c_insert(v_c,A,tc_intdef_oint),tc_set(tc_intdef_oint)),tc_intdef_oint)),inference(resolution,[status(thm)],[191130656,184189344]),[]).
%
% fof(cls_Set_OinsertCI_0,plain,(~c_in(A,B,C)|c_in(A,c_insert(D,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET821-2.tptp',unknown),[]).
%
% cnf(171022496,plain,(~c_in(A,B,C)|c_in(A,c_insert(D,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OinsertCI_0]),[]).
%
% cnf(184168272,plain,(c_in(A,c_insert(C,c_insert(A,D,B),B),B)),inference(resolution,[status(thm)],[171022496,171026592]),[]).
%
% cnf(184353696,plain,(~c_in(A,c_uminus(c_insert(C,c_insert(A,D,B),B),tc_set(B)),B)),inference(resolution,[status(thm)],[171006728,184168272]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[191288904,184353696]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------