TSTP Solution File: SET822-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET822-2 : 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 @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:38:13 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 35 ( 5 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_1,plain,
! [A,B] :
( ~ c_in(v_f(A),B,tc_intdef_oint)
| c_in(v_x(A,B),B,tc_intdef_oint) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
[] ).
cnf(150384752,plain,
( ~ c_in(v_f(A),B,tc_intdef_oint)
| c_in(v_x(A,B),B,tc_intdef_oint) ),
inference(rewrite,[status(thm)],[cls_conjecture_1]),
[] ).
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/SET822-2.tptp',unknown),
[] ).
cnf(150355960,plain,
c_in(A,c_insert(A,B,C),C),
inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),
[] ).
cnf(163487504,plain,
c_in(v_x(A,c_insert(v_f(A),B,tc_intdef_oint)),c_insert(v_f(A),B,tc_intdef_oint),tc_intdef_oint),
inference(resolution,[status(thm)],[150384752,150355960]),
[] ).
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/SET822-2.tptp',unknown),
[] ).
cnf(150370016,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]),
[] ).
fof(cls_Set_OemptyE_0,plain,
! [A,B] : ~ c_in(A,c_emptyset,B),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
[] ).
cnf(150350976,plain,
~ c_in(A,c_emptyset,B),
inference(rewrite,[status(thm)],[cls_Set_OemptyE_0]),
[] ).
cnf(163452624,plain,
( ~ c_in(A,c_insert(B,c_emptyset,C),C)
| $equal(B,A) ),
inference(resolution,[status(thm)],[150370016,150350976]),
[] ).
cnf(163702344,plain,
$equal(v_f(A),v_x(A,c_insert(v_f(A),c_emptyset,tc_intdef_oint))),
inference(resolution,[status(thm)],[163487504,163452624]),
[] ).
fof(cls_conjecture_2,plain,
! [A,B] :
( ~ c_in(v_f(A),B,tc_intdef_oint)
| ~ v_p(v_x(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
[] ).
cnf(150389744,plain,
( ~ c_in(v_f(A),B,tc_intdef_oint)
| ~ v_p(v_x(A,B)) ),
inference(rewrite,[status(thm)],[cls_conjecture_2]),
[] ).
cnf(163474544,plain,
~ v_p(v_x(A,c_insert(v_f(A),B,tc_intdef_oint))),
inference(resolution,[status(thm)],[150389744,150355960]),
[] ).
cnf(163797408,plain,
~ v_p(v_f(A)),
inference(paramodulation,[status(thm)],[163702344,163474544,theory(equality)]),
[] ).
fof(cls_conjecture_0,plain,
v_p(v_f(v_b)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),
[] ).
cnf(150378936,plain,
v_p(v_f(v_b)),
inference(rewrite,[status(thm)],[cls_conjecture_0]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[163797408,150378936]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_1,plain,(~c_in(v_f(A),B,tc_intdef_oint)|c_in(v_x(A,B),B,tc_intdef_oint)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
%
% cnf(150384752,plain,(~c_in(v_f(A),B,tc_intdef_oint)|c_in(v_x(A,B),B,tc_intdef_oint)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
%
% fof(cls_Set_OinsertCI_1,plain,(c_in(A,c_insert(A,B,C),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
%
% cnf(150355960,plain,(c_in(A,c_insert(A,B,C),C)),inference(rewrite,[status(thm)],[cls_Set_OinsertCI_1]),[]).
%
% cnf(163487504,plain,(c_in(v_x(A,c_insert(v_f(A),B,tc_intdef_oint)),c_insert(v_f(A),B,tc_intdef_oint),tc_intdef_oint)),inference(resolution,[status(thm)],[150384752,150355960]),[]).
%
% fof(cls_Set_OinsertE_0,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
%
% cnf(150370016,plain,(~c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|$equal(B,A)),inference(rewrite,[status(thm)],[cls_Set_OinsertE_0]),[]).
%
% fof(cls_Set_OemptyE_0,plain,(~c_in(A,c_emptyset,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
%
% cnf(150350976,plain,(~c_in(A,c_emptyset,B)),inference(rewrite,[status(thm)],[cls_Set_OemptyE_0]),[]).
%
% cnf(163452624,plain,(~c_in(A,c_insert(B,c_emptyset,C),C)|$equal(B,A)),inference(resolution,[status(thm)],[150370016,150350976]),[]).
%
% cnf(163702344,plain,($equal(v_f(A),v_x(A,c_insert(v_f(A),c_emptyset,tc_intdef_oint)))),inference(resolution,[status(thm)],[163487504,163452624]),[]).
%
% fof(cls_conjecture_2,plain,(~c_in(v_f(A),B,tc_intdef_oint)|~v_p(v_x(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
%
% cnf(150389744,plain,(~c_in(v_f(A),B,tc_intdef_oint)|~v_p(v_x(A,B))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
%
% cnf(163474544,plain,(~v_p(v_x(A,c_insert(v_f(A),B,tc_intdef_oint)))),inference(resolution,[status(thm)],[150389744,150355960]),[]).
%
% cnf(163797408,plain,(~v_p(v_f(A))),inference(paramodulation,[status(thm)],[163702344,163474544,theory(equality)]),[]).
%
% fof(cls_conjecture_0,plain,(v_p(v_f(v_b))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET822-2.tptp',unknown),[]).
%
% cnf(150378936,plain,(v_p(v_f(v_b))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[163797408,150378936]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------