TSTP Solution File: SET930+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET930+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:48:15 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 138 ( 66 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 173 ( 76 ~; 51 |; 41 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/tmp/tmp31I0UE/sel_SET930+1.p_1',t73_zfmisc_1) ).
fof(3,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
file('/tmp/tmp31I0UE/sel_SET930+1.p_1',t72_zfmisc_1) ).
fof(4,conjecture,
! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
file('/tmp/tmp31I0UE/sel_SET930+1.p_1',t74_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp31I0UE/sel_SET930+1.p_1',commutativity_k2_tarski) ).
fof(9,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
file('/tmp/tmp31I0UE/sel_SET930+1.p_1',l39_zfmisc_1) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != empty_set
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(12,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).
fof(14,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(15,plain,
! [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != empty_set
| ( in(X1,X3)
& in(X2,X3) ) )
& ( ~ in(X1,X3)
| ~ in(X2,X3)
| set_difference(unordered_pair(X1,X2),X3) = empty_set ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != empty_set
| ( in(X4,X6)
& in(X5,X6) ) )
& ( ~ in(X4,X6)
| ~ in(X5,X6)
| set_difference(unordered_pair(X4,X5),X6) = empty_set ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X5,X6] :
( ( in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) != empty_set )
& ( in(X5,X6)
| set_difference(unordered_pair(X4,X5),X6) != empty_set )
& ( ~ in(X4,X6)
| ~ in(X5,X6)
| set_difference(unordered_pair(X4,X5),X6) = empty_set ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( set_difference(unordered_pair(X1,X2),X3) = empty_set
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(24,plain,
! [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
| ( ~ in(X1,X3)
& ~ in(X2,X3) ) )
& ( in(X1,X3)
| in(X2,X3)
| set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(25,plain,
! [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != unordered_pair(X4,X5)
| ( ~ in(X4,X6)
& ~ in(X5,X6) ) )
& ( in(X4,X6)
| in(X5,X6)
| set_difference(unordered_pair(X4,X5),X6) = unordered_pair(X4,X5) ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) != unordered_pair(X4,X5) )
& ( ~ in(X5,X6)
| set_difference(unordered_pair(X4,X5),X6) != unordered_pair(X4,X5) )
& ( in(X4,X6)
| in(X5,X6)
| set_difference(unordered_pair(X4,X5),X6) = unordered_pair(X4,X5) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(27,plain,
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
| in(X2,X3)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(30,negated_conjecture,
? [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) != empty_set
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(31,negated_conjecture,
? [X4,X5,X6] :
( set_difference(unordered_pair(X4,X5),X6) != empty_set
& set_difference(unordered_pair(X4,X5),X6) != singleton(X4)
& set_difference(unordered_pair(X4,X5),X6) != singleton(X5)
& set_difference(unordered_pair(X4,X5),X6) != unordered_pair(X4,X5) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,negated_conjecture,
( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != empty_set
& set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != singleton(esk2_0)
& set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != singleton(esk3_0)
& set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[31]) ).
cnf(33,negated_conjecture,
set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,negated_conjecture,
set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != singleton(esk3_0),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(35,negated_conjecture,
set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != singleton(esk2_0),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(36,negated_conjecture,
set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[32]) ).
fof(37,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(38,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[37]) ).
fof(46,plain,
! [X1,X2,X3] :
( ( set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
| ( ~ in(X1,X3)
& ( in(X2,X3)
| X1 = X2 ) ) )
& ( in(X1,X3)
| ( ~ in(X2,X3)
& X1 != X2 )
| set_difference(unordered_pair(X1,X2),X3) = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(47,plain,
! [X4,X5,X6] :
( ( set_difference(unordered_pair(X4,X5),X6) != singleton(X4)
| ( ~ in(X4,X6)
& ( in(X5,X6)
| X4 = X5 ) ) )
& ( in(X4,X6)
| ( ~ in(X5,X6)
& X4 != X5 )
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,plain,
! [X4,X5,X6] :
( ( ~ in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( in(X5,X6)
| X4 = X5
| set_difference(unordered_pair(X4,X5),X6) != singleton(X4) )
& ( ~ in(X5,X6)
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) )
& ( X4 != X5
| in(X4,X6)
| set_difference(unordered_pair(X4,X5),X6) = singleton(X4) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(50,plain,
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| in(X1,X3)
| ~ in(X2,X3) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(64,negated_conjecture,
( ~ in(esk3_0,esk4_0)
| ~ in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[36,18,theory(equality)]) ).
cnf(72,plain,
( set_difference(unordered_pair(X2,X1),X3) = singleton(X1)
| in(X1,X3)
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[50,38,theory(equality)]) ).
cnf(75,negated_conjecture,
( in(esk2_0,esk4_0)
| ~ in(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[35,50,theory(equality)]) ).
cnf(92,negated_conjecture,
( in(esk2_0,esk4_0)
| in(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[33,27,theory(equality)]) ).
cnf(107,negated_conjecture,
in(esk2_0,esk4_0),
inference(csr,[status(thm)],[75,92]) ).
cnf(109,negated_conjecture,
( ~ in(esk3_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[64,107,theory(equality)]) ).
cnf(110,negated_conjecture,
~ in(esk3_0,esk4_0),
inference(cn,[status(thm)],[109,theory(equality)]) ).
cnf(230,negated_conjecture,
( in(esk3_0,esk4_0)
| ~ in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[34,72,theory(equality)]) ).
cnf(250,negated_conjecture,
( in(esk3_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[230,107,theory(equality)]) ).
cnf(251,negated_conjecture,
in(esk3_0,esk4_0),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(252,negated_conjecture,
$false,
inference(sr,[status(thm)],[251,110,theory(equality)]) ).
cnf(253,negated_conjecture,
$false,
252,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET930+1.p
% --creating new selector for []
% -running prover on /tmp/tmp31I0UE/sel_SET930+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET930+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET930+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET930+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------