TSTP Solution File: SET906+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET906+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:45:54 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 230 ( 79 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 295 ( 105 ~; 119 |; 63 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 113 ( 7 sgn 76 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmpeGQPGH/sel_SET906+1.p_1',d2_xboole_0) ).
fof(4,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpeGQPGH/sel_SET906+1.p_1',commutativity_k2_xboole_0) ).
fof(7,conjecture,
! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
file('/tmp/tmpeGQPGH/sel_SET906+1.p_1',t47_zfmisc_1) ).
fof(11,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpeGQPGH/sel_SET906+1.p_1',d3_tarski) ).
fof(12,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpeGQPGH/sel_SET906+1.p_1',d2_tarski) ).
fof(14,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(22,plain,
! [X1,X2,X3] :
( ( X3 != set_union2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| in(X4,X1)
| in(X4,X2) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X2) )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) )
& ( in(X4,X3)
| in(X4,X1)
| in(X4,X2) ) )
| X3 = set_union2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(23,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( ~ in(X9,X5)
& ~ in(X9,X6) ) )
& ( in(X9,X7)
| in(X9,X5)
| in(X9,X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
| ( ~ in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) )
& ( in(esk2_3(X5,X6,X7),X7)
| in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[23]) ).
fof(25,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) )
| X7 != set_union2(X5,X6) )
& ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
| ( ~ in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) )
& ( in(esk2_3(X5,X6,X7),X7)
| in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[24]) ).
fof(26,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X6)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X5)
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X6)
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk2_3(X5,X6,X7),X7)
| in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(30,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(36,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(37,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[36]) ).
fof(43,negated_conjecture,
? [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
& ~ in(X1,X3) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(44,negated_conjecture,
? [X4,X5,X6] :
( subset(set_union2(unordered_pair(X4,X5),X6),X6)
& ~ in(X4,X6) ),
inference(variable_rename,[status(thm)],[43]) ).
fof(45,negated_conjecture,
( subset(set_union2(unordered_pair(esk3_0,esk4_0),esk5_0),esk5_0)
& ~ in(esk3_0,esk5_0) ),
inference(skolemize,[status(esa)],[44]) ).
cnf(46,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(47,negated_conjecture,
subset(set_union2(unordered_pair(esk3_0,esk4_0),esk5_0),esk5_0),
inference(split_conjunct,[status(thm)],[45]) ).
fof(56,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(57,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[57]) ).
fof(59,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[58]) ).
fof(60,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk7_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[59]) ).
cnf(63,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(64,plain,
! [X1,X2,X3] :
( ( X3 != unordered_pair(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| X4 = X1
| X4 = X2 )
& ( ( X4 != X1
& X4 != X2 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( X4 != X1
& X4 != X2 ) )
& ( in(X4,X3)
| X4 = X1
| X4 = X2 ) )
| X3 = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(65,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( X9 != X5
& X9 != X6 ) )
& ( in(X9,X7)
| X9 = X5
| X9 = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[65]) ).
fof(67,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) )
| X7 != unordered_pair(X5,X6) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[66]) ).
fof(68,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X5
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X6
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[67]) ).
cnf(73,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(79,negated_conjecture,
subset(set_union2(esk5_0,unordered_pair(esk3_0,esk4_0)),esk5_0),
inference(rw,[status(thm)],[47,37,theory(equality)]) ).
cnf(87,plain,
( in(X1,X2)
| unordered_pair(X1,X3) != X2 ),
inference(er,[status(thm)],[73,theory(equality)]) ).
cnf(94,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[30,theory(equality)]) ).
cnf(126,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,set_union2(esk5_0,unordered_pair(esk3_0,esk4_0))) ),
inference(spm,[status(thm)],[63,79,theory(equality)]) ).
cnf(174,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[87,theory(equality)]) ).
cnf(194,plain,
in(X1,set_union2(X2,unordered_pair(X1,X3))),
inference(spm,[status(thm)],[94,174,theory(equality)]) ).
cnf(285,negated_conjecture,
in(esk3_0,esk5_0),
inference(spm,[status(thm)],[126,194,theory(equality)]) ).
cnf(291,negated_conjecture,
$false,
inference(sr,[status(thm)],[285,46,theory(equality)]) ).
cnf(292,negated_conjecture,
$false,
291,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET906+1.p
% --creating new selector for []
% -running prover on /tmp/tmpeGQPGH/sel_SET906+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET906+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET906+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET906+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
%
%------------------------------------------------------------------------------