TSTP Solution File: SEU149+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU149+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 04:52:54 EST 2010
% Result : Theorem 0.45s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 141 ( 89 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 156 ( 58 ~; 62 |; 30 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 2 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(9,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpEGyEY_/sel_SEU149+2.p_1',t69_enumset1) ).
fof(16,conjecture,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/tmp/tmpEGyEY_/sel_SEU149+2.p_1',t8_zfmisc_1) ).
fof(25,axiom,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/tmp/tmpEGyEY_/sel_SEU149+2.p_1',t6_zfmisc_1) ).
fof(29,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpEGyEY_/sel_SEU149+2.p_1',commutativity_k2_tarski) ).
fof(65,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmpEGyEY_/sel_SEU149+2.p_1',l2_zfmisc_1) ).
fof(71,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpEGyEY_/sel_SEU149+2.p_1',d2_tarski) ).
fof(73,negated_conjecture,
~ ! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[16]) ).
fof(106,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[9]) ).
cnf(107,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[106]) ).
fof(127,negated_conjecture,
? [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[73]) ).
fof(128,negated_conjecture,
? [X4,X5,X6] :
( singleton(X4) = unordered_pair(X5,X6)
& X4 != X5 ),
inference(variable_rename,[status(thm)],[127]) ).
fof(129,negated_conjecture,
( singleton(esk2_0) = unordered_pair(esk3_0,esk4_0)
& esk2_0 != esk3_0 ),
inference(skolemize,[status(esa)],[128]) ).
cnf(130,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[129]) ).
cnf(131,negated_conjecture,
singleton(esk2_0) = unordered_pair(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[129]) ).
fof(160,plain,
! [X1,X2] :
( ~ subset(singleton(X1),singleton(X2))
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(161,plain,
! [X3,X4] :
( ~ subset(singleton(X3),singleton(X4))
| X3 = X4 ),
inference(variable_rename,[status(thm)],[160]) ).
cnf(162,plain,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[161]) ).
fof(176,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[29]) ).
cnf(177,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[176]) ).
fof(292,plain,
! [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| in(X1,X2) )
& ( ~ in(X1,X2)
| subset(singleton(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[65]) ).
fof(293,plain,
! [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(variable_rename,[status(thm)],[292]) ).
cnf(294,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[293]) ).
fof(328,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)],[71]) ).
fof(329,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)],[328]) ).
fof(330,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(esk16_3(X5,X6,X7),X7)
| ( esk16_3(X5,X6,X7) != X5
& esk16_3(X5,X6,X7) != X6 ) )
& ( in(esk16_3(X5,X6,X7),X7)
| esk16_3(X5,X6,X7) = X5
| esk16_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[329]) ).
fof(331,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(esk16_3(X5,X6,X7),X7)
| ( esk16_3(X5,X6,X7) != X5
& esk16_3(X5,X6,X7) != X6 ) )
& ( in(esk16_3(X5,X6,X7),X7)
| esk16_3(X5,X6,X7) = X5
| esk16_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[330]) ).
fof(332,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) )
& ( esk16_3(X5,X6,X7) != X5
| ~ in(esk16_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk16_3(X5,X6,X7) != X6
| ~ in(esk16_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk16_3(X5,X6,X7),X7)
| esk16_3(X5,X6,X7) = X5
| esk16_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[331]) ).
cnf(336,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[332]) ).
cnf(342,negated_conjecture,
unordered_pair(esk3_0,esk4_0) = unordered_pair(esk2_0,esk2_0),
inference(rw,[status(thm)],[131,107,theory(equality)]),
[unfolding] ).
cnf(345,plain,
( X1 = X2
| ~ subset(unordered_pair(X1,X1),unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[162,107,theory(equality)]),107,theory(equality)]),
[unfolding] ).
cnf(348,plain,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[294,107,theory(equality)]),
[unfolding] ).
cnf(535,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[336,theory(equality)]) ).
cnf(4894,negated_conjecture,
( in(esk4_0,X1)
| unordered_pair(esk2_0,esk2_0) != X1 ),
inference(spm,[status(thm)],[535,342,theory(equality)]) ).
cnf(4907,negated_conjecture,
in(esk4_0,unordered_pair(esk2_0,esk2_0)),
inference(er,[status(thm)],[4894,theory(equality)]) ).
cnf(4914,negated_conjecture,
subset(unordered_pair(esk4_0,esk4_0),unordered_pair(esk2_0,esk2_0)),
inference(spm,[status(thm)],[348,4907,theory(equality)]) ).
cnf(4937,negated_conjecture,
esk4_0 = esk2_0,
inference(spm,[status(thm)],[345,4914,theory(equality)]) ).
cnf(4958,negated_conjecture,
unordered_pair(esk2_0,esk3_0) = unordered_pair(esk2_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[342,4937,theory(equality)]),177,theory(equality)]) ).
cnf(4966,negated_conjecture,
( in(esk3_0,X1)
| unordered_pair(esk2_0,esk2_0) != X1 ),
inference(spm,[status(thm)],[535,4958,theory(equality)]) ).
cnf(4967,negated_conjecture,
in(esk3_0,unordered_pair(esk2_0,esk2_0)),
inference(er,[status(thm)],[4966,theory(equality)]) ).
cnf(4974,negated_conjecture,
subset(unordered_pair(esk3_0,esk3_0),unordered_pair(esk2_0,esk2_0)),
inference(spm,[status(thm)],[348,4967,theory(equality)]) ).
cnf(4997,negated_conjecture,
esk3_0 = esk2_0,
inference(spm,[status(thm)],[345,4974,theory(equality)]) ).
cnf(5015,negated_conjecture,
$false,
inference(sr,[status(thm)],[4997,130,theory(equality)]) ).
cnf(5016,negated_conjecture,
$false,
5015,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU149+2.p
% --creating new selector for []
% -running prover on /tmp/tmpEGyEY_/sel_SEU149+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU149+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU149+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU149+2.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
%
%------------------------------------------------------------------------------