TSTP Solution File: SEU149+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU149+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 04:52:50 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 186 ( 130 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 228 ( 83 ~; 96 |; 43 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 96 ( 6 sgn 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,conjecture,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/tmp/tmp7UOQ1r/sel_SEU149+1.p_1',t8_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp7UOQ1r/sel_SEU149+1.p_1',commutativity_k2_tarski) ).
fof(5,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmp7UOQ1r/sel_SEU149+1.p_1',d1_tarski) ).
fof(7,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmp7UOQ1r/sel_SEU149+1.p_1',d2_tarski) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[3]) ).
fof(12,negated_conjecture,
? [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(13,negated_conjecture,
? [X4,X5,X6] :
( singleton(X4) = unordered_pair(X5,X6)
& X4 != X5 ),
inference(variable_rename,[status(thm)],[12]) ).
fof(14,negated_conjecture,
( singleton(esk1_0) = unordered_pair(esk2_0,esk3_0)
& esk1_0 != esk2_0 ),
inference(skolemize,[status(esa)],[13]) ).
cnf(15,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,negated_conjecture,
singleton(esk1_0) = unordered_pair(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[14]) ).
fof(17,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[17]) ).
fof(19,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(20,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[20]) ).
fof(22,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[21]) ).
fof(23,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[22]) ).
cnf(26,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(27,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(31,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)],[7]) ).
fof(32,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)],[31]) ).
fof(33,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(esk5_3(X5,X6,X7),X7)
| ( esk5_3(X5,X6,X7) != X5
& esk5_3(X5,X6,X7) != X6 ) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[32]) ).
fof(34,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(esk5_3(X5,X6,X7),X7)
| ( esk5_3(X5,X6,X7) != X5
& esk5_3(X5,X6,X7) != X6 ) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[33]) ).
fof(35,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) )
& ( esk5_3(X5,X6,X7) != X5
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk5_3(X5,X6,X7) != X6
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| esk5_3(X5,X6,X7) = X5
| esk5_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[34]) ).
cnf(39,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(41,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(42,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[26,theory(equality)]) ).
cnf(43,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[39,theory(equality)]) ).
cnf(45,plain,
( X1 = X2
| X3 = X2
| ~ in(X2,unordered_pair(X1,X3)) ),
inference(er,[status(thm)],[41,theory(equality)]) ).
cnf(55,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[42,theory(equality)]) ).
cnf(57,negated_conjecture,
in(esk1_0,unordered_pair(esk2_0,esk3_0)),
inference(spm,[status(thm)],[55,16,theory(equality)]) ).
cnf(61,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[43,theory(equality)]) ).
cnf(66,plain,
( X1 = X2
| singleton(X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[27,61,theory(equality)]) ).
cnf(90,negated_conjecture,
( esk3_0 = esk1_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[45,57,theory(equality)]) ).
cnf(95,negated_conjecture,
esk3_0 = esk1_0,
inference(sr,[status(thm)],[90,15,theory(equality)]) ).
cnf(97,negated_conjecture,
singleton(esk1_0) = unordered_pair(esk2_0,esk1_0),
inference(rw,[status(thm)],[16,95,theory(equality)]) ).
cnf(105,negated_conjecture,
( esk1_0 = X1
| unordered_pair(esk2_0,esk1_0) != unordered_pair(X2,X1) ),
inference(spm,[status(thm)],[66,97,theory(equality)]) ).
cnf(108,negated_conjecture,
( esk1_0 = X1
| unordered_pair(esk2_0,esk1_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[105,18,theory(equality)]) ).
cnf(110,negated_conjecture,
esk1_0 = esk2_0,
inference(er,[status(thm)],[108,theory(equality)]) ).
cnf(113,negated_conjecture,
$false,
inference(sr,[status(thm)],[110,15,theory(equality)]) ).
cnf(114,negated_conjecture,
$false,
113,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU149+1.p
% --creating new selector for []
% -running prover on /tmp/tmp7UOQ1r/sel_SEU149+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU149+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU149+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU149+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
%
%------------------------------------------------------------------------------