TSTP Solution File: SEU159+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU159+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:56:03 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 209 ( 71 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 252 ( 92 ~; 109 |; 45 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 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 : 100 ( 4 sgn 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',t38_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',commutativity_k2_tarski) ).
fof(5,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',d3_tarski) ).
fof(6,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',d2_tarski) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(11,negated_conjecture,
? [X1,X2,X3] :
( ( ~ subset(unordered_pair(X1,X2),X3)
| ~ in(X1,X3)
| ~ in(X2,X3) )
& ( subset(unordered_pair(X1,X2),X3)
| ( in(X1,X3)
& in(X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(12,negated_conjecture,
? [X4,X5,X6] :
( ( ~ subset(unordered_pair(X4,X5),X6)
| ~ in(X4,X6)
| ~ in(X5,X6) )
& ( subset(unordered_pair(X4,X5),X6)
| ( in(X4,X6)
& in(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,negated_conjecture,
( ( ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk3_0) )
& ( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| ( in(esk1_0,esk3_0)
& in(esk2_0,esk3_0) ) ) ),
inference(skolemize,[status(esa)],[12]) ).
fof(14,negated_conjecture,
( ( ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk3_0) )
& ( in(esk1_0,esk3_0)
| subset(unordered_pair(esk1_0,esk2_0),esk3_0) )
& ( in(esk2_0,esk3_0)
| subset(unordered_pair(esk1_0,esk2_0),esk3_0) ) ),
inference(distribute,[status(thm)],[13]) ).
cnf(15,negated_conjecture,
( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,negated_conjecture,
( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,negated_conjecture,
( ~ in(esk2_0,esk3_0)
| ~ in(esk1_0,esk3_0)
| ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[18]) ).
fof(23,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)],[5]) ).
fof(24,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)],[23]) ).
fof(25,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk4_2(X4,X5),X4)
& ~ in(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk4_2(X4,X5),X4)
& ~ in(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk4_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
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)],[6]) ).
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(45,negated_conjecture,
( in(X1,esk3_0)
| in(esk1_0,esk3_0)
| ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[30,16,theory(equality)]) ).
cnf(46,negated_conjecture,
( in(X1,esk3_0)
| in(esk2_0,esk3_0)
| ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[30,15,theory(equality)]) ).
cnf(50,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[39,theory(equality)]) ).
cnf(54,plain,
( X1 = X2
| X3 = X2
| ~ in(X2,unordered_pair(X1,X3)) ),
inference(er,[status(thm)],[41,theory(equality)]) ).
cnf(64,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[50,theory(equality)]) ).
cnf(67,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[64,19,theory(equality)]) ).
cnf(71,negated_conjecture,
in(esk2_0,esk3_0),
inference(spm,[status(thm)],[46,64,theory(equality)]) ).
cnf(76,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| $false
| ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
inference(rw,[status(thm)],[17,71,theory(equality)]) ).
cnf(77,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
inference(cn,[status(thm)],[76,theory(equality)]) ).
cnf(83,negated_conjecture,
in(esk1_0,esk3_0),
inference(spm,[status(thm)],[45,67,theory(equality)]) ).
cnf(94,negated_conjecture,
( $false
| ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
inference(rw,[status(thm)],[77,83,theory(equality)]) ).
cnf(95,negated_conjecture,
~ subset(unordered_pair(esk1_0,esk2_0),esk3_0),
inference(cn,[status(thm)],[94,theory(equality)]) ).
cnf(101,plain,
( X1 = esk4_2(unordered_pair(X2,X1),X3)
| X2 = esk4_2(unordered_pair(X2,X1),X3)
| subset(unordered_pair(X2,X1),X3) ),
inference(spm,[status(thm)],[54,29,theory(equality)]) ).
cnf(109,plain,
( subset(unordered_pair(X1,X2),X3)
| esk4_2(unordered_pair(X1,X2),X3) = X2
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[28,101,theory(equality)]) ).
cnf(189,plain,
( subset(unordered_pair(X1,X2),X3)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[28,109,theory(equality)]) ).
cnf(194,negated_conjecture,
( ~ in(esk2_0,esk3_0)
| ~ in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[95,189,theory(equality)]) ).
cnf(196,negated_conjecture,
( $false
| ~ in(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[194,71,theory(equality)]) ).
cnf(197,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[196,83,theory(equality)]) ).
cnf(198,negated_conjecture,
$false,
inference(cn,[status(thm)],[197,theory(equality)]) ).
cnf(199,negated_conjecture,
$false,
198,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU159+1.p
% --creating new selector for []
% -running prover on /tmp/tmpx-FJec/sel_SEU159+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU159+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU159+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU159+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
%
%------------------------------------------------------------------------------