TSTP Solution File: SEU125+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU125+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 04:43:34 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 186 ( 20 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 214 ( 76 ~; 89 |; 43 &)
% ( 3 <=>; 3 =>; 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 : 107 ( 8 sgn 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',t8_xboole_1) ).
fof(8,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',d2_xboole_0) ).
fof(13,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',idempotence_k2_xboole_0) ).
fof(16,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpeR65Xk/sel_SEU125+1.p_1',d3_tarski) ).
fof(19,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(26,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& subset(X3,X2)
& ~ subset(set_union2(X1,X3),X2) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(27,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& subset(X6,X5)
& ~ subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,negated_conjecture,
( subset(esk1_0,esk2_0)
& subset(esk3_0,esk2_0)
& ~ subset(set_union2(esk1_0,esk3_0),esk2_0) ),
inference(skolemize,[status(esa)],[27]) ).
cnf(29,negated_conjecture,
~ subset(set_union2(esk1_0,esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,negated_conjecture,
subset(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(31,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[28]) ).
fof(43,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)],[8]) ).
fof(44,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)],[43]) ).
fof(45,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(esk5_3(X5,X6,X7),X7)
| ( ~ in(esk5_3(X5,X6,X7),X5)
& ~ in(esk5_3(X5,X6,X7),X6) ) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| in(esk5_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[44]) ).
fof(46,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(esk5_3(X5,X6,X7),X7)
| ( ~ in(esk5_3(X5,X6,X7),X5)
& ~ in(esk5_3(X5,X6,X7),X6) ) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| in(esk5_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[45]) ).
fof(47,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(esk5_3(X5,X6,X7),X5)
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk5_3(X5,X6,X7),X6)
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| in(esk5_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(51,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(53,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(65,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[13]) ).
cnf(66,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[65]) ).
fof(73,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)],[16]) ).
fof(74,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)],[73]) ).
fof(75,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)],[74]) ).
fof(76,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)],[75]) ).
fof(77,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)],[76]) ).
cnf(78,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(79,plain,
( subset(X1,X2)
| in(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(80,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(104,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[80,31,theory(equality)]) ).
cnf(105,negated_conjecture,
( in(X1,esk2_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[80,30,theory(equality)]) ).
cnf(109,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[51,theory(equality)]) ).
cnf(123,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[53,theory(equality)]) ).
cnf(165,negated_conjecture,
( in(esk7_2(esk1_0,X1),esk2_0)
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[104,79,theory(equality)]) ).
cnf(198,negated_conjecture,
( in(esk7_2(esk3_0,X1),esk2_0)
| subset(esk3_0,X1) ),
inference(spm,[status(thm)],[105,79,theory(equality)]) ).
cnf(217,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk7_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[78,109,theory(equality)]) ).
cnf(316,plain,
( in(esk7_2(set_union2(X1,X2),X3),X2)
| in(esk7_2(set_union2(X1,X2),X3),X1)
| subset(set_union2(X1,X2),X3) ),
inference(spm,[status(thm)],[123,79,theory(equality)]) ).
cnf(430,negated_conjecture,
subset(esk1_0,set_union2(X1,esk2_0)),
inference(spm,[status(thm)],[217,165,theory(equality)]) ).
cnf(431,negated_conjecture,
subset(esk3_0,set_union2(X1,esk2_0)),
inference(spm,[status(thm)],[217,198,theory(equality)]) ).
cnf(438,negated_conjecture,
( in(X1,set_union2(X2,esk2_0))
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[80,430,theory(equality)]) ).
cnf(461,negated_conjecture,
( in(X1,set_union2(X2,esk2_0))
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[80,431,theory(equality)]) ).
cnf(554,negated_conjecture,
( subset(X1,set_union2(X2,esk2_0))
| ~ in(esk7_2(X1,set_union2(X2,esk2_0)),esk1_0) ),
inference(spm,[status(thm)],[78,438,theory(equality)]) ).
cnf(631,negated_conjecture,
( subset(X1,set_union2(X2,esk2_0))
| ~ in(esk7_2(X1,set_union2(X2,esk2_0)),esk3_0) ),
inference(spm,[status(thm)],[78,461,theory(equality)]) ).
cnf(889,negated_conjecture,
( subset(X1,esk2_0)
| ~ in(esk7_2(X1,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[554,66,theory(equality)]) ).
cnf(898,negated_conjecture,
( subset(X1,esk2_0)
| ~ in(esk7_2(X1,esk2_0),esk3_0) ),
inference(spm,[status(thm)],[631,66,theory(equality)]) ).
cnf(1700,negated_conjecture,
( subset(set_union2(esk1_0,X1),esk2_0)
| in(esk7_2(set_union2(esk1_0,X1),esk2_0),X1) ),
inference(spm,[status(thm)],[889,316,theory(equality)]) ).
cnf(1748,negated_conjecture,
subset(set_union2(esk1_0,esk3_0),esk2_0),
inference(spm,[status(thm)],[898,1700,theory(equality)]) ).
cnf(1761,negated_conjecture,
$false,
inference(sr,[status(thm)],[1748,29,theory(equality)]) ).
cnf(1762,negated_conjecture,
$false,
1761,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU125+1.p
% --creating new selector for []
% -running prover on /tmp/tmpeR65Xk/sel_SEU125+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU125+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU125+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU125+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
%
%------------------------------------------------------------------------------