TSTP Solution File: SEU180+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU180+2 : 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 05:09:29 EST 2010
% Result : Theorem 1.88s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 22 unt; 0 def)
% Number of atoms : 244 ( 30 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 286 ( 113 ~; 115 |; 47 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 132 ( 8 sgn 77 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(36,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',t20_relat_1) ).
fof(39,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',t69_enumset1) ).
fof(52,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',t7_xboole_1) ).
fof(64,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',t30_relat_1) ).
fof(68,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',d3_tarski) ).
fof(85,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',commutativity_k2_tarski) ).
fof(103,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',d5_tarski) ).
fof(110,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',d6_relat_1) ).
fof(132,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmpdDQhtT/sel_SEU180+2.p_1',d2_xboole_0) ).
fof(151,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
inference(assume_negation,[status(cth)],[64]) ).
fof(294,plain,
! [X1,X2,X3] :
( ~ relation(X3)
| ~ in(ordered_pair(X1,X2),X3)
| ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(295,plain,
! [X4,X5,X6] :
( ~ relation(X6)
| ~ in(ordered_pair(X4,X5),X6)
| ( in(X4,relation_dom(X6))
& in(X5,relation_rng(X6)) ) ),
inference(variable_rename,[status(thm)],[294]) ).
fof(296,plain,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_rng(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[295]) ).
cnf(297,plain,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[296]) ).
cnf(298,plain,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[296]) ).
fof(308,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[39]) ).
cnf(309,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[308]) ).
fof(357,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[52]) ).
cnf(358,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[357]) ).
fof(405,negated_conjecture,
? [X1,X2,X3] :
( relation(X3)
& in(ordered_pair(X1,X2),X3)
& ( ~ in(X1,relation_field(X3))
| ~ in(X2,relation_field(X3)) ) ),
inference(fof_nnf,[status(thm)],[151]) ).
fof(406,negated_conjecture,
? [X4,X5,X6] :
( relation(X6)
& in(ordered_pair(X4,X5),X6)
& ( ~ in(X4,relation_field(X6))
| ~ in(X5,relation_field(X6)) ) ),
inference(variable_rename,[status(thm)],[405]) ).
fof(407,negated_conjecture,
( relation(esk20_0)
& in(ordered_pair(esk18_0,esk19_0),esk20_0)
& ( ~ in(esk18_0,relation_field(esk20_0))
| ~ in(esk19_0,relation_field(esk20_0)) ) ),
inference(skolemize,[status(esa)],[406]) ).
cnf(408,negated_conjecture,
( ~ in(esk19_0,relation_field(esk20_0))
| ~ in(esk18_0,relation_field(esk20_0)) ),
inference(split_conjunct,[status(thm)],[407]) ).
cnf(409,negated_conjecture,
in(ordered_pair(esk18_0,esk19_0),esk20_0),
inference(split_conjunct,[status(thm)],[407]) ).
cnf(410,negated_conjecture,
relation(esk20_0),
inference(split_conjunct,[status(thm)],[407]) ).
fof(425,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)],[68]) ).
fof(426,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)],[425]) ).
fof(427,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk22_2(X4,X5),X4)
& ~ in(esk22_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[426]) ).
fof(428,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk22_2(X4,X5),X4)
& ~ in(esk22_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[427]) ).
fof(429,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk22_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk22_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[428]) ).
cnf(432,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[429]) ).
fof(490,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[85]) ).
cnf(491,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[490]) ).
fof(552,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[103]) ).
cnf(553,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[552]) ).
fof(584,plain,
! [X1] :
( ~ relation(X1)
| relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
inference(fof_nnf,[status(thm)],[110]) ).
fof(585,plain,
! [X2] :
( ~ relation(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[584]) ).
cnf(586,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[585]) ).
fof(656,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)],[132]) ).
fof(657,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)],[656]) ).
fof(658,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(esk38_3(X5,X6,X7),X7)
| ( ~ in(esk38_3(X5,X6,X7),X5)
& ~ in(esk38_3(X5,X6,X7),X6) ) )
& ( in(esk38_3(X5,X6,X7),X7)
| in(esk38_3(X5,X6,X7),X5)
| in(esk38_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[657]) ).
fof(659,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(esk38_3(X5,X6,X7),X7)
| ( ~ in(esk38_3(X5,X6,X7),X5)
& ~ in(esk38_3(X5,X6,X7),X6) ) )
& ( in(esk38_3(X5,X6,X7),X7)
| in(esk38_3(X5,X6,X7),X5)
| in(esk38_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[658]) ).
fof(660,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(esk38_3(X5,X6,X7),X5)
| ~ in(esk38_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk38_3(X5,X6,X7),X6)
| ~ in(esk38_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk38_3(X5,X6,X7),X7)
| in(esk38_3(X5,X6,X7),X5)
| in(esk38_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[659]) ).
cnf(664,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[660]) ).
cnf(751,plain,
unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[553,309,theory(equality)]),
[unfolding] ).
cnf(795,negated_conjecture,
in(unordered_pair(unordered_pair(esk18_0,esk19_0),unordered_pair(esk18_0,esk18_0)),esk20_0),
inference(rw,[status(thm)],[409,751,theory(equality)]),
[unfolding] ).
cnf(807,plain,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[297,751,theory(equality)]),
[unfolding] ).
cnf(808,plain,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[298,751,theory(equality)]),
[unfolding] ).
cnf(832,negated_conjecture,
in(unordered_pair(unordered_pair(esk18_0,esk18_0),unordered_pair(esk18_0,esk19_0)),esk20_0),
inference(rw,[status(thm)],[795,491,theory(equality)]) ).
cnf(947,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[432,358,theory(equality)]) ).
cnf(1070,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[664,theory(equality)]) ).
cnf(1396,plain,
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X1)),X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[807,491,theory(equality)]) ).
cnf(1404,plain,
( in(X1,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[808,491,theory(equality)]) ).
cnf(5461,plain,
( in(X1,relation_field(X2))
| ~ in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(spm,[status(thm)],[947,586,theory(equality)]) ).
cnf(6134,plain,
( in(X1,relation_field(X2))
| ~ in(X1,relation_rng(X2))
| ~ relation(X2) ),
inference(spm,[status(thm)],[1070,586,theory(equality)]) ).
cnf(6211,negated_conjecture,
( ~ in(esk18_0,relation_field(esk20_0))
| ~ in(esk19_0,relation_rng(esk20_0))
| ~ relation(esk20_0) ),
inference(spm,[status(thm)],[408,6134,theory(equality)]) ).
cnf(6253,negated_conjecture,
( ~ in(esk18_0,relation_field(esk20_0))
| ~ in(esk19_0,relation_rng(esk20_0))
| $false ),
inference(rw,[status(thm)],[6211,410,theory(equality)]) ).
cnf(6254,negated_conjecture,
( ~ in(esk18_0,relation_field(esk20_0))
| ~ in(esk19_0,relation_rng(esk20_0)) ),
inference(cn,[status(thm)],[6253,theory(equality)]) ).
cnf(6259,plain,
( ~ in(esk19_0,relation_rng(esk20_0))
| ~ in(esk18_0,relation_dom(esk20_0))
| ~ relation(esk20_0) ),
inference(spm,[status(thm)],[6254,5461,theory(equality)]) ).
cnf(6261,plain,
( ~ in(esk19_0,relation_rng(esk20_0))
| ~ in(esk18_0,relation_dom(esk20_0))
| $false ),
inference(rw,[status(thm)],[6259,410,theory(equality)]) ).
cnf(6262,plain,
( ~ in(esk19_0,relation_rng(esk20_0))
| ~ in(esk18_0,relation_dom(esk20_0)) ),
inference(cn,[status(thm)],[6261,theory(equality)]) ).
cnf(27030,negated_conjecture,
( in(esk19_0,relation_rng(esk20_0))
| ~ relation(esk20_0) ),
inference(spm,[status(thm)],[1396,832,theory(equality)]) ).
cnf(27183,negated_conjecture,
( in(esk19_0,relation_rng(esk20_0))
| $false ),
inference(rw,[status(thm)],[27030,410,theory(equality)]) ).
cnf(27184,negated_conjecture,
in(esk19_0,relation_rng(esk20_0)),
inference(cn,[status(thm)],[27183,theory(equality)]) ).
cnf(27215,plain,
( $false
| ~ in(esk18_0,relation_dom(esk20_0)) ),
inference(rw,[status(thm)],[6262,27184,theory(equality)]) ).
cnf(27216,plain,
~ in(esk18_0,relation_dom(esk20_0)),
inference(cn,[status(thm)],[27215,theory(equality)]) ).
cnf(28276,negated_conjecture,
( in(esk18_0,relation_dom(esk20_0))
| ~ relation(esk20_0) ),
inference(spm,[status(thm)],[1404,832,theory(equality)]) ).
cnf(28431,negated_conjecture,
( in(esk18_0,relation_dom(esk20_0))
| $false ),
inference(rw,[status(thm)],[28276,410,theory(equality)]) ).
cnf(28432,negated_conjecture,
in(esk18_0,relation_dom(esk20_0)),
inference(cn,[status(thm)],[28431,theory(equality)]) ).
cnf(28433,negated_conjecture,
$false,
inference(sr,[status(thm)],[28432,27216,theory(equality)]) ).
cnf(28434,negated_conjecture,
$false,
28433,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU180+2.p
% --creating new selector for []
% -running prover on /tmp/tmpdDQhtT/sel_SEU180+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU180+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU180+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU180+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
%
%------------------------------------------------------------------------------