TSTP Solution File: SEU180+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU180+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 05:09:25 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 11 unt; 0 def)
% Number of atoms : 312 ( 60 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 409 ( 158 ~; 175 |; 63 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 158 ( 7 sgn 93 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/tmp/tmp_xGChB/sel_SEU180+1.p_1',d5_relat_1) ).
fof(3,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/tmp/tmp_xGChB/sel_SEU180+1.p_1',d6_relat_1) ).
fof(18,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmp_xGChB/sel_SEU180+1.p_1',d2_xboole_0) ).
fof(19,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/tmp/tmp_xGChB/sel_SEU180+1.p_1',d4_relat_1) ).
fof(28,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmp_xGChB/sel_SEU180+1.p_1',d5_tarski) ).
fof(31,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/tmp/tmp_xGChB/sel_SEU180+1.p_1',t30_relat_1) ).
fof(37,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)],[31]) ).
fof(45,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_rng(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) )
& ( ! [X4] : ~ in(ordered_pair(X4,X3),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X4,X3),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) ) )
| X2 = relation_rng(X1) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(46,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X8,X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X11,X10),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X12,X10),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk2_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) )
& ( ( ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) ) )
| X6 != relation_rng(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[47]) ).
fof(49,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5)
| X6 != relation_rng(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[48]) ).
cnf(51,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(ordered_pair(X4,X3),X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(56,plain,
! [X1] :
( ~ relation(X1)
| relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(57,plain,
! [X2] :
( ~ relation(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[56]) ).
cnf(58,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(92,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)],[18]) ).
fof(93,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)],[92]) ).
fof(94,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(esk6_3(X5,X6,X7),X7)
| ( ~ in(esk6_3(X5,X6,X7),X5)
& ~ in(esk6_3(X5,X6,X7),X6) ) )
& ( in(esk6_3(X5,X6,X7),X7)
| in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[93]) ).
fof(95,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(esk6_3(X5,X6,X7),X7)
| ( ~ in(esk6_3(X5,X6,X7),X5)
& ~ in(esk6_3(X5,X6,X7),X6) ) )
& ( in(esk6_3(X5,X6,X7),X7)
| in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[94]) ).
fof(96,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(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk6_3(X5,X6,X7),X6)
| ~ in(esk6_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[95]) ).
cnf(100,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(101,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(103,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_dom(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) )
& ( ! [X4] : ~ in(ordered_pair(X3,X4),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X3,X4),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) ) )
| X2 = relation_dom(X1) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(104,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X7,X8),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X10,X11),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X10,X12),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk7_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk8_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk8_2(X5,X6),X11),X5) )
& ( in(esk8_2(X5,X6),X6)
| in(ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(skolemize,[status(esa)],[104]) ).
fof(106,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk8_2(X5,X6),X11),X5)
| ~ in(esk8_2(X5,X6),X6) )
& ( in(esk8_2(X5,X6),X6)
| in(ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk7_3(X5,X6,X7)),X5) ) )
| X6 != relation_dom(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[105]) ).
fof(107,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk8_2(X5,X6),X11),X5)
| ~ in(esk8_2(X5,X6),X6)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk8_2(X5,X6),X6)
| in(ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6)),X5)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk7_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[106]) ).
cnf(109,plain,
( in(X3,X2)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(ordered_pair(X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[107]) ).
fof(126,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[28]) ).
cnf(127,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[126]) ).
fof(134,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)],[37]) ).
fof(135,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)],[134]) ).
fof(136,negated_conjecture,
( relation(esk13_0)
& in(ordered_pair(esk11_0,esk12_0),esk13_0)
& ( ~ in(esk11_0,relation_field(esk13_0))
| ~ in(esk12_0,relation_field(esk13_0)) ) ),
inference(skolemize,[status(esa)],[135]) ).
cnf(137,negated_conjecture,
( ~ in(esk12_0,relation_field(esk13_0))
| ~ in(esk11_0,relation_field(esk13_0)) ),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(138,negated_conjecture,
in(ordered_pair(esk11_0,esk12_0),esk13_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(139,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[136]) ).
cnf(149,negated_conjecture,
in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0),
inference(rw,[status(thm)],[138,127,theory(equality)]),
[unfolding] ).
cnf(152,plain,
( in(X3,X2)
| relation_rng(X1) != X2
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X1) ),
inference(rw,[status(thm)],[51,127,theory(equality)]),
[unfolding] ).
cnf(153,plain,
( in(X3,X2)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1) ),
inference(rw,[status(thm)],[109,127,theory(equality)]),
[unfolding] ).
cnf(192,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[100,theory(equality)]) ).
cnf(200,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[101,theory(equality)]) ).
cnf(216,negated_conjecture,
( in(esk12_0,X1)
| relation_rng(esk13_0) != X1
| ~ relation(esk13_0) ),
inference(spm,[status(thm)],[152,149,theory(equality)]) ).
cnf(221,negated_conjecture,
( in(esk12_0,X1)
| relation_rng(esk13_0) != X1
| $false ),
inference(rw,[status(thm)],[216,139,theory(equality)]) ).
cnf(222,negated_conjecture,
( in(esk12_0,X1)
| relation_rng(esk13_0) != X1 ),
inference(cn,[status(thm)],[221,theory(equality)]) ).
cnf(223,negated_conjecture,
( in(esk11_0,X1)
| relation_dom(esk13_0) != X1
| ~ relation(esk13_0) ),
inference(spm,[status(thm)],[153,149,theory(equality)]) ).
cnf(228,negated_conjecture,
( in(esk11_0,X1)
| relation_dom(esk13_0) != X1
| $false ),
inference(rw,[status(thm)],[223,139,theory(equality)]) ).
cnf(229,negated_conjecture,
( in(esk11_0,X1)
| relation_dom(esk13_0) != X1 ),
inference(cn,[status(thm)],[228,theory(equality)]) ).
cnf(333,negated_conjecture,
in(esk12_0,relation_rng(esk13_0)),
inference(er,[status(thm)],[222,theory(equality)]) ).
cnf(354,negated_conjecture,
in(esk11_0,relation_dom(esk13_0)),
inference(er,[status(thm)],[229,theory(equality)]) ).
cnf(379,plain,
( in(X1,relation_field(X2))
| ~ in(X1,relation_rng(X2))
| ~ relation(X2) ),
inference(spm,[status(thm)],[192,58,theory(equality)]) ).
cnf(390,negated_conjecture,
( ~ in(esk11_0,relation_field(esk13_0))
| ~ in(esk12_0,relation_rng(esk13_0))
| ~ relation(esk13_0) ),
inference(spm,[status(thm)],[137,379,theory(equality)]) ).
cnf(400,negated_conjecture,
( ~ in(esk11_0,relation_field(esk13_0))
| $false
| ~ relation(esk13_0) ),
inference(rw,[status(thm)],[390,333,theory(equality)]) ).
cnf(401,negated_conjecture,
( ~ in(esk11_0,relation_field(esk13_0))
| $false
| $false ),
inference(rw,[status(thm)],[400,139,theory(equality)]) ).
cnf(402,negated_conjecture,
~ in(esk11_0,relation_field(esk13_0)),
inference(cn,[status(thm)],[401,theory(equality)]) ).
cnf(428,plain,
( in(X1,relation_field(X2))
| ~ in(X1,relation_dom(X2))
| ~ relation(X2) ),
inference(spm,[status(thm)],[200,58,theory(equality)]) ).
cnf(438,negated_conjecture,
( ~ in(esk11_0,relation_dom(esk13_0))
| ~ relation(esk13_0) ),
inference(spm,[status(thm)],[402,428,theory(equality)]) ).
cnf(452,negated_conjecture,
( $false
| ~ relation(esk13_0) ),
inference(rw,[status(thm)],[438,354,theory(equality)]) ).
cnf(453,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[452,139,theory(equality)]) ).
cnf(454,negated_conjecture,
$false,
inference(cn,[status(thm)],[453,theory(equality)]) ).
cnf(455,negated_conjecture,
$false,
454,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU180+1.p
% --creating new selector for []
% -running prover on /tmp/tmp_xGChB/sel_SEU180+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU180+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU180+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU180+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
%
%------------------------------------------------------------------------------