%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU268+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 06:30:07 EST 2010
% Result : Theorem 0.63s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 23 unt; 0 def)
% Number of atoms : 269 ( 49 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 353 ( 144 ~; 155 |; 45 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 120 ( 5 sgn 62 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',reflexivity_r1_tarski) ).
fof(18,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',commutativity_k2_tarski) ).
fof(25,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = inclusion_relation(X1)
<=> ( relation_field(X2) = X1
& ! [X3,X4] :
( ( in(X3,X1)
& in(X4,X1) )
=> ( in(ordered_pair(X3,X4),X2)
<=> subset(X3,X4) ) ) ) ) ),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',d1_wellord2) ).
fof(28,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',d9_relat_2) ).
fof(30,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',d1_relat_2) ).
fof(37,conjecture,
! [X1] : reflexive(inclusion_relation(X1)),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',t2_wellord2) ).
fof(39,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',dt_k1_wellord2) ).
fof(49,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpNkQPlL/sel_SEU268+1.p_1',d5_tarski) ).
fof(52,negated_conjecture,
~ ! [X1] : reflexive(inclusion_relation(X1)),
inference(assume_negation,[status(cth)],[37]) ).
fof(96,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(97,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[96]) ).
fof(127,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[18]) ).
cnf(128,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[127]) ).
fof(148,plain,
! [X1,X2] :
( ~ relation(X2)
| ( ( X2 != inclusion_relation(X1)
| ( relation_field(X2) = X1
& ! [X3,X4] :
( ~ in(X3,X1)
| ~ in(X4,X1)
| ( ( ~ in(ordered_pair(X3,X4),X2)
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| in(ordered_pair(X3,X4),X2) ) ) ) ) )
& ( relation_field(X2) != X1
| ? [X3,X4] :
( in(X3,X1)
& in(X4,X1)
& ( ~ in(ordered_pair(X3,X4),X2)
| ~ subset(X3,X4) )
& ( in(ordered_pair(X3,X4),X2)
| subset(X3,X4) ) )
| X2 = inclusion_relation(X1) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(149,plain,
! [X5,X6] :
( ~ relation(X6)
| ( ( X6 != inclusion_relation(X5)
| ( relation_field(X6) = X5
& ! [X7,X8] :
( ~ in(X7,X5)
| ~ in(X8,X5)
| ( ( ~ in(ordered_pair(X7,X8),X6)
| subset(X7,X8) )
& ( ~ subset(X7,X8)
| in(ordered_pair(X7,X8),X6) ) ) ) ) )
& ( relation_field(X6) != X5
| ? [X9,X10] :
( in(X9,X5)
& in(X10,X5)
& ( ~ in(ordered_pair(X9,X10),X6)
| ~ subset(X9,X10) )
& ( in(ordered_pair(X9,X10),X6)
| subset(X9,X10) ) )
| X6 = inclusion_relation(X5) ) ) ),
inference(variable_rename,[status(thm)],[148]) ).
fof(150,plain,
! [X5,X6] :
( ~ relation(X6)
| ( ( X6 != inclusion_relation(X5)
| ( relation_field(X6) = X5
& ! [X7,X8] :
( ~ in(X7,X5)
| ~ in(X8,X5)
| ( ( ~ in(ordered_pair(X7,X8),X6)
| subset(X7,X8) )
& ( ~ subset(X7,X8)
| in(ordered_pair(X7,X8),X6) ) ) ) ) )
& ( relation_field(X6) != X5
| ( in(esk9_2(X5,X6),X5)
& in(esk10_2(X5,X6),X5)
& ( ~ in(ordered_pair(esk9_2(X5,X6),esk10_2(X5,X6)),X6)
| ~ subset(esk9_2(X5,X6),esk10_2(X5,X6)) )
& ( in(ordered_pair(esk9_2(X5,X6),esk10_2(X5,X6)),X6)
| subset(esk9_2(X5,X6),esk10_2(X5,X6)) ) )
| X6 = inclusion_relation(X5) ) ) ),
inference(skolemize,[status(esa)],[149]) ).
fof(151,plain,
! [X5,X6,X7,X8] :
( ( ( ( ( ~ in(X7,X5)
| ~ in(X8,X5)
| ( ( ~ in(ordered_pair(X7,X8),X6)
| subset(X7,X8) )
& ( ~ subset(X7,X8)
| in(ordered_pair(X7,X8),X6) ) ) )
& relation_field(X6) = X5 )
| X6 != inclusion_relation(X5) )
& ( relation_field(X6) != X5
| ( in(esk9_2(X5,X6),X5)
& in(esk10_2(X5,X6),X5)
& ( ~ in(ordered_pair(esk9_2(X5,X6),esk10_2(X5,X6)),X6)
| ~ subset(esk9_2(X5,X6),esk10_2(X5,X6)) )
& ( in(ordered_pair(esk9_2(X5,X6),esk10_2(X5,X6)),X6)
| subset(esk9_2(X5,X6),esk10_2(X5,X6)) ) )
| X6 = inclusion_relation(X5) ) )
| ~ relation(X6) ),
inference(shift_quantors,[status(thm)],[150]) ).
fof(152,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X6)
| subset(X7,X8)
| ~ in(X7,X5)
| ~ in(X8,X5)
| X6 != inclusion_relation(X5)
| ~ relation(X6) )
& ( ~ subset(X7,X8)
| in(ordered_pair(X7,X8),X6)
| ~ in(X7,X5)
| ~ in(X8,X5)
| X6 != inclusion_relation(X5)
| ~ relation(X6) )
& ( relation_field(X6) = X5
| X6 != inclusion_relation(X5)
| ~ relation(X6) )
& ( in(esk9_2(X5,X6),X5)
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( in(esk10_2(X5,X6),X5)
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( ~ in(ordered_pair(esk9_2(X5,X6),esk10_2(X5,X6)),X6)
| ~ subset(esk9_2(X5,X6),esk10_2(X5,X6))
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) )
& ( in(ordered_pair(esk9_2(X5,X6),esk10_2(X5,X6)),X6)
| subset(esk9_2(X5,X6),esk10_2(X5,X6))
| relation_field(X6) != X5
| X6 = inclusion_relation(X5)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[151]) ).
cnf(157,plain,
( relation_field(X1) = X2
| ~ relation(X1)
| X1 != inclusion_relation(X2) ),
inference(split_conjunct,[status(thm)],[152]) ).
cnf(158,plain,
( in(ordered_pair(X4,X3),X1)
| ~ relation(X1)
| X1 != inclusion_relation(X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ subset(X4,X3) ),
inference(split_conjunct,[status(thm)],[152]) ).
fof(166,plain,
! [X1] :
( ~ relation(X1)
| ( ( ~ reflexive(X1)
| is_reflexive_in(X1,relation_field(X1)) )
& ( ~ is_reflexive_in(X1,relation_field(X1))
| reflexive(X1) ) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(167,plain,
! [X2] :
( ~ relation(X2)
| ( ( ~ reflexive(X2)
| is_reflexive_in(X2,relation_field(X2)) )
& ( ~ is_reflexive_in(X2,relation_field(X2))
| reflexive(X2) ) ) ),
inference(variable_rename,[status(thm)],[166]) ).
fof(168,plain,
! [X2] :
( ( ~ reflexive(X2)
| is_reflexive_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_reflexive_in(X2,relation_field(X2))
| reflexive(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[167]) ).
cnf(169,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[168]) ).
fof(172,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( ~ is_reflexive_in(X1,X2)
| ! [X3] :
( ~ in(X3,X2)
| in(ordered_pair(X3,X3),X1) ) )
& ( ? [X3] :
( in(X3,X2)
& ~ in(ordered_pair(X3,X3),X1) )
| is_reflexive_in(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(173,plain,
! [X4] :
( ~ relation(X4)
| ! [X5] :
( ( ~ is_reflexive_in(X4,X5)
| ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4) ) )
& ( ? [X7] :
( in(X7,X5)
& ~ in(ordered_pair(X7,X7),X4) )
| is_reflexive_in(X4,X5) ) ) ),
inference(variable_rename,[status(thm)],[172]) ).
fof(174,plain,
! [X4] :
( ~ relation(X4)
| ! [X5] :
( ( ~ is_reflexive_in(X4,X5)
| ! [X6] :
( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4) ) )
& ( ( in(esk11_2(X4,X5),X5)
& ~ in(ordered_pair(esk11_2(X4,X5),esk11_2(X4,X5)),X4) )
| is_reflexive_in(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[173]) ).
fof(175,plain,
! [X4,X5,X6] :
( ( ( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4)
| ~ is_reflexive_in(X4,X5) )
& ( ( in(esk11_2(X4,X5),X5)
& ~ in(ordered_pair(esk11_2(X4,X5),esk11_2(X4,X5)),X4) )
| is_reflexive_in(X4,X5) ) )
| ~ relation(X4) ),
inference(shift_quantors,[status(thm)],[174]) ).
fof(176,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| in(ordered_pair(X6,X6),X4)
| ~ is_reflexive_in(X4,X5)
| ~ relation(X4) )
& ( in(esk11_2(X4,X5),X5)
| is_reflexive_in(X4,X5)
| ~ relation(X4) )
& ( ~ in(ordered_pair(esk11_2(X4,X5),esk11_2(X4,X5)),X4)
| is_reflexive_in(X4,X5)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[175]) ).
cnf(177,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(ordered_pair(esk11_2(X1,X2),esk11_2(X1,X2)),X1) ),
inference(split_conjunct,[status(thm)],[176]) ).
cnf(178,plain,
( is_reflexive_in(X1,X2)
| in(esk11_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[176]) ).
fof(196,negated_conjecture,
? [X1] : ~ reflexive(inclusion_relation(X1)),
inference(fof_nnf,[status(thm)],[52]) ).
fof(197,negated_conjecture,
? [X2] : ~ reflexive(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[196]) ).
fof(198,negated_conjecture,
~ reflexive(inclusion_relation(esk12_0)),
inference(skolemize,[status(esa)],[197]) ).
cnf(199,negated_conjecture,
~ reflexive(inclusion_relation(esk12_0)),
inference(split_conjunct,[status(thm)],[198]) ).
fof(204,plain,
! [X2] : relation(inclusion_relation(X2)),
inference(variable_rename,[status(thm)],[39]) ).
cnf(205,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[204]) ).
fof(221,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[49]) ).
cnf(222,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[221]) ).
cnf(231,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk11_2(X1,X2),esk11_2(X1,X2)),singleton(esk11_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[177,222,theory(equality)]),
[unfolding] ).
cnf(236,plain,
( in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X1)
| inclusion_relation(X2) != X1
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ subset(X4,X3) ),
inference(rw,[status(thm)],[158,222,theory(equality)]),
[unfolding] ).
cnf(279,plain,
( relation_field(inclusion_relation(X1)) = X1
| ~ relation(inclusion_relation(X1)) ),
inference(er,[status(thm)],[157,theory(equality)]) ).
cnf(280,plain,
( relation_field(inclusion_relation(X1)) = X1
| $false ),
inference(rw,[status(thm)],[279,205,theory(equality)]) ).
cnf(281,plain,
relation_field(inclusion_relation(X1)) = X1,
inference(cn,[status(thm)],[280,theory(equality)]) ).
cnf(309,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk11_2(X1,X2)),unordered_pair(esk11_2(X1,X2),esk11_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[231,128,theory(equality)]) ).
cnf(312,plain,
( in(unordered_pair(unordered_pair(esk11_2(X1,X2),X3),singleton(esk11_2(X1,X2))),X4)
| is_reflexive_in(X1,X2)
| inclusion_relation(X2) != X4
| ~ subset(esk11_2(X1,X2),X3)
| ~ relation(X4)
| ~ in(X3,X2)
| ~ relation(X1) ),
inference(spm,[status(thm)],[236,178,theory(equality)]) ).
cnf(357,plain,
( reflexive(inclusion_relation(X1))
| ~ is_reflexive_in(inclusion_relation(X1),X1)
| ~ relation(inclusion_relation(X1)) ),
inference(spm,[status(thm)],[169,281,theory(equality)]) ).
cnf(361,plain,
( reflexive(inclusion_relation(X1))
| ~ is_reflexive_in(inclusion_relation(X1),X1)
| $false ),
inference(rw,[status(thm)],[357,205,theory(equality)]) ).
cnf(362,plain,
( reflexive(inclusion_relation(X1))
| ~ is_reflexive_in(inclusion_relation(X1),X1) ),
inference(cn,[status(thm)],[361,theory(equality)]) ).
cnf(737,plain,
( is_reflexive_in(X1,X2)
| in(unordered_pair(singleton(esk11_2(X1,X2)),unordered_pair(esk11_2(X1,X2),X3)),X4)
| inclusion_relation(X2) != X4
| ~ subset(esk11_2(X1,X2),X3)
| ~ relation(X4)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[312,128,theory(equality)]) ).
cnf(6422,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| inclusion_relation(X2) != X1
| ~ subset(esk11_2(X1,X2),esk11_2(X1,X2))
| ~ in(esk11_2(X1,X2),X2) ),
inference(spm,[status(thm)],[309,737,theory(equality)]) ).
cnf(6469,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| inclusion_relation(X2) != X1
| $false
| ~ in(esk11_2(X1,X2),X2) ),
inference(rw,[status(thm)],[6422,97,theory(equality)]) ).
cnf(6470,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| inclusion_relation(X2) != X1
| ~ in(esk11_2(X1,X2),X2) ),
inference(cn,[status(thm)],[6469,theory(equality)]) ).
cnf(7646,plain,
( is_reflexive_in(X1,X2)
| inclusion_relation(X2) != X1
| ~ relation(X1) ),
inference(csr,[status(thm)],[6470,178]) ).
cnf(7649,plain,
( reflexive(inclusion_relation(X1))
| ~ relation(inclusion_relation(X1)) ),
inference(spm,[status(thm)],[362,7646,theory(equality)]) ).
cnf(7650,plain,
( reflexive(inclusion_relation(X1))
| $false ),
inference(rw,[status(thm)],[7649,205,theory(equality)]) ).
cnf(7651,plain,
reflexive(inclusion_relation(X1)),
inference(cn,[status(thm)],[7650,theory(equality)]) ).
cnf(7657,negated_conjecture,
$false,
inference(rw,[status(thm)],[199,7651,theory(equality)]) ).
cnf(7658,negated_conjecture,
$false,
inference(cn,[status(thm)],[7657,theory(equality)]) ).
cnf(7659,negated_conjecture,
$false,
7658,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU268+1.p
% --creating new selector for []
% -running prover on /tmp/tmpNkQPlL/sel_SEU268+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU268+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU268+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU268+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
%
%------------------------------------------------------------------------------