TSTP Solution File: SEU199+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU199+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 05:24:54 EST 2010
% Result : Theorem 27.61s
% Output : CNFRefutation 27.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 12 unt; 0 def)
% Number of atoms : 241 ( 25 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 329 ( 135 ~; 144 |; 39 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 131 ( 6 sgn 72 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/tmp/tmpgEhCbv/sel_SEU199+1.p_1',dt_k8_relat_1) ).
fof(4,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('/tmp/tmpgEhCbv/sel_SEU199+1.p_1',d3_relat_1) ).
fof(13,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpgEhCbv/sel_SEU199+1.p_1',commutativity_k2_tarski) ).
fof(18,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('/tmp/tmpgEhCbv/sel_SEU199+1.p_1',t117_relat_1) ).
fof(28,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpgEhCbv/sel_SEU199+1.p_1',d5_tarski) ).
fof(35,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('/tmp/tmpgEhCbv/sel_SEU199+1.p_1',d12_relat_1) ).
fof(37,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
inference(assume_negation,[status(cth)],[18]) ).
fof(46,plain,
! [X1,X2] :
( ~ relation(X2)
| relation(relation_rng_restriction(X1,X2)) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(47,plain,
! [X3,X4] :
( ~ relation(X4)
| relation(relation_rng_restriction(X3,X4)) ),
inference(variable_rename,[status(thm)],[46]) ).
cnf(48,plain,
( relation(relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(55,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ~ relation(X2)
| ( ( ~ subset(X1,X2)
| ! [X3,X4] :
( ~ in(ordered_pair(X3,X4),X1)
| in(ordered_pair(X3,X4),X2) ) )
& ( ? [X3,X4] :
( in(ordered_pair(X3,X4),X1)
& ~ in(ordered_pair(X3,X4),X2) )
| subset(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(56,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ~ relation(X6)
| ( ( ~ subset(X5,X6)
| ! [X7,X8] :
( ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6) ) )
& ( ? [X9,X10] :
( in(ordered_pair(X9,X10),X5)
& ~ in(ordered_pair(X9,X10),X6) )
| subset(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ~ relation(X6)
| ( ( ~ subset(X5,X6)
| ! [X7,X8] :
( ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6) ) )
& ( ( in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X5)
& ~ in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X6) )
| subset(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[56]) ).
fof(58,plain,
! [X5,X6,X7,X8] :
( ( ( ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| ~ subset(X5,X6) )
& ( ( in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X5)
& ~ in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X6) )
| subset(X5,X6) ) )
| ~ relation(X6)
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[57]) ).
fof(59,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X7,X8),X5)
| in(ordered_pair(X7,X8),X6)
| ~ subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X5)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) )
& ( ~ in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X6)
| subset(X5,X6)
| ~ relation(X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[58]) ).
cnf(60,plain,
( subset(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(61,plain,
( subset(X1,X2)
| in(ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(87,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[13]) ).
cnf(88,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[87]) ).
fof(98,negated_conjecture,
? [X1,X2] :
( relation(X2)
& ~ subset(relation_rng_restriction(X1,X2),X2) ),
inference(fof_nnf,[status(thm)],[37]) ).
fof(99,negated_conjecture,
? [X3,X4] :
( relation(X4)
& ~ subset(relation_rng_restriction(X3,X4),X4) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,negated_conjecture,
( relation(esk7_0)
& ~ subset(relation_rng_restriction(esk6_0,esk7_0),esk7_0) ),
inference(skolemize,[status(esa)],[99]) ).
cnf(101,negated_conjecture,
~ subset(relation_rng_restriction(esk6_0,esk7_0),esk7_0),
inference(split_conjunct,[status(thm)],[100]) ).
cnf(102,negated_conjecture,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[100]) ).
fof(120,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[28]) ).
cnf(121,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[120]) ).
fof(140,plain,
! [X1,X2] :
( ~ relation(X2)
| ! [X3] :
( ~ relation(X3)
| ( ( X3 != relation_rng_restriction(X1,X2)
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X3)
| ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) )
& ( ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X2)
| in(ordered_pair(X4,X5),X3) ) ) )
& ( ? [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X3)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X2) )
& ( in(ordered_pair(X4,X5),X3)
| ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) )
| X3 = relation_rng_restriction(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(141,plain,
! [X6,X7] :
( ~ relation(X7)
| ! [X8] :
( ~ relation(X8)
| ( ( X8 != relation_rng_restriction(X6,X7)
| ! [X9,X10] :
( ( ~ in(ordered_pair(X9,X10),X8)
| ( in(X10,X6)
& in(ordered_pair(X9,X10),X7) ) )
& ( ~ in(X10,X6)
| ~ in(ordered_pair(X9,X10),X7)
| in(ordered_pair(X9,X10),X8) ) ) )
& ( ? [X11,X12] :
( ( ~ in(ordered_pair(X11,X12),X8)
| ~ in(X12,X6)
| ~ in(ordered_pair(X11,X12),X7) )
& ( in(ordered_pair(X11,X12),X8)
| ( in(X12,X6)
& in(ordered_pair(X11,X12),X7) ) ) )
| X8 = relation_rng_restriction(X6,X7) ) ) ) ),
inference(variable_rename,[status(thm)],[140]) ).
fof(142,plain,
! [X6,X7] :
( ~ relation(X7)
| ! [X8] :
( ~ relation(X8)
| ( ( X8 != relation_rng_restriction(X6,X7)
| ! [X9,X10] :
( ( ~ in(ordered_pair(X9,X10),X8)
| ( in(X10,X6)
& in(ordered_pair(X9,X10),X7) ) )
& ( ~ in(X10,X6)
| ~ in(ordered_pair(X9,X10),X7)
| in(ordered_pair(X9,X10),X8) ) ) )
& ( ( ( ~ in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X8)
| ~ in(esk12_3(X6,X7,X8),X6)
| ~ in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X7) )
& ( in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X8)
| ( in(esk12_3(X6,X7,X8),X6)
& in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X7) ) ) )
| X8 = relation_rng_restriction(X6,X7) ) ) ) ),
inference(skolemize,[status(esa)],[141]) ).
fof(143,plain,
! [X6,X7,X8,X9,X10] :
( ( ( ( ( ~ in(ordered_pair(X9,X10),X8)
| ( in(X10,X6)
& in(ordered_pair(X9,X10),X7) ) )
& ( ~ in(X10,X6)
| ~ in(ordered_pair(X9,X10),X7)
| in(ordered_pair(X9,X10),X8) ) )
| X8 != relation_rng_restriction(X6,X7) )
& ( ( ( ~ in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X8)
| ~ in(esk12_3(X6,X7,X8),X6)
| ~ in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X7) )
& ( in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X8)
| ( in(esk12_3(X6,X7,X8),X6)
& in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X7) ) ) )
| X8 = relation_rng_restriction(X6,X7) ) )
| ~ relation(X8)
| ~ relation(X7) ),
inference(shift_quantors,[status(thm)],[142]) ).
fof(144,plain,
! [X6,X7,X8,X9,X10] :
( ( in(X10,X6)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(X9,X10),X7)
| ~ in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(X10,X6)
| ~ in(ordered_pair(X9,X10),X7)
| in(ordered_pair(X9,X10),X8)
| X8 != relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( ~ in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X8)
| ~ in(esk12_3(X6,X7,X8),X6)
| ~ in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X7)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(esk12_3(X6,X7,X8),X6)
| in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) )
& ( in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X7)
| in(ordered_pair(esk11_3(X6,X7,X8),esk12_3(X6,X7,X8)),X8)
| X8 = relation_rng_restriction(X6,X7)
| ~ relation(X8)
| ~ relation(X7) ) ),
inference(distribute,[status(thm)],[143]) ).
cnf(149,plain,
( in(ordered_pair(X4,X5),X1)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_rng_restriction(X3,X1)
| ~ in(ordered_pair(X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[144]) ).
cnf(154,plain,
( subset(X1,X2)
| in(unordered_pair(unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),singleton(esk2_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[61,121,theory(equality)]),
[unfolding] ).
cnf(157,plain,
( subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),singleton(esk2_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[60,121,theory(equality)]),
[unfolding] ).
cnf(159,plain,
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| relation_rng_restriction(X3,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[149,121,theory(equality)]),121,theory(equality)]),
[unfolding] ).
cnf(211,plain,
( subset(X1,X2)
| in(unordered_pair(singleton(esk2_2(X1,X2)),unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[154,88,theory(equality)]) ).
cnf(214,plain,
( subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk2_2(X1,X2)),unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[157,88,theory(equality)]) ).
cnf(218,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| relation_rng_restriction(X4,X3) != X5
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X5)
| ~ relation(X5)
| ~ relation(X3) ),
inference(spm,[status(thm)],[159,88,theory(equality)]) ).
cnf(668,plain,
( in(unordered_pair(singleton(esk2_2(X1,X2)),unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2))),X3)
| subset(X1,X2)
| relation_rng_restriction(X4,X3) != X1
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2) ),
inference(spm,[status(thm)],[218,211,theory(equality)]) ).
cnf(7892,plain,
( subset(relation_rng_restriction(X1,X2),X3)
| in(unordered_pair(singleton(esk2_2(relation_rng_restriction(X1,X2),X3)),unordered_pair(esk2_2(relation_rng_restriction(X1,X2),X3),esk3_2(relation_rng_restriction(X1,X2),X3))),X2)
| ~ relation(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ relation(X3) ),
inference(er,[status(thm)],[668,theory(equality)]) ).
cnf(449629,plain,
( subset(relation_rng_restriction(X1,X2),X3)
| in(unordered_pair(singleton(esk2_2(relation_rng_restriction(X1,X2),X3)),unordered_pair(esk2_2(relation_rng_restriction(X1,X2),X3),esk3_2(relation_rng_restriction(X1,X2),X3))),X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(csr,[status(thm)],[7892,48]) ).
cnf(449634,plain,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X1,X2)) ),
inference(spm,[status(thm)],[214,449629,theory(equality)]) ).
cnf(450092,plain,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
inference(csr,[status(thm)],[449634,48]) ).
cnf(450094,negated_conjecture,
~ relation(esk7_0),
inference(spm,[status(thm)],[101,450092,theory(equality)]) ).
cnf(450429,negated_conjecture,
$false,
inference(rw,[status(thm)],[450094,102,theory(equality)]) ).
cnf(450430,negated_conjecture,
$false,
inference(cn,[status(thm)],[450429,theory(equality)]) ).
cnf(450431,negated_conjecture,
$false,
450430,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU199+1.p
% --creating new selector for []
% -running prover on /tmp/tmpgEhCbv/sel_SEU199+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU199+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU199+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU199+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
%
%------------------------------------------------------------------------------