TSTP Solution File: SEU263+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU263+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 06:27:47 EST 2010
% Result : Theorem 0.92s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 9 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 130 ( 53 ~; 49 |; 16 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 128 ( 5 sgn 80 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',dt_m2_relset_1) ).
fof(2,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',redefinition_m2_relset_1) ).
fof(4,axiom,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t119_zfmisc_1) ).
fof(6,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',cc1_relset_1) ).
fof(7,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t1_xboole_1) ).
fof(8,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',d1_relset_1) ).
fof(9,axiom,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t21_relat_1) ).
fof(12,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t12_relset_1) ).
fof(19,conjecture,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t14_relset_1) ).
fof(21,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(22,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| element(X3,powerset(cartesian_product2(X1,X2))) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(23,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| element(X6,powerset(cartesian_product2(X4,X5))) ),
inference(variable_rename,[status(thm)],[22]) ).
cnf(24,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X1,X2,X3] :
( ( ~ relation_of2_as_subset(X3,X1,X2)
| relation_of2(X3,X1,X2) )
& ( ~ relation_of2(X3,X1,X2)
| relation_of2_as_subset(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ relation_of2_as_subset(X6,X4,X5)
| relation_of2(X6,X4,X5) )
& ( ~ relation_of2(X6,X4,X5)
| relation_of2_as_subset(X6,X4,X5) ) ),
inference(variable_rename,[status(thm)],[25]) ).
cnf(27,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(32,plain,
! [X1,X2,X3,X4] :
( ~ subset(X1,X2)
| ~ subset(X3,X4)
| subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(33,plain,
! [X5,X6,X7,X8] :
( ~ subset(X5,X6)
| ~ subset(X7,X8)
| subset(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
inference(variable_rename,[status(thm)],[32]) ).
cnf(34,plain,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(38,plain,
! [X1,X2,X3] :
( ~ element(X3,powerset(cartesian_product2(X1,X2)))
| relation(X3) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(39,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(cartesian_product2(X4,X5)))
| relation(X6) ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X2,X3)
| subset(X1,X3) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(42,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[41]) ).
cnf(43,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(44,plain,
! [X1,X2,X3] :
( ( ~ relation_of2(X3,X1,X2)
| subset(X3,cartesian_product2(X1,X2)) )
& ( ~ subset(X3,cartesian_product2(X1,X2))
| relation_of2(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(45,plain,
! [X4,X5,X6] :
( ( ~ relation_of2(X6,X4,X5)
| subset(X6,cartesian_product2(X4,X5)) )
& ( ~ subset(X6,cartesian_product2(X4,X5))
| relation_of2(X6,X4,X5) ) ),
inference(variable_rename,[status(thm)],[44]) ).
cnf(46,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(48,plain,
! [X1] :
( ~ relation(X1)
| subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(49,plain,
! [X2] :
( ~ relation(X2)
| subset(X2,cartesian_product2(relation_dom(X2),relation_rng(X2))) ),
inference(variable_rename,[status(thm)],[48]) ).
cnf(50,plain,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(56,plain,
! [X1,X2,X3] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(57,plain,
! [X4,X5,X6] :
( ~ relation_of2_as_subset(X6,X4,X5)
| ( subset(relation_dom(X6),X4)
& subset(relation_rng(X6),X5) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X4,X5,X6] :
( ( subset(relation_dom(X6),X4)
| ~ relation_of2_as_subset(X6,X4,X5) )
& ( subset(relation_rng(X6),X5)
| ~ relation_of2_as_subset(X6,X4,X5) ) ),
inference(distribute,[status(thm)],[57]) ).
cnf(60,plain,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(70,negated_conjecture,
? [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
& subset(relation_rng(X4),X2)
& ~ relation_of2_as_subset(X4,X3,X2) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(71,negated_conjecture,
? [X5,X6,X7,X8] :
( relation_of2_as_subset(X8,X7,X5)
& subset(relation_rng(X8),X6)
& ~ relation_of2_as_subset(X8,X7,X6) ),
inference(variable_rename,[status(thm)],[70]) ).
fof(72,negated_conjecture,
( relation_of2_as_subset(esk7_0,esk6_0,esk4_0)
& subset(relation_rng(esk7_0),esk5_0)
& ~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0) ),
inference(skolemize,[status(esa)],[71]) ).
cnf(73,negated_conjecture,
~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(74,negated_conjecture,
subset(relation_rng(esk7_0),esk5_0),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(75,negated_conjecture,
relation_of2_as_subset(esk7_0,esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[72]) ).
cnf(81,negated_conjecture,
subset(relation_dom(esk7_0),esk6_0),
inference(spm,[status(thm)],[60,75,theory(equality)]) ).
cnf(94,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[27,46,theory(equality)]) ).
cnf(102,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ subset(X1,cartesian_product2(X4,X5))
| ~ subset(X5,X3)
| ~ subset(X4,X2) ),
inference(spm,[status(thm)],[43,34,theory(equality)]) ).
cnf(104,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[40,24,theory(equality)]) ).
cnf(117,negated_conjecture,
relation(esk7_0),
inference(spm,[status(thm)],[104,75,theory(equality)]) ).
cnf(397,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ subset(relation_rng(X1),X3)
| ~ subset(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(spm,[status(thm)],[102,50,theory(equality)]) ).
cnf(10246,negated_conjecture,
( subset(esk7_0,cartesian_product2(X1,esk5_0))
| ~ relation(esk7_0)
| ~ subset(relation_dom(esk7_0),X1) ),
inference(spm,[status(thm)],[397,74,theory(equality)]) ).
cnf(10578,negated_conjecture,
( subset(esk7_0,cartesian_product2(X1,esk5_0))
| $false
| ~ subset(relation_dom(esk7_0),X1) ),
inference(rw,[status(thm)],[10246,117,theory(equality)]) ).
cnf(10579,negated_conjecture,
( subset(esk7_0,cartesian_product2(X1,esk5_0))
| ~ subset(relation_dom(esk7_0),X1) ),
inference(cn,[status(thm)],[10578,theory(equality)]) ).
cnf(11231,negated_conjecture,
subset(esk7_0,cartesian_product2(esk6_0,esk5_0)),
inference(spm,[status(thm)],[10579,81,theory(equality)]) ).
cnf(11241,negated_conjecture,
relation_of2_as_subset(esk7_0,esk6_0,esk5_0),
inference(spm,[status(thm)],[94,11231,theory(equality)]) ).
cnf(11246,negated_conjecture,
$false,
inference(sr,[status(thm)],[11241,73,theory(equality)]) ).
cnf(11247,negated_conjecture,
$false,
11246,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU263+1.p
% --creating new selector for []
% -running prover on /tmp/tmpPO6-YU/sel_SEU263+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU263+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU263+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU263+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
%
%------------------------------------------------------------------------------