TSTP Solution File: SEU243+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU243+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 06:11:42 EST 2010
% Result : Theorem 0.33s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 6 unt; 0 def)
% Number of atoms : 255 ( 34 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 348 ( 140 ~; 148 |; 52 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 89 ( 0 sgn 44 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(12,conjecture,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('/tmp/tmpqHgVc_/sel_SEU243+1.p_1',t5_wellord1) ).
fof(17,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( subset(X3,X2)
& X3 != empty_set
& ! [X4] :
~ ( in(X4,X3)
& disjoint(fiber(X1,X4),X3) ) ) ) ),
file('/tmp/tmpqHgVc_/sel_SEU243+1.p_1',d3_wellord1) ).
fof(33,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( subset(X2,relation_field(X1))
& X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& disjoint(fiber(X1,X3),X2) ) ) ) ),
file('/tmp/tmpqHgVc_/sel_SEU243+1.p_1',d2_wellord1) ).
fof(38,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(75,negated_conjecture,
? [X1] :
( relation(X1)
& ( ~ well_founded_relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) )
& ( well_founded_relation(X1)
| is_well_founded_in(X1,relation_field(X1)) ) ),
inference(fof_nnf,[status(thm)],[38]) ).
fof(76,negated_conjecture,
? [X2] :
( relation(X2)
& ( ~ well_founded_relation(X2)
| ~ is_well_founded_in(X2,relation_field(X2)) )
& ( well_founded_relation(X2)
| is_well_founded_in(X2,relation_field(X2)) ) ),
inference(variable_rename,[status(thm)],[75]) ).
fof(77,negated_conjecture,
( relation(esk4_0)
& ( ~ well_founded_relation(esk4_0)
| ~ is_well_founded_in(esk4_0,relation_field(esk4_0)) )
& ( well_founded_relation(esk4_0)
| is_well_founded_in(esk4_0,relation_field(esk4_0)) ) ),
inference(skolemize,[status(esa)],[76]) ).
cnf(78,negated_conjecture,
( is_well_founded_in(esk4_0,relation_field(esk4_0))
| well_founded_relation(esk4_0) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(79,negated_conjecture,
( ~ is_well_founded_in(esk4_0,relation_field(esk4_0))
| ~ well_founded_relation(esk4_0) ),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(80,negated_conjecture,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[77]) ).
fof(92,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( ~ is_well_founded_in(X1,X2)
| ! [X3] :
( ~ subset(X3,X2)
| X3 = empty_set
| ? [X4] :
( in(X4,X3)
& disjoint(fiber(X1,X4),X3) ) ) )
& ( ? [X3] :
( subset(X3,X2)
& X3 != empty_set
& ! [X4] :
( ~ in(X4,X3)
| ~ disjoint(fiber(X1,X4),X3) ) )
| is_well_founded_in(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(93,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( ~ is_well_founded_in(X5,X6)
| ! [X7] :
( ~ subset(X7,X6)
| X7 = empty_set
| ? [X8] :
( in(X8,X7)
& disjoint(fiber(X5,X8),X7) ) ) )
& ( ? [X9] :
( subset(X9,X6)
& X9 != empty_set
& ! [X10] :
( ~ in(X10,X9)
| ~ disjoint(fiber(X5,X10),X9) ) )
| is_well_founded_in(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[92]) ).
fof(94,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( ~ is_well_founded_in(X5,X6)
| ! [X7] :
( ~ subset(X7,X6)
| X7 = empty_set
| ( in(esk5_3(X5,X6,X7),X7)
& disjoint(fiber(X5,esk5_3(X5,X6,X7)),X7) ) ) )
& ( ( subset(esk6_2(X5,X6),X6)
& esk6_2(X5,X6) != empty_set
& ! [X10] :
( ~ in(X10,esk6_2(X5,X6))
| ~ disjoint(fiber(X5,X10),esk6_2(X5,X6)) ) )
| is_well_founded_in(X5,X6) ) ) ),
inference(skolemize,[status(esa)],[93]) ).
fof(95,plain,
! [X5,X6,X7,X10] :
( ( ( ( ( ~ in(X10,esk6_2(X5,X6))
| ~ disjoint(fiber(X5,X10),esk6_2(X5,X6)) )
& subset(esk6_2(X5,X6),X6)
& esk6_2(X5,X6) != empty_set )
| is_well_founded_in(X5,X6) )
& ( ~ subset(X7,X6)
| X7 = empty_set
| ( in(esk5_3(X5,X6,X7),X7)
& disjoint(fiber(X5,esk5_3(X5,X6,X7)),X7) )
| ~ is_well_founded_in(X5,X6) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[94]) ).
fof(96,plain,
! [X5,X6,X7,X10] :
( ( ~ in(X10,esk6_2(X5,X6))
| ~ disjoint(fiber(X5,X10),esk6_2(X5,X6))
| is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( subset(esk6_2(X5,X6),X6)
| is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( esk6_2(X5,X6) != empty_set
| is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( in(esk5_3(X5,X6,X7),X7)
| ~ subset(X7,X6)
| X7 = empty_set
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) )
& ( disjoint(fiber(X5,esk5_3(X5,X6,X7)),X7)
| ~ subset(X7,X6)
| X7 = empty_set
| ~ is_well_founded_in(X5,X6)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[95]) ).
cnf(97,plain,
( X3 = empty_set
| disjoint(fiber(X1,esk5_3(X1,X2,X3)),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(98,plain,
( X3 = empty_set
| in(esk5_3(X1,X2,X3),X3)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(99,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| esk6_2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(100,plain,
( is_well_founded_in(X1,X2)
| subset(esk6_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[96]) ).
cnf(101,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X3),esk6_2(X1,X2))
| ~ in(X3,esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[96]) ).
fof(138,plain,
! [X1] :
( ~ relation(X1)
| ( ( ~ well_founded_relation(X1)
| ! [X2] :
( ~ subset(X2,relation_field(X1))
| X2 = empty_set
| ? [X3] :
( in(X3,X2)
& disjoint(fiber(X1,X3),X2) ) ) )
& ( ? [X2] :
( subset(X2,relation_field(X1))
& X2 != empty_set
& ! [X3] :
( ~ in(X3,X2)
| ~ disjoint(fiber(X1,X3),X2) ) )
| well_founded_relation(X1) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(139,plain,
! [X4] :
( ~ relation(X4)
| ( ( ~ well_founded_relation(X4)
| ! [X5] :
( ~ subset(X5,relation_field(X4))
| X5 = empty_set
| ? [X6] :
( in(X6,X5)
& disjoint(fiber(X4,X6),X5) ) ) )
& ( ? [X7] :
( subset(X7,relation_field(X4))
& X7 != empty_set
& ! [X8] :
( ~ in(X8,X7)
| ~ disjoint(fiber(X4,X8),X7) ) )
| well_founded_relation(X4) ) ) ),
inference(variable_rename,[status(thm)],[138]) ).
fof(140,plain,
! [X4] :
( ~ relation(X4)
| ( ( ~ well_founded_relation(X4)
| ! [X5] :
( ~ subset(X5,relation_field(X4))
| X5 = empty_set
| ( in(esk8_2(X4,X5),X5)
& disjoint(fiber(X4,esk8_2(X4,X5)),X5) ) ) )
& ( ( subset(esk9_1(X4),relation_field(X4))
& esk9_1(X4) != empty_set
& ! [X8] :
( ~ in(X8,esk9_1(X4))
| ~ disjoint(fiber(X4,X8),esk9_1(X4)) ) )
| well_founded_relation(X4) ) ) ),
inference(skolemize,[status(esa)],[139]) ).
fof(141,plain,
! [X4,X5,X8] :
( ( ( ( ( ~ in(X8,esk9_1(X4))
| ~ disjoint(fiber(X4,X8),esk9_1(X4)) )
& subset(esk9_1(X4),relation_field(X4))
& esk9_1(X4) != empty_set )
| well_founded_relation(X4) )
& ( ~ subset(X5,relation_field(X4))
| X5 = empty_set
| ( in(esk8_2(X4,X5),X5)
& disjoint(fiber(X4,esk8_2(X4,X5)),X5) )
| ~ well_founded_relation(X4) ) )
| ~ relation(X4) ),
inference(shift_quantors,[status(thm)],[140]) ).
fof(142,plain,
! [X4,X5,X8] :
( ( ~ in(X8,esk9_1(X4))
| ~ disjoint(fiber(X4,X8),esk9_1(X4))
| well_founded_relation(X4)
| ~ relation(X4) )
& ( subset(esk9_1(X4),relation_field(X4))
| well_founded_relation(X4)
| ~ relation(X4) )
& ( esk9_1(X4) != empty_set
| well_founded_relation(X4)
| ~ relation(X4) )
& ( in(esk8_2(X4,X5),X5)
| ~ subset(X5,relation_field(X4))
| X5 = empty_set
| ~ well_founded_relation(X4)
| ~ relation(X4) )
& ( disjoint(fiber(X4,esk8_2(X4,X5)),X5)
| ~ subset(X5,relation_field(X4))
| X5 = empty_set
| ~ well_founded_relation(X4)
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[141]) ).
cnf(143,plain,
( X2 = empty_set
| disjoint(fiber(X1,esk8_2(X1,X2)),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(144,plain,
( X2 = empty_set
| in(esk8_2(X1,X2),X2)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(X2,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(145,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| esk9_1(X1) != empty_set ),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(146,plain,
( well_founded_relation(X1)
| subset(esk9_1(X1),relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(147,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ disjoint(fiber(X1,X2),esk9_1(X1))
| ~ in(X2,esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(200,plain,
( is_well_founded_in(X1,X2)
| empty_set = esk6_2(X1,X2)
| ~ in(esk8_2(X1,esk6_2(X1,X2)),esk6_2(X1,X2))
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ subset(esk6_2(X1,X2),relation_field(X1)) ),
inference(spm,[status(thm)],[101,143,theory(equality)]) ).
cnf(202,plain,
( well_founded_relation(X1)
| empty_set = esk9_1(X1)
| ~ in(esk5_3(X1,X2,esk9_1(X1)),esk9_1(X1))
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(esk9_1(X1),X2) ),
inference(spm,[status(thm)],[147,97,theory(equality)]) ).
cnf(373,plain,
( esk6_2(X1,X2) = empty_set
| is_well_founded_in(X1,X2)
| ~ well_founded_relation(X1)
| ~ subset(esk6_2(X1,X2),relation_field(X1))
| ~ relation(X1) ),
inference(csr,[status(thm)],[200,144]) ).
cnf(374,plain,
( is_well_founded_in(X1,X2)
| ~ well_founded_relation(X1)
| ~ subset(esk6_2(X1,X2),relation_field(X1))
| ~ relation(X1) ),
inference(csr,[status(thm)],[373,99]) ).
cnf(375,plain,
( is_well_founded_in(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[374,100,theory(equality)]) ).
cnf(380,negated_conjecture,
( ~ well_founded_relation(esk4_0)
| ~ relation(esk4_0) ),
inference(spm,[status(thm)],[79,375,theory(equality)]) ).
cnf(381,negated_conjecture,
( ~ well_founded_relation(esk4_0)
| $false ),
inference(rw,[status(thm)],[380,80,theory(equality)]) ).
cnf(382,negated_conjecture,
~ well_founded_relation(esk4_0),
inference(cn,[status(thm)],[381,theory(equality)]) ).
cnf(387,negated_conjecture,
is_well_founded_in(esk4_0,relation_field(esk4_0)),
inference(sr,[status(thm)],[78,382,theory(equality)]) ).
cnf(440,plain,
( esk9_1(X1) = empty_set
| well_founded_relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(esk9_1(X1),X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[202,98]) ).
cnf(441,plain,
( well_founded_relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(esk9_1(X1),X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[440,145]) ).
cnf(443,plain,
( well_founded_relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[441,146,theory(equality)]) ).
cnf(456,negated_conjecture,
( well_founded_relation(esk4_0)
| ~ relation(esk4_0) ),
inference(spm,[status(thm)],[443,387,theory(equality)]) ).
cnf(459,negated_conjecture,
( well_founded_relation(esk4_0)
| $false ),
inference(rw,[status(thm)],[456,80,theory(equality)]) ).
cnf(460,negated_conjecture,
well_founded_relation(esk4_0),
inference(cn,[status(thm)],[459,theory(equality)]) ).
cnf(461,negated_conjecture,
$false,
inference(sr,[status(thm)],[460,382,theory(equality)]) ).
cnf(462,negated_conjecture,
$false,
461,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU243+1.p
% --creating new selector for []
% -running prover on /tmp/tmpqHgVc_/sel_SEU243+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU243+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU243+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU243+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
%
%------------------------------------------------------------------------------