TSTP Solution File: SEU131+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU131+2 : 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 04:45:10 EST 2010
% Result : Theorem 1.05s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 84 ( 16 unt; 0 def)
% Number of atoms : 286 ( 64 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 338 ( 136 ~; 132 |; 56 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 172 ( 13 sgn 100 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',t2_boole) ).
fof(17,conjecture,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',l32_xboole_1) ).
fof(20,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',t7_xboole_1) ).
fof(23,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',d4_xboole_0) ).
fof(24,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',d7_xboole_0) ).
fof(29,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',d1_xboole_0) ).
fof(40,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',t12_xboole_1) ).
fof(42,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',d3_tarski) ).
fof(43,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/tmp/tmpI73Gky/sel_SEU131+2.p_1',t4_xboole_0) ).
fof(45,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[17]) ).
fof(50,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[23,theory(equality)]) ).
fof(52,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[29,theory(equality)]) ).
fof(53,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[43,theory(equality)]) ).
fof(56,plain,
! [X2] : set_intersection2(X2,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[2]) ).
cnf(57,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[56]) ).
fof(110,negated_conjecture,
? [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| ~ subset(X1,X2) )
& ( set_difference(X1,X2) = empty_set
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(111,negated_conjecture,
? [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| ~ subset(X3,X4) )
& ( set_difference(X3,X4) = empty_set
| subset(X3,X4) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,negated_conjecture,
( ( set_difference(esk5_0,esk6_0) != empty_set
| ~ subset(esk5_0,esk6_0) )
& ( set_difference(esk5_0,esk6_0) = empty_set
| subset(esk5_0,esk6_0) ) ),
inference(skolemize,[status(esa)],[111]) ).
cnf(113,negated_conjecture,
( subset(esk5_0,esk6_0)
| set_difference(esk5_0,esk6_0) = empty_set ),
inference(split_conjunct,[status(thm)],[112]) ).
cnf(114,negated_conjecture,
( ~ subset(esk5_0,esk6_0)
| set_difference(esk5_0,esk6_0) != empty_set ),
inference(split_conjunct,[status(thm)],[112]) ).
fof(121,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[20]) ).
cnf(122,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[121]) ).
fof(127,plain,
! [X1,X2,X3] :
( ( X3 != set_difference(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_difference(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[50]) ).
fof(128,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(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_difference(X5,X6) ) ),
inference(variable_rename,[status(thm)],[127]) ).
fof(129,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| ( in(esk7_3(X5,X6,X7),X5)
& ~ in(esk7_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(skolemize,[status(esa)],[128]) ).
fof(130,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_difference(X5,X6) )
& ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| ( in(esk7_3(X5,X6,X7),X5)
& ~ in(esk7_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[129]) ).
fof(131,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X6)
| X7 = set_difference(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) )
& ( ~ in(esk7_3(X5,X6,X7),X6)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) ) ),
inference(distribute,[status(thm)],[130]) ).
cnf(132,plain,
( X1 = set_difference(X2,X3)
| in(esk7_3(X2,X3,X1),X1)
| ~ in(esk7_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(133,plain,
( X1 = set_difference(X2,X3)
| in(esk7_3(X2,X3,X1),X1)
| in(esk7_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[131]) ).
cnf(135,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[131]) ).
fof(138,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set )
& ( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(139,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X3,X4) != empty_set
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[138]) ).
cnf(140,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[139]) ).
fof(161,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[52]) ).
fof(162,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[161]) ).
fof(163,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk9_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[162]) ).
fof(164,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk9_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[163]) ).
cnf(166,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[164]) ).
fof(191,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| set_union2(X1,X2) = X2 ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(192,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[191]) ).
cnf(193,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[192]) ).
fof(197,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(198,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[197]) ).
fof(199,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk11_2(X4,X5),X4)
& ~ in(esk11_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[198]) ).
fof(200,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk11_2(X4,X5),X4)
& ~ in(esk11_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[199]) ).
fof(201,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk11_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk11_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[200]) ).
cnf(202,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(203,plain,
( subset(X1,X2)
| in(esk11_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
cnf(204,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[201]) ).
fof(205,plain,
! [X1,X2] :
( ( disjoint(X1,X2)
| ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[53]) ).
fof(206,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| ? [X6] : in(X6,set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(variable_rename,[status(thm)],[205]) ).
fof(207,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| in(esk12_2(X4,X5),set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(skolemize,[status(esa)],[206]) ).
fof(208,plain,
! [X4,X5,X7] :
( ( ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) )
& ( disjoint(X4,X5)
| in(esk12_2(X4,X5),set_intersection2(X4,X5)) ) ),
inference(shift_quantors,[status(thm)],[207]) ).
cnf(210,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[208]) ).
cnf(302,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[204,122,theory(equality)]) ).
cnf(327,plain,
( ~ disjoint(X1,empty_set)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[210,57,theory(equality)]) ).
cnf(413,negated_conjecture,
( in(X1,X2)
| in(X1,esk6_0)
| subset(esk5_0,esk6_0)
| empty_set != X2
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[135,113,theory(equality)]) ).
fof(1017,plain,
( ~ epred1_0
<=> ! [X1] : ~ disjoint(X1,empty_set) ),
introduced(definition),
[split] ).
cnf(1018,plain,
( epred1_0
| ~ disjoint(X1,empty_set) ),
inference(split_equiv,[status(thm)],[1017]) ).
fof(1019,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition),
[split] ).
cnf(1020,plain,
( epred2_0
| ~ in(X2,empty_set) ),
inference(split_equiv,[status(thm)],[1019]) ).
cnf(1021,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[327,1017,theory(equality)]),1019,theory(equality)]),
[split] ).
cnf(1022,plain,
( epred1_0
| set_intersection2(X1,empty_set) != empty_set ),
inference(spm,[status(thm)],[1018,140,theory(equality)]) ).
cnf(1028,plain,
( epred1_0
| $false ),
inference(rw,[status(thm)],[1022,57,theory(equality)]) ).
cnf(1029,plain,
epred1_0,
inference(cn,[status(thm)],[1028,theory(equality)]) ).
cnf(1035,plain,
( ~ epred2_0
| $false ),
inference(rw,[status(thm)],[1021,1029,theory(equality)]) ).
cnf(1036,plain,
~ epred2_0,
inference(cn,[status(thm)],[1035,theory(equality)]) ).
cnf(1037,plain,
~ in(X2,empty_set),
inference(sr,[status(thm)],[1020,1036,theory(equality)]) ).
cnf(1044,plain,
( set_difference(X1,X2) = empty_set
| in(esk7_3(X1,X2,empty_set),X1) ),
inference(spm,[status(thm)],[1037,133,theory(equality)]) ).
cnf(1406,plain,
( set_difference(X1,set_union2(X2,X3)) = X4
| in(esk7_3(X1,set_union2(X2,X3),X4),X4)
| ~ in(esk7_3(X1,set_union2(X2,X3),X4),X2) ),
inference(spm,[status(thm)],[132,302,theory(equality)]) ).
cnf(3793,negated_conjecture,
( in(X1,esk6_0)
| in(X1,X2)
| empty_set != X2
| ~ in(X1,esk5_0) ),
inference(csr,[status(thm)],[413,204]) ).
cnf(3794,negated_conjecture,
( in(X1,esk6_0)
| empty_set != X2
| ~ in(X1,esk5_0) ),
inference(csr,[status(thm)],[3793,166]) ).
cnf(3795,negated_conjecture,
( in(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(er,[status(thm)],[3794,theory(equality)]) ).
cnf(3799,negated_conjecture,
( subset(X1,esk6_0)
| ~ in(esk11_2(X1,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[202,3795,theory(equality)]) ).
cnf(5695,negated_conjecture,
subset(esk5_0,esk6_0),
inference(spm,[status(thm)],[3799,203,theory(equality)]) ).
cnf(5714,negated_conjecture,
( set_difference(esk5_0,esk6_0) != empty_set
| $false ),
inference(rw,[status(thm)],[114,5695,theory(equality)]) ).
cnf(5715,negated_conjecture,
set_difference(esk5_0,esk6_0) != empty_set,
inference(cn,[status(thm)],[5714,theory(equality)]) ).
cnf(19722,plain,
( set_difference(X1,set_union2(X1,X2)) = empty_set
| in(esk7_3(X1,set_union2(X1,X2),empty_set),empty_set) ),
inference(spm,[status(thm)],[1406,1044,theory(equality)]) ).
cnf(19729,plain,
set_difference(X1,set_union2(X1,X2)) = empty_set,
inference(sr,[status(thm)],[19722,1037,theory(equality)]) ).
cnf(19737,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[19729,193,theory(equality)]) ).
cnf(19759,plain,
~ subset(esk5_0,esk6_0),
inference(spm,[status(thm)],[5715,19737,theory(equality)]) ).
cnf(19769,plain,
$false,
inference(rw,[status(thm)],[19759,5695,theory(equality)]) ).
cnf(19770,plain,
$false,
inference(cn,[status(thm)],[19769,theory(equality)]) ).
cnf(19771,plain,
$false,
19770,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU131+2.p
% --creating new selector for []
% -running prover on /tmp/tmpI73Gky/sel_SEU131+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU131+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU131+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU131+2.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
%
%------------------------------------------------------------------------------