TSTP Solution File: SET935+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET935+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:48:47 EST 2010
% Result : Theorem 0.34s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 19 unt; 0 def)
% Number of atoms : 259 ( 60 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 299 ( 104 ~; 131 |; 56 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 118 ( 6 sgn 74 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',d10_xboole_0) ).
fof(4,conjecture,
! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',t82_zfmisc_1) ).
fof(5,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',d2_xboole_0) ).
fof(6,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',d1_zfmisc_1) ).
fof(8,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',commutativity_k2_xboole_0) ).
fof(10,axiom,
! [X1,X2] :
( inclusion_comparable(X1,X2)
<=> ( subset(X1,X2)
| subset(X2,X1) ) ),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',d9_xboole_0) ).
fof(15,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',t7_xboole_1) ).
fof(16,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpLbIp8J/sel_SET935+1.p_1',reflexivity_r1_tarski) ).
fof(17,negated_conjecture,
~ ! [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
=> inclusion_comparable(X1,X2) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(22,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(23,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(25,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(34,negated_conjecture,
? [X1,X2] :
( set_union2(powerset(X1),powerset(X2)) = powerset(set_union2(X1,X2))
& ~ inclusion_comparable(X1,X2) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(35,negated_conjecture,
? [X3,X4] :
( set_union2(powerset(X3),powerset(X4)) = powerset(set_union2(X3,X4))
& ~ inclusion_comparable(X3,X4) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( set_union2(powerset(esk2_0),powerset(esk3_0)) = powerset(set_union2(esk2_0,esk3_0))
& ~ inclusion_comparable(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[35]) ).
cnf(37,negated_conjecture,
~ inclusion_comparable(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
set_union2(powerset(esk2_0),powerset(esk3_0)) = powerset(set_union2(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[36]) ).
fof(39,plain,
! [X1,X2,X3] :
( ( X3 != set_union2(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_union2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(40,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(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_union2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk4_3(X5,X6,X7),X7)
| ( ~ in(esk4_3(X5,X6,X7),X5)
& ~ in(esk4_3(X5,X6,X7),X6) ) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,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_union2(X5,X6) )
& ( ( ( ~ in(esk4_3(X5,X6,X7),X7)
| ( ~ in(esk4_3(X5,X6,X7),X5)
& ~ in(esk4_3(X5,X6,X7),X6) ) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X6)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X5)
| ~ in(esk4_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X6)
| ~ in(esk4_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(49,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(50,plain,
! [X1,X2] :
( ( X2 != powerset(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| subset(X3,X1) )
& ( ~ subset(X3,X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ subset(X3,X1) )
& ( in(X3,X2)
| subset(X3,X1) ) )
| X2 = powerset(X1) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(51,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ subset(X7,X4) )
& ( in(X7,X5)
| subset(X7,X4) ) )
| X5 = powerset(X4) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| ~ subset(esk5_2(X4,X5),X4) )
& ( in(esk5_2(X4,X5),X5)
| subset(esk5_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(skolemize,[status(esa)],[51]) ).
fof(53,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) )
| X5 != powerset(X4) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| ~ subset(esk5_2(X4,X5),X4) )
& ( in(esk5_2(X4,X5),X5)
| subset(esk5_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(shift_quantors,[status(thm)],[52]) ).
fof(54,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk5_2(X4,X5),X5)
| ~ subset(esk5_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk5_2(X4,X5),X5)
| subset(esk5_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(57,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(58,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(62,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[8]) ).
cnf(63,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[62]) ).
fof(67,plain,
! [X1,X2] :
( ( ~ inclusion_comparable(X1,X2)
| subset(X1,X2)
| subset(X2,X1) )
& ( ( ~ subset(X1,X2)
& ~ subset(X2,X1) )
| inclusion_comparable(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(68,plain,
! [X3,X4] :
( ( ~ inclusion_comparable(X3,X4)
| subset(X3,X4)
| subset(X4,X3) )
& ( ( ~ subset(X3,X4)
& ~ subset(X4,X3) )
| inclusion_comparable(X3,X4) ) ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,plain,
! [X3,X4] :
( ( ~ inclusion_comparable(X3,X4)
| subset(X3,X4)
| subset(X4,X3) )
& ( ~ subset(X3,X4)
| inclusion_comparable(X3,X4) )
& ( ~ subset(X4,X3)
| inclusion_comparable(X3,X4) ) ),
inference(distribute,[status(thm)],[68]) ).
cnf(70,plain,
( inclusion_comparable(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(71,plain,
( inclusion_comparable(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[69]) ).
fof(83,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[15]) ).
cnf(84,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[83]) ).
fof(85,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[16]) ).
cnf(86,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[85]) ).
cnf(99,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[84,63,theory(equality)]) ).
cnf(106,plain,
inclusion_comparable(X1,set_union2(X1,X2)),
inference(spm,[status(thm)],[71,84,theory(equality)]) ).
cnf(116,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[58,theory(equality)]) ).
cnf(120,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[57,theory(equality)]) ).
cnf(133,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[49,theory(equality)]) ).
cnf(179,plain,
inclusion_comparable(set_union2(X1,X2),X2),
inference(spm,[status(thm)],[70,99,theory(equality)]) ).
cnf(243,plain,
in(X1,powerset(X1)),
inference(spm,[status(thm)],[120,86,theory(equality)]) ).
cnf(667,negated_conjecture,
( in(X1,powerset(esk3_0))
| in(X1,powerset(esk2_0))
| ~ in(X1,powerset(set_union2(esk2_0,esk3_0))) ),
inference(spm,[status(thm)],[133,38,theory(equality)]) ).
cnf(5437,negated_conjecture,
( in(set_union2(esk2_0,esk3_0),powerset(esk2_0))
| in(set_union2(esk2_0,esk3_0),powerset(esk3_0)) ),
inference(spm,[status(thm)],[667,243,theory(equality)]) ).
cnf(5475,negated_conjecture,
( subset(set_union2(esk2_0,esk3_0),esk3_0)
| in(set_union2(esk2_0,esk3_0),powerset(esk2_0)) ),
inference(spm,[status(thm)],[116,5437,theory(equality)]) ).
cnf(5481,negated_conjecture,
( subset(set_union2(esk2_0,esk3_0),esk2_0)
| subset(set_union2(esk2_0,esk3_0),esk3_0) ),
inference(spm,[status(thm)],[116,5475,theory(equality)]) ).
cnf(5488,negated_conjecture,
( esk3_0 = set_union2(esk2_0,esk3_0)
| subset(set_union2(esk2_0,esk3_0),esk2_0)
| ~ subset(esk3_0,set_union2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[25,5481,theory(equality)]) ).
cnf(5493,negated_conjecture,
( esk3_0 = set_union2(esk2_0,esk3_0)
| subset(set_union2(esk2_0,esk3_0),esk2_0)
| $false ),
inference(rw,[status(thm)],[5488,99,theory(equality)]) ).
cnf(5494,negated_conjecture,
( esk3_0 = set_union2(esk2_0,esk3_0)
| subset(set_union2(esk2_0,esk3_0),esk2_0) ),
inference(cn,[status(thm)],[5493,theory(equality)]) ).
cnf(5498,negated_conjecture,
( esk2_0 = set_union2(esk2_0,esk3_0)
| set_union2(esk2_0,esk3_0) = esk3_0
| ~ subset(esk2_0,set_union2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[25,5494,theory(equality)]) ).
cnf(5503,negated_conjecture,
( esk2_0 = set_union2(esk2_0,esk3_0)
| set_union2(esk2_0,esk3_0) = esk3_0
| $false ),
inference(rw,[status(thm)],[5498,84,theory(equality)]) ).
cnf(5504,negated_conjecture,
( esk2_0 = set_union2(esk2_0,esk3_0)
| set_union2(esk2_0,esk3_0) = esk3_0 ),
inference(cn,[status(thm)],[5503,theory(equality)]) ).
cnf(5508,negated_conjecture,
( inclusion_comparable(esk2_0,esk3_0)
| set_union2(esk2_0,esk3_0) = esk2_0 ),
inference(spm,[status(thm)],[106,5504,theory(equality)]) ).
cnf(5695,negated_conjecture,
set_union2(esk2_0,esk3_0) = esk2_0,
inference(sr,[status(thm)],[5508,37,theory(equality)]) ).
cnf(5771,negated_conjecture,
inclusion_comparable(esk2_0,esk3_0),
inference(spm,[status(thm)],[179,5695,theory(equality)]) ).
cnf(5974,negated_conjecture,
$false,
inference(sr,[status(thm)],[5771,37,theory(equality)]) ).
cnf(5975,negated_conjecture,
$false,
5974,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET935+1.p
% --creating new selector for []
% -running prover on /tmp/tmpLbIp8J/sel_SET935+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET935+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET935+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET935+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
%
%------------------------------------------------------------------------------