TSTP Solution File: SET632+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET632+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:05:57 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 16 unt; 0 def)
% Number of atoms : 220 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 241 ( 95 ~; 88 |; 47 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 6 sgn 78 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',subset_defn) ).
fof(2,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',empty_defn) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',equal_defn) ).
fof(4,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',intersect_defn) ).
fof(5,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3)
& disjoint(X2,X3) )
=> X1 = empty_set ),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',prove_th114) ).
fof(6,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',symmetry_of_intersect) ).
fof(7,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',disjoint_defn) ).
fof(9,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpCzYAn0/sel_SET632+3.p_1',empty_set_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3)
& disjoint(X2,X3) )
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[5]) ).
fof(11,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(12,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(13,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(14,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(15,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[17]) ).
cnf(20,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(21,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(22,plain,
! [X1] :
( ( ~ empty(X1)
| ! [X2] : ~ member(X2,X1) )
& ( ? [X2] : member(X2,X1)
| empty(X1) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(23,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( ? [X5] : member(X5,X3)
| empty(X3) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X3] :
( ( ~ empty(X3)
| ! [X4] : ~ member(X4,X3) )
& ( member(esk2_1(X3),X3)
| empty(X3) ) ),
inference(skolemize,[status(esa)],[23]) ).
fof(25,plain,
! [X3,X4] :
( ( ~ member(X4,X3)
| ~ empty(X3) )
& ( member(esk2_1(X3),X3)
| empty(X3) ) ),
inference(shift_quantors,[status(thm)],[24]) ).
cnf(26,plain,
( empty(X1)
| member(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(28,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(29,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,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)],[29]) ).
cnf(31,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(34,plain,
! [X1,X2] :
( ( ~ intersect(X1,X2)
| ? [X3] :
( member(X3,X1)
& member(X3,X2) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X2) )
| intersect(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(35,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ? [X6] :
( member(X6,X4)
& member(X6,X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ( member(esk3_2(X4,X5),X4)
& member(esk3_2(X4,X5),X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( ~ intersect(X4,X5)
| ( member(esk3_2(X4,X5),X4)
& member(esk3_2(X4,X5),X5) ) ) ),
inference(shift_quantors,[status(thm)],[36]) ).
fof(38,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( member(esk3_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk3_2(X4,X5),X5)
| ~ intersect(X4,X5) ) ),
inference(distribute,[status(thm)],[37]) ).
cnf(39,plain,
( member(esk3_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(41,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(42,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& subset(X1,X3)
& disjoint(X2,X3)
& X1 != empty_set ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(43,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& subset(X4,X6)
& disjoint(X5,X6)
& X4 != empty_set ),
inference(variable_rename,[status(thm)],[42]) ).
fof(44,negated_conjecture,
( subset(esk4_0,esk5_0)
& subset(esk4_0,esk6_0)
& disjoint(esk5_0,esk6_0)
& esk4_0 != empty_set ),
inference(skolemize,[status(esa)],[43]) ).
cnf(45,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,negated_conjecture,
disjoint(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(47,negated_conjecture,
subset(esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(48,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[44]) ).
fof(49,plain,
! [X1,X2] :
( ~ intersect(X1,X2)
| intersect(X2,X1) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(50,plain,
! [X3,X4] :
( ~ intersect(X3,X4)
| intersect(X4,X3) ),
inference(variable_rename,[status(thm)],[49]) ).
cnf(51,plain,
( intersect(X1,X2)
| ~ intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(52,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) )
& ( intersect(X1,X2)
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(53,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| ~ intersect(X3,X4) )
& ( intersect(X3,X4)
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[52]) ).
cnf(55,plain,
( ~ intersect(X1,X2)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(58,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[13]) ).
cnf(59,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(66,negated_conjecture,
~ intersect(esk5_0,esk6_0),
inference(spm,[status(thm)],[55,46,theory(equality)]) ).
cnf(70,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[59,20,theory(equality)]) ).
cnf(71,plain,
( subset(X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[27,20,theory(equality)]) ).
cnf(75,plain,
( ~ empty(X1)
| ~ intersect(X2,X1) ),
inference(spm,[status(thm)],[27,39,theory(equality)]) ).
cnf(76,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[21,48,theory(equality)]) ).
cnf(77,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[21,47,theory(equality)]) ).
cnf(81,plain,
( intersect(X1,X2)
| empty(X2)
| ~ member(esk2_1(X2),X1) ),
inference(spm,[status(thm)],[41,26,theory(equality)]) ).
cnf(91,negated_conjecture,
( intersect(X1,esk5_0)
| ~ member(X2,X1)
| ~ member(X2,esk4_0) ),
inference(spm,[status(thm)],[41,76,theory(equality)]) ).
cnf(98,negated_conjecture,
( intersect(esk5_0,X1)
| empty(X1)
| ~ member(esk2_1(X1),esk4_0) ),
inference(spm,[status(thm)],[81,76,theory(equality)]) ).
cnf(152,negated_conjecture,
( intersect(X1,esk5_0)
| empty(esk4_0)
| ~ member(esk2_1(esk4_0),X1) ),
inference(spm,[status(thm)],[91,26,theory(equality)]) ).
cnf(202,negated_conjecture,
( intersect(esk5_0,esk4_0)
| empty(esk4_0) ),
inference(spm,[status(thm)],[98,26,theory(equality)]) ).
cnf(203,negated_conjecture,
( subset(esk4_0,X1)
| intersect(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[71,202,theory(equality)]) ).
cnf(205,negated_conjecture,
( X1 = esk4_0
| intersect(esk5_0,esk4_0)
| ~ subset(X1,esk4_0) ),
inference(spm,[status(thm)],[31,203,theory(equality)]) ).
cnf(221,negated_conjecture,
( empty_set = esk4_0
| intersect(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[205,70,theory(equality)]) ).
cnf(222,negated_conjecture,
intersect(esk5_0,esk4_0),
inference(sr,[status(thm)],[221,45,theory(equality)]) ).
cnf(224,negated_conjecture,
~ empty(esk4_0),
inference(spm,[status(thm)],[75,222,theory(equality)]) ).
cnf(271,negated_conjecture,
( intersect(X1,esk5_0)
| ~ member(esk2_1(esk4_0),X1) ),
inference(sr,[status(thm)],[152,224,theory(equality)]) ).
cnf(274,negated_conjecture,
( intersect(esk6_0,esk5_0)
| ~ member(esk2_1(esk4_0),esk4_0) ),
inference(spm,[status(thm)],[271,77,theory(equality)]) ).
cnf(277,negated_conjecture,
( intersect(esk6_0,esk5_0)
| empty(esk4_0) ),
inference(spm,[status(thm)],[274,26,theory(equality)]) ).
cnf(278,negated_conjecture,
intersect(esk6_0,esk5_0),
inference(sr,[status(thm)],[277,224,theory(equality)]) ).
cnf(279,negated_conjecture,
intersect(esk5_0,esk6_0),
inference(spm,[status(thm)],[51,278,theory(equality)]) ).
cnf(285,negated_conjecture,
$false,
inference(sr,[status(thm)],[279,66,theory(equality)]) ).
cnf(286,negated_conjecture,
$false,
285,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET632+3.p
% --creating new selector for []
% -running prover on /tmp/tmpCzYAn0/sel_SET632+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET632+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET632+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET632+3.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
%
%------------------------------------------------------------------------------