TSTP Solution File: SET175+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET175+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 02:53:53 EST 2010
% Result : Theorem 2.86s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 27 unt; 0 def)
% Number of atoms : 249 ( 55 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 266 ( 96 ~; 118 |; 45 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 188 ( 17 sgn 80 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',commutativity_of_intersection) ).
fof(2,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',commutativity_of_union) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',equal_defn) ).
fof(4,conjecture,
! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',prove_absorbtion_for_union) ).
fof(5,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',union_defn) ).
fof(6,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',subset_defn) ).
fof(7,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',equal_member_defn) ).
fof(8,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpLOW9e_/sel_SET175+3.p_1',intersection_defn) ).
fof(10,negated_conjecture,
~ ! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
inference(assume_negation,[status(cth)],[4]) ).
fof(11,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(12,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[11]) ).
fof(13,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(14,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[13]) ).
fof(15,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(16,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,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)],[16]) ).
cnf(18,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,negated_conjecture,
? [X1,X2] : union(X1,intersection(X1,X2)) != X1,
inference(fof_nnf,[status(thm)],[10]) ).
fof(22,negated_conjecture,
? [X3,X4] : union(X3,intersection(X3,X4)) != X3,
inference(variable_rename,[status(thm)],[21]) ).
fof(23,negated_conjecture,
union(esk1_0,intersection(esk1_0,esk2_0)) != esk1_0,
inference(skolemize,[status(esa)],[22]) ).
cnf(24,negated_conjecture,
union(esk1_0,intersection(esk1_0,esk2_0)) != esk1_0,
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X1,X2,X3] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(31,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)],[6]) ).
fof(32,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)],[31]) ).
fof(33,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk3_2(X4,X5),X4)
& ~ member(esk3_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[32]) ).
fof(34,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk3_2(X4,X5),X4)
& ~ member(esk3_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[33]) ).
fof(35,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk3_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk3_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[34]) ).
cnf(36,plain,
( subset(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(39,plain,
! [X1,X2] :
( ( X1 != X2
| ! [X3] :
( ( ~ member(X3,X1)
| member(X3,X2) )
& ( ~ member(X3,X2)
| member(X3,X1) ) ) )
& ( ? [X3] :
( ( ~ member(X3,X1)
| ~ member(X3,X2) )
& ( member(X3,X1)
| member(X3,X2) ) )
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(40,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ? [X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5) )
& ( member(X7,X4)
| member(X7,X5) ) )
| X4 = X5 ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ( ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5) )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X4,X5,X6] :
( ( ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5) )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(44,plain,
( X1 = X2
| member(esk4_2(X1,X2),X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,plain,
( X1 = X2
| ~ member(esk4_2(X1,X2),X2)
| ~ member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(48,plain,
! [X1,X2,X3] :
( ( ~ member(X3,intersection(X1,X2))
| ( member(X3,X1)
& member(X3,X2) ) )
& ( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(49,plain,
! [X4,X5,X6] :
( ( ~ member(X6,intersection(X4,X5))
| ( member(X6,X4)
& member(X6,X5) ) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[48]) ).
fof(50,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[49]) ).
cnf(51,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(52,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(66,plain,
( member(esk3_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[52,37,theory(equality)]) ).
cnf(70,plain,
( subset(X1,union(X2,X3))
| ~ member(esk3_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[36,28,theory(equality)]) ).
cnf(79,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk3_2(X1,intersection(X2,X3)),X3)
| ~ member(esk3_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[36,51,theory(equality)]) ).
cnf(87,plain,
( member(esk4_2(intersection(X1,X2),X3),X2)
| intersection(X1,X2) = X3
| member(esk4_2(intersection(X1,X2),X3),X3) ),
inference(spm,[status(thm)],[52,44,theory(equality)]) ).
cnf(92,plain,
( member(esk4_2(X1,union(X2,X3)),X3)
| member(esk4_2(X1,union(X2,X3)),X2)
| X1 = union(X2,X3)
| member(esk4_2(X1,union(X2,X3)),X1) ),
inference(spm,[status(thm)],[30,44,theory(equality)]) ).
cnf(101,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[36,66,theory(equality)]) ).
cnf(103,plain,
subset(intersection(X2,X1),X2),
inference(spm,[status(thm)],[101,12,theory(equality)]) ).
cnf(131,plain,
subset(intersection(X1,X2),union(X3,X2)),
inference(spm,[status(thm)],[70,66,theory(equality)]) ).
cnf(156,plain,
( member(X1,union(X2,X3))
| ~ member(X1,intersection(X4,X3)) ),
inference(spm,[status(thm)],[38,131,theory(equality)]) ).
cnf(188,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk3_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[79,37,theory(equality)]) ).
cnf(223,plain,
( intersection(X4,X5) = X5
| member(esk4_2(intersection(X4,X5),X5),X5) ),
inference(ef,[status(thm)],[87,theory(equality)]) ).
cnf(239,plain,
( intersection(X1,X2) = X2
| ~ member(esk4_2(intersection(X1,X2),X2),intersection(X1,X2)) ),
inference(spm,[status(thm)],[45,223,theory(equality)]) ).
cnf(252,plain,
( member(esk3_2(intersection(X1,X2),X3),union(X4,X2))
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[156,37,theory(equality)]) ).
cnf(469,plain,
( X6 = union(X7,X6)
| member(esk4_2(X6,union(X7,X6)),X7)
| member(esk4_2(X6,union(X7,X6)),X6) ),
inference(ef,[status(thm)],[92,theory(equality)]) ).
cnf(1837,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[188,37,theory(equality)]) ).
cnf(1844,plain,
subset(intersection(X1,X2),intersection(union(X3,X2),intersection(X1,X2))),
inference(spm,[status(thm)],[188,252,theory(equality)]) ).
cnf(1862,plain,
( intersection(X1,X1) = X1
| ~ subset(intersection(X1,X1),X1) ),
inference(spm,[status(thm)],[18,1837,theory(equality)]) ).
cnf(1868,plain,
( intersection(X1,X1) = X1
| $false ),
inference(rw,[status(thm)],[1862,103,theory(equality)]) ).
cnf(1869,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[1868,theory(equality)]) ).
cnf(2606,plain,
( intersection(union(X1,X2),intersection(X3,X2)) = intersection(X3,X2)
| ~ subset(intersection(union(X1,X2),intersection(X3,X2)),intersection(X3,X2)) ),
inference(spm,[status(thm)],[18,1844,theory(equality)]) ).
cnf(2613,plain,
( intersection(union(X1,X2),intersection(X3,X2)) = intersection(X3,X2)
| $false ),
inference(rw,[status(thm)],[2606,101,theory(equality)]) ).
cnf(2614,plain,
intersection(union(X1,X2),intersection(X3,X2)) = intersection(X3,X2),
inference(cn,[status(thm)],[2613,theory(equality)]) ).
cnf(2687,plain,
intersection(union(X1,X2),X2) = X2,
inference(spm,[status(thm)],[2614,1869,theory(equality)]) ).
cnf(2796,plain,
intersection(X2,union(X1,X2)) = X2,
inference(rw,[status(thm)],[2687,12,theory(equality)]) ).
cnf(12599,plain,
( X1 = union(X2,X1)
| ~ member(esk4_2(X1,union(X2,X1)),X1) ),
inference(spm,[status(thm)],[239,2796,theory(equality)]) ).
cnf(90151,plain,
( union(X1,X2) = X2
| member(esk4_2(X2,union(X1,X2)),X1) ),
inference(spm,[status(thm)],[12599,469,theory(equality)]) ).
cnf(96126,plain,
( member(esk4_2(X1,union(intersection(X2,X3),X1)),X3)
| union(intersection(X2,X3),X1) = X1 ),
inference(spm,[status(thm)],[52,90151,theory(equality)]) ).
cnf(96275,plain,
union(intersection(X1,X2),X2) = X2,
inference(spm,[status(thm)],[12599,96126,theory(equality)]) ).
cnf(96287,plain,
union(X2,intersection(X1,X2)) = X2,
inference(rw,[status(thm)],[96275,14,theory(equality)]) ).
cnf(96859,plain,
union(X1,intersection(X1,X2)) = X1,
inference(spm,[status(thm)],[96287,12,theory(equality)]) ).
cnf(98411,negated_conjecture,
$false,
inference(rw,[status(thm)],[24,96859,theory(equality)]) ).
cnf(98412,negated_conjecture,
$false,
inference(cn,[status(thm)],[98411,theory(equality)]) ).
cnf(98413,negated_conjecture,
$false,
98412,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET175+3.p
% --creating new selector for []
% -running prover on /tmp/tmpLOW9e_/sel_SET175+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET175+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET175+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET175+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
%
%------------------------------------------------------------------------------