TSTP Solution File: SET607+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET607+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:00:55 EST 2010
% Result : Theorem 26.45s
% Output : CNFRefutation 26.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 92 ( 33 unt; 0 def)
% Number of atoms : 225 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 214 ( 81 ~; 96 |; 31 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 231 ( 25 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmp1Jax_9/sel_SET607+3.p_1',commutativity_of_union) ).
fof(2,conjecture,
! [X1,X2] : union(X1,difference(X2,X1)) = union(X1,X2),
file('/tmp/tmp1Jax_9/sel_SET607+3.p_1',prove_th79) ).
fof(3,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmp1Jax_9/sel_SET607+3.p_1',equal_defn) ).
fof(4,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmp1Jax_9/sel_SET607+3.p_1',union_defn) ).
fof(5,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmp1Jax_9/sel_SET607+3.p_1',subset_defn) ).
fof(7,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmp1Jax_9/sel_SET607+3.p_1',difference_defn) ).
fof(9,negated_conjecture,
~ ! [X1,X2] : union(X1,difference(X2,X1)) = union(X1,X2),
inference(assume_negation,[status(cth)],[2]) ).
fof(10,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(11,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(12,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[11]) ).
fof(13,negated_conjecture,
? [X1,X2] : union(X1,difference(X2,X1)) != union(X1,X2),
inference(fof_nnf,[status(thm)],[9]) ).
fof(14,negated_conjecture,
? [X3,X4] : union(X3,difference(X4,X3)) != union(X3,X4),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
union(esk1_0,difference(esk2_0,esk1_0)) != union(esk1_0,esk2_0),
inference(skolemize,[status(esa)],[14]) ).
cnf(16,negated_conjecture,
union(esk1_0,difference(esk2_0,esk1_0)) != union(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,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(18,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,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)],[18]) ).
cnf(20,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,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)],[4]) ).
fof(24,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)],[23]) ).
fof(25,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)],[24]) ).
cnf(26,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(28,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(29,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)],[5]) ).
fof(30,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)],[29]) ).
fof(31,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)],[30]) ).
fof(32,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)],[31]) ).
fof(33,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)],[32]) ).
cnf(34,plain,
( subset(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(46,plain,
! [X1,X2,X3] :
( ( ~ member(X3,difference(X1,X2))
| ( member(X3,X1)
& ~ member(X3,X2) ) )
& ( ~ member(X3,X1)
| member(X3,X2)
| member(X3,difference(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(47,plain,
! [X4,X5,X6] :
( ( ~ member(X6,difference(X4,X5))
| ( member(X6,X4)
& ~ member(X6,X5) ) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(X4,X5)) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(49,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(51,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(62,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[51,35,theory(equality)]) ).
cnf(63,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk3_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[50,35,theory(equality)]) ).
cnf(64,plain,
( subset(X1,union(X2,X3))
| ~ member(esk3_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[34,26,theory(equality)]) ).
cnf(65,plain,
( subset(X1,union(X2,X3))
| ~ member(esk3_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[34,27,theory(equality)]) ).
cnf(71,plain,
( subset(X1,difference(X2,X3))
| member(esk3_2(X1,difference(X2,X3)),X3)
| ~ member(esk3_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[34,49,theory(equality)]) ).
cnf(76,plain,
( member(esk3_2(union(X1,X2),X3),X2)
| member(esk3_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[28,35,theory(equality)]) ).
cnf(91,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[34,62,theory(equality)]) ).
cnf(92,plain,
( member(esk3_2(difference(union(X1,X2),X3),X4),X2)
| member(esk3_2(difference(union(X1,X2),X3),X4),X1)
| subset(difference(union(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[28,62,theory(equality)]) ).
cnf(93,plain,
( X1 = difference(X1,X2)
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[20,91,theory(equality)]) ).
cnf(97,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk3_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk3_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[63,49,theory(equality)]) ).
cnf(98,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[63,62,theory(equality)]) ).
cnf(99,plain,
( X1 = difference(X2,X2)
| ~ subset(X1,difference(X2,X2)) ),
inference(spm,[status(thm)],[20,98,theory(equality)]) ).
cnf(100,plain,
( member(X1,X2)
| ~ member(X1,difference(X3,X3)) ),
inference(spm,[status(thm)],[36,98,theory(equality)]) ).
cnf(101,plain,
difference(difference(X1,X1),X2) = difference(X1,X1),
inference(spm,[status(thm)],[93,98,theory(equality)]) ).
cnf(106,plain,
( ~ member(X1,difference(X2,X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[50,101,theory(equality)]) ).
cnf(157,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk3_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[64,26,theory(equality)]) ).
cnf(159,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[64,35,theory(equality)]) ).
cnf(162,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[159,12,theory(equality)]) ).
cnf(201,plain,
( subset(X1,union(difference(X2,X3),X4))
| member(esk3_2(X1,union(difference(X2,X3),X4)),X3)
| ~ member(esk3_2(X1,union(difference(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[65,49,theory(equality)]) ).
cnf(225,plain,
( member(esk3_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[71,35,theory(equality)]) ).
cnf(231,plain,
( member(esk3_2(X1,difference(X1,difference(X2,X3))),X2)
| subset(X1,difference(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[51,225,theory(equality)]) ).
cnf(238,plain,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[106,100]) ).
cnf(247,plain,
subset(X1,difference(X1,difference(X2,X2))),
inference(spm,[status(thm)],[238,225,theory(equality)]) ).
cnf(256,plain,
( difference(X1,difference(X2,X2)) = X1
| ~ subset(difference(X1,difference(X2,X2)),X1) ),
inference(spm,[status(thm)],[20,247,theory(equality)]) ).
cnf(266,plain,
( difference(X1,difference(X2,X2)) = X1
| $false ),
inference(rw,[status(thm)],[256,91,theory(equality)]) ).
cnf(267,plain,
difference(X1,difference(X2,X2)) = X1,
inference(cn,[status(thm)],[266,theory(equality)]) ).
cnf(317,plain,
( subset(union(X1,X2),union(X3,X1))
| member(esk3_2(union(X1,X2),union(X3,X1)),X2) ),
inference(spm,[status(thm)],[64,76,theory(equality)]) ).
cnf(319,plain,
( subset(union(X1,X2),union(X1,X3))
| member(esk3_2(union(X1,X2),union(X1,X3)),X2) ),
inference(spm,[status(thm)],[65,76,theory(equality)]) ).
cnf(1640,plain,
( subset(difference(union(X1,X2),X1),X3)
| member(esk3_2(difference(union(X1,X2),X1),X3),X2) ),
inference(spm,[status(thm)],[63,92,theory(equality)]) ).
cnf(2503,plain,
( member(esk3_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[97,62,theory(equality)]) ).
cnf(4915,plain,
subset(difference(X1,X2),difference(difference(X1,X2),difference(X2,X3))),
inference(spm,[status(thm)],[63,231,theory(equality)]) ).
cnf(5042,plain,
( difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2)
| ~ subset(difference(difference(X1,X2),difference(X2,X3)),difference(X1,X2)) ),
inference(spm,[status(thm)],[20,4915,theory(equality)]) ).
cnf(5110,plain,
( difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2)
| $false ),
inference(rw,[status(thm)],[5042,91,theory(equality)]) ).
cnf(5111,plain,
difference(difference(X1,X2),difference(X2,X3)) = difference(X1,X2),
inference(cn,[status(thm)],[5110,theory(equality)]) ).
cnf(5224,plain,
( subset(difference(X1,X2),X4)
| ~ member(esk3_2(difference(X1,X2),X4),difference(X2,X3)) ),
inference(spm,[status(thm)],[63,5111,theory(equality)]) ).
cnf(10983,plain,
( member(esk3_2(union(X1,X2),union(difference(X2,X3),X1)),X3)
| subset(union(X1,X2),union(difference(X2,X3),X1)) ),
inference(spm,[status(thm)],[201,317,theory(equality)]) ).
cnf(11462,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[157,319,theory(equality)]) ).
cnf(158825,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[34,2503,theory(equality)]) ).
cnf(390926,plain,
subset(difference(union(X1,difference(X1,X2)),X1),X3),
inference(spm,[status(thm)],[5224,1640,theory(equality)]) ).
cnf(392170,plain,
difference(union(X1,difference(X1,X2)),X1) = difference(X3,X3),
inference(spm,[status(thm)],[99,390926,theory(equality)]) ).
cnf(392681,plain,
subset(difference(union(X1,difference(X1,X2)),difference(X3,X3)),X1),
inference(spm,[status(thm)],[158825,392170,theory(equality)]) ).
cnf(394379,plain,
subset(union(X1,difference(X1,X2)),X1),
inference(rw,[status(thm)],[392681,267,theory(equality)]) ).
cnf(395595,plain,
( X1 = union(X1,difference(X1,X2))
| ~ subset(X1,union(X1,difference(X1,X2))) ),
inference(spm,[status(thm)],[20,394379,theory(equality)]) ).
cnf(395749,plain,
( X1 = union(X1,difference(X1,X2))
| $false ),
inference(rw,[status(thm)],[395595,162,theory(equality)]) ).
cnf(395750,plain,
X1 = union(X1,difference(X1,X2)),
inference(cn,[status(thm)],[395749,theory(equality)]) ).
cnf(395827,plain,
subset(union(X1,difference(X2,X3)),union(X1,X2)),
inference(spm,[status(thm)],[11462,395750,theory(equality)]) ).
cnf(922417,plain,
subset(union(X1,X2),union(difference(X2,X1),X1)),
inference(spm,[status(thm)],[64,10983,theory(equality)]) ).
cnf(922896,plain,
subset(union(X1,X2),union(X1,difference(X2,X1))),
inference(rw,[status(thm)],[922417,12,theory(equality)]) ).
cnf(923240,plain,
( union(X1,difference(X2,X1)) = union(X1,X2)
| ~ subset(union(X1,difference(X2,X1)),union(X1,X2)) ),
inference(spm,[status(thm)],[20,922896,theory(equality)]) ).
cnf(923547,plain,
( union(X1,difference(X2,X1)) = union(X1,X2)
| $false ),
inference(rw,[status(thm)],[923240,395827,theory(equality)]) ).
cnf(923548,plain,
union(X1,difference(X2,X1)) = union(X1,X2),
inference(cn,[status(thm)],[923547,theory(equality)]) ).
cnf(925884,negated_conjecture,
$false,
inference(rw,[status(thm)],[16,923548,theory(equality)]) ).
cnf(925885,negated_conjecture,
$false,
inference(cn,[status(thm)],[925884,theory(equality)]) ).
cnf(925886,negated_conjecture,
$false,
925885,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET607+3.p
% --creating new selector for []
% -running prover on /tmp/tmp1Jax_9/sel_SET607+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET607+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET607+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET607+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
%
%------------------------------------------------------------------------------