TSTP Solution File: SET615+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET615+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 03:02:56 EST 2010
% Result : Theorem 95.31s
% Output : CNFRefutation 95.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 6
% Syntax : Number of formulae : 149 ( 67 unt; 0 def)
% Number of atoms : 307 ( 70 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 251 ( 93 ~; 121 |; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 398 ( 37 sgn 63 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpYyBYm3/sel_SET615+3.p_2',commutativity_of_union) ).
fof(2,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpYyBYm3/sel_SET615+3.p_2',equal_defn) ).
fof(3,conjecture,
! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
file('/tmp/tmpYyBYm3/sel_SET615+3.p_2',prove_difference_distributes_over_union) ).
fof(4,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpYyBYm3/sel_SET615+3.p_2',union_defn) ).
fof(5,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpYyBYm3/sel_SET615+3.p_2',subset_defn) ).
fof(7,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/tmp/tmpYyBYm3/sel_SET615+3.p_2',difference_defn) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
inference(assume_negation,[status(cth)],[3]) ).
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,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(14,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,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)],[14]) ).
cnf(16,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(19,negated_conjecture,
? [X1,X2,X3] : difference(union(X1,X2),X3) != union(difference(X1,X3),difference(X2,X3)),
inference(fof_nnf,[status(thm)],[9]) ).
fof(20,negated_conjecture,
? [X4,X5,X6] : difference(union(X4,X5),X6) != union(difference(X4,X6),difference(X5,X6)),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,negated_conjecture,
difference(union(esk1_0,esk2_0),esk3_0) != union(difference(esk1_0,esk3_0),difference(esk2_0,esk3_0)),
inference(skolemize,[status(esa)],[20]) ).
cnf(22,negated_conjecture,
difference(union(esk1_0,esk2_0),esk3_0) != union(difference(esk1_0,esk3_0),difference(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[21]) ).
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(esk4_2(X4,X5),X4)
& ~ member(esk4_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(esk4_2(X4,X5),X4)
& ~ member(esk4_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(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk4_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[32]) ).
cnf(34,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,plain,
( subset(X1,X2)
| member(esk4_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(esk4_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(esk4_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[50,35,theory(equality)]) ).
cnf(64,plain,
( subset(X1,union(X2,X3))
| ~ member(esk4_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[34,26,theory(equality)]) ).
cnf(65,plain,
( subset(X1,union(X2,X3))
| ~ member(esk4_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[34,27,theory(equality)]) ).
cnf(71,plain,
( subset(X1,difference(X2,X3))
| member(esk4_2(X1,difference(X2,X3)),X3)
| ~ member(esk4_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[34,49,theory(equality)]) ).
cnf(76,plain,
( member(esk4_2(union(X1,X2),X3),X2)
| member(esk4_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(esk4_2(difference(union(X1,X2),X3),X4),X2)
| member(esk4_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)],[16,91,theory(equality)]) ).
cnf(97,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk4_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk4_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)],[16,98,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(esk4_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(160,plain,
( subset(X1,union(X2,difference(X3,X4)))
| member(esk4_2(X1,union(X2,difference(X3,X4))),X4)
| ~ member(esk4_2(X1,union(X2,difference(X3,X4))),X3) ),
inference(spm,[status(thm)],[64,49,theory(equality)]) ).
cnf(162,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[159,12,theory(equality)]) ).
cnf(199,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk4_2(X1,union(union(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[65,27,theory(equality)]) ).
cnf(201,plain,
( subset(X1,union(difference(X2,X3),X4))
| member(esk4_2(X1,union(difference(X2,X3),X4)),X3)
| ~ member(esk4_2(X1,union(difference(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[65,49,theory(equality)]) ).
cnf(224,plain,
( member(esk4_2(X1,difference(union(X2,X3),X4)),X4)
| subset(X1,difference(union(X2,X3),X4))
| ~ member(esk4_2(X1,difference(union(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[71,27,theory(equality)]) ).
cnf(225,plain,
( member(esk4_2(X1,difference(X1,X2)),X2)
| subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[71,35,theory(equality)]) ).
cnf(231,plain,
( member(esk4_2(X1,difference(X1,difference(X2,X3))),X2)
| subset(X1,difference(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[51,225,theory(equality)]) ).
cnf(232,plain,
( subset(X1,difference(X1,difference(X2,X3)))
| ~ member(esk4_2(X1,difference(X1,difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[50,225,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)],[16,247,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(esk4_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(esk4_2(union(X1,X2),union(X1,X3)),X2) ),
inference(spm,[status(thm)],[65,76,theory(equality)]) ).
cnf(320,plain,
( subset(union(X1,X2),union(X2,X3))
| member(esk4_2(union(X1,X2),union(X2,X3)),X1) ),
inference(spm,[status(thm)],[65,76,theory(equality)]) ).
cnf(1636,plain,
( subset(difference(union(X1,X2),X3),X1)
| member(esk4_2(difference(union(X1,X2),X3),X1),X2) ),
inference(spm,[status(thm)],[34,92,theory(equality)]) ).
cnf(1640,plain,
( subset(difference(union(X1,X2),X1),X3)
| member(esk4_2(difference(union(X1,X2),X1),X3),X2) ),
inference(spm,[status(thm)],[63,92,theory(equality)]) ).
cnf(2503,plain,
( member(esk4_2(difference(X1,difference(X1,X2)),X3),X2)
| subset(difference(X1,difference(X1,X2)),X3) ),
inference(spm,[status(thm)],[97,62,theory(equality)]) ).
cnf(4326,plain,
( member(esk4_2(X1,difference(union(X1,X2),X3)),X3)
| subset(X1,difference(union(X1,X2),X3)) ),
inference(spm,[status(thm)],[224,35,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)],[16,4915,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(esk4_2(difference(X1,X2),X4),difference(X2,X3)) ),
inference(spm,[status(thm)],[63,5111,theory(equality)]) ).
cnf(5393,plain,
subset(X1,difference(X1,difference(X2,X1))),
inference(spm,[status(thm)],[232,35,theory(equality)]) ).
cnf(5395,plain,
subset(difference(X1,X2),difference(difference(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[232,62,theory(equality)]) ).
cnf(5396,plain,
( subset(union(X1,X2),difference(union(X1,X2),difference(X3,X1)))
| member(esk4_2(union(X1,X2),difference(union(X1,X2),difference(X3,X1))),X2) ),
inference(spm,[status(thm)],[232,76,theory(equality)]) ).
cnf(5481,plain,
( difference(X1,difference(X2,X1)) = X1
| ~ subset(difference(X1,difference(X2,X1)),X1) ),
inference(spm,[status(thm)],[16,5393,theory(equality)]) ).
cnf(5514,plain,
( difference(X1,difference(X2,X1)) = X1
| $false ),
inference(rw,[status(thm)],[5481,91,theory(equality)]) ).
cnf(5515,plain,
difference(X1,difference(X2,X1)) = X1,
inference(cn,[status(thm)],[5514,theory(equality)]) ).
cnf(5586,plain,
( subset(X1,X3)
| ~ member(esk4_2(X1,X3),difference(X2,X1)) ),
inference(spm,[status(thm)],[63,5515,theory(equality)]) ).
cnf(6036,plain,
( difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2)
| ~ subset(difference(difference(X1,X2),difference(X3,X1)),difference(X1,X2)) ),
inference(spm,[status(thm)],[16,5395,theory(equality)]) ).
cnf(6109,plain,
( difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2)
| $false ),
inference(rw,[status(thm)],[6036,91,theory(equality)]) ).
cnf(6110,plain,
difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2),
inference(cn,[status(thm)],[6109,theory(equality)]) ).
cnf(6264,plain,
( subset(X1,difference(X1,difference(X2,X3)))
| ~ member(esk4_2(X1,difference(X1,difference(X2,X3))),difference(X4,X2)) ),
inference(spm,[status(thm)],[232,6110,theory(equality)]) ).
cnf(10983,plain,
( member(esk4_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(11464,plain,
( member(esk4_2(union(X1,X2),union(X1,difference(X2,X3))),X3)
| subset(union(X1,X2),union(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[160,319,theory(equality)]) ).
cnf(11682,plain,
subset(union(X1,X2),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[157,320,theory(equality)]) ).
cnf(111991,plain,
subset(difference(union(X1,X2),X2),X1),
inference(spm,[status(thm)],[63,1636,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)],[16,394379,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(395831,plain,
subset(union(difference(X1,X2),X3),union(X3,X1)),
inference(spm,[status(thm)],[11682,395750,theory(equality)]) ).
cnf(428536,plain,
subset(X1,difference(union(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[5586,4326,theory(equality)]) ).
cnf(494996,plain,
subset(union(X1,difference(X2,X3)),difference(union(X1,difference(X2,X3)),difference(X3,X1))),
inference(spm,[status(thm)],[6264,5396,theory(equality)]) ).
cnf(922417,plain,
subset(union(X1,X2),union(difference(X2,X1),X1)),
inference(spm,[status(thm)],[64,10983,theory(equality)]) ).
cnf(922420,plain,
subset(union(union(X1,X2),X3),union(difference(X3,X2),union(X1,X2))),
inference(spm,[status(thm)],[157,10983,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)],[16,922896,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(923717,plain,
subset(difference(union(X1,X2),difference(X2,X1)),X1),
inference(spm,[status(thm)],[111991,923548,theory(equality)]) ).
cnf(983000,plain,
subset(union(union(X1,X2),X3),union(union(X1,X2),difference(X3,X1))),
inference(spm,[status(thm)],[199,11464,theory(equality)]) ).
cnf(1205321,plain,
( X1 = difference(union(X1,X2),difference(X2,X1))
| ~ subset(X1,difference(union(X1,X2),difference(X2,X1))) ),
inference(spm,[status(thm)],[16,923717,theory(equality)]) ).
cnf(1205631,plain,
( X1 = difference(union(X1,X2),difference(X2,X1))
| $false ),
inference(rw,[status(thm)],[1205321,428536,theory(equality)]) ).
cnf(1205632,plain,
X1 = difference(union(X1,X2),difference(X2,X1)),
inference(cn,[status(thm)],[1205631,theory(equality)]) ).
cnf(1205675,plain,
difference(union(difference(X1,X2),X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[1205632,5515,theory(equality)]) ).
cnf(1207321,plain,
difference(union(X2,X1),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1205675,12,theory(equality)]),923548,theory(equality)]) ).
cnf(1208673,plain,
difference(union(X2,X1),X1) = difference(X2,X1),
inference(spm,[status(thm)],[1207321,12,theory(equality)]) ).
cnf(1340743,plain,
( union(difference(X1,X2),union(X3,X2)) = union(union(X3,X2),X1)
| ~ subset(union(difference(X1,X2),union(X3,X2)),union(union(X3,X2),X1)) ),
inference(spm,[status(thm)],[16,922420,theory(equality)]) ).
cnf(1341082,plain,
( union(difference(X1,X2),union(X3,X2)) = union(union(X3,X2),X1)
| $false ),
inference(rw,[status(thm)],[1340743,395831,theory(equality)]) ).
cnf(1341083,plain,
union(difference(X1,X2),union(X3,X2)) = union(union(X3,X2),X1),
inference(cn,[status(thm)],[1341082,theory(equality)]) ).
cnf(1342479,plain,
union(difference(X1,X2),union(X3,X2)) = union(union(X3,X2),union(X1,X2)),
inference(spm,[status(thm)],[1341083,1208673,theory(equality)]) ).
cnf(1344883,plain,
union(union(X3,X2),X1) = union(union(X3,X2),union(X1,X2)),
inference(rw,[status(thm)],[1342479,1341083,theory(equality)]) ).
cnf(1383389,plain,
( union(union(X1,X2),difference(X3,X1)) = union(union(X1,X2),X3)
| ~ subset(union(union(X1,X2),difference(X3,X1)),union(union(X1,X2),X3)) ),
inference(spm,[status(thm)],[16,983000,theory(equality)]) ).
cnf(1383716,plain,
( union(union(X1,X2),difference(X3,X1)) = union(union(X1,X2),X3)
| $false ),
inference(rw,[status(thm)],[1383389,395827,theory(equality)]) ).
cnf(1383717,plain,
union(union(X1,X2),difference(X3,X1)) = union(union(X1,X2),X3),
inference(cn,[status(thm)],[1383716,theory(equality)]) ).
cnf(1946354,plain,
union(union(X1,X2),X3) = union(union(X3,X2),union(X1,X2)),
inference(spm,[status(thm)],[12,1344883,theory(equality)]) ).
cnf(1948819,plain,
union(union(X1,X2),X3) = union(union(X3,X2),X1),
inference(rw,[status(thm)],[1946354,1344883,theory(equality)]) ).
cnf(1953589,plain,
union(union(X3,X2),X1) = union(X3,union(X1,X2)),
inference(spm,[status(thm)],[12,1948819,theory(equality)]) ).
cnf(1957972,plain,
union(union(X1,X2),X3) = union(X1,union(X3,difference(X2,X1))),
inference(spm,[status(thm)],[1953589,923548,theory(equality)]) ).
cnf(1959229,plain,
union(X1,union(difference(X3,X1),X2)) = union(union(X1,X2),X3),
inference(rw,[status(thm)],[1383717,1953589,theory(equality)]) ).
cnf(1959230,plain,
union(X1,union(difference(X3,X1),X2)) = union(X1,union(X3,X2)),
inference(rw,[status(thm)],[1959229,1953589,theory(equality)]) ).
cnf(1960519,plain,
union(X1,union(X3,X2)) = union(X1,union(X3,difference(X2,X1))),
inference(rw,[status(thm)],[1957972,1953589,theory(equality)]) ).
cnf(1967277,plain,
difference(union(X1,union(X2,X3)),X1) = difference(union(difference(X2,X1),X3),X1),
inference(spm,[status(thm)],[1207321,1959230,theory(equality)]) ).
cnf(1968936,plain,
difference(union(X2,X3),X1) = difference(union(difference(X2,X1),X3),X1),
inference(rw,[status(thm)],[1967277,1207321,theory(equality)]) ).
cnf(1996826,plain,
difference(union(X1,union(X2,X3)),X1) = difference(union(X2,difference(X3,X1)),X1),
inference(spm,[status(thm)],[1207321,1960519,theory(equality)]) ).
cnf(1998270,plain,
difference(union(X2,X3),X1) = difference(union(X2,difference(X3,X1)),X1),
inference(rw,[status(thm)],[1996826,1207321,theory(equality)]) ).
cnf(2076834,plain,
( difference(union(X1,difference(X2,X3)),difference(X3,X1)) = union(X1,difference(X2,X3))
| ~ subset(difference(union(X1,difference(X2,X3)),difference(X3,X1)),union(X1,difference(X2,X3))) ),
inference(spm,[status(thm)],[16,494996,theory(equality)]) ).
cnf(2076993,plain,
( difference(union(X1,difference(X2,X3)),difference(X3,X1)) = union(X1,difference(X2,X3))
| $false ),
inference(rw,[status(thm)],[2076834,91,theory(equality)]) ).
cnf(2076994,plain,
difference(union(X1,difference(X2,X3)),difference(X3,X1)) = union(X1,difference(X2,X3)),
inference(cn,[status(thm)],[2076993,theory(equality)]) ).
cnf(2077010,plain,
difference(union(difference(X1,X2),difference(X3,X2)),X2) = union(difference(X1,X2),difference(X3,X2)),
inference(spm,[status(thm)],[2076994,5515,theory(equality)]) ).
cnf(2078223,plain,
difference(union(X1,X3),X2) = union(difference(X1,X2),difference(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2077010,1968936,theory(equality)]),1998270,theory(equality)]) ).
cnf(2081905,negated_conjecture,
$false,
inference(rw,[status(thm)],[22,2078223,theory(equality)]) ).
cnf(2081906,negated_conjecture,
$false,
inference(cn,[status(thm)],[2081905,theory(equality)]) ).
cnf(2081907,negated_conjecture,
$false,
2081906,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET615+3.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpYyBYm3/sel_SET615+3.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpYyBYm3/sel_SET615+3.p_2 with time limit 81
% -prover status Theorem
% Problem SET615+3.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET615+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET615+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
%
%------------------------------------------------------------------------------