TSTP Solution File: SET795+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET795+4 : 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 03:39:50 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 12 unt; 0 def)
% Number of atoms : 625 ( 43 equ)
% Maximal formula atoms : 256 ( 10 avg)
% Number of connectives : 784 ( 221 ~; 351 |; 192 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 75 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 213 ( 3 sgn 136 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( member(X1,unordered_pair(X2,X3))
<=> ( X1 = X2
| X1 = X3 ) ),
file('/tmp/tmpIW3U4f/sel_SET795+4.p_1',unordered_pair) ).
fof(2,axiom,
! [X2,X1,X4,X5] :
( least_upper_bound(X2,X1,X4,X5)
<=> ( member(X2,X1)
& upper_bound(X2,X4,X1)
& ! [X6] :
( ( member(X6,X5)
& upper_bound(X6,X4,X1) )
=> apply(X4,X2,X6) ) ) ),
file('/tmp/tmpIW3U4f/sel_SET795+4.p_1',least_upper_bound) ).
fof(3,axiom,
! [X4,X5] :
( order(X4,X5)
<=> ( ! [X1] :
( member(X1,X5)
=> apply(X4,X1,X1) )
& ! [X1,X7] :
( ( member(X1,X5)
& member(X7,X5) )
=> ( ( apply(X4,X1,X7)
& apply(X4,X7,X1) )
=> X1 = X7 ) )
& ! [X1,X7,X8] :
( ( member(X1,X5)
& member(X7,X5)
& member(X8,X5) )
=> ( ( apply(X4,X1,X7)
& apply(X4,X7,X8) )
=> apply(X4,X1,X8) ) ) ) ),
file('/tmp/tmpIW3U4f/sel_SET795+4.p_1',order) ).
fof(4,axiom,
! [X4,X5,X6] :
( upper_bound(X6,X4,X5)
<=> ! [X1] :
( member(X1,X5)
=> apply(X4,X1,X6) ) ),
file('/tmp/tmpIW3U4f/sel_SET795+4.p_1',upper_bound) ).
fof(5,conjecture,
! [X4,X5,X2,X3] :
( ( order(X4,X5)
& member(X2,X5)
& member(X3,X5)
& apply(X4,X2,X3) )
=> least_upper_bound(X3,unordered_pair(X2,X3),X4,X5) ),
file('/tmp/tmpIW3U4f/sel_SET795+4.p_1',thIV7) ).
fof(6,negated_conjecture,
~ ! [X4,X5,X2,X3] :
( ( order(X4,X5)
& member(X2,X5)
& member(X3,X5)
& apply(X4,X2,X3) )
=> least_upper_bound(X3,unordered_pair(X2,X3),X4,X5) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(7,plain,
! [X5,X4] :
( epred1_2(X4,X5)
<=> ( ! [X1] :
( member(X1,X5)
=> apply(X4,X1,X1) )
& ! [X1,X7] :
( ( member(X1,X5)
& member(X7,X5) )
=> ( ( apply(X4,X1,X7)
& apply(X4,X7,X1) )
=> X1 = X7 ) )
& ! [X1,X7,X8] :
( ( member(X1,X5)
& member(X7,X5)
& member(X8,X5) )
=> ( ( apply(X4,X1,X7)
& apply(X4,X7,X8) )
=> apply(X4,X1,X8) ) ) ) ),
introduced(definition) ).
fof(8,plain,
! [X4,X5] :
( order(X4,X5)
<=> epred1_2(X4,X5) ),
inference(apply_def,[status(esa)],[3,7,theory(equality)]) ).
fof(9,plain,
! [X1,X2,X3] :
( ( ~ member(X1,unordered_pair(X2,X3))
| X1 = X2
| X1 = X3 )
& ( ( X1 != X2
& X1 != X3 )
| member(X1,unordered_pair(X2,X3)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(10,plain,
! [X4,X5,X6] :
( ( ~ member(X4,unordered_pair(X5,X6))
| X4 = X5
| X4 = X6 )
& ( ( X4 != X5
& X4 != X6 )
| member(X4,unordered_pair(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[9]) ).
fof(11,plain,
! [X4,X5,X6] :
( ( ~ member(X4,unordered_pair(X5,X6))
| X4 = X5
| X4 = X6 )
& ( X4 != X5
| member(X4,unordered_pair(X5,X6)) )
& ( X4 != X6
| member(X4,unordered_pair(X5,X6)) ) ),
inference(distribute,[status(thm)],[10]) ).
cnf(12,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X3 ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(14,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(15,plain,
! [X2,X1,X4,X5] :
( ( ~ least_upper_bound(X2,X1,X4,X5)
| ( member(X2,X1)
& upper_bound(X2,X4,X1)
& ! [X6] :
( ~ member(X6,X5)
| ~ upper_bound(X6,X4,X1)
| apply(X4,X2,X6) ) ) )
& ( ~ member(X2,X1)
| ~ upper_bound(X2,X4,X1)
| ? [X6] :
( member(X6,X5)
& upper_bound(X6,X4,X1)
& ~ apply(X4,X2,X6) )
| least_upper_bound(X2,X1,X4,X5) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X7,X8,X9,X10] :
( ( ~ least_upper_bound(X7,X8,X9,X10)
| ( member(X7,X8)
& upper_bound(X7,X9,X8)
& ! [X11] :
( ~ member(X11,X10)
| ~ upper_bound(X11,X9,X8)
| apply(X9,X7,X11) ) ) )
& ( ~ member(X7,X8)
| ~ upper_bound(X7,X9,X8)
| ? [X12] :
( member(X12,X10)
& upper_bound(X12,X9,X8)
& ~ apply(X9,X7,X12) )
| least_upper_bound(X7,X8,X9,X10) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X7,X8,X9,X10] :
( ( ~ least_upper_bound(X7,X8,X9,X10)
| ( member(X7,X8)
& upper_bound(X7,X9,X8)
& ! [X11] :
( ~ member(X11,X10)
| ~ upper_bound(X11,X9,X8)
| apply(X9,X7,X11) ) ) )
& ( ~ member(X7,X8)
| ~ upper_bound(X7,X9,X8)
| ( member(esk1_4(X7,X8,X9,X10),X10)
& upper_bound(esk1_4(X7,X8,X9,X10),X9,X8)
& ~ apply(X9,X7,esk1_4(X7,X8,X9,X10)) )
| least_upper_bound(X7,X8,X9,X10) ) ),
inference(skolemize,[status(esa)],[16]) ).
fof(18,plain,
! [X7,X8,X9,X10,X11] :
( ( ( ( ~ member(X11,X10)
| ~ upper_bound(X11,X9,X8)
| apply(X9,X7,X11) )
& member(X7,X8)
& upper_bound(X7,X9,X8) )
| ~ least_upper_bound(X7,X8,X9,X10) )
& ( ~ member(X7,X8)
| ~ upper_bound(X7,X9,X8)
| ( member(esk1_4(X7,X8,X9,X10),X10)
& upper_bound(esk1_4(X7,X8,X9,X10),X9,X8)
& ~ apply(X9,X7,esk1_4(X7,X8,X9,X10)) )
| least_upper_bound(X7,X8,X9,X10) ) ),
inference(shift_quantors,[status(thm)],[17]) ).
fof(19,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ member(X11,X10)
| ~ upper_bound(X11,X9,X8)
| apply(X9,X7,X11)
| ~ least_upper_bound(X7,X8,X9,X10) )
& ( member(X7,X8)
| ~ least_upper_bound(X7,X8,X9,X10) )
& ( upper_bound(X7,X9,X8)
| ~ least_upper_bound(X7,X8,X9,X10) )
& ( member(esk1_4(X7,X8,X9,X10),X10)
| ~ member(X7,X8)
| ~ upper_bound(X7,X9,X8)
| least_upper_bound(X7,X8,X9,X10) )
& ( upper_bound(esk1_4(X7,X8,X9,X10),X9,X8)
| ~ member(X7,X8)
| ~ upper_bound(X7,X9,X8)
| least_upper_bound(X7,X8,X9,X10) )
& ( ~ apply(X9,X7,esk1_4(X7,X8,X9,X10))
| ~ member(X7,X8)
| ~ upper_bound(X7,X9,X8)
| least_upper_bound(X7,X8,X9,X10) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(20,plain,
( least_upper_bound(X1,X2,X3,X4)
| ~ upper_bound(X1,X3,X2)
| ~ member(X1,X2)
| ~ apply(X3,X1,esk1_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( least_upper_bound(X1,X2,X3,X4)
| upper_bound(esk1_4(X1,X2,X3,X4),X3,X2)
| ~ upper_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(26,plain,
! [X4,X5] :
( ( ~ order(X4,X5)
| epred1_2(X4,X5) )
& ( ~ epred1_2(X4,X5)
| order(X4,X5) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(27,plain,
! [X6,X7] :
( ( ~ order(X6,X7)
| epred1_2(X6,X7) )
& ( ~ epred1_2(X6,X7)
| order(X6,X7) ) ),
inference(variable_rename,[status(thm)],[26]) ).
cnf(29,plain,
( epred1_2(X1,X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(30,plain,
! [X4,X5,X6] :
( ( ~ upper_bound(X6,X4,X5)
| ! [X1] :
( ~ member(X1,X5)
| apply(X4,X1,X6) ) )
& ( ? [X1] :
( member(X1,X5)
& ~ apply(X4,X1,X6) )
| upper_bound(X6,X4,X5) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(31,plain,
! [X7,X8,X9] :
( ( ~ upper_bound(X9,X7,X8)
| ! [X10] :
( ~ member(X10,X8)
| apply(X7,X10,X9) ) )
& ( ? [X11] :
( member(X11,X8)
& ~ apply(X7,X11,X9) )
| upper_bound(X9,X7,X8) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X7,X8,X9] :
( ( ~ upper_bound(X9,X7,X8)
| ! [X10] :
( ~ member(X10,X8)
| apply(X7,X10,X9) ) )
& ( ( member(esk2_3(X7,X8,X9),X8)
& ~ apply(X7,esk2_3(X7,X8,X9),X9) )
| upper_bound(X9,X7,X8) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| apply(X7,X10,X9)
| ~ upper_bound(X9,X7,X8) )
& ( ( member(esk2_3(X7,X8,X9),X8)
& ~ apply(X7,esk2_3(X7,X8,X9),X9) )
| upper_bound(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| apply(X7,X10,X9)
| ~ upper_bound(X9,X7,X8) )
& ( member(esk2_3(X7,X8,X9),X8)
| upper_bound(X9,X7,X8) )
& ( ~ apply(X7,esk2_3(X7,X8,X9),X9)
| upper_bound(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( upper_bound(X1,X2,X3)
| ~ apply(X2,esk2_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( upper_bound(X1,X2,X3)
| member(esk2_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(37,plain,
( apply(X2,X4,X1)
| ~ upper_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(38,negated_conjecture,
? [X4,X5,X2,X3] :
( order(X4,X5)
& member(X2,X5)
& member(X3,X5)
& apply(X4,X2,X3)
& ~ least_upper_bound(X3,unordered_pair(X2,X3),X4,X5) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(39,negated_conjecture,
? [X6,X7,X8,X9] :
( order(X6,X7)
& member(X8,X7)
& member(X9,X7)
& apply(X6,X8,X9)
& ~ least_upper_bound(X9,unordered_pair(X8,X9),X6,X7) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,negated_conjecture,
( order(esk3_0,esk4_0)
& member(esk5_0,esk4_0)
& member(esk6_0,esk4_0)
& apply(esk3_0,esk5_0,esk6_0)
& ~ least_upper_bound(esk6_0,unordered_pair(esk5_0,esk6_0),esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[39]) ).
cnf(41,negated_conjecture,
~ least_upper_bound(esk6_0,unordered_pair(esk5_0,esk6_0),esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(42,negated_conjecture,
apply(esk3_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(43,negated_conjecture,
member(esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(45,negated_conjecture,
order(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[40]) ).
fof(46,plain,
! [X5,X4] :
( ( ~ epred1_2(X4,X5)
| ( ! [X1] :
( ~ member(X1,X5)
| apply(X4,X1,X1) )
& ! [X1,X7] :
( ~ member(X1,X5)
| ~ member(X7,X5)
| ~ apply(X4,X1,X7)
| ~ apply(X4,X7,X1)
| X1 = X7 )
& ! [X1,X7,X8] :
( ~ member(X1,X5)
| ~ member(X7,X5)
| ~ member(X8,X5)
| ~ apply(X4,X1,X7)
| ~ apply(X4,X7,X8)
| apply(X4,X1,X8) ) ) )
& ( ? [X1] :
( member(X1,X5)
& ~ apply(X4,X1,X1) )
| ? [X1,X7] :
( member(X1,X5)
& member(X7,X5)
& apply(X4,X1,X7)
& apply(X4,X7,X1)
& X1 != X7 )
| ? [X1,X7,X8] :
( member(X1,X5)
& member(X7,X5)
& member(X8,X5)
& apply(X4,X1,X7)
& apply(X4,X7,X8)
& ~ apply(X4,X1,X8) )
| epred1_2(X4,X5) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(47,plain,
! [X9,X10] :
( ( ~ epred1_2(X10,X9)
| ( ! [X11] :
( ~ member(X11,X9)
| apply(X10,X11,X11) )
& ! [X12,X13] :
( ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X10,X12,X13)
| ~ apply(X10,X13,X12)
| X12 = X13 )
& ! [X14,X15,X16] :
( ~ member(X14,X9)
| ~ member(X15,X9)
| ~ member(X16,X9)
| ~ apply(X10,X14,X15)
| ~ apply(X10,X15,X16)
| apply(X10,X14,X16) ) ) )
& ( ? [X17] :
( member(X17,X9)
& ~ apply(X10,X17,X17) )
| ? [X18,X19] :
( member(X18,X9)
& member(X19,X9)
& apply(X10,X18,X19)
& apply(X10,X19,X18)
& X18 != X19 )
| ? [X20,X21,X22] :
( member(X20,X9)
& member(X21,X9)
& member(X22,X9)
& apply(X10,X20,X21)
& apply(X10,X21,X22)
& ~ apply(X10,X20,X22) )
| epred1_2(X10,X9) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,plain,
! [X9,X10] :
( ( ~ epred1_2(X10,X9)
| ( ! [X11] :
( ~ member(X11,X9)
| apply(X10,X11,X11) )
& ! [X12,X13] :
( ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X10,X12,X13)
| ~ apply(X10,X13,X12)
| X12 = X13 )
& ! [X14,X15,X16] :
( ~ member(X14,X9)
| ~ member(X15,X9)
| ~ member(X16,X9)
| ~ apply(X10,X14,X15)
| ~ apply(X10,X15,X16)
| apply(X10,X14,X16) ) ) )
& ( ( member(esk7_2(X9,X10),X9)
& ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10)) )
| ( member(esk8_2(X9,X10),X9)
& member(esk9_2(X9,X10),X9)
& apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
& apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
& esk8_2(X9,X10) != esk9_2(X9,X10) )
| ( member(esk10_2(X9,X10),X9)
& member(esk11_2(X9,X10),X9)
& member(esk12_2(X9,X10),X9)
& apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
& apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
& ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10)) )
| epred1_2(X10,X9) ) ),
inference(skolemize,[status(esa)],[47]) ).
fof(49,plain,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( ( ( ~ member(X14,X9)
| ~ member(X15,X9)
| ~ member(X16,X9)
| ~ apply(X10,X14,X15)
| ~ apply(X10,X15,X16)
| apply(X10,X14,X16) )
& ( ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X10,X12,X13)
| ~ apply(X10,X13,X12)
| X12 = X13 )
& ( ~ member(X11,X9)
| apply(X10,X11,X11) ) )
| ~ epred1_2(X10,X9) )
& ( ( member(esk7_2(X9,X10),X9)
& ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10)) )
| ( member(esk8_2(X9,X10),X9)
& member(esk9_2(X9,X10),X9)
& apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
& apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
& esk8_2(X9,X10) != esk9_2(X9,X10) )
| ( member(esk10_2(X9,X10),X9)
& member(esk11_2(X9,X10),X9)
& member(esk12_2(X9,X10),X9)
& apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
& apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
& ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10)) )
| epred1_2(X10,X9) ) ),
inference(shift_quantors,[status(thm)],[48]) ).
fof(50,plain,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( ~ member(X14,X9)
| ~ member(X15,X9)
| ~ member(X16,X9)
| ~ apply(X10,X14,X15)
| ~ apply(X10,X15,X16)
| apply(X10,X14,X16)
| ~ epred1_2(X10,X9) )
& ( ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X10,X12,X13)
| ~ apply(X10,X13,X12)
| X12 = X13
| ~ epred1_2(X10,X9) )
& ( ~ member(X11,X9)
| apply(X10,X11,X11)
| ~ epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| member(esk8_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| member(esk8_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| member(esk8_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| member(esk8_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| member(esk8_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| member(esk8_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| member(esk9_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| member(esk9_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| member(esk9_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| member(esk9_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| member(esk9_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| member(esk9_2(X9,X10),X9)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| esk8_2(X9,X10) != esk9_2(X9,X10)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| esk8_2(X9,X10) != esk9_2(X9,X10)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| esk8_2(X9,X10) != esk9_2(X9,X10)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| esk8_2(X9,X10) != esk9_2(X9,X10)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| esk8_2(X9,X10) != esk9_2(X9,X10)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| esk8_2(X9,X10) != esk9_2(X9,X10)
| member(esk7_2(X9,X10),X9)
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| member(esk8_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| member(esk8_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| member(esk8_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| member(esk8_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| member(esk8_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| member(esk8_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| member(esk9_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| member(esk9_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| member(esk9_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| member(esk9_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| member(esk9_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| member(esk9_2(X9,X10),X9)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk8_2(X9,X10),esk9_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| apply(X10,esk9_2(X9,X10),esk8_2(X9,X10))
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk10_2(X9,X10),X9)
| esk8_2(X9,X10) != esk9_2(X9,X10)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk11_2(X9,X10),X9)
| esk8_2(X9,X10) != esk9_2(X9,X10)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( member(esk12_2(X9,X10),X9)
| esk8_2(X9,X10) != esk9_2(X9,X10)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk10_2(X9,X10),esk11_2(X9,X10))
| esk8_2(X9,X10) != esk9_2(X9,X10)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( apply(X10,esk11_2(X9,X10),esk12_2(X9,X10))
| esk8_2(X9,X10) != esk9_2(X9,X10)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) )
& ( ~ apply(X10,esk10_2(X9,X10),esk12_2(X9,X10))
| esk8_2(X9,X10) != esk9_2(X9,X10)
| ~ apply(X10,esk7_2(X9,X10),esk7_2(X9,X10))
| epred1_2(X10,X9) ) ),
inference(distribute,[status(thm)],[49]) ).
cnf(111,plain,
( apply(X1,X3,X3)
| ~ epred1_2(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(114,plain,
member(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[12,theory(equality)]) ).
cnf(116,negated_conjecture,
epred1_2(esk3_0,esk4_0),
inference(spm,[status(thm)],[29,45,theory(equality)]) ).
cnf(118,plain,
( esk2_3(X1,unordered_pair(X2,X3),X4) = X3
| esk2_3(X1,unordered_pair(X2,X3),X4) = X2
| upper_bound(X4,X1,unordered_pair(X2,X3)) ),
inference(spm,[status(thm)],[14,36,theory(equality)]) ).
cnf(130,plain,
( apply(X1,X2,esk1_4(X3,X4,X1,X5))
| least_upper_bound(X3,X4,X1,X5)
| ~ member(X2,X4)
| ~ upper_bound(X3,X1,X4)
| ~ member(X3,X4) ),
inference(spm,[status(thm)],[37,21,theory(equality)]) ).
cnf(196,negated_conjecture,
( apply(esk3_0,X1,X1)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[111,116,theory(equality)]) ).
cnf(216,plain,
( upper_bound(X1,X2,unordered_pair(X3,X4))
| esk2_3(X2,unordered_pair(X3,X4),X1) = X4
| ~ apply(X2,X3,X1) ),
inference(spm,[status(thm)],[35,118,theory(equality)]) ).
cnf(253,plain,
( upper_bound(X1,X2,unordered_pair(X3,X4))
| ~ apply(X2,X4,X1)
| ~ apply(X2,X3,X1) ),
inference(spm,[status(thm)],[35,216,theory(equality)]) ).
cnf(307,plain,
( least_upper_bound(X1,X2,X3,X4)
| ~ upper_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[20,130,theory(equality)]) ).
cnf(309,negated_conjecture,
( ~ upper_bound(esk6_0,esk3_0,unordered_pair(esk5_0,esk6_0))
| ~ member(esk6_0,unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[41,307,theory(equality)]) ).
cnf(313,negated_conjecture,
( ~ upper_bound(esk6_0,esk3_0,unordered_pair(esk5_0,esk6_0))
| $false ),
inference(rw,[status(thm)],[309,114,theory(equality)]) ).
cnf(314,negated_conjecture,
~ upper_bound(esk6_0,esk3_0,unordered_pair(esk5_0,esk6_0)),
inference(cn,[status(thm)],[313,theory(equality)]) ).
cnf(315,negated_conjecture,
( ~ apply(esk3_0,esk6_0,esk6_0)
| ~ apply(esk3_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[314,253,theory(equality)]) ).
cnf(316,negated_conjecture,
( ~ apply(esk3_0,esk6_0,esk6_0)
| $false ),
inference(rw,[status(thm)],[315,42,theory(equality)]) ).
cnf(317,negated_conjecture,
~ apply(esk3_0,esk6_0,esk6_0),
inference(cn,[status(thm)],[316,theory(equality)]) ).
cnf(321,negated_conjecture,
~ member(esk6_0,esk4_0),
inference(spm,[status(thm)],[317,196,theory(equality)]) ).
cnf(322,negated_conjecture,
$false,
inference(rw,[status(thm)],[321,43,theory(equality)]) ).
cnf(323,negated_conjecture,
$false,
inference(cn,[status(thm)],[322,theory(equality)]) ).
cnf(324,negated_conjecture,
$false,
323,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET795+4.p
% --creating new selector for [SET006+0.ax, SET006+3.ax]
% -running prover on /tmp/tmpIW3U4f/sel_SET795+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET795+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET795+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET795+4.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
%
%------------------------------------------------------------------------------