TSTP Solution File: SET796+4 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET796+4 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:39:57 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% 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/tmp68b75-/sel_SET796+4.p_1',unordered_pair) ).
fof(2,axiom,
! [X4,X5] :
( order(X4,X5)
<=> ( ! [X1] :
( member(X1,X5)
=> apply(X4,X1,X1) )
& ! [X1,X6] :
( ( member(X1,X5)
& member(X6,X5) )
=> ( ( apply(X4,X1,X6)
& apply(X4,X6,X1) )
=> X1 = X6 ) )
& ! [X1,X6,X7] :
( ( member(X1,X5)
& member(X6,X5)
& member(X7,X5) )
=> ( ( apply(X4,X1,X6)
& apply(X4,X6,X7) )
=> apply(X4,X1,X7) ) ) ) ),
file('/tmp/tmp68b75-/sel_SET796+4.p_1',order) ).
fof(3,axiom,
! [X2,X1,X4,X5] :
( greatest_lower_bound(X2,X1,X4,X5)
<=> ( member(X2,X1)
& lower_bound(X2,X4,X1)
& ! [X8] :
( ( member(X8,X5)
& lower_bound(X8,X4,X1) )
=> apply(X4,X8,X2) ) ) ),
file('/tmp/tmp68b75-/sel_SET796+4.p_1',greatest_lower_bound) ).
fof(4,axiom,
! [X4,X5,X8] :
( lower_bound(X8,X4,X5)
<=> ! [X1] :
( member(X1,X5)
=> apply(X4,X8,X1) ) ),
file('/tmp/tmp68b75-/sel_SET796+4.p_1',lower_bound) ).
fof(5,conjecture,
! [X4,X5,X2,X3] :
( ( order(X4,X5)
& member(X2,X5)
& member(X3,X5)
& apply(X4,X2,X3) )
=> greatest_lower_bound(X2,unordered_pair(X2,X3),X4,X5) ),
file('/tmp/tmp68b75-/sel_SET796+4.p_1',thIV8) ).
fof(6,negated_conjecture,
~ ! [X4,X5,X2,X3] :
( ( order(X4,X5)
& member(X2,X5)
& member(X3,X5)
& apply(X4,X2,X3) )
=> greatest_lower_bound(X2,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,X6] :
( ( member(X1,X5)
& member(X6,X5) )
=> ( ( apply(X4,X1,X6)
& apply(X4,X6,X1) )
=> X1 = X6 ) )
& ! [X1,X6,X7] :
( ( member(X1,X5)
& member(X6,X5)
& member(X7,X5) )
=> ( ( apply(X4,X1,X6)
& apply(X4,X6,X7) )
=> apply(X4,X1,X7) ) ) ) ),
introduced(definition) ).
fof(8,plain,
! [X4,X5] :
( order(X4,X5)
<=> epred1_2(X4,X5) ),
inference(apply_def,[status(esa)],[2,7,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(13,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
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,
! [X4,X5] :
( ( ~ order(X4,X5)
| epred1_2(X4,X5) )
& ( ~ epred1_2(X4,X5)
| order(X4,X5) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(16,plain,
! [X6,X7] :
( ( ~ order(X6,X7)
| epred1_2(X6,X7) )
& ( ~ epred1_2(X6,X7)
| order(X6,X7) ) ),
inference(variable_rename,[status(thm)],[15]) ).
cnf(18,plain,
( epred1_2(X1,X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(19,plain,
! [X2,X1,X4,X5] :
( ( ~ greatest_lower_bound(X2,X1,X4,X5)
| ( member(X2,X1)
& lower_bound(X2,X4,X1)
& ! [X8] :
( ~ member(X8,X5)
| ~ lower_bound(X8,X4,X1)
| apply(X4,X8,X2) ) ) )
& ( ~ member(X2,X1)
| ~ lower_bound(X2,X4,X1)
| ? [X8] :
( member(X8,X5)
& lower_bound(X8,X4,X1)
& ~ apply(X4,X8,X2) )
| greatest_lower_bound(X2,X1,X4,X5) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(20,plain,
! [X9,X10,X11,X12] :
( ( ~ greatest_lower_bound(X9,X10,X11,X12)
| ( member(X9,X10)
& lower_bound(X9,X11,X10)
& ! [X13] :
( ~ member(X13,X12)
| ~ lower_bound(X13,X11,X10)
| apply(X11,X13,X9) ) ) )
& ( ~ member(X9,X10)
| ~ lower_bound(X9,X11,X10)
| ? [X14] :
( member(X14,X12)
& lower_bound(X14,X11,X10)
& ~ apply(X11,X14,X9) )
| greatest_lower_bound(X9,X10,X11,X12) ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,plain,
! [X9,X10,X11,X12] :
( ( ~ greatest_lower_bound(X9,X10,X11,X12)
| ( member(X9,X10)
& lower_bound(X9,X11,X10)
& ! [X13] :
( ~ member(X13,X12)
| ~ lower_bound(X13,X11,X10)
| apply(X11,X13,X9) ) ) )
& ( ~ member(X9,X10)
| ~ lower_bound(X9,X11,X10)
| ( member(esk1_4(X9,X10,X11,X12),X12)
& lower_bound(esk1_4(X9,X10,X11,X12),X11,X10)
& ~ apply(X11,esk1_4(X9,X10,X11,X12),X9) )
| greatest_lower_bound(X9,X10,X11,X12) ) ),
inference(skolemize,[status(esa)],[20]) ).
fof(22,plain,
! [X9,X10,X11,X12,X13] :
( ( ( ( ~ member(X13,X12)
| ~ lower_bound(X13,X11,X10)
| apply(X11,X13,X9) )
& member(X9,X10)
& lower_bound(X9,X11,X10) )
| ~ greatest_lower_bound(X9,X10,X11,X12) )
& ( ~ member(X9,X10)
| ~ lower_bound(X9,X11,X10)
| ( member(esk1_4(X9,X10,X11,X12),X12)
& lower_bound(esk1_4(X9,X10,X11,X12),X11,X10)
& ~ apply(X11,esk1_4(X9,X10,X11,X12),X9) )
| greatest_lower_bound(X9,X10,X11,X12) ) ),
inference(shift_quantors,[status(thm)],[21]) ).
fof(23,plain,
! [X9,X10,X11,X12,X13] :
( ( ~ member(X13,X12)
| ~ lower_bound(X13,X11,X10)
| apply(X11,X13,X9)
| ~ greatest_lower_bound(X9,X10,X11,X12) )
& ( member(X9,X10)
| ~ greatest_lower_bound(X9,X10,X11,X12) )
& ( lower_bound(X9,X11,X10)
| ~ greatest_lower_bound(X9,X10,X11,X12) )
& ( member(esk1_4(X9,X10,X11,X12),X12)
| ~ member(X9,X10)
| ~ lower_bound(X9,X11,X10)
| greatest_lower_bound(X9,X10,X11,X12) )
& ( lower_bound(esk1_4(X9,X10,X11,X12),X11,X10)
| ~ member(X9,X10)
| ~ lower_bound(X9,X11,X10)
| greatest_lower_bound(X9,X10,X11,X12) )
& ( ~ apply(X11,esk1_4(X9,X10,X11,X12),X9)
| ~ member(X9,X10)
| ~ lower_bound(X9,X11,X10)
| greatest_lower_bound(X9,X10,X11,X12) ) ),
inference(distribute,[status(thm)],[22]) ).
cnf(24,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2)
| ~ apply(X3,esk1_4(X1,X2,X3,X4),X1) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| lower_bound(esk1_4(X1,X2,X3,X4),X3,X2)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(30,plain,
! [X4,X5,X8] :
( ( ~ lower_bound(X8,X4,X5)
| ! [X1] :
( ~ member(X1,X5)
| apply(X4,X8,X1) ) )
& ( ? [X1] :
( member(X1,X5)
& ~ apply(X4,X8,X1) )
| lower_bound(X8,X4,X5) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(31,plain,
! [X9,X10,X11] :
( ( ~ lower_bound(X11,X9,X10)
| ! [X12] :
( ~ member(X12,X10)
| apply(X9,X11,X12) ) )
& ( ? [X13] :
( member(X13,X10)
& ~ apply(X9,X11,X13) )
| lower_bound(X11,X9,X10) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X9,X10,X11] :
( ( ~ lower_bound(X11,X9,X10)
| ! [X12] :
( ~ member(X12,X10)
| apply(X9,X11,X12) ) )
& ( ( member(esk2_3(X9,X10,X11),X10)
& ~ apply(X9,X11,esk2_3(X9,X10,X11)) )
| lower_bound(X11,X9,X10) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X9,X10,X11,X12] :
( ( ~ member(X12,X10)
| apply(X9,X11,X12)
| ~ lower_bound(X11,X9,X10) )
& ( ( member(esk2_3(X9,X10,X11),X10)
& ~ apply(X9,X11,esk2_3(X9,X10,X11)) )
| lower_bound(X11,X9,X10) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X9,X10,X11,X12] :
( ( ~ member(X12,X10)
| apply(X9,X11,X12)
| ~ lower_bound(X11,X9,X10) )
& ( member(esk2_3(X9,X10,X11),X10)
| lower_bound(X11,X9,X10) )
& ( ~ apply(X9,X11,esk2_3(X9,X10,X11))
| lower_bound(X11,X9,X10) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( lower_bound(X1,X2,X3)
| ~ apply(X2,X1,esk2_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( lower_bound(X1,X2,X3)
| member(esk2_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(37,plain,
( apply(X2,X1,X4)
| ~ lower_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)
& ~ greatest_lower_bound(X2,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)
& ~ greatest_lower_bound(X8,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)
& ~ greatest_lower_bound(esk5_0,unordered_pair(esk5_0,esk6_0),esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[39]) ).
cnf(41,negated_conjecture,
~ greatest_lower_bound(esk5_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(44,negated_conjecture,
member(esk5_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,X6] :
( ~ member(X1,X5)
| ~ member(X6,X5)
| ~ apply(X4,X1,X6)
| ~ apply(X4,X6,X1)
| X1 = X6 )
& ! [X1,X6,X7] :
( ~ member(X1,X5)
| ~ member(X6,X5)
| ~ member(X7,X5)
| ~ apply(X4,X1,X6)
| ~ apply(X4,X6,X7)
| apply(X4,X1,X7) ) ) )
& ( ? [X1] :
( member(X1,X5)
& ~ apply(X4,X1,X1) )
| ? [X1,X6] :
( member(X1,X5)
& member(X6,X5)
& apply(X4,X1,X6)
& apply(X4,X6,X1)
& X1 != X6 )
| ? [X1,X6,X7] :
( member(X1,X5)
& member(X6,X5)
& member(X7,X5)
& apply(X4,X1,X6)
& apply(X4,X6,X7)
& ~ apply(X4,X1,X7) )
| epred1_2(X4,X5) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(47,plain,
! [X8,X9] :
( ( ~ epred1_2(X9,X8)
| ( ! [X10] :
( ~ member(X10,X8)
| apply(X9,X10,X10) )
& ! [X11,X12] :
( ~ member(X11,X8)
| ~ member(X12,X8)
| ~ apply(X9,X11,X12)
| ~ apply(X9,X12,X11)
| X11 = X12 )
& ! [X13,X14,X15] :
( ~ member(X13,X8)
| ~ member(X14,X8)
| ~ member(X15,X8)
| ~ apply(X9,X13,X14)
| ~ apply(X9,X14,X15)
| apply(X9,X13,X15) ) ) )
& ( ? [X16] :
( member(X16,X8)
& ~ apply(X9,X16,X16) )
| ? [X17,X18] :
( member(X17,X8)
& member(X18,X8)
& apply(X9,X17,X18)
& apply(X9,X18,X17)
& X17 != X18 )
| ? [X19,X20,X21] :
( member(X19,X8)
& member(X20,X8)
& member(X21,X8)
& apply(X9,X19,X20)
& apply(X9,X20,X21)
& ~ apply(X9,X19,X21) )
| epred1_2(X9,X8) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,plain,
! [X8,X9] :
( ( ~ epred1_2(X9,X8)
| ( ! [X10] :
( ~ member(X10,X8)
| apply(X9,X10,X10) )
& ! [X11,X12] :
( ~ member(X11,X8)
| ~ member(X12,X8)
| ~ apply(X9,X11,X12)
| ~ apply(X9,X12,X11)
| X11 = X12 )
& ! [X13,X14,X15] :
( ~ member(X13,X8)
| ~ member(X14,X8)
| ~ member(X15,X8)
| ~ apply(X9,X13,X14)
| ~ apply(X9,X14,X15)
| apply(X9,X13,X15) ) ) )
& ( ( member(esk7_2(X8,X9),X8)
& ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9)) )
| ( member(esk8_2(X8,X9),X8)
& member(esk9_2(X8,X9),X8)
& apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
& apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
& esk8_2(X8,X9) != esk9_2(X8,X9) )
| ( member(esk10_2(X8,X9),X8)
& member(esk11_2(X8,X9),X8)
& member(esk12_2(X8,X9),X8)
& apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
& apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
& ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9)) )
| epred1_2(X9,X8) ) ),
inference(skolemize,[status(esa)],[47]) ).
fof(49,plain,
! [X8,X9,X10,X11,X12,X13,X14,X15] :
( ( ( ( ~ member(X13,X8)
| ~ member(X14,X8)
| ~ member(X15,X8)
| ~ apply(X9,X13,X14)
| ~ apply(X9,X14,X15)
| apply(X9,X13,X15) )
& ( ~ member(X11,X8)
| ~ member(X12,X8)
| ~ apply(X9,X11,X12)
| ~ apply(X9,X12,X11)
| X11 = X12 )
& ( ~ member(X10,X8)
| apply(X9,X10,X10) ) )
| ~ epred1_2(X9,X8) )
& ( ( member(esk7_2(X8,X9),X8)
& ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9)) )
| ( member(esk8_2(X8,X9),X8)
& member(esk9_2(X8,X9),X8)
& apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
& apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
& esk8_2(X8,X9) != esk9_2(X8,X9) )
| ( member(esk10_2(X8,X9),X8)
& member(esk11_2(X8,X9),X8)
& member(esk12_2(X8,X9),X8)
& apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
& apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
& ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9)) )
| epred1_2(X9,X8) ) ),
inference(shift_quantors,[status(thm)],[48]) ).
fof(50,plain,
! [X8,X9,X10,X11,X12,X13,X14,X15] :
( ( ~ member(X13,X8)
| ~ member(X14,X8)
| ~ member(X15,X8)
| ~ apply(X9,X13,X14)
| ~ apply(X9,X14,X15)
| apply(X9,X13,X15)
| ~ epred1_2(X9,X8) )
& ( ~ member(X11,X8)
| ~ member(X12,X8)
| ~ apply(X9,X11,X12)
| ~ apply(X9,X12,X11)
| X11 = X12
| ~ epred1_2(X9,X8) )
& ( ~ member(X10,X8)
| apply(X9,X10,X10)
| ~ epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| member(esk8_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| member(esk8_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| member(esk8_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| member(esk8_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| member(esk8_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| member(esk8_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| member(esk9_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| member(esk9_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| member(esk9_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| member(esk9_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| member(esk9_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| member(esk9_2(X8,X9),X8)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| esk8_2(X8,X9) != esk9_2(X8,X9)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| esk8_2(X8,X9) != esk9_2(X8,X9)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| esk8_2(X8,X9) != esk9_2(X8,X9)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| esk8_2(X8,X9) != esk9_2(X8,X9)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| esk8_2(X8,X9) != esk9_2(X8,X9)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| esk8_2(X8,X9) != esk9_2(X8,X9)
| member(esk7_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| member(esk9_2(X8,X9),X8)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk8_2(X8,X9),esk9_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| apply(X9,esk9_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk10_2(X8,X9),X8)
| esk8_2(X8,X9) != esk9_2(X8,X9)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk11_2(X8,X9),X8)
| esk8_2(X8,X9) != esk9_2(X8,X9)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk12_2(X8,X9),X8)
| esk8_2(X8,X9) != esk9_2(X8,X9)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk10_2(X8,X9),esk11_2(X8,X9))
| esk8_2(X8,X9) != esk9_2(X8,X9)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk11_2(X8,X9),esk12_2(X8,X9))
| esk8_2(X8,X9) != esk9_2(X8,X9)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk10_2(X8,X9),esk12_2(X8,X9))
| esk8_2(X8,X9) != esk9_2(X8,X9)
| ~ apply(X9,esk7_2(X8,X9),esk7_2(X8,X9))
| epred1_2(X9,X8) ) ),
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(115,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[13,theory(equality)]) ).
cnf(116,negated_conjecture,
epred1_2(esk3_0,esk4_0),
inference(spm,[status(thm)],[18,45,theory(equality)]) ).
cnf(118,plain,
( esk2_3(X1,unordered_pair(X2,X3),X4) = X3
| esk2_3(X1,unordered_pair(X2,X3),X4) = X2
| lower_bound(X4,X1,unordered_pair(X2,X3)) ),
inference(spm,[status(thm)],[14,36,theory(equality)]) ).
cnf(130,plain,
( apply(X1,esk1_4(X2,X3,X1,X4),X5)
| greatest_lower_bound(X2,X3,X1,X4)
| ~ member(X5,X3)
| ~ lower_bound(X2,X1,X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[37,25,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,
( lower_bound(X1,X2,unordered_pair(X3,X4))
| esk2_3(X2,unordered_pair(X3,X4),X1) = X4
| ~ apply(X2,X1,X3) ),
inference(spm,[status(thm)],[35,118,theory(equality)]) ).
cnf(254,plain,
( lower_bound(X1,X2,unordered_pair(X3,X4))
| ~ apply(X2,X1,X4)
| ~ apply(X2,X1,X3) ),
inference(spm,[status(thm)],[35,216,theory(equality)]) ).
cnf(310,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[24,130,theory(equality)]) ).
cnf(315,negated_conjecture,
( ~ lower_bound(esk5_0,esk3_0,unordered_pair(esk5_0,esk6_0))
| ~ member(esk5_0,unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[41,310,theory(equality)]) ).
cnf(319,negated_conjecture,
( ~ lower_bound(esk5_0,esk3_0,unordered_pair(esk5_0,esk6_0))
| $false ),
inference(rw,[status(thm)],[315,115,theory(equality)]) ).
cnf(320,negated_conjecture,
~ lower_bound(esk5_0,esk3_0,unordered_pair(esk5_0,esk6_0)),
inference(cn,[status(thm)],[319,theory(equality)]) ).
cnf(321,negated_conjecture,
( ~ apply(esk3_0,esk5_0,esk6_0)
| ~ apply(esk3_0,esk5_0,esk5_0) ),
inference(spm,[status(thm)],[320,254,theory(equality)]) ).
cnf(322,negated_conjecture,
( $false
| ~ apply(esk3_0,esk5_0,esk5_0) ),
inference(rw,[status(thm)],[321,42,theory(equality)]) ).
cnf(323,negated_conjecture,
~ apply(esk3_0,esk5_0,esk5_0),
inference(cn,[status(thm)],[322,theory(equality)]) ).
cnf(324,negated_conjecture,
~ member(esk5_0,esk4_0),
inference(spm,[status(thm)],[323,196,theory(equality)]) ).
cnf(325,negated_conjecture,
$false,
inference(rw,[status(thm)],[324,44,theory(equality)]) ).
cnf(326,negated_conjecture,
$false,
inference(cn,[status(thm)],[325,theory(equality)]) ).
cnf(327,negated_conjecture,
$false,
326,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET796+4.p
% --creating new selector for [SET006+0.ax, SET006+3.ax]
% -running prover on /tmp/tmp68b75-/sel_SET796+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET796+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET796+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET796+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
%
%------------------------------------------------------------------------------