TSTP Solution File: SET806+4 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET806+4 : TPTP v5.0.0. Released v3.2.0.
% 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 03:40:45 EST 2010
% Result : Theorem 1.38s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 6
% Syntax : Number of formulae : 111 ( 13 unt; 0 def)
% Number of atoms : 684 ( 0 equ)
% Maximal formula atoms : 207 ( 6 avg)
% Number of connectives : 810 ( 237 ~; 425 |; 131 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 251 ( 1 sgn 96 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',equal_set) ).
fof(3,axiom,
! [X1,X4] :
( equivalence(X4,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X4,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X4,X3,X5)
=> apply(X4,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X4,X3,X5)
& apply(X4,X5,X6) )
=> apply(X4,X3,X6) ) ) ) ),
file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',equivalence) ).
fof(5,conjecture,
! [X7] : equivalence(equal_set_predicate,power_set(X7)),
file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',thIII13) ).
fof(6,axiom,
! [X3,X5] :
( apply(equal_set_predicate,X3,X5)
<=> equal_set(X3,X5) ),
file('/tmp/tmpsfS2ZG/sel_SET806+4.p_1',rel_equal_set) ).
fof(7,negated_conjecture,
~ ! [X7] : equivalence(equal_set_predicate,power_set(X7)),
inference(assume_negation,[status(cth)],[5]) ).
fof(8,plain,
! [X1,X4] :
( epred1_2(X4,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X4,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X4,X3,X5)
=> apply(X4,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X4,X3,X5)
& apply(X4,X5,X6) )
=> apply(X4,X3,X6) ) ) ) ),
introduced(definition) ).
fof(9,plain,
! [X1,X4] :
( equivalence(X4,X1)
<=> epred1_2(X4,X1) ),
inference(apply_def,[status(esa)],[3,8,theory(equality)]) ).
fof(10,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)],[1]) ).
fof(11,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)],[10]) ).
fof(12,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[11]) ).
fof(13,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[12]) ).
fof(14,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[13]) ).
cnf(15,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(19,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[19]) ).
cnf(21,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,plain,
( subset(X2,X1)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(23,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,plain,
! [X1,X4] :
( ( ~ equivalence(X4,X1)
| epred1_2(X4,X1) )
& ( ~ epred1_2(X4,X1)
| equivalence(X4,X1) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(25,plain,
! [X5,X6] :
( ( ~ equivalence(X6,X5)
| epred1_2(X6,X5) )
& ( ~ epred1_2(X6,X5)
| equivalence(X6,X5) ) ),
inference(variable_rename,[status(thm)],[24]) ).
cnf(26,plain,
( equivalence(X1,X2)
| ~ epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(32,negated_conjecture,
? [X7] : ~ equivalence(equal_set_predicate,power_set(X7)),
inference(fof_nnf,[status(thm)],[7]) ).
fof(33,negated_conjecture,
? [X8] : ~ equivalence(equal_set_predicate,power_set(X8)),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,negated_conjecture,
~ equivalence(equal_set_predicate,power_set(esk2_0)),
inference(skolemize,[status(esa)],[33]) ).
cnf(35,negated_conjecture,
~ equivalence(equal_set_predicate,power_set(esk2_0)),
inference(split_conjunct,[status(thm)],[34]) ).
fof(36,plain,
! [X3,X5] :
( ( ~ apply(equal_set_predicate,X3,X5)
| equal_set(X3,X5) )
& ( ~ equal_set(X3,X5)
| apply(equal_set_predicate,X3,X5) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(37,plain,
! [X6,X7] :
( ( ~ apply(equal_set_predicate,X6,X7)
| equal_set(X6,X7) )
& ( ~ equal_set(X6,X7)
| apply(equal_set_predicate,X6,X7) ) ),
inference(variable_rename,[status(thm)],[36]) ).
cnf(38,plain,
( apply(equal_set_predicate,X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,plain,
( equal_set(X1,X2)
| ~ apply(equal_set_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(40,plain,
! [X1,X4] :
( ( ~ epred1_2(X4,X1)
| ( ! [X3] :
( ~ member(X3,X1)
| apply(X4,X3,X3) )
& ! [X3,X5] :
( ~ member(X3,X1)
| ~ member(X5,X1)
| ~ apply(X4,X3,X5)
| apply(X4,X5,X3) )
& ! [X3,X5,X6] :
( ~ member(X3,X1)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ apply(X4,X3,X5)
| ~ apply(X4,X5,X6)
| apply(X4,X3,X6) ) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X4,X3,X3) )
| ? [X3,X5] :
( member(X3,X1)
& member(X5,X1)
& apply(X4,X3,X5)
& ~ apply(X4,X5,X3) )
| ? [X3,X5,X6] :
( member(X3,X1)
& member(X5,X1)
& member(X6,X1)
& apply(X4,X3,X5)
& apply(X4,X5,X6)
& ~ apply(X4,X3,X6) )
| epred1_2(X4,X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(41,plain,
! [X7,X8] :
( ( ~ epred1_2(X8,X7)
| ( ! [X9] :
( ~ member(X9,X7)
| apply(X8,X9,X9) )
& ! [X10,X11] :
( ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X8,X10,X11)
| apply(X8,X11,X10) )
& ! [X12,X13,X14] :
( ~ member(X12,X7)
| ~ member(X13,X7)
| ~ member(X14,X7)
| ~ apply(X8,X12,X13)
| ~ apply(X8,X13,X14)
| apply(X8,X12,X14) ) ) )
& ( ? [X15] :
( member(X15,X7)
& ~ apply(X8,X15,X15) )
| ? [X16,X17] :
( member(X16,X7)
& member(X17,X7)
& apply(X8,X16,X17)
& ~ apply(X8,X17,X16) )
| ? [X18,X19,X20] :
( member(X18,X7)
& member(X19,X7)
& member(X20,X7)
& apply(X8,X18,X19)
& apply(X8,X19,X20)
& ~ apply(X8,X18,X20) )
| epred1_2(X8,X7) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,plain,
! [X7,X8] :
( ( ~ epred1_2(X8,X7)
| ( ! [X9] :
( ~ member(X9,X7)
| apply(X8,X9,X9) )
& ! [X10,X11] :
( ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X8,X10,X11)
| apply(X8,X11,X10) )
& ! [X12,X13,X14] :
( ~ member(X12,X7)
| ~ member(X13,X7)
| ~ member(X14,X7)
| ~ apply(X8,X12,X13)
| ~ apply(X8,X13,X14)
| apply(X8,X12,X14) ) ) )
& ( ( member(esk3_2(X7,X8),X7)
& ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8)) )
| ( member(esk4_2(X7,X8),X7)
& member(esk5_2(X7,X8),X7)
& apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
& ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8)) )
| ( member(esk6_2(X7,X8),X7)
& member(esk7_2(X7,X8),X7)
& member(esk8_2(X7,X8),X7)
& apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
& apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
& ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8)) )
| epred1_2(X8,X7) ) ),
inference(skolemize,[status(esa)],[41]) ).
fof(43,plain,
! [X7,X8,X9,X10,X11,X12,X13,X14] :
( ( ( ( ~ member(X12,X7)
| ~ member(X13,X7)
| ~ member(X14,X7)
| ~ apply(X8,X12,X13)
| ~ apply(X8,X13,X14)
| apply(X8,X12,X14) )
& ( ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X8,X10,X11)
| apply(X8,X11,X10) )
& ( ~ member(X9,X7)
| apply(X8,X9,X9) ) )
| ~ epred1_2(X8,X7) )
& ( ( member(esk3_2(X7,X8),X7)
& ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8)) )
| ( member(esk4_2(X7,X8),X7)
& member(esk5_2(X7,X8),X7)
& apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
& ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8)) )
| ( member(esk6_2(X7,X8),X7)
& member(esk7_2(X7,X8),X7)
& member(esk8_2(X7,X8),X7)
& apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
& apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
& ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8)) )
| epred1_2(X8,X7) ) ),
inference(shift_quantors,[status(thm)],[42]) ).
fof(44,plain,
! [X7,X8,X9,X10,X11,X12,X13,X14] :
( ( ~ member(X12,X7)
| ~ member(X13,X7)
| ~ member(X14,X7)
| ~ apply(X8,X12,X13)
| ~ apply(X8,X13,X14)
| apply(X8,X12,X14)
| ~ epred1_2(X8,X7) )
& ( ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X8,X10,X11)
| apply(X8,X11,X10)
| ~ epred1_2(X8,X7) )
& ( ~ member(X9,X7)
| apply(X8,X9,X9)
| ~ epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| member(esk4_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| member(esk4_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| member(esk4_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| member(esk4_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk4_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| member(esk4_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| member(esk5_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| member(esk5_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| member(esk5_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| member(esk5_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk5_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| member(esk5_2(X7,X8),X7)
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| member(esk3_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| member(esk4_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| member(esk4_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| member(esk4_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| member(esk4_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk4_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| member(esk4_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| member(esk5_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| member(esk5_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| member(esk5_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| member(esk5_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk5_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| member(esk5_2(X7,X8),X7)
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| apply(X8,esk4_2(X7,X8),esk5_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk6_2(X7,X8),X7)
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk6_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk6_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk5_2(X7,X8),esk4_2(X7,X8))
| ~ apply(X8,esk3_2(X7,X8),esk3_2(X7,X8))
| epred1_2(X8,X7) ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(45,plain,
( epred1_2(X1,X2)
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1))
| ~ apply(X1,esk6_2(X2,X1),esk8_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,plain,
( epred1_2(X1,X2)
| apply(X1,esk7_2(X2,X1),esk8_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(47,plain,
( epred1_2(X1,X2)
| apply(X1,esk6_2(X2,X1),esk7_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(51,plain,
( epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk6_2(X2,X1),esk8_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(52,plain,
( epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| apply(X1,esk7_2(X2,X1),esk8_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(53,plain,
( epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| apply(X1,esk6_2(X2,X1),esk7_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(96,negated_conjecture,
~ epred1_2(equal_set_predicate,power_set(esk2_0)),
inference(spm,[status(thm)],[35,26,theory(equality)]) ).
cnf(100,plain,
( subset(X1,X2)
| ~ apply(equal_set_predicate,X2,X1) ),
inference(spm,[status(thm)],[22,39,theory(equality)]) ).
cnf(101,plain,
( subset(X1,X2)
| ~ apply(equal_set_predicate,X1,X2) ),
inference(spm,[status(thm)],[23,39,theory(equality)]) ).
cnf(104,plain,
subset(X1,X1),
inference(spm,[status(thm)],[15,16,theory(equality)]) ).
cnf(107,plain,
( apply(equal_set_predicate,X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[38,21,theory(equality)]) ).
cnf(159,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ apply(equal_set_predicate,X2,X3) ),
inference(spm,[status(thm)],[17,100,theory(equality)]) ).
cnf(160,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ apply(equal_set_predicate,X3,X2) ),
inference(spm,[status(thm)],[17,101,theory(equality)]) ).
cnf(166,plain,
( apply(equal_set_predicate,X1,X1)
| ~ subset(X1,X1) ),
inference(spm,[status(thm)],[107,104,theory(equality)]) ).
cnf(168,plain,
( apply(equal_set_predicate,X1,X2)
| ~ subset(X1,X2)
| ~ apply(equal_set_predicate,X2,X1) ),
inference(spm,[status(thm)],[107,101,theory(equality)]) ).
cnf(170,plain,
( apply(equal_set_predicate,X1,X1)
| $false ),
inference(rw,[status(thm)],[166,104,theory(equality)]) ).
cnf(171,plain,
apply(equal_set_predicate,X1,X1),
inference(cn,[status(thm)],[170,theory(equality)]) ).
cnf(182,plain,
( apply(equal_set_predicate,X1,X2)
| ~ apply(equal_set_predicate,X2,X1) ),
inference(csr,[status(thm)],[168,100]) ).
cnf(251,plain,
( member(X1,esk6_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[159,53,theory(equality)]) ).
cnf(252,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk8_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[159,52,theory(equality)]) ).
cnf(253,plain,
( member(X1,esk6_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[159,47,theory(equality)]) ).
cnf(254,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk8_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[159,46,theory(equality)]) ).
cnf(269,plain,
( member(X1,esk6_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| $false ),
inference(rw,[status(thm)],[251,171,theory(equality)]) ).
cnf(270,plain,
( member(X1,esk6_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk7_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[269,theory(equality)]) ).
cnf(271,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk8_2(X2,equal_set_predicate))
| $false ),
inference(rw,[status(thm)],[252,171,theory(equality)]) ).
cnf(272,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk8_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[271,theory(equality)]) ).
cnf(273,plain,
( member(X1,esk6_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| $false
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(rw,[status(thm)],[253,171,theory(equality)]) ).
cnf(274,plain,
( member(X1,esk6_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[273,theory(equality)]) ).
cnf(275,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk8_2(X2,equal_set_predicate))
| $false
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(rw,[status(thm)],[254,171,theory(equality)]) ).
cnf(276,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk8_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[275,theory(equality)]) ).
cnf(300,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk6_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[160,53,theory(equality)]) ).
cnf(301,plain,
( member(X1,esk8_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[160,52,theory(equality)]) ).
cnf(302,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk6_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[160,47,theory(equality)]) ).
cnf(303,plain,
( member(X1,esk8_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X2,equal_set_predicate),esk3_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[160,46,theory(equality)]) ).
cnf(318,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk6_2(X2,equal_set_predicate))
| $false ),
inference(rw,[status(thm)],[300,171,theory(equality)]) ).
cnf(319,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk6_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[318,theory(equality)]) ).
cnf(320,plain,
( member(X1,esk8_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| $false ),
inference(rw,[status(thm)],[301,171,theory(equality)]) ).
cnf(321,plain,
( member(X1,esk8_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| apply(equal_set_predicate,esk4_2(X2,equal_set_predicate),esk5_2(X2,equal_set_predicate))
| ~ member(X1,esk7_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[320,theory(equality)]) ).
cnf(322,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk6_2(X2,equal_set_predicate))
| $false
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(rw,[status(thm)],[302,171,theory(equality)]) ).
cnf(323,plain,
( member(X1,esk7_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk6_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[322,theory(equality)]) ).
cnf(324,plain,
( member(X1,esk8_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| $false
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(rw,[status(thm)],[303,171,theory(equality)]) ).
cnf(325,plain,
( member(X1,esk8_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(X1,esk7_2(X2,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X2,equal_set_predicate),esk4_2(X2,equal_set_predicate)) ),
inference(cn,[status(thm)],[324,theory(equality)]) ).
cnf(2233,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[272,16,theory(equality)]) ).
cnf(2403,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[270,2233,theory(equality)]) ).
cnf(2525,plain,
( subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[15,2403,theory(equality)]) ).
cnf(2532,plain,
( apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| ~ subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[107,2525,theory(equality)]) ).
cnf(2568,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(esk1_2(esk6_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| subset(esk6_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[319,16,theory(equality)]) ).
cnf(2709,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(esk1_2(esk6_2(X1,equal_set_predicate),X2),esk8_2(X1,equal_set_predicate))
| subset(esk6_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[321,2568,theory(equality)]) ).
cnf(2878,plain,
( subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[15,2709,theory(equality)]) ).
cnf(14914,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
inference(csr,[status(thm)],[2532,2878]) ).
cnf(14923,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk3_2(X1,equal_set_predicate),esk3_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[51,14914,theory(equality)]) ).
cnf(14934,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| $false ),
inference(rw,[status(thm)],[14923,171,theory(equality)]) ).
cnf(14935,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[14934,theory(equality)]) ).
cnf(14970,plain,
( apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[182,14935,theory(equality)]) ).
cnf(14986,plain,
( epred1_2(equal_set_predicate,X1)
| member(X2,esk6_2(X1,equal_set_predicate))
| ~ member(X2,esk7_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[274,14970,theory(equality)]) ).
cnf(14988,plain,
( epred1_2(equal_set_predicate,X1)
| member(X2,esk7_2(X1,equal_set_predicate))
| ~ member(X2,esk8_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[276,14970,theory(equality)]) ).
cnf(14990,plain,
( epred1_2(equal_set_predicate,X1)
| member(X2,esk7_2(X1,equal_set_predicate))
| ~ member(X2,esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[323,14970,theory(equality)]) ).
cnf(14991,plain,
( epred1_2(equal_set_predicate,X1)
| member(X2,esk8_2(X1,equal_set_predicate))
| ~ member(X2,esk7_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[325,14970,theory(equality)]) ).
cnf(15276,plain,
( epred1_2(equal_set_predicate,X1)
| member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[14988,16,theory(equality)]) ).
cnf(15439,plain,
( subset(X1,esk8_2(X2,equal_set_predicate))
| epred1_2(equal_set_predicate,X2)
| ~ member(esk1_2(X1,esk8_2(X2,equal_set_predicate)),esk7_2(X2,equal_set_predicate)) ),
inference(spm,[status(thm)],[15,14991,theory(equality)]) ).
cnf(15863,plain,
( epred1_2(equal_set_predicate,X1)
| member(esk1_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[14986,15276,theory(equality)]) ).
cnf(16219,plain,
( epred1_2(equal_set_predicate,X1)
| subset(X2,esk8_2(X1,equal_set_predicate))
| ~ member(esk1_2(X2,esk8_2(X1,equal_set_predicate)),esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[15439,14990,theory(equality)]) ).
cnf(16279,plain,
( subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[15,15863,theory(equality)]) ).
cnf(16300,plain,
( apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1)
| ~ subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[107,16279,theory(equality)]) ).
cnf(16589,plain,
( epred1_2(equal_set_predicate,X1)
| subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[16219,16,theory(equality)]) ).
cnf(18201,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
inference(csr,[status(thm)],[16300,16589]) ).
cnf(18211,plain,
( epred1_2(equal_set_predicate,X1)
| ~ apply(equal_set_predicate,esk3_2(X1,equal_set_predicate),esk3_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[45,18201,theory(equality)]) ).
cnf(18225,plain,
( epred1_2(equal_set_predicate,X1)
| $false
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(rw,[status(thm)],[18211,171,theory(equality)]) ).
cnf(18226,plain,
( epred1_2(equal_set_predicate,X1)
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[18225,theory(equality)]) ).
cnf(18240,plain,
epred1_2(equal_set_predicate,X1),
inference(csr,[status(thm)],[18226,14970]) ).
cnf(18242,negated_conjecture,
$false,
inference(rw,[status(thm)],[96,18240,theory(equality)]) ).
cnf(18243,negated_conjecture,
$false,
inference(cn,[status(thm)],[18242,theory(equality)]) ).
cnf(18244,negated_conjecture,
$false,
18243,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET806+4.p
% --creating new selector for [SET006+0.ax, SET006+2.ax]
% -running prover on /tmp/tmpsfS2ZG/sel_SET806+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET806+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET806+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET806+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
%
%------------------------------------------------------------------------------