%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET768+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:35:32 EST 2010
% Result : Theorem 11.49s
% Output : CNFRefutation 11.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 10 unt; 0 def)
% Number of atoms : 629 ( 0 equ)
% Maximal formula atoms : 207 ( 7 avg)
% Number of connectives : 785 ( 245 ~; 367 |; 152 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 241 ( 9 sgn 112 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpMDH-4l/sel_SET768+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpMDH-4l/sel_SET768+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/tmpMDH-4l/sel_SET768+4.p_1',equivalence) ).
fof(4,axiom,
! [X4,X7,X1,X3] :
( member(X3,equivalence_class(X1,X7,X4))
<=> ( member(X3,X7)
& apply(X4,X1,X3) ) ),
file('/tmp/tmpMDH-4l/sel_SET768+4.p_1',equivalence_class) ).
fof(5,conjecture,
! [X7,X4,X1,X2] :
( ( equivalence(X4,X7)
& member(X1,X7)
& member(X2,X7) )
=> ( equal_set(equivalence_class(X1,X7,X4),equivalence_class(X2,X7,X4))
<=> apply(X4,X1,X2) ) ),
file('/tmp/tmpMDH-4l/sel_SET768+4.p_1',thIII04) ).
fof(6,negated_conjecture,
~ ! [X7,X4,X1,X2] :
( ( equivalence(X4,X7)
& member(X1,X7)
& member(X2,X7) )
=> ( equal_set(equivalence_class(X1,X7,X4),equivalence_class(X2,X7,X4))
<=> apply(X4,X1,X2) ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(7,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(8,plain,
! [X1,X4] :
( equivalence(X4,X1)
<=> epred1_2(X4,X1) ),
inference(apply_def,[status(esa)],[3,7,theory(equality)]) ).
fof(9,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(10,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)],[9]) ).
fof(11,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)],[10]) ).
fof(12,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)],[11]) ).
fof(13,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)],[12]) ).
cnf(14,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(15,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
cnf(16,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,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(18,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)],[17]) ).
fof(19,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)],[18]) ).
cnf(20,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( subset(X2,X1)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,plain,
! [X1,X4] :
( ( ~ equivalence(X4,X1)
| epred1_2(X4,X1) )
& ( ~ epred1_2(X4,X1)
| equivalence(X4,X1) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(24,plain,
! [X5,X6] :
( ( ~ equivalence(X6,X5)
| epred1_2(X6,X5) )
& ( ~ epred1_2(X6,X5)
| equivalence(X6,X5) ) ),
inference(variable_rename,[status(thm)],[23]) ).
cnf(26,plain,
( epred1_2(X1,X2)
| ~ equivalence(X1,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(27,plain,
! [X4,X7,X1,X3] :
( ( ~ member(X3,equivalence_class(X1,X7,X4))
| ( member(X3,X7)
& apply(X4,X1,X3) ) )
& ( ~ member(X3,X7)
| ~ apply(X4,X1,X3)
| member(X3,equivalence_class(X1,X7,X4)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(28,plain,
! [X8,X9,X10,X11] :
( ( ~ member(X11,equivalence_class(X10,X9,X8))
| ( member(X11,X9)
& apply(X8,X10,X11) ) )
& ( ~ member(X11,X9)
| ~ apply(X8,X10,X11)
| member(X11,equivalence_class(X10,X9,X8)) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X8,X9,X10,X11] :
( ( member(X11,X9)
| ~ member(X11,equivalence_class(X10,X9,X8)) )
& ( apply(X8,X10,X11)
| ~ member(X11,equivalence_class(X10,X9,X8)) )
& ( ~ member(X11,X9)
| ~ apply(X8,X10,X11)
| member(X11,equivalence_class(X10,X9,X8)) ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(30,plain,
( member(X1,equivalence_class(X2,X3,X4))
| ~ apply(X4,X2,X1)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,plain,
( apply(X4,X2,X1)
| ~ member(X1,equivalence_class(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(32,plain,
( member(X1,X3)
| ~ member(X1,equivalence_class(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(33,negated_conjecture,
? [X7,X4,X1,X2] :
( equivalence(X4,X7)
& member(X1,X7)
& member(X2,X7)
& ( ~ equal_set(equivalence_class(X1,X7,X4),equivalence_class(X2,X7,X4))
| ~ apply(X4,X1,X2) )
& ( equal_set(equivalence_class(X1,X7,X4),equivalence_class(X2,X7,X4))
| apply(X4,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(34,negated_conjecture,
? [X8,X9,X10,X11] :
( equivalence(X9,X8)
& member(X10,X8)
& member(X11,X8)
& ( ~ equal_set(equivalence_class(X10,X8,X9),equivalence_class(X11,X8,X9))
| ~ apply(X9,X10,X11) )
& ( equal_set(equivalence_class(X10,X8,X9),equivalence_class(X11,X8,X9))
| apply(X9,X10,X11) ) ),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
( equivalence(esk3_0,esk2_0)
& member(esk4_0,esk2_0)
& member(esk5_0,esk2_0)
& ( ~ equal_set(equivalence_class(esk4_0,esk2_0,esk3_0),equivalence_class(esk5_0,esk2_0,esk3_0))
| ~ apply(esk3_0,esk4_0,esk5_0) )
& ( equal_set(equivalence_class(esk4_0,esk2_0,esk3_0),equivalence_class(esk5_0,esk2_0,esk3_0))
| apply(esk3_0,esk4_0,esk5_0) ) ),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
( apply(esk3_0,esk4_0,esk5_0)
| equal_set(equivalence_class(esk4_0,esk2_0,esk3_0),equivalence_class(esk5_0,esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(37,negated_conjecture,
( ~ apply(esk3_0,esk4_0,esk5_0)
| ~ equal_set(equivalence_class(esk4_0,esk2_0,esk3_0),equivalence_class(esk5_0,esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,negated_conjecture,
member(esk5_0,esk2_0),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(39,negated_conjecture,
member(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(40,negated_conjecture,
equivalence(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[35]) ).
fof(41,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)],[7]) ).
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) ) ) )
& ( ? [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)],[41]) ).
fof(43,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(esk6_2(X7,X8),X7)
& ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8)) )
| ( member(esk7_2(X7,X8),X7)
& member(esk8_2(X7,X8),X7)
& apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
& ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8)) )
| ( member(esk9_2(X7,X8),X7)
& member(esk10_2(X7,X8),X7)
& member(esk11_2(X7,X8),X7)
& apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
& apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
& ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8)) )
| epred1_2(X8,X7) ) ),
inference(skolemize,[status(esa)],[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) )
& ( ~ 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(esk6_2(X7,X8),X7)
& ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8)) )
| ( member(esk7_2(X7,X8),X7)
& member(esk8_2(X7,X8),X7)
& apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
& ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8)) )
| ( member(esk9_2(X7,X8),X7)
& member(esk10_2(X7,X8),X7)
& member(esk11_2(X7,X8),X7)
& apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
& apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
& ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8)) )
| epred1_2(X8,X7) ) ),
inference(shift_quantors,[status(thm)],[43]) ).
fof(45,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(esk9_2(X7,X8),X7)
| member(esk7_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| member(esk7_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| member(esk7_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| member(esk7_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| member(esk7_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| member(esk7_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk9_2(X7,X8),X7)
| member(esk8_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| member(esk8_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| member(esk8_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| member(esk8_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| member(esk8_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| member(esk8_2(X7,X8),X7)
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk9_2(X7,X8),X7)
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk9_2(X7,X8),X7)
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| member(esk6_2(X7,X8),X7)
| epred1_2(X8,X7) )
& ( member(esk9_2(X7,X8),X7)
| member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| member(esk7_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk9_2(X7,X8),X7)
| member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| member(esk8_2(X7,X8),X7)
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk9_2(X7,X8),X7)
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| apply(X8,esk7_2(X7,X8),esk8_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk9_2(X7,X8),X7)
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk10_2(X7,X8),X7)
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( member(esk11_2(X7,X8),X7)
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk9_2(X7,X8),esk10_2(X7,X8))
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( apply(X8,esk10_2(X7,X8),esk11_2(X7,X8))
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) )
& ( ~ apply(X8,esk9_2(X7,X8),esk11_2(X7,X8))
| ~ apply(X8,esk8_2(X7,X8),esk7_2(X7,X8))
| ~ apply(X8,esk6_2(X7,X8),esk6_2(X7,X8))
| epred1_2(X8,X7) ) ),
inference(distribute,[status(thm)],[44]) ).
cnf(94,plain,
( apply(X1,X3,X3)
| ~ epred1_2(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(95,plain,
( apply(X1,X3,X4)
| ~ epred1_2(X1,X2)
| ~ apply(X1,X4,X3)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(96,plain,
( apply(X1,X3,X4)
| ~ epred1_2(X1,X2)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X5)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(97,negated_conjecture,
( subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| apply(esk3_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[21,36,theory(equality)]) ).
cnf(99,negated_conjecture,
epred1_2(esk3_0,esk2_0),
inference(spm,[status(thm)],[26,40,theory(equality)]) ).
cnf(101,plain,
( member(esk1_2(equivalence_class(X1,X2,X3),X4),X2)
| subset(equivalence_class(X1,X2,X3),X4) ),
inference(spm,[status(thm)],[32,15,theory(equality)]) ).
cnf(102,plain,
( apply(X1,X2,esk1_2(equivalence_class(X2,X3,X1),X4))
| subset(equivalence_class(X2,X3,X1),X4) ),
inference(spm,[status(thm)],[31,15,theory(equality)]) ).
cnf(106,plain,
( subset(X1,equivalence_class(X2,X3,X4))
| ~ apply(X4,X2,esk1_2(X1,equivalence_class(X2,X3,X4)))
| ~ member(esk1_2(X1,equivalence_class(X2,X3,X4)),X3) ),
inference(spm,[status(thm)],[14,30,theory(equality)]) ).
cnf(110,negated_conjecture,
( ~ apply(esk3_0,esk4_0,esk5_0)
| ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| ~ subset(equivalence_class(esk4_0,esk2_0,esk3_0),equivalence_class(esk5_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[37,20,theory(equality)]) ).
cnf(167,negated_conjecture,
( apply(esk3_0,X1,X1)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[94,99,theory(equality)]) ).
cnf(177,negated_conjecture,
( member(X1,equivalence_class(esk4_0,esk2_0,esk3_0))
| apply(esk3_0,esk4_0,esk5_0)
| ~ member(X1,equivalence_class(esk5_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[16,97,theory(equality)]) ).
cnf(180,plain,
( member(esk1_2(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),X6),X3)
| subset(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),X6) ),
inference(spm,[status(thm)],[32,101,theory(equality)]) ).
cnf(185,negated_conjecture,
( apply(esk3_0,esk4_0,X1)
| apply(esk3_0,esk4_0,esk5_0)
| ~ member(X1,equivalence_class(esk5_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[31,177,theory(equality)]) ).
cnf(189,negated_conjecture,
( apply(esk3_0,esk4_0,esk5_0)
| apply(esk3_0,esk4_0,X1)
| ~ apply(esk3_0,esk5_0,X1)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[185,30,theory(equality)]) ).
cnf(199,plain,
( apply(X1,X2,esk1_2(equivalence_class(X3,X4,X1),X5))
| subset(equivalence_class(X3,X4,X1),X5)
| ~ epred1_2(X1,X6)
| ~ apply(X1,X2,X3)
| ~ member(X3,X6)
| ~ member(esk1_2(equivalence_class(X3,X4,X1),X5),X6)
| ~ member(X2,X6) ),
inference(spm,[status(thm)],[96,102,theory(equality)]) ).
cnf(200,negated_conjecture,
( apply(esk3_0,esk4_0,esk5_0)
| ~ member(esk5_0,esk2_0) ),
inference(spm,[status(thm)],[189,167,theory(equality)]) ).
cnf(202,negated_conjecture,
( apply(esk3_0,esk4_0,esk5_0)
| $false ),
inference(rw,[status(thm)],[200,38,theory(equality)]) ).
cnf(203,negated_conjecture,
apply(esk3_0,esk4_0,esk5_0),
inference(cn,[status(thm)],[202,theory(equality)]) ).
cnf(204,negated_conjecture,
( apply(esk3_0,esk5_0,esk4_0)
| ~ epred1_2(esk3_0,X1)
| ~ member(esk4_0,X1)
| ~ member(esk5_0,X1) ),
inference(spm,[status(thm)],[95,203,theory(equality)]) ).
cnf(209,negated_conjecture,
( $false
| ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| ~ subset(equivalence_class(esk4_0,esk2_0,esk3_0),equivalence_class(esk5_0,esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[110,203,theory(equality)]) ).
cnf(210,negated_conjecture,
( ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| ~ subset(equivalence_class(esk4_0,esk2_0,esk3_0),equivalence_class(esk5_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[209,theory(equality)]) ).
cnf(217,negated_conjecture,
( apply(esk3_0,esk5_0,esk4_0)
| ~ member(esk4_0,esk2_0)
| ~ member(esk5_0,esk2_0) ),
inference(spm,[status(thm)],[204,99,theory(equality)]) ).
cnf(218,negated_conjecture,
( apply(esk3_0,esk5_0,esk4_0)
| $false
| ~ member(esk5_0,esk2_0) ),
inference(rw,[status(thm)],[217,39,theory(equality)]) ).
cnf(219,negated_conjecture,
( apply(esk3_0,esk5_0,esk4_0)
| $false
| $false ),
inference(rw,[status(thm)],[218,38,theory(equality)]) ).
cnf(220,negated_conjecture,
apply(esk3_0,esk5_0,esk4_0),
inference(cn,[status(thm)],[219,theory(equality)]) ).
cnf(231,plain,
( subset(equivalence_class(X1,X2,X3),equivalence_class(X1,X4,X3))
| ~ member(esk1_2(equivalence_class(X1,X2,X3),equivalence_class(X1,X4,X3)),X4) ),
inference(spm,[status(thm)],[106,102,theory(equality)]) ).
cnf(291,plain,
subset(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),equivalence_class(X1,X3,X5)),
inference(spm,[status(thm)],[231,180,theory(equality)]) ).
cnf(294,plain,
( member(X1,equivalence_class(X2,X3,X4))
| ~ member(X1,equivalence_class(X2,equivalence_class(X5,X3,X6),X4)) ),
inference(spm,[status(thm)],[16,291,theory(equality)]) ).
cnf(301,plain,
( member(X1,equivalence_class(X2,X3,X4))
| ~ apply(X4,X2,X1)
| ~ member(X1,equivalence_class(X5,X3,X6)) ),
inference(spm,[status(thm)],[294,30,theory(equality)]) ).
cnf(323,plain,
( member(esk1_2(equivalence_class(X1,X2,X3),X4),equivalence_class(X5,X2,X6))
| subset(equivalence_class(X1,X2,X3),X4)
| ~ apply(X6,X5,esk1_2(equivalence_class(X1,X2,X3),X4)) ),
inference(spm,[status(thm)],[301,15,theory(equality)]) ).
cnf(2414,plain,
( apply(X1,X2,esk1_2(equivalence_class(X3,X4,X1),X5))
| subset(equivalence_class(X3,X4,X1),X5)
| ~ epred1_2(X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X3,X4)
| ~ member(X2,X4) ),
inference(spm,[status(thm)],[199,101,theory(equality)]) ).
cnf(5593,plain,
( subset(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X5))
| ~ apply(X5,X4,esk1_2(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X5))) ),
inference(spm,[status(thm)],[14,323,theory(equality)]) ).
cnf(123598,plain,
( subset(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X3))
| ~ epred1_2(X3,X2)
| ~ apply(X3,X4,X1)
| ~ member(X1,X2)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[5593,2414,theory(equality)]) ).
cnf(123619,plain,
( ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| ~ epred1_2(esk3_0,esk2_0)
| ~ apply(esk3_0,esk5_0,esk4_0)
| ~ member(esk4_0,esk2_0)
| ~ member(esk5_0,esk2_0) ),
inference(spm,[status(thm)],[210,123598,theory(equality)]) ).
cnf(123620,plain,
( ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| $false
| ~ apply(esk3_0,esk5_0,esk4_0)
| ~ member(esk4_0,esk2_0)
| ~ member(esk5_0,esk2_0) ),
inference(rw,[status(thm)],[123619,99,theory(equality)]) ).
cnf(123621,plain,
( ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| $false
| $false
| ~ member(esk4_0,esk2_0)
| ~ member(esk5_0,esk2_0) ),
inference(rw,[status(thm)],[123620,220,theory(equality)]) ).
cnf(123622,plain,
( ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| $false
| $false
| $false
| ~ member(esk5_0,esk2_0) ),
inference(rw,[status(thm)],[123621,39,theory(equality)]) ).
cnf(123623,plain,
( ~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0))
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[123622,38,theory(equality)]) ).
cnf(123624,plain,
~ subset(equivalence_class(esk5_0,esk2_0,esk3_0),equivalence_class(esk4_0,esk2_0,esk3_0)),
inference(cn,[status(thm)],[123623,theory(equality)]) ).
cnf(124865,plain,
( ~ epred1_2(esk3_0,esk2_0)
| ~ apply(esk3_0,esk4_0,esk5_0)
| ~ member(esk5_0,esk2_0)
| ~ member(esk4_0,esk2_0) ),
inference(spm,[status(thm)],[123624,123598,theory(equality)]) ).
cnf(124866,plain,
( $false
| ~ apply(esk3_0,esk4_0,esk5_0)
| ~ member(esk5_0,esk2_0)
| ~ member(esk4_0,esk2_0) ),
inference(rw,[status(thm)],[124865,99,theory(equality)]) ).
cnf(124867,plain,
( $false
| $false
| ~ member(esk5_0,esk2_0)
| ~ member(esk4_0,esk2_0) ),
inference(rw,[status(thm)],[124866,203,theory(equality)]) ).
cnf(124868,plain,
( $false
| $false
| $false
| ~ member(esk4_0,esk2_0) ),
inference(rw,[status(thm)],[124867,38,theory(equality)]) ).
cnf(124869,plain,
( $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[124868,39,theory(equality)]) ).
cnf(124870,plain,
$false,
inference(cn,[status(thm)],[124869,theory(equality)]) ).
cnf(124871,plain,
$false,
124870,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET768+4.p
% --creating new selector for [SET006+0.ax, SET006+2.ax]
% -running prover on /tmp/tmpMDH-4l/sel_SET768+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET768+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET768+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET768+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
%
%------------------------------------------------------------------------------