TSTP Solution File: SET790+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET790+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 03:39:11 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 9 unt; 0 def)
% Number of atoms : 536 ( 35 equ)
% Maximal formula atoms : 256 ( 11 avg)
% Number of connectives : 680 ( 189 ~; 315 |; 157 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 75 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 138 ( 1 sgn 94 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( order(X1,X2)
<=> ( ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X3) )
& ! [X3,X4] :
( ( member(X3,X2)
& member(X4,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
=> X3 = X4 ) )
& ! [X3,X4,X5] :
( ( member(X3,X2)
& member(X4,X2)
& member(X5,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X5) )
=> apply(X1,X3,X5) ) ) ) ),
file('/tmp/tmpnnmK6x/sel_SET790+4.p_1',order) ).
fof(2,axiom,
! [X1,X2,X6] :
( least(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X6,X3) ) ) ),
file('/tmp/tmpnnmK6x/sel_SET790+4.p_1',least) ).
fof(3,conjecture,
! [X1,X2,X6] :
( ( order(X1,X2)
& least(X6,X1,X2) )
=> ! [X3] :
( least(X3,X1,X2)
=> X6 = X3 ) ),
file('/tmp/tmpnnmK6x/sel_SET790+4.p_1',thIV2) ).
fof(4,negated_conjecture,
~ ! [X1,X2,X6] :
( ( order(X1,X2)
& least(X6,X1,X2) )
=> ! [X3] :
( least(X3,X1,X2)
=> X6 = X3 ) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(5,plain,
! [X2,X1] :
( epred1_2(X1,X2)
<=> ( ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X3) )
& ! [X3,X4] :
( ( member(X3,X2)
& member(X4,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
=> X3 = X4 ) )
& ! [X3,X4,X5] :
( ( member(X3,X2)
& member(X4,X2)
& member(X5,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X5) )
=> apply(X1,X3,X5) ) ) ) ),
introduced(definition) ).
fof(6,plain,
! [X1,X2] :
( order(X1,X2)
<=> epred1_2(X1,X2) ),
inference(apply_def,[status(esa)],[1,5,theory(equality)]) ).
fof(7,plain,
! [X1,X2] :
( ( ~ order(X1,X2)
| epred1_2(X1,X2) )
& ( ~ epred1_2(X1,X2)
| order(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(8,plain,
! [X3,X4] :
( ( ~ order(X3,X4)
| epred1_2(X3,X4) )
& ( ~ epred1_2(X3,X4)
| order(X3,X4) ) ),
inference(variable_rename,[status(thm)],[7]) ).
cnf(10,plain,
( epred1_2(X1,X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[8]) ).
fof(11,plain,
! [X1,X2,X6] :
( ( ~ least(X6,X1,X2)
| ( member(X6,X2)
& ! [X3] :
( ~ member(X3,X2)
| apply(X1,X6,X3) ) ) )
& ( ~ member(X6,X2)
| ? [X3] :
( member(X3,X2)
& ~ apply(X1,X6,X3) )
| least(X6,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(12,plain,
! [X7,X8,X9] :
( ( ~ least(X9,X7,X8)
| ( member(X9,X8)
& ! [X10] :
( ~ member(X10,X8)
| apply(X7,X9,X10) ) ) )
& ( ~ member(X9,X8)
| ? [X11] :
( member(X11,X8)
& ~ apply(X7,X9,X11) )
| least(X9,X7,X8) ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X7,X8,X9] :
( ( ~ least(X9,X7,X8)
| ( member(X9,X8)
& ! [X10] :
( ~ member(X10,X8)
| apply(X7,X9,X10) ) ) )
& ( ~ member(X9,X8)
| ( member(esk1_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk1_3(X7,X8,X9)) )
| least(X9,X7,X8) ) ),
inference(skolemize,[status(esa)],[12]) ).
fof(14,plain,
! [X7,X8,X9,X10] :
( ( ( ( ~ member(X10,X8)
| apply(X7,X9,X10) )
& member(X9,X8) )
| ~ least(X9,X7,X8) )
& ( ~ member(X9,X8)
| ( member(esk1_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk1_3(X7,X8,X9)) )
| least(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[13]) ).
fof(15,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| apply(X7,X9,X10)
| ~ least(X9,X7,X8) )
& ( member(X9,X8)
| ~ least(X9,X7,X8) )
& ( member(esk1_3(X7,X8,X9),X8)
| ~ member(X9,X8)
| least(X9,X7,X8) )
& ( ~ apply(X7,X9,esk1_3(X7,X8,X9))
| ~ member(X9,X8)
| least(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[14]) ).
cnf(18,plain,
( member(X1,X3)
| ~ least(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(19,plain,
( apply(X2,X1,X4)
| ~ least(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(20,negated_conjecture,
? [X1,X2,X6] :
( order(X1,X2)
& least(X6,X1,X2)
& ? [X3] :
( least(X3,X1,X2)
& X6 != X3 ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(21,negated_conjecture,
? [X7,X8,X9] :
( order(X7,X8)
& least(X9,X7,X8)
& ? [X10] :
( least(X10,X7,X8)
& X9 != X10 ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,negated_conjecture,
( order(esk2_0,esk3_0)
& least(esk4_0,esk2_0,esk3_0)
& least(esk5_0,esk2_0,esk3_0)
& esk4_0 != esk5_0 ),
inference(skolemize,[status(esa)],[21]) ).
cnf(23,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,negated_conjecture,
least(esk5_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(25,negated_conjecture,
least(esk4_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(26,negated_conjecture,
order(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[22]) ).
fof(27,plain,
! [X2,X1] :
( ( ~ epred1_2(X1,X2)
| ( ! [X3] :
( ~ member(X3,X2)
| apply(X1,X3,X3) )
& ! [X3,X4] :
( ~ member(X3,X2)
| ~ member(X4,X2)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3)
| X3 = X4 )
& ! [X3,X4,X5] :
( ~ member(X3,X2)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X5)
| apply(X1,X3,X5) ) ) )
& ( ? [X3] :
( member(X3,X2)
& ~ apply(X1,X3,X3) )
| ? [X3,X4] :
( member(X3,X2)
& member(X4,X2)
& apply(X1,X3,X4)
& apply(X1,X4,X3)
& X3 != X4 )
| ? [X3,X4,X5] :
( member(X3,X2)
& member(X4,X2)
& member(X5,X2)
& apply(X1,X3,X4)
& apply(X1,X4,X5)
& ~ apply(X1,X3,X5) )
| epred1_2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(28,plain,
! [X6,X7] :
( ( ~ epred1_2(X7,X6)
| ( ! [X8] :
( ~ member(X8,X6)
| apply(X7,X8,X8) )
& ! [X9,X10] :
( ~ member(X9,X6)
| ~ member(X10,X6)
| ~ apply(X7,X9,X10)
| ~ apply(X7,X10,X9)
| X9 = X10 )
& ! [X11,X12,X13] :
( ~ member(X11,X6)
| ~ member(X12,X6)
| ~ member(X13,X6)
| ~ apply(X7,X11,X12)
| ~ apply(X7,X12,X13)
| apply(X7,X11,X13) ) ) )
& ( ? [X14] :
( member(X14,X6)
& ~ apply(X7,X14,X14) )
| ? [X15,X16] :
( member(X15,X6)
& member(X16,X6)
& apply(X7,X15,X16)
& apply(X7,X16,X15)
& X15 != X16 )
| ? [X17,X18,X19] :
( member(X17,X6)
& member(X18,X6)
& member(X19,X6)
& apply(X7,X17,X18)
& apply(X7,X18,X19)
& ~ apply(X7,X17,X19) )
| epred1_2(X7,X6) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,plain,
! [X6,X7] :
( ( ~ epred1_2(X7,X6)
| ( ! [X8] :
( ~ member(X8,X6)
| apply(X7,X8,X8) )
& ! [X9,X10] :
( ~ member(X9,X6)
| ~ member(X10,X6)
| ~ apply(X7,X9,X10)
| ~ apply(X7,X10,X9)
| X9 = X10 )
& ! [X11,X12,X13] :
( ~ member(X11,X6)
| ~ member(X12,X6)
| ~ member(X13,X6)
| ~ apply(X7,X11,X12)
| ~ apply(X7,X12,X13)
| apply(X7,X11,X13) ) ) )
& ( ( member(esk6_2(X6,X7),X6)
& ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7)) )
| ( member(esk7_2(X6,X7),X6)
& member(esk8_2(X6,X7),X6)
& apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
& apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
& esk7_2(X6,X7) != esk8_2(X6,X7) )
| ( member(esk9_2(X6,X7),X6)
& member(esk10_2(X6,X7),X6)
& member(esk11_2(X6,X7),X6)
& apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
& apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
& ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7)) )
| epred1_2(X7,X6) ) ),
inference(skolemize,[status(esa)],[28]) ).
fof(30,plain,
! [X6,X7,X8,X9,X10,X11,X12,X13] :
( ( ( ( ~ member(X11,X6)
| ~ member(X12,X6)
| ~ member(X13,X6)
| ~ apply(X7,X11,X12)
| ~ apply(X7,X12,X13)
| apply(X7,X11,X13) )
& ( ~ member(X9,X6)
| ~ member(X10,X6)
| ~ apply(X7,X9,X10)
| ~ apply(X7,X10,X9)
| X9 = X10 )
& ( ~ member(X8,X6)
| apply(X7,X8,X8) ) )
| ~ epred1_2(X7,X6) )
& ( ( member(esk6_2(X6,X7),X6)
& ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7)) )
| ( member(esk7_2(X6,X7),X6)
& member(esk8_2(X6,X7),X6)
& apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
& apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
& esk7_2(X6,X7) != esk8_2(X6,X7) )
| ( member(esk9_2(X6,X7),X6)
& member(esk10_2(X6,X7),X6)
& member(esk11_2(X6,X7),X6)
& apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
& apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
& ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7)) )
| epred1_2(X7,X6) ) ),
inference(shift_quantors,[status(thm)],[29]) ).
fof(31,plain,
! [X6,X7,X8,X9,X10,X11,X12,X13] :
( ( ~ member(X11,X6)
| ~ member(X12,X6)
| ~ member(X13,X6)
| ~ apply(X7,X11,X12)
| ~ apply(X7,X12,X13)
| apply(X7,X11,X13)
| ~ epred1_2(X7,X6) )
& ( ~ member(X9,X6)
| ~ member(X10,X6)
| ~ apply(X7,X9,X10)
| ~ apply(X7,X10,X9)
| X9 = X10
| ~ epred1_2(X7,X6) )
& ( ~ member(X8,X6)
| apply(X7,X8,X8)
| ~ epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| member(esk7_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| member(esk7_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| member(esk7_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| member(esk7_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| member(esk7_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| member(esk7_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| member(esk8_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| member(esk8_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| member(esk8_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| member(esk8_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| member(esk8_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| member(esk8_2(X6,X7),X6)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| esk7_2(X6,X7) != esk8_2(X6,X7)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| esk7_2(X6,X7) != esk8_2(X6,X7)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| esk7_2(X6,X7) != esk8_2(X6,X7)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| esk7_2(X6,X7) != esk8_2(X6,X7)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| esk7_2(X6,X7) != esk8_2(X6,X7)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| esk7_2(X6,X7) != esk8_2(X6,X7)
| member(esk6_2(X6,X7),X6)
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| member(esk7_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| member(esk7_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| member(esk7_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| member(esk7_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| member(esk7_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| member(esk7_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| member(esk8_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| member(esk8_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| member(esk8_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| member(esk8_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| member(esk8_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| member(esk8_2(X6,X7),X6)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk7_2(X6,X7),esk8_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| apply(X7,esk8_2(X6,X7),esk7_2(X6,X7))
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk9_2(X6,X7),X6)
| esk7_2(X6,X7) != esk8_2(X6,X7)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk10_2(X6,X7),X6)
| esk7_2(X6,X7) != esk8_2(X6,X7)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( member(esk11_2(X6,X7),X6)
| esk7_2(X6,X7) != esk8_2(X6,X7)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk9_2(X6,X7),esk10_2(X6,X7))
| esk7_2(X6,X7) != esk8_2(X6,X7)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( apply(X7,esk10_2(X6,X7),esk11_2(X6,X7))
| esk7_2(X6,X7) != esk8_2(X6,X7)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) )
& ( ~ apply(X7,esk9_2(X6,X7),esk11_2(X6,X7))
| esk7_2(X6,X7) != esk8_2(X6,X7)
| ~ apply(X7,esk6_2(X6,X7),esk6_2(X6,X7))
| epred1_2(X7,X6) ) ),
inference(distribute,[status(thm)],[30]) ).
cnf(93,plain,
( X3 = X4
| ~ epred1_2(X1,X2)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X4,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(95,negated_conjecture,
epred1_2(esk2_0,esk3_0),
inference(spm,[status(thm)],[10,26,theory(equality)]) ).
cnf(97,negated_conjecture,
member(esk4_0,esk3_0),
inference(spm,[status(thm)],[18,25,theory(equality)]) ).
cnf(98,negated_conjecture,
member(esk5_0,esk3_0),
inference(spm,[status(thm)],[18,24,theory(equality)]) ).
cnf(99,negated_conjecture,
( apply(esk2_0,esk4_0,X1)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[19,25,theory(equality)]) ).
cnf(100,negated_conjecture,
( apply(esk2_0,esk5_0,X1)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[19,24,theory(equality)]) ).
cnf(167,negated_conjecture,
( X1 = esk4_0
| ~ epred1_2(esk2_0,X2)
| ~ apply(esk2_0,X1,esk4_0)
| ~ member(esk4_0,X2)
| ~ member(X1,X2)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[93,99,theory(equality)]) ).
cnf(190,negated_conjecture,
( esk5_0 = esk4_0
| ~ epred1_2(esk2_0,X1)
| ~ member(esk4_0,X1)
| ~ member(esk5_0,esk3_0)
| ~ member(esk5_0,X1)
| ~ member(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[167,100,theory(equality)]) ).
cnf(191,negated_conjecture,
( esk5_0 = esk4_0
| ~ epred1_2(esk2_0,X1)
| ~ member(esk4_0,X1)
| $false
| ~ member(esk5_0,X1)
| ~ member(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[190,98,theory(equality)]) ).
cnf(192,negated_conjecture,
( esk5_0 = esk4_0
| ~ epred1_2(esk2_0,X1)
| ~ member(esk4_0,X1)
| $false
| ~ member(esk5_0,X1)
| $false ),
inference(rw,[status(thm)],[191,97,theory(equality)]) ).
cnf(193,negated_conjecture,
( esk5_0 = esk4_0
| ~ epred1_2(esk2_0,X1)
| ~ member(esk4_0,X1)
| ~ member(esk5_0,X1) ),
inference(cn,[status(thm)],[192,theory(equality)]) ).
cnf(194,negated_conjecture,
( ~ epred1_2(esk2_0,X1)
| ~ member(esk4_0,X1)
| ~ member(esk5_0,X1) ),
inference(sr,[status(thm)],[193,23,theory(equality)]) ).
cnf(195,negated_conjecture,
( ~ member(esk4_0,esk3_0)
| ~ member(esk5_0,esk3_0) ),
inference(spm,[status(thm)],[194,95,theory(equality)]) ).
cnf(196,negated_conjecture,
( $false
| ~ member(esk5_0,esk3_0) ),
inference(rw,[status(thm)],[195,97,theory(equality)]) ).
cnf(197,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[196,98,theory(equality)]) ).
cnf(198,negated_conjecture,
$false,
inference(cn,[status(thm)],[197,theory(equality)]) ).
cnf(199,negated_conjecture,
$false,
198,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET790+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmpnnmK6x/sel_SET790+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET790+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET790+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET790+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
%
%------------------------------------------------------------------------------