%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET792+4 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:39:30 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 8 unt; 0 def)
% Number of atoms : 605 ( 37 equ)
% Maximal formula atoms : 256 ( 11 avg)
% Number of connectives : 777 ( 225 ~; 357 |; 176 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 75 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 175 ( 1 sgn 116 !; 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/tmp4kBg8p/sel_SET792+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/tmp4kBg8p/sel_SET792+4.p_1',least) ).
fof(3,axiom,
! [X1,X2,X6] :
( min(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X3,X6) )
=> X6 = X3 ) ) ),
file('/tmp/tmp4kBg8p/sel_SET792+4.p_1',min) ).
fof(4,conjecture,
! [X1,X2,X6] :
( ( order(X1,X2)
& least(X6,X1,X2) )
=> min(X6,X1,X2) ),
file('/tmp/tmp4kBg8p/sel_SET792+4.p_1',thIV4) ).
fof(5,negated_conjecture,
~ ! [X1,X2,X6] :
( ( order(X1,X2)
& least(X6,X1,X2) )
=> min(X6,X1,X2) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(6,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(7,plain,
! [X1,X2] :
( order(X1,X2)
<=> epred1_2(X1,X2) ),
inference(apply_def,[status(esa)],[1,6,theory(equality)]) ).
fof(8,plain,
! [X1,X2] :
( ( ~ order(X1,X2)
| epred1_2(X1,X2) )
& ( ~ epred1_2(X1,X2)
| order(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(9,plain,
! [X3,X4] :
( ( ~ order(X3,X4)
| epred1_2(X3,X4) )
& ( ~ epred1_2(X3,X4)
| order(X3,X4) ) ),
inference(variable_rename,[status(thm)],[8]) ).
cnf(11,plain,
( epred1_2(X1,X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[9]) ).
fof(12,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(13,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)],[12]) ).
fof(14,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)],[13]) ).
fof(15,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)],[14]) ).
fof(16,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)],[15]) ).
cnf(19,plain,
( member(X1,X3)
| ~ least(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(20,plain,
( apply(X2,X1,X4)
| ~ least(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(21,plain,
! [X1,X2,X6] :
( ( ~ min(X6,X1,X2)
| ( member(X6,X2)
& ! [X3] :
( ~ member(X3,X2)
| ~ apply(X1,X3,X6)
| X6 = X3 ) ) )
& ( ~ member(X6,X2)
| ? [X3] :
( member(X3,X2)
& apply(X1,X3,X6)
& X6 != X3 )
| min(X6,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(22,plain,
! [X7,X8,X9] :
( ( ~ min(X9,X7,X8)
| ( member(X9,X8)
& ! [X10] :
( ~ member(X10,X8)
| ~ apply(X7,X10,X9)
| X9 = X10 ) ) )
& ( ~ member(X9,X8)
| ? [X11] :
( member(X11,X8)
& apply(X7,X11,X9)
& X9 != X11 )
| min(X9,X7,X8) ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,plain,
! [X7,X8,X9] :
( ( ~ min(X9,X7,X8)
| ( member(X9,X8)
& ! [X10] :
( ~ member(X10,X8)
| ~ apply(X7,X10,X9)
| X9 = X10 ) ) )
& ( ~ member(X9,X8)
| ( member(esk2_3(X7,X8,X9),X8)
& apply(X7,esk2_3(X7,X8,X9),X9)
& X9 != esk2_3(X7,X8,X9) )
| min(X9,X7,X8) ) ),
inference(skolemize,[status(esa)],[22]) ).
fof(24,plain,
! [X7,X8,X9,X10] :
( ( ( ( ~ member(X10,X8)
| ~ apply(X7,X10,X9)
| X9 = X10 )
& member(X9,X8) )
| ~ min(X9,X7,X8) )
& ( ~ member(X9,X8)
| ( member(esk2_3(X7,X8,X9),X8)
& apply(X7,esk2_3(X7,X8,X9),X9)
& X9 != esk2_3(X7,X8,X9) )
| min(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[23]) ).
fof(25,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| ~ apply(X7,X10,X9)
| X9 = X10
| ~ min(X9,X7,X8) )
& ( member(X9,X8)
| ~ min(X9,X7,X8) )
& ( member(esk2_3(X7,X8,X9),X8)
| ~ member(X9,X8)
| min(X9,X7,X8) )
& ( apply(X7,esk2_3(X7,X8,X9),X9)
| ~ member(X9,X8)
| min(X9,X7,X8) )
& ( X9 != esk2_3(X7,X8,X9)
| ~ member(X9,X8)
| min(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[24]) ).
cnf(26,plain,
( min(X1,X2,X3)
| ~ member(X1,X3)
| X1 != esk2_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,plain,
( min(X1,X2,X3)
| apply(X2,esk2_3(X2,X3,X1),X1)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(28,plain,
( min(X1,X2,X3)
| member(esk2_3(X2,X3,X1),X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(31,negated_conjecture,
? [X1,X2,X6] :
( order(X1,X2)
& least(X6,X1,X2)
& ~ min(X6,X1,X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,negated_conjecture,
? [X7,X8,X9] :
( order(X7,X8)
& least(X9,X7,X8)
& ~ min(X9,X7,X8) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( order(esk3_0,esk4_0)
& least(esk5_0,esk3_0,esk4_0)
& ~ min(esk5_0,esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
~ min(esk5_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,negated_conjecture,
least(esk5_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,negated_conjecture,
order(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
fof(37,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)],[6]) ).
fof(38,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)],[37]) ).
fof(39,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)],[38]) ).
fof(40,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)],[39]) ).
fof(41,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)],[40]) ).
cnf(103,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)],[41]) ).
cnf(105,negated_conjecture,
epred1_2(esk3_0,esk4_0),
inference(spm,[status(thm)],[11,36,theory(equality)]) ).
cnf(107,negated_conjecture,
member(esk5_0,esk4_0),
inference(spm,[status(thm)],[19,35,theory(equality)]) ).
cnf(108,negated_conjecture,
( apply(esk3_0,esk5_0,X1)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[20,35,theory(equality)]) ).
cnf(109,plain,
( X1 = esk2_3(X2,X3,X1)
| min(X1,X2,X3)
| ~ epred1_2(X2,X4)
| ~ apply(X2,X1,esk2_3(X2,X3,X1))
| ~ member(esk2_3(X2,X3,X1),X4)
| ~ member(X1,X4)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[103,27,theory(equality)]) ).
cnf(179,plain,
( min(X1,X2,X3)
| ~ epred1_2(X2,X4)
| ~ apply(X2,X1,esk2_3(X2,X3,X1))
| ~ member(esk2_3(X2,X3,X1),X4)
| ~ member(X1,X4)
| ~ member(X1,X3) ),
inference(csr,[status(thm)],[109,26]) ).
cnf(180,negated_conjecture,
( min(esk5_0,esk3_0,X1)
| ~ epred1_2(esk3_0,X2)
| ~ member(esk2_3(esk3_0,X1,esk5_0),X2)
| ~ member(esk5_0,X2)
| ~ member(esk5_0,X1)
| ~ member(esk2_3(esk3_0,X1,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[179,108,theory(equality)]) ).
cnf(196,negated_conjecture,
( min(esk5_0,esk3_0,esk4_0)
| ~ epred1_2(esk3_0,X1)
| ~ member(esk2_3(esk3_0,esk4_0,esk5_0),X1)
| ~ member(esk5_0,X1)
| ~ member(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[180,28,theory(equality)]) ).
cnf(197,negated_conjecture,
( min(esk5_0,esk3_0,esk4_0)
| ~ epred1_2(esk3_0,X1)
| ~ member(esk2_3(esk3_0,esk4_0,esk5_0),X1)
| ~ member(esk5_0,X1)
| $false ),
inference(rw,[status(thm)],[196,107,theory(equality)]) ).
cnf(198,negated_conjecture,
( min(esk5_0,esk3_0,esk4_0)
| ~ epred1_2(esk3_0,X1)
| ~ member(esk2_3(esk3_0,esk4_0,esk5_0),X1)
| ~ member(esk5_0,X1) ),
inference(cn,[status(thm)],[197,theory(equality)]) ).
cnf(199,negated_conjecture,
( ~ epred1_2(esk3_0,X1)
| ~ member(esk2_3(esk3_0,esk4_0,esk5_0),X1)
| ~ member(esk5_0,X1) ),
inference(sr,[status(thm)],[198,34,theory(equality)]) ).
cnf(210,negated_conjecture,
( min(esk5_0,esk3_0,esk4_0)
| ~ epred1_2(esk3_0,esk4_0)
| ~ member(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[199,28,theory(equality)]) ).
cnf(211,negated_conjecture,
( min(esk5_0,esk3_0,esk4_0)
| $false
| ~ member(esk5_0,esk4_0) ),
inference(rw,[status(thm)],[210,105,theory(equality)]) ).
cnf(212,negated_conjecture,
( min(esk5_0,esk3_0,esk4_0)
| $false
| $false ),
inference(rw,[status(thm)],[211,107,theory(equality)]) ).
cnf(213,negated_conjecture,
min(esk5_0,esk3_0,esk4_0),
inference(cn,[status(thm)],[212,theory(equality)]) ).
cnf(214,negated_conjecture,
$false,
inference(sr,[status(thm)],[213,34,theory(equality)]) ).
cnf(215,negated_conjecture,
$false,
214,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET792+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmp4kBg8p/sel_SET792+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET792+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET792+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET792+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
%
%------------------------------------------------------------------------------