TSTP Solution File: SET776+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET776+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 03:38:38 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 51 ( 15 unt; 0 def)
% Number of atoms : 349 ( 0 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 439 ( 141 ~; 164 |; 120 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 64 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( pre_order(X1,X2)
<=> ( ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X3) )
& ! [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/tmpMt-fW3/sel_SET776+4.p_1',pre_order) ).
fof(2,conjecture,
! [X2,X6,X1] :
( ( pre_order(X6,X2)
& ! [X7,X8] :
( ( member(X7,X2)
& member(X8,X2) )
=> ( apply(X1,X7,X8)
<=> ( apply(X6,X7,X8)
& apply(X6,X8,X7) ) ) ) )
=> ! [X9,X10,X11,X12] :
( ( member(X9,X2)
& member(X10,X2)
& member(X11,X2)
& member(X12,X2) )
=> ( ( apply(X1,X9,X11)
& apply(X1,X10,X12)
& apply(X6,X9,X10) )
=> apply(X6,X11,X12) ) ) ),
file('/tmp/tmpMt-fW3/sel_SET776+4.p_1',thIII12) ).
fof(3,negated_conjecture,
~ ! [X2,X6,X1] :
( ( pre_order(X6,X2)
& ! [X7,X8] :
( ( member(X7,X2)
& member(X8,X2) )
=> ( apply(X1,X7,X8)
<=> ( apply(X6,X7,X8)
& apply(X6,X8,X7) ) ) ) )
=> ! [X9,X10,X11,X12] :
( ( member(X9,X2)
& member(X10,X2)
& member(X11,X2)
& member(X12,X2) )
=> ( ( apply(X1,X9,X11)
& apply(X1,X10,X12)
& apply(X6,X9,X10) )
=> apply(X6,X11,X12) ) ) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(4,plain,
! [X1,X2] :
( ( ~ pre_order(X1,X2)
| ( ! [X3] :
( ~ member(X3,X2)
| apply(X1,X3,X3) )
& ! [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,X5] :
( member(X3,X2)
& member(X4,X2)
& member(X5,X2)
& apply(X1,X3,X4)
& apply(X1,X4,X5)
& ~ apply(X1,X3,X5) )
| pre_order(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(5,plain,
! [X6,X7] :
( ( ~ pre_order(X6,X7)
| ( ! [X8] :
( ~ member(X8,X7)
| apply(X6,X8,X8) )
& ! [X9,X10,X11] :
( ~ member(X9,X7)
| ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X6,X9,X10)
| ~ apply(X6,X10,X11)
| apply(X6,X9,X11) ) ) )
& ( ? [X12] :
( member(X12,X7)
& ~ apply(X6,X12,X12) )
| ? [X13,X14,X15] :
( member(X13,X7)
& member(X14,X7)
& member(X15,X7)
& apply(X6,X13,X14)
& apply(X6,X14,X15)
& ~ apply(X6,X13,X15) )
| pre_order(X6,X7) ) ),
inference(variable_rename,[status(thm)],[4]) ).
fof(6,plain,
! [X6,X7] :
( ( ~ pre_order(X6,X7)
| ( ! [X8] :
( ~ member(X8,X7)
| apply(X6,X8,X8) )
& ! [X9,X10,X11] :
( ~ member(X9,X7)
| ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X6,X9,X10)
| ~ apply(X6,X10,X11)
| apply(X6,X9,X11) ) ) )
& ( ( member(esk1_2(X6,X7),X7)
& ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7)) )
| ( member(esk2_2(X6,X7),X7)
& member(esk3_2(X6,X7),X7)
& member(esk4_2(X6,X7),X7)
& apply(X6,esk2_2(X6,X7),esk3_2(X6,X7))
& apply(X6,esk3_2(X6,X7),esk4_2(X6,X7))
& ~ apply(X6,esk2_2(X6,X7),esk4_2(X6,X7)) )
| pre_order(X6,X7) ) ),
inference(skolemize,[status(esa)],[5]) ).
fof(7,plain,
! [X6,X7,X8,X9,X10,X11] :
( ( ( ( ~ member(X9,X7)
| ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X6,X9,X10)
| ~ apply(X6,X10,X11)
| apply(X6,X9,X11) )
& ( ~ member(X8,X7)
| apply(X6,X8,X8) ) )
| ~ pre_order(X6,X7) )
& ( ( member(esk1_2(X6,X7),X7)
& ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7)) )
| ( member(esk2_2(X6,X7),X7)
& member(esk3_2(X6,X7),X7)
& member(esk4_2(X6,X7),X7)
& apply(X6,esk2_2(X6,X7),esk3_2(X6,X7))
& apply(X6,esk3_2(X6,X7),esk4_2(X6,X7))
& ~ apply(X6,esk2_2(X6,X7),esk4_2(X6,X7)) )
| pre_order(X6,X7) ) ),
inference(shift_quantors,[status(thm)],[6]) ).
fof(8,plain,
! [X6,X7,X8,X9,X10,X11] :
( ( ~ member(X9,X7)
| ~ member(X10,X7)
| ~ member(X11,X7)
| ~ apply(X6,X9,X10)
| ~ apply(X6,X10,X11)
| apply(X6,X9,X11)
| ~ pre_order(X6,X7) )
& ( ~ member(X8,X7)
| apply(X6,X8,X8)
| ~ pre_order(X6,X7) )
& ( member(esk2_2(X6,X7),X7)
| member(esk1_2(X6,X7),X7)
| pre_order(X6,X7) )
& ( member(esk3_2(X6,X7),X7)
| member(esk1_2(X6,X7),X7)
| pre_order(X6,X7) )
& ( member(esk4_2(X6,X7),X7)
| member(esk1_2(X6,X7),X7)
| pre_order(X6,X7) )
& ( apply(X6,esk2_2(X6,X7),esk3_2(X6,X7))
| member(esk1_2(X6,X7),X7)
| pre_order(X6,X7) )
& ( apply(X6,esk3_2(X6,X7),esk4_2(X6,X7))
| member(esk1_2(X6,X7),X7)
| pre_order(X6,X7) )
& ( ~ apply(X6,esk2_2(X6,X7),esk4_2(X6,X7))
| member(esk1_2(X6,X7),X7)
| pre_order(X6,X7) )
& ( member(esk2_2(X6,X7),X7)
| ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7))
| pre_order(X6,X7) )
& ( member(esk3_2(X6,X7),X7)
| ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7))
| pre_order(X6,X7) )
& ( member(esk4_2(X6,X7),X7)
| ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7))
| pre_order(X6,X7) )
& ( apply(X6,esk2_2(X6,X7),esk3_2(X6,X7))
| ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7))
| pre_order(X6,X7) )
& ( apply(X6,esk3_2(X6,X7),esk4_2(X6,X7))
| ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7))
| pre_order(X6,X7) )
& ( ~ apply(X6,esk2_2(X6,X7),esk4_2(X6,X7))
| ~ apply(X6,esk1_2(X6,X7),esk1_2(X6,X7))
| pre_order(X6,X7) ) ),
inference(distribute,[status(thm)],[7]) ).
cnf(22,plain,
( apply(X1,X3,X4)
| ~ pre_order(X1,X2)
| ~ apply(X1,X5,X4)
| ~ apply(X1,X3,X5)
| ~ member(X4,X2)
| ~ member(X5,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[8]) ).
fof(23,negated_conjecture,
? [X2,X6,X1] :
( pre_order(X6,X2)
& ! [X7,X8] :
( ~ member(X7,X2)
| ~ member(X8,X2)
| ( ( ~ apply(X1,X7,X8)
| ( apply(X6,X7,X8)
& apply(X6,X8,X7) ) )
& ( ~ apply(X6,X7,X8)
| ~ apply(X6,X8,X7)
| apply(X1,X7,X8) ) ) )
& ? [X9,X10,X11,X12] :
( member(X9,X2)
& member(X10,X2)
& member(X11,X2)
& member(X12,X2)
& apply(X1,X9,X11)
& apply(X1,X10,X12)
& apply(X6,X9,X10)
& ~ apply(X6,X11,X12) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(24,negated_conjecture,
? [X13,X14,X15] :
( pre_order(X14,X13)
& ! [X16,X17] :
( ~ member(X16,X13)
| ~ member(X17,X13)
| ( ( ~ apply(X15,X16,X17)
| ( apply(X14,X16,X17)
& apply(X14,X17,X16) ) )
& ( ~ apply(X14,X16,X17)
| ~ apply(X14,X17,X16)
| apply(X15,X16,X17) ) ) )
& ? [X18,X19,X20,X21] :
( member(X18,X13)
& member(X19,X13)
& member(X20,X13)
& member(X21,X13)
& apply(X15,X18,X20)
& apply(X15,X19,X21)
& apply(X14,X18,X19)
& ~ apply(X14,X20,X21) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,negated_conjecture,
( pre_order(esk6_0,esk5_0)
& ! [X16,X17] :
( ~ member(X16,esk5_0)
| ~ member(X17,esk5_0)
| ( ( ~ apply(esk7_0,X16,X17)
| ( apply(esk6_0,X16,X17)
& apply(esk6_0,X17,X16) ) )
& ( ~ apply(esk6_0,X16,X17)
| ~ apply(esk6_0,X17,X16)
| apply(esk7_0,X16,X17) ) ) )
& member(esk8_0,esk5_0)
& member(esk9_0,esk5_0)
& member(esk10_0,esk5_0)
& member(esk11_0,esk5_0)
& apply(esk7_0,esk8_0,esk10_0)
& apply(esk7_0,esk9_0,esk11_0)
& apply(esk6_0,esk8_0,esk9_0)
& ~ apply(esk6_0,esk10_0,esk11_0) ),
inference(skolemize,[status(esa)],[24]) ).
fof(26,negated_conjecture,
! [X16,X17] :
( ( ~ member(X16,esk5_0)
| ~ member(X17,esk5_0)
| ( ( ~ apply(esk7_0,X16,X17)
| ( apply(esk6_0,X16,X17)
& apply(esk6_0,X17,X16) ) )
& ( ~ apply(esk6_0,X16,X17)
| ~ apply(esk6_0,X17,X16)
| apply(esk7_0,X16,X17) ) ) )
& pre_order(esk6_0,esk5_0)
& member(esk8_0,esk5_0)
& member(esk9_0,esk5_0)
& member(esk10_0,esk5_0)
& member(esk11_0,esk5_0)
& apply(esk7_0,esk8_0,esk10_0)
& apply(esk7_0,esk9_0,esk11_0)
& apply(esk6_0,esk8_0,esk9_0)
& ~ apply(esk6_0,esk10_0,esk11_0) ),
inference(shift_quantors,[status(thm)],[25]) ).
fof(27,negated_conjecture,
! [X16,X17] :
( ( apply(esk6_0,X16,X17)
| ~ apply(esk7_0,X16,X17)
| ~ member(X16,esk5_0)
| ~ member(X17,esk5_0) )
& ( apply(esk6_0,X17,X16)
| ~ apply(esk7_0,X16,X17)
| ~ member(X16,esk5_0)
| ~ member(X17,esk5_0) )
& ( ~ apply(esk6_0,X16,X17)
| ~ apply(esk6_0,X17,X16)
| apply(esk7_0,X16,X17)
| ~ member(X16,esk5_0)
| ~ member(X17,esk5_0) )
& pre_order(esk6_0,esk5_0)
& member(esk8_0,esk5_0)
& member(esk9_0,esk5_0)
& member(esk10_0,esk5_0)
& member(esk11_0,esk5_0)
& apply(esk7_0,esk8_0,esk10_0)
& apply(esk7_0,esk9_0,esk11_0)
& apply(esk6_0,esk8_0,esk9_0)
& ~ apply(esk6_0,esk10_0,esk11_0) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,negated_conjecture,
~ apply(esk6_0,esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,negated_conjecture,
apply(esk6_0,esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,negated_conjecture,
apply(esk7_0,esk9_0,esk11_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(31,negated_conjecture,
apply(esk7_0,esk8_0,esk10_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(32,negated_conjecture,
member(esk11_0,esk5_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(33,negated_conjecture,
member(esk10_0,esk5_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(34,negated_conjecture,
member(esk9_0,esk5_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(35,negated_conjecture,
member(esk8_0,esk5_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(36,negated_conjecture,
pre_order(esk6_0,esk5_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(38,negated_conjecture,
( apply(esk6_0,X1,X2)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ apply(esk7_0,X2,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(39,negated_conjecture,
( apply(esk6_0,X2,X1)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ apply(esk7_0,X2,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(45,negated_conjecture,
( apply(esk6_0,esk9_0,esk11_0)
| ~ member(esk9_0,esk5_0)
| ~ member(esk11_0,esk5_0) ),
inference(spm,[status(thm)],[39,30,theory(equality)]) ).
cnf(49,negated_conjecture,
( apply(esk6_0,esk9_0,esk11_0)
| $false
| ~ member(esk11_0,esk5_0) ),
inference(rw,[status(thm)],[45,34,theory(equality)]) ).
cnf(50,negated_conjecture,
( apply(esk6_0,esk9_0,esk11_0)
| $false
| $false ),
inference(rw,[status(thm)],[49,32,theory(equality)]) ).
cnf(51,negated_conjecture,
apply(esk6_0,esk9_0,esk11_0),
inference(cn,[status(thm)],[50,theory(equality)]) ).
cnf(52,negated_conjecture,
( apply(esk6_0,esk10_0,esk8_0)
| ~ member(esk8_0,esk5_0)
| ~ member(esk10_0,esk5_0) ),
inference(spm,[status(thm)],[38,31,theory(equality)]) ).
cnf(54,negated_conjecture,
( apply(esk6_0,esk10_0,esk8_0)
| $false
| ~ member(esk10_0,esk5_0) ),
inference(rw,[status(thm)],[52,35,theory(equality)]) ).
cnf(55,negated_conjecture,
( apply(esk6_0,esk10_0,esk8_0)
| $false
| $false ),
inference(rw,[status(thm)],[54,33,theory(equality)]) ).
cnf(56,negated_conjecture,
apply(esk6_0,esk10_0,esk8_0),
inference(cn,[status(thm)],[55,theory(equality)]) ).
cnf(74,negated_conjecture,
( apply(esk6_0,X1,esk9_0)
| ~ apply(esk6_0,X1,esk8_0)
| ~ member(esk8_0,X2)
| ~ member(esk9_0,X2)
| ~ member(X1,X2)
| ~ pre_order(esk6_0,X2) ),
inference(spm,[status(thm)],[22,29,theory(equality)]) ).
cnf(87,negated_conjecture,
( apply(esk6_0,X1,esk11_0)
| ~ apply(esk6_0,X1,esk9_0)
| ~ member(esk9_0,X2)
| ~ member(esk11_0,X2)
| ~ member(X1,X2)
| ~ pre_order(esk6_0,X2) ),
inference(spm,[status(thm)],[22,51,theory(equality)]) ).
cnf(273,negated_conjecture,
( apply(esk6_0,X1,esk9_0)
| ~ apply(esk6_0,X1,esk8_0)
| ~ member(esk8_0,esk5_0)
| ~ member(esk9_0,esk5_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[74,36,theory(equality)]) ).
cnf(274,negated_conjecture,
( apply(esk6_0,X1,esk9_0)
| ~ apply(esk6_0,X1,esk8_0)
| $false
| ~ member(esk9_0,esk5_0)
| ~ member(X1,esk5_0) ),
inference(rw,[status(thm)],[273,35,theory(equality)]) ).
cnf(275,negated_conjecture,
( apply(esk6_0,X1,esk9_0)
| ~ apply(esk6_0,X1,esk8_0)
| $false
| $false
| ~ member(X1,esk5_0) ),
inference(rw,[status(thm)],[274,34,theory(equality)]) ).
cnf(276,negated_conjecture,
( apply(esk6_0,X1,esk9_0)
| ~ apply(esk6_0,X1,esk8_0)
| ~ member(X1,esk5_0) ),
inference(cn,[status(thm)],[275,theory(equality)]) ).
cnf(279,negated_conjecture,
( apply(esk6_0,esk10_0,esk9_0)
| ~ apply(esk6_0,esk10_0,esk8_0) ),
inference(spm,[status(thm)],[276,33,theory(equality)]) ).
cnf(288,negated_conjecture,
( apply(esk6_0,esk10_0,esk9_0)
| $false ),
inference(rw,[status(thm)],[279,56,theory(equality)]) ).
cnf(289,negated_conjecture,
apply(esk6_0,esk10_0,esk9_0),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(335,negated_conjecture,
( apply(esk6_0,X1,esk11_0)
| ~ apply(esk6_0,X1,esk9_0)
| ~ member(esk9_0,esk5_0)
| ~ member(esk11_0,esk5_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[87,36,theory(equality)]) ).
cnf(336,negated_conjecture,
( apply(esk6_0,X1,esk11_0)
| ~ apply(esk6_0,X1,esk9_0)
| $false
| ~ member(esk11_0,esk5_0)
| ~ member(X1,esk5_0) ),
inference(rw,[status(thm)],[335,34,theory(equality)]) ).
cnf(337,negated_conjecture,
( apply(esk6_0,X1,esk11_0)
| ~ apply(esk6_0,X1,esk9_0)
| $false
| $false
| ~ member(X1,esk5_0) ),
inference(rw,[status(thm)],[336,32,theory(equality)]) ).
cnf(338,negated_conjecture,
( apply(esk6_0,X1,esk11_0)
| ~ apply(esk6_0,X1,esk9_0)
| ~ member(X1,esk5_0) ),
inference(cn,[status(thm)],[337,theory(equality)]) ).
cnf(341,negated_conjecture,
( apply(esk6_0,esk10_0,esk11_0)
| ~ apply(esk6_0,esk10_0,esk9_0) ),
inference(spm,[status(thm)],[338,33,theory(equality)]) ).
cnf(351,negated_conjecture,
( apply(esk6_0,esk10_0,esk11_0)
| $false ),
inference(rw,[status(thm)],[341,289,theory(equality)]) ).
cnf(352,negated_conjecture,
apply(esk6_0,esk10_0,esk11_0),
inference(cn,[status(thm)],[351,theory(equality)]) ).
cnf(353,negated_conjecture,
$false,
inference(sr,[status(thm)],[352,28,theory(equality)]) ).
cnf(354,negated_conjecture,
$false,
353,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET776+4.p
% --creating new selector for [SET006+0.ax, SET006+2.ax]
% -running prover on /tmp/tmpMt-fW3/sel_SET776+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET776+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET776+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET776+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
%
%------------------------------------------------------------------------------