TSTP Solution File: SET804+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET804+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 03:40:36 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 182 ( 28 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 218 ( 78 ~; 78 |; 54 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 90 ( 2 sgn 56 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2,X6] :
( least(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X6,X3) ) ) ),
file('/tmp/tmpseEQNZ/sel_SET804+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/tmpseEQNZ/sel_SET804+4.p_1',min) ).
fof(4,conjecture,
! [X1,X2] :
( order(X1,X2)
=> ! [X7,X8] :
( ( min(X7,X1,X2)
& min(X8,X1,X2)
& X7 != X8 )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
file('/tmp/tmpseEQNZ/sel_SET804+4.p_1',thIV16) ).
fof(5,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X7,X8] :
( ( min(X7,X1,X2)
& min(X8,X1,X2)
& X7 != X8 )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
inference(assume_negation,[status(cth)],[4]) ).
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(29,plain,
( member(X1,X3)
| ~ min(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(30,plain,
( X1 = X4
| ~ min(X1,X2,X3)
| ~ apply(X2,X4,X1)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(31,negated_conjecture,
? [X1,X2] :
( order(X1,X2)
& ? [X7,X8] :
( min(X7,X1,X2)
& min(X8,X1,X2)
& X7 != X8
& ? [X6] : least(X6,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,negated_conjecture,
? [X9,X10] :
( order(X9,X10)
& ? [X11,X12] :
( min(X11,X9,X10)
& min(X12,X9,X10)
& X11 != X12
& ? [X13] : least(X13,X9,X10) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( order(esk3_0,esk4_0)
& min(esk5_0,esk3_0,esk4_0)
& min(esk6_0,esk3_0,esk4_0)
& esk5_0 != esk6_0
& least(esk7_0,esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
least(esk7_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,negated_conjecture,
esk5_0 != esk6_0,
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,negated_conjecture,
min(esk6_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(37,negated_conjecture,
min(esk5_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(109,negated_conjecture,
member(esk7_0,esk4_0),
inference(spm,[status(thm)],[19,34,theory(equality)]) ).
cnf(110,negated_conjecture,
member(esk5_0,esk4_0),
inference(spm,[status(thm)],[29,37,theory(equality)]) ).
cnf(111,negated_conjecture,
member(esk6_0,esk4_0),
inference(spm,[status(thm)],[29,36,theory(equality)]) ).
cnf(112,negated_conjecture,
( apply(esk3_0,esk7_0,X1)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[20,34,theory(equality)]) ).
cnf(113,negated_conjecture,
( esk5_0 = X1
| ~ apply(esk3_0,X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[30,37,theory(equality)]) ).
cnf(114,negated_conjecture,
( esk6_0 = X1
| ~ apply(esk3_0,X1,esk6_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[30,36,theory(equality)]) ).
cnf(196,negated_conjecture,
( esk5_0 = esk7_0
| ~ member(esk7_0,esk4_0)
| ~ member(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[113,112,theory(equality)]) ).
cnf(197,negated_conjecture,
( esk5_0 = esk7_0
| $false
| ~ member(esk5_0,esk4_0) ),
inference(rw,[status(thm)],[196,109,theory(equality)]) ).
cnf(198,negated_conjecture,
( esk5_0 = esk7_0
| $false
| $false ),
inference(rw,[status(thm)],[197,110,theory(equality)]) ).
cnf(199,negated_conjecture,
esk5_0 = esk7_0,
inference(cn,[status(thm)],[198,theory(equality)]) ).
cnf(203,negated_conjecture,
( apply(esk3_0,esk5_0,X1)
| ~ member(X1,esk4_0) ),
inference(rw,[status(thm)],[112,199,theory(equality)]) ).
cnf(211,negated_conjecture,
( esk6_0 = esk5_0
| ~ member(esk5_0,esk4_0)
| ~ member(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[114,203,theory(equality)]) ).
cnf(212,negated_conjecture,
( esk6_0 = esk5_0
| $false
| ~ member(esk6_0,esk4_0) ),
inference(rw,[status(thm)],[211,110,theory(equality)]) ).
cnf(213,negated_conjecture,
( esk6_0 = esk5_0
| $false
| $false ),
inference(rw,[status(thm)],[212,111,theory(equality)]) ).
cnf(214,negated_conjecture,
esk6_0 = esk5_0,
inference(cn,[status(thm)],[213,theory(equality)]) ).
cnf(215,negated_conjecture,
$false,
inference(sr,[status(thm)],[214,35,theory(equality)]) ).
cnf(216,negated_conjecture,
$false,
215,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET804+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmpseEQNZ/sel_SET804+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET804+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET804+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET804+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
%
%------------------------------------------------------------------------------