%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET794+4 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:39:46 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 261 ( 19 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 324 ( 112 ~; 131 |; 73 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 119 ( 1 sgn 78 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( total_order(X1,X2)
<=> ( order(X1,X2)
& ! [X3,X4] :
( ( member(X3,X2)
& member(X4,X2) )
=> ( apply(X1,X3,X4)
| apply(X1,X4,X3) ) ) ) ),
file('/tmp/tmpEbsFKv/sel_SET794+4.p_1',total_order) ).
fof(3,axiom,
! [X1,X2,X6] :
( least(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X6,X3) ) ) ),
file('/tmp/tmpEbsFKv/sel_SET794+4.p_1',least) ).
fof(4,axiom,
! [X1,X2,X6] :
( min(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X3,X6) )
=> X6 = X3 ) ) ),
file('/tmp/tmpEbsFKv/sel_SET794+4.p_1',min) ).
fof(5,conjecture,
! [X1,X2,X6] :
( ( total_order(X1,X2)
& min(X6,X1,X2) )
=> least(X6,X1,X2) ),
file('/tmp/tmpEbsFKv/sel_SET794+4.p_1',thIV6) ).
fof(6,negated_conjecture,
~ ! [X1,X2,X6] :
( ( total_order(X1,X2)
& min(X6,X1,X2) )
=> least(X6,X1,X2) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(9,plain,
! [X1,X2] :
( ( ~ total_order(X1,X2)
| ( order(X1,X2)
& ! [X3,X4] :
( ~ member(X3,X2)
| ~ member(X4,X2)
| apply(X1,X3,X4)
| apply(X1,X4,X3) ) ) )
& ( ~ order(X1,X2)
| ? [X3,X4] :
( member(X3,X2)
& member(X4,X2)
& ~ apply(X1,X3,X4)
& ~ apply(X1,X4,X3) )
| total_order(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(10,plain,
! [X5,X6] :
( ( ~ total_order(X5,X6)
| ( order(X5,X6)
& ! [X7,X8] :
( ~ member(X7,X6)
| ~ member(X8,X6)
| apply(X5,X7,X8)
| apply(X5,X8,X7) ) ) )
& ( ~ order(X5,X6)
| ? [X9,X10] :
( member(X9,X6)
& member(X10,X6)
& ~ apply(X5,X9,X10)
& ~ apply(X5,X10,X9) )
| total_order(X5,X6) ) ),
inference(variable_rename,[status(thm)],[9]) ).
fof(11,plain,
! [X5,X6] :
( ( ~ total_order(X5,X6)
| ( order(X5,X6)
& ! [X7,X8] :
( ~ member(X7,X6)
| ~ member(X8,X6)
| apply(X5,X7,X8)
| apply(X5,X8,X7) ) ) )
& ( ~ order(X5,X6)
| ( member(esk1_2(X5,X6),X6)
& member(esk2_2(X5,X6),X6)
& ~ apply(X5,esk1_2(X5,X6),esk2_2(X5,X6))
& ~ apply(X5,esk2_2(X5,X6),esk1_2(X5,X6)) )
| total_order(X5,X6) ) ),
inference(skolemize,[status(esa)],[10]) ).
fof(12,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ member(X7,X6)
| ~ member(X8,X6)
| apply(X5,X7,X8)
| apply(X5,X8,X7) )
& order(X5,X6) )
| ~ total_order(X5,X6) )
& ( ~ order(X5,X6)
| ( member(esk1_2(X5,X6),X6)
& member(esk2_2(X5,X6),X6)
& ~ apply(X5,esk1_2(X5,X6),esk2_2(X5,X6))
& ~ apply(X5,esk2_2(X5,X6),esk1_2(X5,X6)) )
| total_order(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[11]) ).
fof(13,plain,
! [X5,X6,X7,X8] :
( ( ~ member(X7,X6)
| ~ member(X8,X6)
| apply(X5,X7,X8)
| apply(X5,X8,X7)
| ~ total_order(X5,X6) )
& ( order(X5,X6)
| ~ total_order(X5,X6) )
& ( member(esk1_2(X5,X6),X6)
| ~ order(X5,X6)
| total_order(X5,X6) )
& ( member(esk2_2(X5,X6),X6)
| ~ order(X5,X6)
| total_order(X5,X6) )
& ( ~ apply(X5,esk1_2(X5,X6),esk2_2(X5,X6))
| ~ order(X5,X6)
| total_order(X5,X6) )
& ( ~ apply(X5,esk2_2(X5,X6),esk1_2(X5,X6))
| ~ order(X5,X6)
| total_order(X5,X6) ) ),
inference(distribute,[status(thm)],[12]) ).
cnf(19,plain,
( apply(X1,X3,X4)
| apply(X1,X4,X3)
| ~ total_order(X1,X2)
| ~ member(X3,X2)
| ~ member(X4,X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(24,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)],[3]) ).
fof(25,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)],[24]) ).
fof(26,plain,
! [X7,X8,X9] :
( ( ~ least(X9,X7,X8)
| ( member(X9,X8)
& ! [X10] :
( ~ member(X10,X8)
| apply(X7,X9,X10) ) ) )
& ( ~ member(X9,X8)
| ( member(esk3_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk3_3(X7,X8,X9)) )
| least(X9,X7,X8) ) ),
inference(skolemize,[status(esa)],[25]) ).
fof(27,plain,
! [X7,X8,X9,X10] :
( ( ( ( ~ member(X10,X8)
| apply(X7,X9,X10) )
& member(X9,X8) )
| ~ least(X9,X7,X8) )
& ( ~ member(X9,X8)
| ( member(esk3_3(X7,X8,X9),X8)
& ~ apply(X7,X9,esk3_3(X7,X8,X9)) )
| least(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[26]) ).
fof(28,plain,
! [X7,X8,X9,X10] :
( ( ~ member(X10,X8)
| apply(X7,X9,X10)
| ~ least(X9,X7,X8) )
& ( member(X9,X8)
| ~ least(X9,X7,X8) )
& ( member(esk3_3(X7,X8,X9),X8)
| ~ member(X9,X8)
| least(X9,X7,X8) )
& ( ~ apply(X7,X9,esk3_3(X7,X8,X9))
| ~ member(X9,X8)
| least(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[27]) ).
cnf(29,plain,
( least(X1,X2,X3)
| ~ member(X1,X3)
| ~ apply(X2,X1,esk3_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,plain,
( least(X1,X2,X3)
| member(esk3_3(X2,X3,X1),X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(33,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)],[4]) ).
fof(34,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)],[33]) ).
fof(35,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(esk4_3(X7,X8,X9),X8)
& apply(X7,esk4_3(X7,X8,X9),X9)
& X9 != esk4_3(X7,X8,X9) )
| min(X9,X7,X8) ) ),
inference(skolemize,[status(esa)],[34]) ).
fof(36,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(esk4_3(X7,X8,X9),X8)
& apply(X7,esk4_3(X7,X8,X9),X9)
& X9 != esk4_3(X7,X8,X9) )
| min(X9,X7,X8) ) ),
inference(shift_quantors,[status(thm)],[35]) ).
fof(37,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(esk4_3(X7,X8,X9),X8)
| ~ member(X9,X8)
| min(X9,X7,X8) )
& ( apply(X7,esk4_3(X7,X8,X9),X9)
| ~ member(X9,X8)
| min(X9,X7,X8) )
& ( X9 != esk4_3(X7,X8,X9)
| ~ member(X9,X8)
| min(X9,X7,X8) ) ),
inference(distribute,[status(thm)],[36]) ).
cnf(41,plain,
( member(X1,X3)
| ~ min(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(42,plain,
( X1 = X4
| ~ min(X1,X2,X3)
| ~ apply(X2,X4,X1)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(43,negated_conjecture,
? [X1,X2,X6] :
( total_order(X1,X2)
& min(X6,X1,X2)
& ~ least(X6,X1,X2) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(44,negated_conjecture,
? [X7,X8,X9] :
( total_order(X7,X8)
& min(X9,X7,X8)
& ~ least(X9,X7,X8) ),
inference(variable_rename,[status(thm)],[43]) ).
fof(45,negated_conjecture,
( total_order(esk5_0,esk6_0)
& min(esk7_0,esk5_0,esk6_0)
& ~ least(esk7_0,esk5_0,esk6_0) ),
inference(skolemize,[status(esa)],[44]) ).
cnf(46,negated_conjecture,
~ least(esk7_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(47,negated_conjecture,
min(esk7_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(48,negated_conjecture,
total_order(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(117,negated_conjecture,
member(esk7_0,esk6_0),
inference(spm,[status(thm)],[41,47,theory(equality)]) ).
cnf(120,negated_conjecture,
( esk7_0 = X1
| ~ apply(esk5_0,X1,esk7_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[42,47,theory(equality)]) ).
cnf(200,negated_conjecture,
( apply(X1,X2,esk7_0)
| apply(X1,esk7_0,X2)
| ~ member(X2,esk6_0)
| ~ total_order(X1,esk6_0) ),
inference(spm,[status(thm)],[19,117,theory(equality)]) ).
cnf(214,negated_conjecture,
( apply(esk5_0,esk7_0,X1)
| apply(esk5_0,X1,esk7_0)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[200,48,theory(equality)]) ).
cnf(229,negated_conjecture,
apply(esk5_0,esk7_0,esk7_0),
inference(spm,[status(thm)],[214,117,theory(equality)]) ).
cnf(232,negated_conjecture,
( apply(esk5_0,esk3_3(X1,esk6_0,X2),esk7_0)
| apply(esk5_0,esk7_0,esk3_3(X1,esk6_0,X2))
| least(X2,X1,esk6_0)
| ~ member(X2,esk6_0) ),
inference(spm,[status(thm)],[214,30,theory(equality)]) ).
cnf(356,negated_conjecture,
( esk7_0 = esk3_3(X1,esk6_0,X2)
| least(X2,X1,esk6_0)
| apply(esk5_0,esk7_0,esk3_3(X1,esk6_0,X2))
| ~ member(esk3_3(X1,esk6_0,X2),esk6_0)
| ~ member(X2,esk6_0) ),
inference(spm,[status(thm)],[120,232,theory(equality)]) ).
cnf(412,negated_conjecture,
( esk3_3(X1,esk6_0,X2) = esk7_0
| least(X2,X1,esk6_0)
| apply(esk5_0,esk7_0,esk3_3(X1,esk6_0,X2))
| ~ member(X2,esk6_0) ),
inference(csr,[status(thm)],[356,30]) ).
cnf(413,negated_conjecture,
( least(esk7_0,esk5_0,esk6_0)
| esk3_3(esk5_0,esk6_0,esk7_0) = esk7_0
| ~ member(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[29,412,theory(equality)]) ).
cnf(416,negated_conjecture,
( least(esk7_0,esk5_0,esk6_0)
| esk3_3(esk5_0,esk6_0,esk7_0) = esk7_0
| $false ),
inference(rw,[status(thm)],[413,117,theory(equality)]) ).
cnf(417,negated_conjecture,
( least(esk7_0,esk5_0,esk6_0)
| esk3_3(esk5_0,esk6_0,esk7_0) = esk7_0 ),
inference(cn,[status(thm)],[416,theory(equality)]) ).
cnf(418,negated_conjecture,
esk3_3(esk5_0,esk6_0,esk7_0) = esk7_0,
inference(sr,[status(thm)],[417,46,theory(equality)]) ).
cnf(420,negated_conjecture,
( least(esk7_0,esk5_0,esk6_0)
| ~ apply(esk5_0,esk7_0,esk7_0)
| ~ member(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[29,418,theory(equality)]) ).
cnf(426,negated_conjecture,
( least(esk7_0,esk5_0,esk6_0)
| $false
| ~ member(esk7_0,esk6_0) ),
inference(rw,[status(thm)],[420,229,theory(equality)]) ).
cnf(427,negated_conjecture,
( least(esk7_0,esk5_0,esk6_0)
| $false
| $false ),
inference(rw,[status(thm)],[426,117,theory(equality)]) ).
cnf(428,negated_conjecture,
least(esk7_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[427,theory(equality)]) ).
cnf(429,negated_conjecture,
$false,
inference(sr,[status(thm)],[428,46,theory(equality)]) ).
cnf(430,negated_conjecture,
$false,
429,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET794+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmpEbsFKv/sel_SET794+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET794+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET794+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET794+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
%
%------------------------------------------------------------------------------