TSTP Solution File: SET793+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET793+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 03:39:39 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of formulae : 56 ( 11 unt; 0 def)
% Number of atoms : 271 ( 18 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 329 ( 114 ~; 134 |; 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 : 115 ( 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/tmpQHhoWH/sel_SET793+4.p_1',total_order) ).
fof(2,axiom,
! [X1,X2,X5] :
( max(X5,X1,X2)
<=> ( member(X5,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X5,X3) )
=> X5 = X3 ) ) ),
file('/tmp/tmpQHhoWH/sel_SET793+4.p_1',max) ).
fof(3,axiom,
! [X1,X2,X5] :
( greatest(X5,X1,X2)
<=> ( member(X5,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X5) ) ) ),
file('/tmp/tmpQHhoWH/sel_SET793+4.p_1',greatest) ).
fof(5,conjecture,
! [X1,X2,X5] :
( ( total_order(X1,X2)
& max(X5,X1,X2) )
=> greatest(X5,X1,X2) ),
file('/tmp/tmpQHhoWH/sel_SET793+4.p_1',thIV5) ).
fof(6,negated_conjecture,
~ ! [X1,X2,X5] :
( ( total_order(X1,X2)
& max(X5,X1,X2) )
=> greatest(X5,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(20,plain,
! [X1,X2,X5] :
( ( ~ max(X5,X1,X2)
| ( member(X5,X2)
& ! [X3] :
( ~ member(X3,X2)
| ~ apply(X1,X5,X3)
| X5 = X3 ) ) )
& ( ~ member(X5,X2)
| ? [X3] :
( member(X3,X2)
& apply(X1,X5,X3)
& X5 != X3 )
| max(X5,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(21,plain,
! [X6,X7,X8] :
( ( ~ max(X8,X6,X7)
| ( member(X8,X7)
& ! [X9] :
( ~ member(X9,X7)
| ~ apply(X6,X8,X9)
| X8 = X9 ) ) )
& ( ~ member(X8,X7)
| ? [X10] :
( member(X10,X7)
& apply(X6,X8,X10)
& X8 != X10 )
| max(X8,X6,X7) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X6,X7,X8] :
( ( ~ max(X8,X6,X7)
| ( member(X8,X7)
& ! [X9] :
( ~ member(X9,X7)
| ~ apply(X6,X8,X9)
| X8 = X9 ) ) )
& ( ~ member(X8,X7)
| ( member(esk3_3(X6,X7,X8),X7)
& apply(X6,X8,esk3_3(X6,X7,X8))
& X8 != esk3_3(X6,X7,X8) )
| max(X8,X6,X7) ) ),
inference(skolemize,[status(esa)],[21]) ).
fof(23,plain,
! [X6,X7,X8,X9] :
( ( ( ( ~ member(X9,X7)
| ~ apply(X6,X8,X9)
| X8 = X9 )
& member(X8,X7) )
| ~ max(X8,X6,X7) )
& ( ~ member(X8,X7)
| ( member(esk3_3(X6,X7,X8),X7)
& apply(X6,X8,esk3_3(X6,X7,X8))
& X8 != esk3_3(X6,X7,X8) )
| max(X8,X6,X7) ) ),
inference(shift_quantors,[status(thm)],[22]) ).
fof(24,plain,
! [X6,X7,X8,X9] :
( ( ~ member(X9,X7)
| ~ apply(X6,X8,X9)
| X8 = X9
| ~ max(X8,X6,X7) )
& ( member(X8,X7)
| ~ max(X8,X6,X7) )
& ( member(esk3_3(X6,X7,X8),X7)
| ~ member(X8,X7)
| max(X8,X6,X7) )
& ( apply(X6,X8,esk3_3(X6,X7,X8))
| ~ member(X8,X7)
| max(X8,X6,X7) )
& ( X8 != esk3_3(X6,X7,X8)
| ~ member(X8,X7)
| max(X8,X6,X7) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(28,plain,
( member(X1,X3)
| ~ max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(29,plain,
( X1 = X4
| ~ max(X1,X2,X3)
| ~ apply(X2,X1,X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(30,plain,
! [X1,X2,X5] :
( ( ~ greatest(X5,X1,X2)
| ( member(X5,X2)
& ! [X3] :
( ~ member(X3,X2)
| apply(X1,X3,X5) ) ) )
& ( ~ member(X5,X2)
| ? [X3] :
( member(X3,X2)
& ~ apply(X1,X3,X5) )
| greatest(X5,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(31,plain,
! [X6,X7,X8] :
( ( ~ greatest(X8,X6,X7)
| ( member(X8,X7)
& ! [X9] :
( ~ member(X9,X7)
| apply(X6,X9,X8) ) ) )
& ( ~ member(X8,X7)
| ? [X10] :
( member(X10,X7)
& ~ apply(X6,X10,X8) )
| greatest(X8,X6,X7) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X6,X7,X8] :
( ( ~ greatest(X8,X6,X7)
| ( member(X8,X7)
& ! [X9] :
( ~ member(X9,X7)
| apply(X6,X9,X8) ) ) )
& ( ~ member(X8,X7)
| ( member(esk4_3(X6,X7,X8),X7)
& ~ apply(X6,esk4_3(X6,X7,X8),X8) )
| greatest(X8,X6,X7) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X6,X7,X8,X9] :
( ( ( ( ~ member(X9,X7)
| apply(X6,X9,X8) )
& member(X8,X7) )
| ~ greatest(X8,X6,X7) )
& ( ~ member(X8,X7)
| ( member(esk4_3(X6,X7,X8),X7)
& ~ apply(X6,esk4_3(X6,X7,X8),X8) )
| greatest(X8,X6,X7) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X6,X7,X8,X9] :
( ( ~ member(X9,X7)
| apply(X6,X9,X8)
| ~ greatest(X8,X6,X7) )
& ( member(X8,X7)
| ~ greatest(X8,X6,X7) )
& ( member(esk4_3(X6,X7,X8),X7)
| ~ member(X8,X7)
| greatest(X8,X6,X7) )
& ( ~ apply(X6,esk4_3(X6,X7,X8),X8)
| ~ member(X8,X7)
| greatest(X8,X6,X7) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( greatest(X1,X2,X3)
| ~ member(X1,X3)
| ~ apply(X2,esk4_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( greatest(X1,X2,X3)
| member(esk4_3(X2,X3,X1),X3)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(43,negated_conjecture,
? [X1,X2,X5] :
( total_order(X1,X2)
& max(X5,X1,X2)
& ~ greatest(X5,X1,X2) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(44,negated_conjecture,
? [X6,X7,X8] :
( total_order(X6,X7)
& max(X8,X6,X7)
& ~ greatest(X8,X6,X7) ),
inference(variable_rename,[status(thm)],[43]) ).
fof(45,negated_conjecture,
( total_order(esk5_0,esk6_0)
& max(esk7_0,esk5_0,esk6_0)
& ~ greatest(esk7_0,esk5_0,esk6_0) ),
inference(skolemize,[status(esa)],[44]) ).
cnf(46,negated_conjecture,
~ greatest(esk7_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[45]) ).
cnf(47,negated_conjecture,
max(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)],[28,47,theory(equality)]) ).
cnf(120,negated_conjecture,
( esk7_0 = X1
| ~ apply(esk5_0,esk7_0,X1)
| ~ member(X1,esk6_0) ),
inference(spm,[status(thm)],[29,47,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(233,negated_conjecture,
( apply(esk5_0,esk4_3(X1,esk6_0,X2),esk7_0)
| apply(esk5_0,esk7_0,esk4_3(X1,esk6_0,X2))
| greatest(X2,X1,esk6_0)
| ~ member(X2,esk6_0) ),
inference(spm,[status(thm)],[214,36,theory(equality)]) ).
cnf(298,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| apply(esk5_0,esk7_0,esk4_3(esk5_0,esk6_0,esk7_0))
| ~ member(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[35,233,theory(equality)]) ).
cnf(301,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| apply(esk5_0,esk7_0,esk4_3(esk5_0,esk6_0,esk7_0))
| $false ),
inference(rw,[status(thm)],[298,117,theory(equality)]) ).
cnf(302,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| apply(esk5_0,esk7_0,esk4_3(esk5_0,esk6_0,esk7_0)) ),
inference(cn,[status(thm)],[301,theory(equality)]) ).
cnf(303,negated_conjecture,
apply(esk5_0,esk7_0,esk4_3(esk5_0,esk6_0,esk7_0)),
inference(sr,[status(thm)],[302,46,theory(equality)]) ).
cnf(306,negated_conjecture,
( esk7_0 = esk4_3(esk5_0,esk6_0,esk7_0)
| ~ member(esk4_3(esk5_0,esk6_0,esk7_0),esk6_0) ),
inference(spm,[status(thm)],[120,303,theory(equality)]) ).
cnf(307,negated_conjecture,
( esk4_3(esk5_0,esk6_0,esk7_0) = esk7_0
| greatest(esk7_0,esk5_0,esk6_0)
| ~ member(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[306,36,theory(equality)]) ).
cnf(308,negated_conjecture,
( esk4_3(esk5_0,esk6_0,esk7_0) = esk7_0
| greatest(esk7_0,esk5_0,esk6_0)
| $false ),
inference(rw,[status(thm)],[307,117,theory(equality)]) ).
cnf(309,negated_conjecture,
( esk4_3(esk5_0,esk6_0,esk7_0) = esk7_0
| greatest(esk7_0,esk5_0,esk6_0) ),
inference(cn,[status(thm)],[308,theory(equality)]) ).
cnf(310,negated_conjecture,
esk4_3(esk5_0,esk6_0,esk7_0) = esk7_0,
inference(sr,[status(thm)],[309,46,theory(equality)]) ).
cnf(331,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| ~ apply(esk5_0,esk7_0,esk7_0)
| ~ member(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[35,310,theory(equality)]) ).
cnf(332,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| apply(esk5_0,esk7_0,esk7_0)
| ~ member(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[233,310,theory(equality)]) ).
cnf(340,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| ~ apply(esk5_0,esk7_0,esk7_0)
| $false ),
inference(rw,[status(thm)],[331,117,theory(equality)]) ).
cnf(341,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| ~ apply(esk5_0,esk7_0,esk7_0) ),
inference(cn,[status(thm)],[340,theory(equality)]) ).
cnf(342,negated_conjecture,
~ apply(esk5_0,esk7_0,esk7_0),
inference(sr,[status(thm)],[341,46,theory(equality)]) ).
cnf(343,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| apply(esk5_0,esk7_0,esk7_0)
| $false ),
inference(rw,[status(thm)],[332,117,theory(equality)]) ).
cnf(344,negated_conjecture,
( greatest(esk7_0,esk5_0,esk6_0)
| apply(esk5_0,esk7_0,esk7_0) ),
inference(cn,[status(thm)],[343,theory(equality)]) ).
cnf(345,negated_conjecture,
apply(esk5_0,esk7_0,esk7_0),
inference(sr,[status(thm)],[344,46,theory(equality)]) ).
cnf(349,negated_conjecture,
$false,
inference(rw,[status(thm)],[342,345,theory(equality)]) ).
cnf(350,negated_conjecture,
$false,
inference(cn,[status(thm)],[349,theory(equality)]) ).
cnf(351,negated_conjecture,
$false,
350,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET793+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmpQHhoWH/sel_SET793+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET793+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET793+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET793+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
%
%------------------------------------------------------------------------------