TSTP Solution File: SET803+4 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET803+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 03:40:30 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 186 ( 29 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 226 ( 82 ~; 82 |; 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 : 93 ( 2 sgn 56 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( max(X3,X1,X2)
<=> ( member(X3,X2)
& ! [X4] :
( ( member(X4,X2)
& apply(X1,X3,X4) )
=> X3 = X4 ) ) ),
file('/tmp/tmpqVfkts/sel_SET803+4.p_1',max) ).
fof(2,axiom,
! [X1,X2,X3] :
( greatest(X3,X1,X2)
<=> ( member(X3,X2)
& ! [X4] :
( member(X4,X2)
=> apply(X1,X4,X3) ) ) ),
file('/tmp/tmpqVfkts/sel_SET803+4.p_1',greatest) ).
fof(4,conjecture,
! [X1,X2] :
( order(X1,X2)
=> ! [X7,X8] :
( ( max(X7,X1,X2)
& max(X8,X1,X2)
& X7 != X8 )
=> ~ ? [X3] : greatest(X3,X1,X2) ) ),
file('/tmp/tmpqVfkts/sel_SET803+4.p_1',thIV15) ).
fof(5,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X7,X8] :
( ( max(X7,X1,X2)
& max(X8,X1,X2)
& X7 != X8 )
=> ~ ? [X3] : greatest(X3,X1,X2) ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(8,plain,
! [X1,X2,X3] :
( ( ~ max(X3,X1,X2)
| ( member(X3,X2)
& ! [X4] :
( ~ member(X4,X2)
| ~ apply(X1,X3,X4)
| X3 = X4 ) ) )
& ( ~ member(X3,X2)
| ? [X4] :
( member(X4,X2)
& apply(X1,X3,X4)
& X3 != X4 )
| max(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(9,plain,
! [X5,X6,X7] :
( ( ~ max(X7,X5,X6)
| ( member(X7,X6)
& ! [X8] :
( ~ member(X8,X6)
| ~ apply(X5,X7,X8)
| X7 = X8 ) ) )
& ( ~ member(X7,X6)
| ? [X9] :
( member(X9,X6)
& apply(X5,X7,X9)
& X7 != X9 )
| max(X7,X5,X6) ) ),
inference(variable_rename,[status(thm)],[8]) ).
fof(10,plain,
! [X5,X6,X7] :
( ( ~ max(X7,X5,X6)
| ( member(X7,X6)
& ! [X8] :
( ~ member(X8,X6)
| ~ apply(X5,X7,X8)
| X7 = X8 ) ) )
& ( ~ member(X7,X6)
| ( member(esk1_3(X5,X6,X7),X6)
& apply(X5,X7,esk1_3(X5,X6,X7))
& X7 != esk1_3(X5,X6,X7) )
| max(X7,X5,X6) ) ),
inference(skolemize,[status(esa)],[9]) ).
fof(11,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ member(X8,X6)
| ~ apply(X5,X7,X8)
| X7 = X8 )
& member(X7,X6) )
| ~ max(X7,X5,X6) )
& ( ~ member(X7,X6)
| ( member(esk1_3(X5,X6,X7),X6)
& apply(X5,X7,esk1_3(X5,X6,X7))
& X7 != esk1_3(X5,X6,X7) )
| max(X7,X5,X6) ) ),
inference(shift_quantors,[status(thm)],[10]) ).
fof(12,plain,
! [X5,X6,X7,X8] :
( ( ~ member(X8,X6)
| ~ apply(X5,X7,X8)
| X7 = X8
| ~ max(X7,X5,X6) )
& ( member(X7,X6)
| ~ max(X7,X5,X6) )
& ( member(esk1_3(X5,X6,X7),X6)
| ~ member(X7,X6)
| max(X7,X5,X6) )
& ( apply(X5,X7,esk1_3(X5,X6,X7))
| ~ member(X7,X6)
| max(X7,X5,X6) )
& ( X7 != esk1_3(X5,X6,X7)
| ~ member(X7,X6)
| max(X7,X5,X6) ) ),
inference(distribute,[status(thm)],[11]) ).
cnf(16,plain,
( member(X1,X3)
| ~ max(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(17,plain,
( X1 = X4
| ~ max(X1,X2,X3)
| ~ apply(X2,X1,X4)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[12]) ).
fof(18,plain,
! [X1,X2,X3] :
( ( ~ greatest(X3,X1,X2)
| ( member(X3,X2)
& ! [X4] :
( ~ member(X4,X2)
| apply(X1,X4,X3) ) ) )
& ( ~ member(X3,X2)
| ? [X4] :
( member(X4,X2)
& ~ apply(X1,X4,X3) )
| greatest(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(19,plain,
! [X5,X6,X7] :
( ( ~ greatest(X7,X5,X6)
| ( member(X7,X6)
& ! [X8] :
( ~ member(X8,X6)
| apply(X5,X8,X7) ) ) )
& ( ~ member(X7,X6)
| ? [X9] :
( member(X9,X6)
& ~ apply(X5,X9,X7) )
| greatest(X7,X5,X6) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,plain,
! [X5,X6,X7] :
( ( ~ greatest(X7,X5,X6)
| ( member(X7,X6)
& ! [X8] :
( ~ member(X8,X6)
| apply(X5,X8,X7) ) ) )
& ( ~ member(X7,X6)
| ( member(esk2_3(X5,X6,X7),X6)
& ~ apply(X5,esk2_3(X5,X6,X7),X7) )
| greatest(X7,X5,X6) ) ),
inference(skolemize,[status(esa)],[19]) ).
fof(21,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ member(X8,X6)
| apply(X5,X8,X7) )
& member(X7,X6) )
| ~ greatest(X7,X5,X6) )
& ( ~ member(X7,X6)
| ( member(esk2_3(X5,X6,X7),X6)
& ~ apply(X5,esk2_3(X5,X6,X7),X7) )
| greatest(X7,X5,X6) ) ),
inference(shift_quantors,[status(thm)],[20]) ).
fof(22,plain,
! [X5,X6,X7,X8] :
( ( ~ member(X8,X6)
| apply(X5,X8,X7)
| ~ greatest(X7,X5,X6) )
& ( member(X7,X6)
| ~ greatest(X7,X5,X6) )
& ( member(esk2_3(X5,X6,X7),X6)
| ~ member(X7,X6)
| greatest(X7,X5,X6) )
& ( ~ apply(X5,esk2_3(X5,X6,X7),X7)
| ~ member(X7,X6)
| greatest(X7,X5,X6) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(25,plain,
( member(X1,X3)
| ~ greatest(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(26,plain,
( apply(X2,X4,X1)
| ~ greatest(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(31,negated_conjecture,
? [X1,X2] :
( order(X1,X2)
& ? [X7,X8] :
( max(X7,X1,X2)
& max(X8,X1,X2)
& X7 != X8
& ? [X3] : greatest(X3,X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,negated_conjecture,
? [X9,X10] :
( order(X9,X10)
& ? [X11,X12] :
( max(X11,X9,X10)
& max(X12,X9,X10)
& X11 != X12
& ? [X13] : greatest(X13,X9,X10) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( order(esk3_0,esk4_0)
& max(esk5_0,esk3_0,esk4_0)
& max(esk6_0,esk3_0,esk4_0)
& esk5_0 != esk6_0
& greatest(esk7_0,esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
greatest(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,
max(esk6_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(37,negated_conjecture,
max(esk5_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(109,negated_conjecture,
member(esk5_0,esk4_0),
inference(spm,[status(thm)],[16,37,theory(equality)]) ).
cnf(110,negated_conjecture,
member(esk6_0,esk4_0),
inference(spm,[status(thm)],[16,36,theory(equality)]) ).
cnf(111,negated_conjecture,
member(esk7_0,esk4_0),
inference(spm,[status(thm)],[25,34,theory(equality)]) ).
cnf(112,negated_conjecture,
( apply(esk3_0,X1,esk7_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[26,34,theory(equality)]) ).
cnf(213,negated_conjecture,
( X1 = esk7_0
| ~ member(esk7_0,X2)
| ~ max(X1,esk3_0,X2)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[17,112,theory(equality)]) ).
cnf(227,negated_conjecture,
( esk5_0 = esk7_0
| ~ member(esk7_0,esk4_0)
| ~ member(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[213,37,theory(equality)]) ).
cnf(229,negated_conjecture,
( esk5_0 = esk7_0
| $false
| ~ member(esk5_0,esk4_0) ),
inference(rw,[status(thm)],[227,111,theory(equality)]) ).
cnf(230,negated_conjecture,
( esk5_0 = esk7_0
| $false
| $false ),
inference(rw,[status(thm)],[229,109,theory(equality)]) ).
cnf(231,negated_conjecture,
esk5_0 = esk7_0,
inference(cn,[status(thm)],[230,theory(equality)]) ).
cnf(238,negated_conjecture,
( X1 = esk5_0
| ~ member(esk7_0,X2)
| ~ member(X1,esk4_0)
| ~ max(X1,esk3_0,X2) ),
inference(rw,[status(thm)],[213,231,theory(equality)]) ).
cnf(239,negated_conjecture,
( X1 = esk5_0
| ~ member(esk5_0,X2)
| ~ member(X1,esk4_0)
| ~ max(X1,esk3_0,X2) ),
inference(rw,[status(thm)],[238,231,theory(equality)]) ).
cnf(248,negated_conjecture,
( esk6_0 = esk5_0
| ~ member(esk5_0,esk4_0)
| ~ member(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[239,36,theory(equality)]) ).
cnf(249,negated_conjecture,
( esk6_0 = esk5_0
| $false
| ~ member(esk6_0,esk4_0) ),
inference(rw,[status(thm)],[248,109,theory(equality)]) ).
cnf(250,negated_conjecture,
( esk6_0 = esk5_0
| $false
| $false ),
inference(rw,[status(thm)],[249,110,theory(equality)]) ).
cnf(251,negated_conjecture,
esk6_0 = esk5_0,
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(252,negated_conjecture,
$false,
inference(sr,[status(thm)],[251,35,theory(equality)]) ).
cnf(253,negated_conjecture,
$false,
252,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET803+4.p
% --creating new selector for [SET006+3.ax]
% -running prover on /tmp/tmpqVfkts/sel_SET803+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET803+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET803+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET803+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
%
%------------------------------------------------------------------------------