TSTP Solution File: ALG227+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG227+1 : TPTP v5.0.0. Released v3.4.0.
% 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 : Sat Dec 25 04:44:59 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 214 ( 66 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 255 ( 91 ~; 89 |; 52 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 56 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
file('/tmp/tmpdHza_a/sel_ALG227+1.p_1',d3_closure3) ).
fof(4,axiom,
? [X1] :
( v1_xboole_0(X1)
& v1_relat_1(X1)
& v1_funct_1(X1)
& v2_funct_1(X1)
& v1_finset_1(X1)
& v1_fraenkel(X1) ),
file('/tmp/tmpdHza_a/sel_ALG227+1.p_1',rc1_closure2) ).
fof(10,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_pboole(X3,X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,X2)
& X1 = X4
& k1_funct_1(X3,X4) != k1_xboole_0 ) ) ),
file('/tmp/tmpdHza_a/sel_ALG227+1.p_1',fraenkel_a_2_0_closure3) ).
fof(22,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
file('/tmp/tmpdHza_a/sel_ALG227+1.p_1',t8_closure3) ).
fof(26,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/tmp/tmpdHza_a/sel_ALG227+1.p_1',t6_boole) ).
fof(30,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
inference(assume_negation,[status(cth)],[22]) ).
fof(31,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(33,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_pboole(X3,X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( m1_subset_1(X4,X2)
& X1 = X4
& k1_funct_1(X3,X4) != k1_xboole_0 ) ) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(36,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,X1)
=> ( ~ r2_hidden(X3,k1_closure3(X1,X2))
=> k1_funct_1(X2,X3) = k1_xboole_0 ) ) ) ),
inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).
fof(40,plain,
! [X1] :
( v1_xboole_0(X1)
| ! [X2] :
( ~ m1_pboole(X2,X1)
| ! [X3] :
( ( X3 != k1_closure3(X1,X2)
| X3 = a_2_0_closure3(X1,X2) )
& ( X3 != a_2_0_closure3(X1,X2)
| X3 = k1_closure3(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(41,plain,
! [X4] :
( v1_xboole_0(X4)
| ! [X5] :
( ~ m1_pboole(X5,X4)
| ! [X6] :
( ( X6 != k1_closure3(X4,X5)
| X6 = a_2_0_closure3(X4,X5) )
& ( X6 != a_2_0_closure3(X4,X5)
| X6 = k1_closure3(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,plain,
! [X4,X5,X6] :
( ( ( X6 != k1_closure3(X4,X5)
| X6 = a_2_0_closure3(X4,X5) )
& ( X6 != a_2_0_closure3(X4,X5)
| X6 = k1_closure3(X4,X5) ) )
| ~ m1_pboole(X5,X4)
| v1_xboole_0(X4) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X4,X5,X6] :
( ( X6 != k1_closure3(X4,X5)
| X6 = a_2_0_closure3(X4,X5)
| ~ m1_pboole(X5,X4)
| v1_xboole_0(X4) )
& ( X6 != a_2_0_closure3(X4,X5)
| X6 = k1_closure3(X4,X5)
| ~ m1_pboole(X5,X4)
| v1_xboole_0(X4) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(44,plain,
( v1_xboole_0(X1)
| X3 = k1_closure3(X1,X2)
| ~ m1_pboole(X2,X1)
| X3 != a_2_0_closure3(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(49,plain,
? [X2] :
( v1_xboole_0(X2)
& v1_relat_1(X2)
& v1_funct_1(X2)
& v2_funct_1(X2)
& v1_finset_1(X2)
& v1_fraenkel(X2) ),
inference(variable_rename,[status(thm)],[4]) ).
fof(50,plain,
( v1_xboole_0(esk2_0)
& v1_relat_1(esk2_0)
& v1_funct_1(esk2_0)
& v2_funct_1(esk2_0)
& v1_finset_1(esk2_0)
& v1_fraenkel(esk2_0) ),
inference(skolemize,[status(esa)],[49]) ).
cnf(56,plain,
v1_xboole_0(esk2_0),
inference(split_conjunct,[status(thm)],[50]) ).
fof(75,plain,
! [X1,X2,X3] :
( v1_xboole_0(X2)
| ~ m1_pboole(X3,X2)
| ( ( ~ r2_hidden(X1,a_2_0_closure3(X2,X3))
| ? [X4] :
( m1_subset_1(X4,X2)
& X1 = X4
& k1_funct_1(X3,X4) != k1_xboole_0 ) )
& ( ! [X4] :
( ~ m1_subset_1(X4,X2)
| X1 != X4
| k1_funct_1(X3,X4) = k1_xboole_0 )
| r2_hidden(X1,a_2_0_closure3(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(76,plain,
! [X5,X6,X7] :
( v1_xboole_0(X6)
| ~ m1_pboole(X7,X6)
| ( ( ~ r2_hidden(X5,a_2_0_closure3(X6,X7))
| ? [X8] :
( m1_subset_1(X8,X6)
& X5 = X8
& k1_funct_1(X7,X8) != k1_xboole_0 ) )
& ( ! [X9] :
( ~ m1_subset_1(X9,X6)
| X5 != X9
| k1_funct_1(X7,X9) = k1_xboole_0 )
| r2_hidden(X5,a_2_0_closure3(X6,X7)) ) ) ),
inference(variable_rename,[status(thm)],[75]) ).
fof(77,plain,
! [X5,X6,X7] :
( v1_xboole_0(X6)
| ~ m1_pboole(X7,X6)
| ( ( ~ r2_hidden(X5,a_2_0_closure3(X6,X7))
| ( m1_subset_1(esk5_3(X5,X6,X7),X6)
& X5 = esk5_3(X5,X6,X7)
& k1_funct_1(X7,esk5_3(X5,X6,X7)) != k1_xboole_0 ) )
& ( ! [X9] :
( ~ m1_subset_1(X9,X6)
| X5 != X9
| k1_funct_1(X7,X9) = k1_xboole_0 )
| r2_hidden(X5,a_2_0_closure3(X6,X7)) ) ) ),
inference(skolemize,[status(esa)],[76]) ).
fof(78,plain,
! [X5,X6,X7,X9] :
( ( ( ~ m1_subset_1(X9,X6)
| X5 != X9
| k1_funct_1(X7,X9) = k1_xboole_0
| r2_hidden(X5,a_2_0_closure3(X6,X7)) )
& ( ~ r2_hidden(X5,a_2_0_closure3(X6,X7))
| ( m1_subset_1(esk5_3(X5,X6,X7),X6)
& X5 = esk5_3(X5,X6,X7)
& k1_funct_1(X7,esk5_3(X5,X6,X7)) != k1_xboole_0 ) ) )
| v1_xboole_0(X6)
| ~ m1_pboole(X7,X6) ),
inference(shift_quantors,[status(thm)],[77]) ).
fof(79,plain,
! [X5,X6,X7,X9] :
( ( ~ m1_subset_1(X9,X6)
| X5 != X9
| k1_funct_1(X7,X9) = k1_xboole_0
| r2_hidden(X5,a_2_0_closure3(X6,X7))
| v1_xboole_0(X6)
| ~ m1_pboole(X7,X6) )
& ( m1_subset_1(esk5_3(X5,X6,X7),X6)
| ~ r2_hidden(X5,a_2_0_closure3(X6,X7))
| v1_xboole_0(X6)
| ~ m1_pboole(X7,X6) )
& ( X5 = esk5_3(X5,X6,X7)
| ~ r2_hidden(X5,a_2_0_closure3(X6,X7))
| v1_xboole_0(X6)
| ~ m1_pboole(X7,X6) )
& ( k1_funct_1(X7,esk5_3(X5,X6,X7)) != k1_xboole_0
| ~ r2_hidden(X5,a_2_0_closure3(X6,X7))
| v1_xboole_0(X6)
| ~ m1_pboole(X7,X6) ) ),
inference(distribute,[status(thm)],[78]) ).
cnf(83,plain,
( v1_xboole_0(X2)
| r2_hidden(X3,a_2_0_closure3(X2,X1))
| k1_funct_1(X1,X4) = k1_xboole_0
| ~ m1_pboole(X1,X2)
| X3 != X4
| ~ m1_subset_1(X4,X2) ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(120,negated_conjecture,
? [X1] :
( ~ v1_xboole_0(X1)
& ? [X2] :
( m1_pboole(X2,X1)
& ? [X3] :
( m1_subset_1(X3,X1)
& ~ r2_hidden(X3,k1_closure3(X1,X2))
& k1_funct_1(X2,X3) != k1_xboole_0 ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(121,negated_conjecture,
? [X4] :
( ~ v1_xboole_0(X4)
& ? [X5] :
( m1_pboole(X5,X4)
& ? [X6] :
( m1_subset_1(X6,X4)
& ~ r2_hidden(X6,k1_closure3(X4,X5))
& k1_funct_1(X5,X6) != k1_xboole_0 ) ) ),
inference(variable_rename,[status(thm)],[120]) ).
fof(122,negated_conjecture,
( ~ v1_xboole_0(esk9_0)
& m1_pboole(esk10_0,esk9_0)
& m1_subset_1(esk11_0,esk9_0)
& ~ r2_hidden(esk11_0,k1_closure3(esk9_0,esk10_0))
& k1_funct_1(esk10_0,esk11_0) != k1_xboole_0 ),
inference(skolemize,[status(esa)],[121]) ).
cnf(123,negated_conjecture,
k1_funct_1(esk10_0,esk11_0) != k1_xboole_0,
inference(split_conjunct,[status(thm)],[122]) ).
cnf(124,negated_conjecture,
~ r2_hidden(esk11_0,k1_closure3(esk9_0,esk10_0)),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(125,negated_conjecture,
m1_subset_1(esk11_0,esk9_0),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(126,negated_conjecture,
m1_pboole(esk10_0,esk9_0),
inference(split_conjunct,[status(thm)],[122]) ).
cnf(127,negated_conjecture,
~ v1_xboole_0(esk9_0),
inference(split_conjunct,[status(thm)],[122]) ).
fof(133,plain,
! [X1] :
( ~ v1_xboole_0(X1)
| X1 = k1_xboole_0 ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(134,plain,
! [X2] :
( ~ v1_xboole_0(X2)
| X2 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[133]) ).
cnf(135,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[134]) ).
cnf(147,plain,
k1_xboole_0 = esk2_0,
inference(spm,[status(thm)],[135,56,theory(equality)]) ).
cnf(163,plain,
( k1_closure3(X1,X2) = a_2_0_closure3(X1,X2)
| v1_xboole_0(X1)
| ~ m1_pboole(X2,X1) ),
inference(er,[status(thm)],[44,theory(equality)]) ).
cnf(174,plain,
( k1_funct_1(X1,X2) = k1_xboole_0
| r2_hidden(X2,a_2_0_closure3(X3,X1))
| v1_xboole_0(X3)
| ~ m1_subset_1(X2,X3)
| ~ m1_pboole(X1,X3) ),
inference(er,[status(thm)],[83,theory(equality)]) ).
cnf(179,negated_conjecture,
k1_funct_1(esk10_0,esk11_0) != esk2_0,
inference(rw,[status(thm)],[123,147,theory(equality)]) ).
cnf(208,negated_conjecture,
( v1_xboole_0(esk9_0)
| ~ r2_hidden(esk11_0,a_2_0_closure3(esk9_0,esk10_0))
| ~ m1_pboole(esk10_0,esk9_0) ),
inference(spm,[status(thm)],[124,163,theory(equality)]) ).
cnf(210,negated_conjecture,
( v1_xboole_0(esk9_0)
| ~ r2_hidden(esk11_0,a_2_0_closure3(esk9_0,esk10_0))
| $false ),
inference(rw,[status(thm)],[208,126,theory(equality)]) ).
cnf(211,negated_conjecture,
( v1_xboole_0(esk9_0)
| ~ r2_hidden(esk11_0,a_2_0_closure3(esk9_0,esk10_0)) ),
inference(cn,[status(thm)],[210,theory(equality)]) ).
cnf(212,negated_conjecture,
~ r2_hidden(esk11_0,a_2_0_closure3(esk9_0,esk10_0)),
inference(sr,[status(thm)],[211,127,theory(equality)]) ).
cnf(242,plain,
( k1_funct_1(X1,X2) = esk2_0
| r2_hidden(X2,a_2_0_closure3(X3,X1))
| v1_xboole_0(X3)
| ~ m1_subset_1(X2,X3)
| ~ m1_pboole(X1,X3) ),
inference(rw,[status(thm)],[174,147,theory(equality)]) ).
cnf(243,negated_conjecture,
( k1_funct_1(X1,esk11_0) = esk2_0
| r2_hidden(esk11_0,a_2_0_closure3(esk9_0,X1))
| v1_xboole_0(esk9_0)
| ~ m1_pboole(X1,esk9_0) ),
inference(spm,[status(thm)],[242,125,theory(equality)]) ).
cnf(248,negated_conjecture,
( k1_funct_1(X1,esk11_0) = esk2_0
| r2_hidden(esk11_0,a_2_0_closure3(esk9_0,X1))
| ~ m1_pboole(X1,esk9_0) ),
inference(sr,[status(thm)],[243,127,theory(equality)]) ).
cnf(249,negated_conjecture,
( r2_hidden(esk11_0,a_2_0_closure3(esk9_0,esk10_0))
| ~ m1_pboole(esk10_0,esk9_0) ),
inference(spm,[status(thm)],[179,248,theory(equality)]) ).
cnf(250,negated_conjecture,
( r2_hidden(esk11_0,a_2_0_closure3(esk9_0,esk10_0))
| $false ),
inference(rw,[status(thm)],[249,126,theory(equality)]) ).
cnf(251,negated_conjecture,
r2_hidden(esk11_0,a_2_0_closure3(esk9_0,esk10_0)),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(252,negated_conjecture,
$false,
inference(sr,[status(thm)],[251,212,theory(equality)]) ).
cnf(253,negated_conjecture,
$false,
252,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG227+1.p
% --creating new selector for []
% -running prover on /tmp/tmpdHza_a/sel_ALG227+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG227+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG227+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG227+1.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
%
%------------------------------------------------------------------------------