TSTP Solution File: LAT300+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : LAT300+2 : TPTP v5.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 14:14:16 EST 2010
% Result : Theorem 8.64s
% Output : CNFRefutation 8.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 12 unt; 0 def)
% Number of atoms : 255 ( 16 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 313 ( 120 ~; 123 |; 53 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 104 ( 1 sgn 81 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(130,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/tmp/tmpH8Qslh/sel_LAT300+2.p_1',t4_subset) ).
fof(226,axiom,
! [X1] :
~ ( X1 != k1_xboole_0
& ! [X2] :
~ ( r2_hidden(X2,X1)
& ! [X3,X4,X5,X6,X7] :
( ( r2_hidden(X3,X4)
& r2_hidden(X4,X5)
& r2_hidden(X5,X6)
& r2_hidden(X6,X7)
& r2_hidden(X7,X2) )
=> r1_xboole_0(X3,X1) ) ) ),
file('/tmp/tmpH8Qslh/sel_LAT300+2.p_1',t6_mcart_1) ).
fof(927,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/tmp/tmpH8Qslh/sel_LAT300+2.p_1',dt_m2_lattice4) ).
fof(1021,axiom,
! [X1] :
( v1_xboole_0(X1)
<=> X1 = k1_xboole_0 ),
file('/tmp/tmpH8Qslh/sel_LAT300+2.p_1',d5_xboole_0) ).
fof(1718,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& r2_hidden(X3,X2) ) ) ),
file('/tmp/tmpH8Qslh/sel_LAT300+2.p_1',t24_filter_2) ).
fof(1728,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
file('/tmp/tmpH8Qslh/sel_LAT300+2.p_1',dt_m2_filter_2) ).
fof(1733,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& r2_hidden(X3,X2) ) ) ),
inference(assume_negation,[status(cth)],[1718]) ).
fof(1905,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_lattice4(X2,X1)
=> m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[927,theory(equality)]) ).
fof(2094,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ? [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
& r2_hidden(X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[1733,theory(equality)]) ).
fof(2104,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1) )
=> ! [X2] :
( m2_filter_2(X2,X1)
=> ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[1728,theory(equality)]) ).
fof(2529,plain,
! [X1,X2,X3] :
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| m1_subset_1(X1,X3) ),
inference(fof_nnf,[status(thm)],[130]) ).
fof(2530,plain,
! [X4,X5,X6] :
( ~ r2_hidden(X4,X5)
| ~ m1_subset_1(X5,k1_zfmisc_1(X6))
| m1_subset_1(X4,X6) ),
inference(variable_rename,[status(thm)],[2529]) ).
cnf(2531,plain,
( m1_subset_1(X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X2))
| ~ r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[2530]) ).
fof(2837,plain,
! [X1] :
( X1 = k1_xboole_0
| ? [X2] :
( r2_hidden(X2,X1)
& ! [X3,X4,X5,X6,X7] :
( ~ r2_hidden(X3,X4)
| ~ r2_hidden(X4,X5)
| ~ r2_hidden(X5,X6)
| ~ r2_hidden(X6,X7)
| ~ r2_hidden(X7,X2)
| r1_xboole_0(X3,X1) ) ) ),
inference(fof_nnf,[status(thm)],[226]) ).
fof(2838,plain,
! [X8] :
( X8 = k1_xboole_0
| ? [X9] :
( r2_hidden(X9,X8)
& ! [X10,X11,X12,X13,X14] :
( ~ r2_hidden(X10,X11)
| ~ r2_hidden(X11,X12)
| ~ r2_hidden(X12,X13)
| ~ r2_hidden(X13,X14)
| ~ r2_hidden(X14,X9)
| r1_xboole_0(X10,X8) ) ) ),
inference(variable_rename,[status(thm)],[2837]) ).
fof(2839,plain,
! [X8] :
( X8 = k1_xboole_0
| ( r2_hidden(esk38_1(X8),X8)
& ! [X10,X11,X12,X13,X14] :
( ~ r2_hidden(X10,X11)
| ~ r2_hidden(X11,X12)
| ~ r2_hidden(X12,X13)
| ~ r2_hidden(X13,X14)
| ~ r2_hidden(X14,esk38_1(X8))
| r1_xboole_0(X10,X8) ) ) ),
inference(skolemize,[status(esa)],[2838]) ).
fof(2840,plain,
! [X8,X10,X11,X12,X13,X14] :
( ( ( ~ r2_hidden(X10,X11)
| ~ r2_hidden(X11,X12)
| ~ r2_hidden(X12,X13)
| ~ r2_hidden(X13,X14)
| ~ r2_hidden(X14,esk38_1(X8))
| r1_xboole_0(X10,X8) )
& r2_hidden(esk38_1(X8),X8) )
| X8 = k1_xboole_0 ),
inference(shift_quantors,[status(thm)],[2839]) ).
fof(2841,plain,
! [X8,X10,X11,X12,X13,X14] :
( ( ~ r2_hidden(X10,X11)
| ~ r2_hidden(X11,X12)
| ~ r2_hidden(X12,X13)
| ~ r2_hidden(X13,X14)
| ~ r2_hidden(X14,esk38_1(X8))
| r1_xboole_0(X10,X8)
| X8 = k1_xboole_0 )
& ( r2_hidden(esk38_1(X8),X8)
| X8 = k1_xboole_0 ) ),
inference(distribute,[status(thm)],[2840]) ).
cnf(2842,plain,
( X1 = k1_xboole_0
| r2_hidden(esk38_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[2841]) ).
fof(5190,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ! [X2] :
( ~ m2_lattice4(X2,X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_nnf,[status(thm)],[1905]) ).
fof(5191,plain,
! [X3] :
( v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| ! [X4] :
( ~ m2_lattice4(X4,X3)
| m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3))) ) ),
inference(variable_rename,[status(thm)],[5190]) ).
fof(5192,plain,
! [X3,X4] :
( ~ m2_lattice4(X4,X3)
| m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
| v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ),
inference(shift_quantors,[status(thm)],[5191]) ).
cnf(5193,plain,
( v3_struct_0(X1)
| m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_lattice4(X2,X1) ),
inference(split_conjunct,[status(thm)],[5192]) ).
fof(5498,plain,
! [X1] :
( ( ~ v1_xboole_0(X1)
| X1 = k1_xboole_0 )
& ( X1 != k1_xboole_0
| v1_xboole_0(X1) ) ),
inference(fof_nnf,[status(thm)],[1021]) ).
fof(5499,plain,
! [X2] :
( ( ~ v1_xboole_0(X2)
| X2 = k1_xboole_0 )
& ( X2 != k1_xboole_0
| v1_xboole_0(X2) ) ),
inference(variable_rename,[status(thm)],[5498]) ).
cnf(5500,plain,
( v1_xboole_0(X1)
| X1 != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[5499]) ).
fof(7830,negated_conjecture,
? [X1] :
( ~ v3_struct_0(X1)
& v10_lattices(X1)
& l3_lattices(X1)
& ? [X2] :
( m2_filter_2(X2,X1)
& ! [X3] :
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ r2_hidden(X3,X2) ) ) ),
inference(fof_nnf,[status(thm)],[2094]) ).
fof(7831,negated_conjecture,
? [X4] :
( ~ v3_struct_0(X4)
& v10_lattices(X4)
& l3_lattices(X4)
& ? [X5] :
( m2_filter_2(X5,X4)
& ! [X6] :
( ~ m1_subset_1(X6,u1_struct_0(X4))
| ~ r2_hidden(X6,X5) ) ) ),
inference(variable_rename,[status(thm)],[7830]) ).
fof(7832,negated_conjecture,
( ~ v3_struct_0(esk333_0)
& v10_lattices(esk333_0)
& l3_lattices(esk333_0)
& m2_filter_2(esk334_0,esk333_0)
& ! [X6] :
( ~ m1_subset_1(X6,u1_struct_0(esk333_0))
| ~ r2_hidden(X6,esk334_0) ) ),
inference(skolemize,[status(esa)],[7831]) ).
fof(7833,negated_conjecture,
! [X6] :
( ( ~ m1_subset_1(X6,u1_struct_0(esk333_0))
| ~ r2_hidden(X6,esk334_0) )
& m2_filter_2(esk334_0,esk333_0)
& ~ v3_struct_0(esk333_0)
& v10_lattices(esk333_0)
& l3_lattices(esk333_0) ),
inference(shift_quantors,[status(thm)],[7832]) ).
cnf(7834,negated_conjecture,
l3_lattices(esk333_0),
inference(split_conjunct,[status(thm)],[7833]) ).
cnf(7835,negated_conjecture,
v10_lattices(esk333_0),
inference(split_conjunct,[status(thm)],[7833]) ).
cnf(7836,negated_conjecture,
~ v3_struct_0(esk333_0),
inference(split_conjunct,[status(thm)],[7833]) ).
cnf(7837,negated_conjecture,
m2_filter_2(esk334_0,esk333_0),
inference(split_conjunct,[status(thm)],[7833]) ).
cnf(7838,negated_conjecture,
( ~ r2_hidden(X1,esk334_0)
| ~ m1_subset_1(X1,u1_struct_0(esk333_0)) ),
inference(split_conjunct,[status(thm)],[7833]) ).
fof(7880,plain,
! [X1] :
( v3_struct_0(X1)
| ~ v10_lattices(X1)
| ~ l3_lattices(X1)
| ! [X2] :
( ~ m2_filter_2(X2,X1)
| ( ~ v1_xboole_0(X2)
& m2_lattice4(X2,X1) ) ) ),
inference(fof_nnf,[status(thm)],[2104]) ).
fof(7881,plain,
! [X3] :
( v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3)
| ! [X4] :
( ~ m2_filter_2(X4,X3)
| ( ~ v1_xboole_0(X4)
& m2_lattice4(X4,X3) ) ) ),
inference(variable_rename,[status(thm)],[7880]) ).
fof(7882,plain,
! [X3,X4] :
( ~ m2_filter_2(X4,X3)
| ( ~ v1_xboole_0(X4)
& m2_lattice4(X4,X3) )
| v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ),
inference(shift_quantors,[status(thm)],[7881]) ).
fof(7883,plain,
! [X3,X4] :
( ( ~ v1_xboole_0(X4)
| ~ m2_filter_2(X4,X3)
| v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) )
& ( m2_lattice4(X4,X3)
| ~ m2_filter_2(X4,X3)
| v3_struct_0(X3)
| ~ v10_lattices(X3)
| ~ l3_lattices(X3) ) ),
inference(distribute,[status(thm)],[7882]) ).
cnf(7884,plain,
( v3_struct_0(X1)
| m2_lattice4(X2,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[7883]) ).
cnf(7885,plain,
( v3_struct_0(X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| ~ m2_filter_2(X2,X1)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[7883]) ).
cnf(8643,negated_conjecture,
( v3_struct_0(esk333_0)
| ~ v1_xboole_0(esk334_0)
| ~ l3_lattices(esk333_0)
| ~ v10_lattices(esk333_0) ),
inference(spm,[status(thm)],[7885,7837,theory(equality)]) ).
cnf(8644,negated_conjecture,
( v3_struct_0(esk333_0)
| ~ v1_xboole_0(esk334_0)
| $false
| ~ v10_lattices(esk333_0) ),
inference(rw,[status(thm)],[8643,7834,theory(equality)]) ).
cnf(8645,negated_conjecture,
( v3_struct_0(esk333_0)
| ~ v1_xboole_0(esk334_0)
| $false
| $false ),
inference(rw,[status(thm)],[8644,7835,theory(equality)]) ).
cnf(8646,negated_conjecture,
( v3_struct_0(esk333_0)
| ~ v1_xboole_0(esk334_0) ),
inference(cn,[status(thm)],[8645,theory(equality)]) ).
cnf(8647,negated_conjecture,
~ v1_xboole_0(esk334_0),
inference(sr,[status(thm)],[8646,7836,theory(equality)]) ).
cnf(9557,negated_conjecture,
( m2_lattice4(esk334_0,esk333_0)
| v3_struct_0(esk333_0)
| ~ l3_lattices(esk333_0)
| ~ v10_lattices(esk333_0) ),
inference(spm,[status(thm)],[7884,7837,theory(equality)]) ).
cnf(9560,negated_conjecture,
( m2_lattice4(esk334_0,esk333_0)
| v3_struct_0(esk333_0)
| $false
| ~ v10_lattices(esk333_0) ),
inference(rw,[status(thm)],[9557,7834,theory(equality)]) ).
cnf(9561,negated_conjecture,
( m2_lattice4(esk334_0,esk333_0)
| v3_struct_0(esk333_0)
| $false
| $false ),
inference(rw,[status(thm)],[9560,7835,theory(equality)]) ).
cnf(9562,negated_conjecture,
( m2_lattice4(esk334_0,esk333_0)
| v3_struct_0(esk333_0) ),
inference(cn,[status(thm)],[9561,theory(equality)]) ).
cnf(9563,negated_conjecture,
m2_lattice4(esk334_0,esk333_0),
inference(sr,[status(thm)],[9562,7836,theory(equality)]) ).
cnf(70802,negated_conjecture,
k1_xboole_0 != esk334_0,
inference(spm,[status(thm)],[8647,5500,theory(equality)]) ).
cnf(70803,negated_conjecture,
( m1_subset_1(esk334_0,k1_zfmisc_1(u1_struct_0(esk333_0)))
| v3_struct_0(esk333_0)
| ~ l3_lattices(esk333_0)
| ~ v10_lattices(esk333_0) ),
inference(spm,[status(thm)],[5193,9563,theory(equality)]) ).
cnf(70806,negated_conjecture,
( m1_subset_1(esk334_0,k1_zfmisc_1(u1_struct_0(esk333_0)))
| v3_struct_0(esk333_0)
| $false
| ~ v10_lattices(esk333_0) ),
inference(rw,[status(thm)],[70803,7834,theory(equality)]) ).
cnf(70807,negated_conjecture,
( m1_subset_1(esk334_0,k1_zfmisc_1(u1_struct_0(esk333_0)))
| v3_struct_0(esk333_0)
| $false
| $false ),
inference(rw,[status(thm)],[70806,7835,theory(equality)]) ).
cnf(70808,negated_conjecture,
( m1_subset_1(esk334_0,k1_zfmisc_1(u1_struct_0(esk333_0)))
| v3_struct_0(esk333_0) ),
inference(cn,[status(thm)],[70807,theory(equality)]) ).
cnf(70809,negated_conjecture,
m1_subset_1(esk334_0,k1_zfmisc_1(u1_struct_0(esk333_0))),
inference(sr,[status(thm)],[70808,7836,theory(equality)]) ).
cnf(70822,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk333_0))
| ~ r2_hidden(X1,esk334_0) ),
inference(spm,[status(thm)],[2531,70809,theory(equality)]) ).
cnf(71450,negated_conjecture,
~ r2_hidden(X1,esk334_0),
inference(csr,[status(thm)],[70822,7838]) ).
cnf(71451,negated_conjecture,
k1_xboole_0 = esk334_0,
inference(spm,[status(thm)],[71450,2842,theory(equality)]) ).
cnf(71577,negated_conjecture,
$false,
inference(sr,[status(thm)],[71451,70802,theory(equality)]) ).
cnf(71578,negated_conjecture,
$false,
71577,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/LAT/LAT300+2.p
% --creating new selector for [SET007+3.ax, SET007+0.ax, SET007+1.ax, SET007+2.ax, SET007+4.ax, SET007+5.ax, SET007+6.ax, SET007+7.ax, SET007+9.ax, SET007+10.ax, SET007+11.ax, SET007+13.ax, SET007+14.ax, SET007+16.ax, SET007+17.ax, SET007+18.ax, SET007+20.ax, SET007+22.ax, SET007+23.ax, SET007+26.ax, SET007+32.ax, SET007+35.ax, SET007+117.ax, SET007+200.ax, SET007+205.ax, SET007+242.ax, SET007+253.ax, SET007+297.ax, SET007+375.ax]
% -running prover on /tmp/tmpH8Qslh/sel_LAT300+2.p_1 with time limit 29
% -prover status Theorem
% Problem LAT300+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/LAT/LAT300+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/LAT/LAT300+2.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
%
%------------------------------------------------------------------------------