TSTP Solution File: SEU344+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU344+1 : TPTP v5.0.0. Released v3.3.0.
% 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 07:33:57 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 14 unt; 0 def)
% Number of atoms : 242 ( 46 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 269 ( 97 ~; 125 |; 29 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 81 ( 4 sgn 58 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(17,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',dt_l3_lattices) ).
fof(35,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',t7_xboole_1) ).
fof(38,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',d3_lattices) ).
fof(63,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',fc1_lattice3) ).
fof(66,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',dt_k1_lattice3) ).
fof(67,axiom,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',t1_lattice3) ).
fof(75,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',t12_xboole_1) ).
fof(79,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
file('/tmp/tmp-c8auj/sel_SEU344+1.p_1',t2_lattice3) ).
fof(82,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X2,X3)
<=> subset(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[79]) ).
fof(96,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[38,theory(equality)]) ).
fof(101,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[63,theory(equality)]) ).
fof(160,plain,
! [X1] :
( ~ latt_str(X1)
| ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(161,plain,
! [X2] :
( ~ latt_str(X2)
| ( meet_semilatt_str(X2)
& join_semilatt_str(X2) ) ),
inference(variable_rename,[status(thm)],[160]) ).
fof(162,plain,
! [X2] :
( ( meet_semilatt_str(X2)
| ~ latt_str(X2) )
& ( join_semilatt_str(X2)
| ~ latt_str(X2) ) ),
inference(distribute,[status(thm)],[161]) ).
cnf(163,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[162]) ).
fof(209,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[35]) ).
cnf(210,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[209]) ).
fof(217,plain,
! [X1] :
( empty_carrier(X1)
| ~ join_semilatt_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| ( ( ~ below(X1,X2,X3)
| join(X1,X2,X3) = X3 )
& ( join(X1,X2,X3) != X3
| below(X1,X2,X3) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[96]) ).
fof(218,plain,
! [X4] :
( empty_carrier(X4)
| ~ join_semilatt_str(X4)
| ! [X5] :
( ~ element(X5,the_carrier(X4))
| ! [X6] :
( ~ element(X6,the_carrier(X4))
| ( ( ~ below(X4,X5,X6)
| join(X4,X5,X6) = X6 )
& ( join(X4,X5,X6) != X6
| below(X4,X5,X6) ) ) ) ) ),
inference(variable_rename,[status(thm)],[217]) ).
fof(219,plain,
! [X4,X5,X6] :
( ~ element(X6,the_carrier(X4))
| ( ( ~ below(X4,X5,X6)
| join(X4,X5,X6) = X6 )
& ( join(X4,X5,X6) != X6
| below(X4,X5,X6) ) )
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) ),
inference(shift_quantors,[status(thm)],[218]) ).
fof(220,plain,
! [X4,X5,X6] :
( ( ~ below(X4,X5,X6)
| join(X4,X5,X6) = X6
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) )
& ( join(X4,X5,X6) != X6
| below(X4,X5,X6)
| ~ element(X6,the_carrier(X4))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ join_semilatt_str(X4) ) ),
inference(distribute,[status(thm)],[219]) ).
cnf(221,plain,
( empty_carrier(X1)
| below(X1,X2,X3)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| join(X1,X2,X3) != X3 ),
inference(split_conjunct,[status(thm)],[220]) ).
cnf(222,plain,
( empty_carrier(X1)
| join(X1,X2,X3) = X3
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[220]) ).
fof(289,plain,
! [X2] :
( ~ empty_carrier(boole_lattice(X2))
& strict_latt_str(boole_lattice(X2)) ),
inference(variable_rename,[status(thm)],[101]) ).
cnf(291,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[289]) ).
fof(294,plain,
! [X2] :
( strict_latt_str(boole_lattice(X2))
& latt_str(boole_lattice(X2)) ),
inference(variable_rename,[status(thm)],[66]) ).
cnf(295,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[294]) ).
fof(297,plain,
! [X1,X2] :
( ~ element(X2,the_carrier(boole_lattice(X1)))
| ! [X3] :
( ~ element(X3,the_carrier(boole_lattice(X1)))
| ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[67]) ).
fof(298,plain,
! [X4,X5] :
( ~ element(X5,the_carrier(boole_lattice(X4)))
| ! [X6] :
( ~ element(X6,the_carrier(boole_lattice(X4)))
| ( join(boole_lattice(X4),X5,X6) = set_union2(X5,X6)
& meet(boole_lattice(X4),X5,X6) = set_intersection2(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[297]) ).
fof(299,plain,
! [X4,X5,X6] :
( ~ element(X6,the_carrier(boole_lattice(X4)))
| ( join(boole_lattice(X4),X5,X6) = set_union2(X5,X6)
& meet(boole_lattice(X4),X5,X6) = set_intersection2(X5,X6) )
| ~ element(X5,the_carrier(boole_lattice(X4))) ),
inference(shift_quantors,[status(thm)],[298]) ).
fof(300,plain,
! [X4,X5,X6] :
( ( join(boole_lattice(X4),X5,X6) = set_union2(X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(X4))) )
& ( meet(boole_lattice(X4),X5,X6) = set_intersection2(X5,X6)
| ~ element(X6,the_carrier(boole_lattice(X4)))
| ~ element(X5,the_carrier(boole_lattice(X4))) ) ),
inference(distribute,[status(thm)],[299]) ).
cnf(302,plain,
( join(boole_lattice(X2),X1,X3) = set_union2(X1,X3)
| ~ element(X1,the_carrier(boole_lattice(X2)))
| ~ element(X3,the_carrier(boole_lattice(X2))) ),
inference(split_conjunct,[status(thm)],[300]) ).
fof(324,plain,
! [X1,X2] :
( ~ subset(X1,X2)
| set_union2(X1,X2) = X2 ),
inference(fof_nnf,[status(thm)],[75]) ).
fof(325,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| set_union2(X3,X4) = X4 ),
inference(variable_rename,[status(thm)],[324]) ).
cnf(326,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[325]) ).
fof(334,negated_conjecture,
? [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
& ? [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
& ( ~ below(boole_lattice(X1),X2,X3)
| ~ subset(X2,X3) )
& ( below(boole_lattice(X1),X2,X3)
| subset(X2,X3) ) ) ),
inference(fof_nnf,[status(thm)],[82]) ).
fof(335,negated_conjecture,
? [X4,X5] :
( element(X5,the_carrier(boole_lattice(X4)))
& ? [X6] :
( element(X6,the_carrier(boole_lattice(X4)))
& ( ~ below(boole_lattice(X4),X5,X6)
| ~ subset(X5,X6) )
& ( below(boole_lattice(X4),X5,X6)
| subset(X5,X6) ) ) ),
inference(variable_rename,[status(thm)],[334]) ).
fof(336,negated_conjecture,
( element(esk17_0,the_carrier(boole_lattice(esk16_0)))
& element(esk18_0,the_carrier(boole_lattice(esk16_0)))
& ( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
| ~ subset(esk17_0,esk18_0) )
& ( below(boole_lattice(esk16_0),esk17_0,esk18_0)
| subset(esk17_0,esk18_0) ) ),
inference(skolemize,[status(esa)],[335]) ).
cnf(337,negated_conjecture,
( subset(esk17_0,esk18_0)
| below(boole_lattice(esk16_0),esk17_0,esk18_0) ),
inference(split_conjunct,[status(thm)],[336]) ).
cnf(338,negated_conjecture,
( ~ subset(esk17_0,esk18_0)
| ~ below(boole_lattice(esk16_0),esk17_0,esk18_0) ),
inference(split_conjunct,[status(thm)],[336]) ).
cnf(339,negated_conjecture,
element(esk18_0,the_carrier(boole_lattice(esk16_0))),
inference(split_conjunct,[status(thm)],[336]) ).
cnf(340,negated_conjecture,
element(esk17_0,the_carrier(boole_lattice(esk16_0))),
inference(split_conjunct,[status(thm)],[336]) ).
cnf(362,plain,
join_semilatt_str(boole_lattice(X1)),
inference(spm,[status(thm)],[163,295,theory(equality)]) ).
cnf(429,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0
| empty_carrier(boole_lattice(esk16_0))
| subset(esk17_0,esk18_0)
| ~ element(esk18_0,the_carrier(boole_lattice(esk16_0)))
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0)))
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(spm,[status(thm)],[222,337,theory(equality)]) ).
cnf(430,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0
| empty_carrier(boole_lattice(esk16_0))
| subset(esk17_0,esk18_0)
| $false
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0)))
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(rw,[status(thm)],[429,339,theory(equality)]) ).
cnf(431,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0
| empty_carrier(boole_lattice(esk16_0))
| subset(esk17_0,esk18_0)
| $false
| $false
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(rw,[status(thm)],[430,340,theory(equality)]) ).
cnf(432,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0
| empty_carrier(boole_lattice(esk16_0))
| subset(esk17_0,esk18_0)
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(cn,[status(thm)],[431,theory(equality)]) ).
cnf(433,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0
| subset(esk17_0,esk18_0)
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(sr,[status(thm)],[432,291,theory(equality)]) ).
cnf(739,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0
| subset(esk17_0,esk18_0)
| $false ),
inference(rw,[status(thm)],[433,362,theory(equality)]) ).
cnf(740,negated_conjecture,
( join(boole_lattice(esk16_0),esk17_0,esk18_0) = esk18_0
| subset(esk17_0,esk18_0) ),
inference(cn,[status(thm)],[739,theory(equality)]) ).
cnf(741,negated_conjecture,
( esk18_0 = set_union2(esk17_0,esk18_0)
| subset(esk17_0,esk18_0)
| ~ element(esk18_0,the_carrier(boole_lattice(esk16_0)))
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0))) ),
inference(spm,[status(thm)],[302,740,theory(equality)]) ).
cnf(743,negated_conjecture,
( esk18_0 = set_union2(esk17_0,esk18_0)
| subset(esk17_0,esk18_0)
| $false
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0))) ),
inference(rw,[status(thm)],[741,339,theory(equality)]) ).
cnf(744,negated_conjecture,
( esk18_0 = set_union2(esk17_0,esk18_0)
| subset(esk17_0,esk18_0)
| $false
| $false ),
inference(rw,[status(thm)],[743,340,theory(equality)]) ).
cnf(745,negated_conjecture,
( esk18_0 = set_union2(esk17_0,esk18_0)
| subset(esk17_0,esk18_0) ),
inference(cn,[status(thm)],[744,theory(equality)]) ).
cnf(751,negated_conjecture,
set_union2(esk17_0,esk18_0) = esk18_0,
inference(csr,[status(thm)],[745,326]) ).
cnf(752,negated_conjecture,
subset(esk17_0,esk18_0),
inference(spm,[status(thm)],[210,751,theory(equality)]) ).
cnf(771,negated_conjecture,
( ~ below(boole_lattice(esk16_0),esk17_0,esk18_0)
| $false ),
inference(rw,[status(thm)],[338,752,theory(equality)]) ).
cnf(772,negated_conjecture,
~ below(boole_lattice(esk16_0),esk17_0,esk18_0),
inference(cn,[status(thm)],[771,theory(equality)]) ).
cnf(781,negated_conjecture,
( empty_carrier(boole_lattice(esk16_0))
| join(boole_lattice(esk16_0),esk17_0,esk18_0) != esk18_0
| ~ element(esk18_0,the_carrier(boole_lattice(esk16_0)))
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0)))
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(spm,[status(thm)],[772,221,theory(equality)]) ).
cnf(782,negated_conjecture,
( empty_carrier(boole_lattice(esk16_0))
| join(boole_lattice(esk16_0),esk17_0,esk18_0) != esk18_0
| $false
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0)))
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(rw,[status(thm)],[781,339,theory(equality)]) ).
cnf(783,negated_conjecture,
( empty_carrier(boole_lattice(esk16_0))
| join(boole_lattice(esk16_0),esk17_0,esk18_0) != esk18_0
| $false
| $false
| ~ join_semilatt_str(boole_lattice(esk16_0)) ),
inference(rw,[status(thm)],[782,340,theory(equality)]) ).
cnf(784,negated_conjecture,
( empty_carrier(boole_lattice(esk16_0))
| join(boole_lattice(esk16_0),esk17_0,esk18_0) != esk18_0
| $false
| $false
| $false ),
inference(rw,[status(thm)],[783,362,theory(equality)]) ).
cnf(785,negated_conjecture,
( empty_carrier(boole_lattice(esk16_0))
| join(boole_lattice(esk16_0),esk17_0,esk18_0) != esk18_0 ),
inference(cn,[status(thm)],[784,theory(equality)]) ).
cnf(786,negated_conjecture,
join(boole_lattice(esk16_0),esk17_0,esk18_0) != esk18_0,
inference(sr,[status(thm)],[785,291,theory(equality)]) ).
cnf(792,negated_conjecture,
( set_union2(esk17_0,esk18_0) != esk18_0
| ~ element(esk18_0,the_carrier(boole_lattice(esk16_0)))
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0))) ),
inference(spm,[status(thm)],[786,302,theory(equality)]) ).
cnf(793,negated_conjecture,
( $false
| ~ element(esk18_0,the_carrier(boole_lattice(esk16_0)))
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0))) ),
inference(rw,[status(thm)],[792,751,theory(equality)]) ).
cnf(794,negated_conjecture,
( $false
| $false
| ~ element(esk17_0,the_carrier(boole_lattice(esk16_0))) ),
inference(rw,[status(thm)],[793,339,theory(equality)]) ).
cnf(795,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[794,340,theory(equality)]) ).
cnf(796,negated_conjecture,
$false,
inference(cn,[status(thm)],[795,theory(equality)]) ).
cnf(797,negated_conjecture,
$false,
796,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU344+1.p
% --creating new selector for []
% -running prover on /tmp/tmp-c8auj/sel_SEU344+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU344+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU344+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU344+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
%
%------------------------------------------------------------------------------