TSTP Solution File: SEU118+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU118+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 04:42:10 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 193 ( 21 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 239 ( 91 ~; 94 |; 43 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 1 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/tmp/tmpqOQ_1N/sel_SEU118+1.p_1',t1_subset) ).
fof(20,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/tmp/tmpqOQ_1N/sel_SEU118+1.p_1',cc2_finset_1) ).
fof(22,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('/tmp/tmpqOQ_1N/sel_SEU118+1.p_1',d5_finsub_1) ).
fof(24,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/tmp/tmpqOQ_1N/sel_SEU118+1.p_1',t3_subset) ).
fof(25,axiom,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
file('/tmp/tmpqOQ_1N/sel_SEU118+1.p_1',fc2_finsub_1) ).
fof(31,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ( finite(X1)
=> element(X2,finite_subsets(X1)) ) ),
file('/tmp/tmpqOQ_1N/sel_SEU118+1.p_1',t34_finsub_1) ).
fof(34,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( finite(X1)
=> element(X2,finite_subsets(X1)) ) ),
inference(assume_negation,[status(cth)],[31]) ).
fof(43,plain,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(55,plain,
! [X1,X2] :
( ~ in(X1,X2)
| element(X1,X2) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(56,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[55]) ).
cnf(57,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(121,plain,
! [X1] :
( ~ finite(X1)
| ! [X2] :
( ~ element(X2,powerset(X1))
| finite(X2) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(122,plain,
! [X3] :
( ~ finite(X3)
| ! [X4] :
( ~ element(X4,powerset(X3))
| finite(X4) ) ),
inference(variable_rename,[status(thm)],[121]) ).
fof(123,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| finite(X4)
| ~ finite(X3) ),
inference(shift_quantors,[status(thm)],[122]) ).
cnf(124,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[123]) ).
fof(130,plain,
! [X1,X2] :
( ~ preboolean(X2)
| ( ( X2 != finite_subsets(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ( subset(X3,X1)
& finite(X3) ) )
& ( ~ subset(X3,X1)
| ~ finite(X3)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ subset(X3,X1)
| ~ finite(X3) )
& ( in(X3,X2)
| ( subset(X3,X1)
& finite(X3) ) ) )
| X2 = finite_subsets(X1) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(131,plain,
! [X4,X5] :
( ~ preboolean(X5)
| ( ( X5 != finite_subsets(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| ( subset(X6,X4)
& finite(X6) ) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ subset(X7,X4)
| ~ finite(X7) )
& ( in(X7,X5)
| ( subset(X7,X4)
& finite(X7) ) ) )
| X5 = finite_subsets(X4) ) ) ),
inference(variable_rename,[status(thm)],[130]) ).
fof(132,plain,
! [X4,X5] :
( ~ preboolean(X5)
| ( ( X5 != finite_subsets(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| ( subset(X6,X4)
& finite(X6) ) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk7_2(X4,X5),X5)
| ~ subset(esk7_2(X4,X5),X4)
| ~ finite(esk7_2(X4,X5)) )
& ( in(esk7_2(X4,X5),X5)
| ( subset(esk7_2(X4,X5),X4)
& finite(esk7_2(X4,X5)) ) ) )
| X5 = finite_subsets(X4) ) ) ),
inference(skolemize,[status(esa)],[131]) ).
fof(133,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ in(X6,X5)
| ( subset(X6,X4)
& finite(X6) ) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5) ) )
| X5 != finite_subsets(X4) )
& ( ( ( ~ in(esk7_2(X4,X5),X5)
| ~ subset(esk7_2(X4,X5),X4)
| ~ finite(esk7_2(X4,X5)) )
& ( in(esk7_2(X4,X5),X5)
| ( subset(esk7_2(X4,X5),X4)
& finite(esk7_2(X4,X5)) ) ) )
| X5 = finite_subsets(X4) ) )
| ~ preboolean(X5) ),
inference(shift_quantors,[status(thm)],[132]) ).
fof(134,plain,
! [X4,X5,X6] :
( ( subset(X6,X4)
| ~ in(X6,X5)
| X5 != finite_subsets(X4)
| ~ preboolean(X5) )
& ( finite(X6)
| ~ in(X6,X5)
| X5 != finite_subsets(X4)
| ~ preboolean(X5) )
& ( ~ subset(X6,X4)
| ~ finite(X6)
| in(X6,X5)
| X5 != finite_subsets(X4)
| ~ preboolean(X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| ~ subset(esk7_2(X4,X5),X4)
| ~ finite(esk7_2(X4,X5))
| X5 = finite_subsets(X4)
| ~ preboolean(X5) )
& ( subset(esk7_2(X4,X5),X4)
| in(esk7_2(X4,X5),X5)
| X5 = finite_subsets(X4)
| ~ preboolean(X5) )
& ( finite(esk7_2(X4,X5))
| in(esk7_2(X4,X5),X5)
| X5 = finite_subsets(X4)
| ~ preboolean(X5) ) ),
inference(distribute,[status(thm)],[133]) ).
cnf(138,plain,
( in(X3,X1)
| ~ preboolean(X1)
| X1 != finite_subsets(X2)
| ~ finite(X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[134]) ).
fof(144,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(145,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[144]) ).
cnf(147,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[145]) ).
fof(148,plain,
! [X2] :
( ~ empty(finite_subsets(X2))
& cup_closed(finite_subsets(X2))
& diff_closed(finite_subsets(X2))
& preboolean(finite_subsets(X2)) ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(149,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[148]) ).
fof(173,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(X1))
& finite(X1)
& ~ element(X2,finite_subsets(X1)) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(174,negated_conjecture,
? [X3,X4] :
( element(X4,powerset(X3))
& finite(X3)
& ~ element(X4,finite_subsets(X3)) ),
inference(variable_rename,[status(thm)],[173]) ).
fof(175,negated_conjecture,
( element(esk12_0,powerset(esk11_0))
& finite(esk11_0)
& ~ element(esk12_0,finite_subsets(esk11_0)) ),
inference(skolemize,[status(esa)],[174]) ).
cnf(176,negated_conjecture,
~ element(esk12_0,finite_subsets(esk11_0)),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(177,negated_conjecture,
finite(esk11_0),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(178,negated_conjecture,
element(esk12_0,powerset(esk11_0)),
inference(split_conjunct,[status(thm)],[175]) ).
cnf(189,negated_conjecture,
( finite(esk12_0)
| ~ finite(esk11_0) ),
inference(spm,[status(thm)],[124,178,theory(equality)]) ).
cnf(193,negated_conjecture,
( finite(esk12_0)
| $false ),
inference(rw,[status(thm)],[189,177,theory(equality)]) ).
cnf(194,negated_conjecture,
finite(esk12_0),
inference(cn,[status(thm)],[193,theory(equality)]) ).
cnf(240,plain,
( in(X1,X2)
| finite_subsets(X3) != X2
| ~ preboolean(X2)
| ~ finite(X1)
| ~ element(X1,powerset(X3)) ),
inference(spm,[status(thm)],[138,147,theory(equality)]) ).
cnf(530,negated_conjecture,
( in(esk12_0,X1)
| finite_subsets(esk11_0) != X1
| ~ preboolean(X1)
| ~ finite(esk12_0) ),
inference(spm,[status(thm)],[240,178,theory(equality)]) ).
cnf(541,negated_conjecture,
( in(esk12_0,X1)
| finite_subsets(esk11_0) != X1
| ~ preboolean(X1)
| $false ),
inference(rw,[status(thm)],[530,194,theory(equality)]) ).
cnf(542,negated_conjecture,
( in(esk12_0,X1)
| finite_subsets(esk11_0) != X1
| ~ preboolean(X1) ),
inference(cn,[status(thm)],[541,theory(equality)]) ).
cnf(579,negated_conjecture,
( element(esk12_0,X1)
| finite_subsets(esk11_0) != X1
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[57,542,theory(equality)]) ).
cnf(600,negated_conjecture,
( element(esk12_0,finite_subsets(esk11_0))
| ~ preboolean(finite_subsets(esk11_0)) ),
inference(er,[status(thm)],[579,theory(equality)]) ).
cnf(601,negated_conjecture,
( element(esk12_0,finite_subsets(esk11_0))
| $false ),
inference(rw,[status(thm)],[600,149,theory(equality)]) ).
cnf(602,negated_conjecture,
element(esk12_0,finite_subsets(esk11_0)),
inference(cn,[status(thm)],[601,theory(equality)]) ).
cnf(603,negated_conjecture,
$false,
inference(sr,[status(thm)],[602,176,theory(equality)]) ).
cnf(604,negated_conjecture,
$false,
603,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU118+1.p
% --creating new selector for []
% -running prover on /tmp/tmpqOQ_1N/sel_SEU118+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU118+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU118+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU118+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
%
%------------------------------------------------------------------------------