TSTP Solution File: SEU131+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU131+1 : TPTP v5.0.0. Released v3.3.0.
% 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 : Sun Dec 26 04:45:05 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 202 ( 41 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 240 ( 89 ~; 103 |; 40 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 106 ( 8 sgn 52 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/tmp/tmpaoxjkR/sel_SEU131+1.p_1',t3_boole) ).
fof(8,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/tmp/tmpaoxjkR/sel_SEU131+1.p_1',d4_xboole_0) ).
fof(11,conjecture,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpaoxjkR/sel_SEU131+1.p_1',l32_xboole_1) ).
fof(14,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpaoxjkR/sel_SEU131+1.p_1',d3_tarski) ).
fof(17,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(19,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(30,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[3]) ).
cnf(31,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[30]) ).
fof(40,plain,
! [X1,X2,X3] :
( ( X3 != set_difference(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) )
& ( ~ in(X4,X1)
| in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) ) )
| X3 = set_difference(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(41,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& ~ in(X9,X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
| ~ in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X6) )
& ( in(esk3_3(X5,X6,X7),X7)
| ( in(esk3_3(X5,X6,X7),X5)
& ~ in(esk3_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(skolemize,[status(esa)],[41]) ).
fof(43,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) )
| X7 != set_difference(X5,X6) )
& ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
| ~ in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X6) )
& ( in(esk3_3(X5,X6,X7),X7)
| ( in(esk3_3(X5,X6,X7),X5)
& ~ in(esk3_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[42]) ).
fof(44,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk3_3(X5,X6,X7),X7)
| ~ in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X6)
| X7 = set_difference(X5,X6) )
& ( in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) )
& ( ~ in(esk3_3(X5,X6,X7),X6)
| in(esk3_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(45,plain,
( X1 = set_difference(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| ~ in(esk3_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(46,plain,
( X1 = set_difference(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(esk3_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(48,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(49,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(56,negated_conjecture,
? [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| ~ subset(X1,X2) )
& ( set_difference(X1,X2) = empty_set
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(57,negated_conjecture,
? [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| ~ subset(X3,X4) )
& ( set_difference(X3,X4) = empty_set
| subset(X3,X4) ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,negated_conjecture,
( ( set_difference(esk4_0,esk5_0) != empty_set
| ~ subset(esk4_0,esk5_0) )
& ( set_difference(esk4_0,esk5_0) = empty_set
| subset(esk4_0,esk5_0) ) ),
inference(skolemize,[status(esa)],[57]) ).
cnf(59,negated_conjecture,
( subset(esk4_0,esk5_0)
| set_difference(esk4_0,esk5_0) = empty_set ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| set_difference(esk4_0,esk5_0) != empty_set ),
inference(split_conjunct,[status(thm)],[58]) ).
fof(67,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(68,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[68]) ).
fof(70,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[69]) ).
fof(71,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk7_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[70]) ).
cnf(72,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(73,plain,
( subset(X1,X2)
| in(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(74,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(87,negated_conjecture,
( in(X1,esk5_0)
| set_difference(esk4_0,esk5_0) = empty_set
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[74,59,theory(equality)]) ).
cnf(94,plain,
( X1 != X2
| ~ in(X3,empty_set)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[49,31,theory(equality)]) ).
cnf(95,plain,
( ~ in(X1,empty_set)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[94,theory(equality)]) ).
cnf(96,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[48,theory(equality)]) ).
cnf(120,plain,
( subset(empty_set,X1)
| ~ in(esk7_2(empty_set,X1),X2) ),
inference(spm,[status(thm)],[95,73,theory(equality)]) ).
cnf(123,plain,
( set_difference(X1,X2) = empty_set
| in(esk3_3(X1,X2,empty_set),X1)
| ~ in(esk3_3(X1,X2,empty_set),X3) ),
inference(spm,[status(thm)],[95,46,theory(equality)]) ).
cnf(126,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[120,73,theory(equality)]) ).
cnf(127,plain,
( in(X1,X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[74,126,theory(equality)]) ).
cnf(129,plain,
~ in(X1,empty_set),
inference(csr,[status(thm)],[127,95]) ).
cnf(619,plain,
( set_difference(X1,X2) = empty_set
| in(esk3_3(X1,X2,empty_set),X1) ),
inference(spm,[status(thm)],[123,46,theory(equality)]) ).
cnf(643,negated_conjecture,
( set_difference(esk4_0,esk5_0) = empty_set
| in(esk3_3(esk4_0,X1,empty_set),esk5_0)
| set_difference(esk4_0,X1) = empty_set ),
inference(spm,[status(thm)],[87,619,theory(equality)]) ).
cnf(666,negated_conjecture,
( set_difference(esk4_0,esk5_0) = empty_set
| in(esk3_3(esk4_0,esk5_0,empty_set),empty_set) ),
inference(spm,[status(thm)],[45,643,theory(equality)]) ).
cnf(668,negated_conjecture,
set_difference(esk4_0,esk5_0) = empty_set,
inference(sr,[status(thm)],[666,129,theory(equality)]) ).
cnf(675,negated_conjecture,
( in(X1,empty_set)
| in(X1,esk5_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[96,668,theory(equality)]) ).
cnf(707,negated_conjecture,
( $false
| ~ subset(esk4_0,esk5_0) ),
inference(rw,[status(thm)],[60,668,theory(equality)]) ).
cnf(708,negated_conjecture,
~ subset(esk4_0,esk5_0),
inference(cn,[status(thm)],[707,theory(equality)]) ).
cnf(711,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk4_0) ),
inference(sr,[status(thm)],[675,129,theory(equality)]) ).
cnf(720,negated_conjecture,
( subset(X1,esk5_0)
| ~ in(esk7_2(X1,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[72,711,theory(equality)]) ).
cnf(725,negated_conjecture,
subset(esk4_0,esk5_0),
inference(spm,[status(thm)],[720,73,theory(equality)]) ).
cnf(727,negated_conjecture,
$false,
inference(sr,[status(thm)],[725,708,theory(equality)]) ).
cnf(728,negated_conjecture,
$false,
727,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU131+1.p
% --creating new selector for []
% -running prover on /tmp/tmpaoxjkR/sel_SEU131+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU131+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU131+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU131+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
%
%------------------------------------------------------------------------------