%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU125+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 04:48:02 EST 2010
% Result : Theorem 24.66s
% Output : CNFRefutation 24.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 22 unt; 0 def)
% Number of atoms : 237 ( 35 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 264 ( 96 ~; 109 |; 51 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 160 ( 12 sgn 75 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',t1_boole) ).
fof(2,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',t1_xboole_1) ).
fof(5,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',t8_xboole_1) ).
fof(12,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',commutativity_k2_xboole_0) ).
fof(14,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',t7_xboole_1) ).
fof(17,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',d2_xboole_0) ).
fof(24,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',d10_xboole_0) ).
fof(30,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpYL2COf/sel_SEU125+2.p_1',d3_tarski) ).
fof(33,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(41,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[1]) ).
cnf(42,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[41]) ).
fof(43,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X2,X3)
| subset(X1,X3) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(44,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[43]) ).
cnf(45,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(52,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& subset(X3,X2)
& ~ subset(set_union2(X1,X3),X2) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(53,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& subset(X6,X5)
& ~ subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[52]) ).
fof(54,negated_conjecture,
( subset(esk2_0,esk3_0)
& subset(esk4_0,esk3_0)
& ~ subset(set_union2(esk2_0,esk4_0),esk3_0) ),
inference(skolemize,[status(esa)],[53]) ).
cnf(55,negated_conjecture,
~ subset(set_union2(esk2_0,esk4_0),esk3_0),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(56,negated_conjecture,
subset(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(57,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[54]) ).
fof(86,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[12]) ).
cnf(87,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[86]) ).
fof(91,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[14]) ).
cnf(92,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[91]) ).
fof(98,plain,
! [X1,X2,X3] :
( ( X3 != set_union2(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_union2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(99,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(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_union2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[98]) ).
fof(100,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
| ( ~ in(esk7_3(X5,X6,X7),X5)
& ~ in(esk7_3(X5,X6,X7),X6) ) )
& ( in(esk7_3(X5,X6,X7),X7)
| in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[99]) ).
fof(101,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_union2(X5,X6) )
& ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
| ( ~ in(esk7_3(X5,X6,X7),X5)
& ~ in(esk7_3(X5,X6,X7),X6) ) )
& ( in(esk7_3(X5,X6,X7),X7)
| in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[100]) ).
fof(102,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X6)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk7_3(X5,X6,X7),X6)
| ~ in(esk7_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[101]) ).
cnf(106,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(108,plain,
( in(X4,X3)
| in(X4,X2)
| X1 != set_union2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[102]) ).
fof(127,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(128,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[127]) ).
fof(129,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[128]) ).
cnf(130,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[129]) ).
fof(144,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)],[30]) ).
fof(145,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)],[144]) ).
fof(146,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk10_2(X4,X5),X4)
& ~ in(esk10_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[145]) ).
fof(147,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk10_2(X4,X5),X4)
& ~ in(esk10_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[146]) ).
fof(148,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk10_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk10_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[147]) ).
cnf(149,plain,
( subset(X1,X2)
| ~ in(esk10_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[148]) ).
cnf(150,plain,
( subset(X1,X2)
| in(esk10_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[148]) ).
cnf(151,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[148]) ).
cnf(173,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[92,87,theory(equality)]) ).
cnf(187,plain,
( subset(X1,set_union2(X2,X3))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[45,92,theory(equality)]) ).
cnf(215,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[151,92,theory(equality)]) ).
cnf(234,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[106,theory(equality)]) ).
cnf(261,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[108,theory(equality)]) ).
cnf(404,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X4)
| ~ subset(X4,X2) ),
inference(spm,[status(thm)],[151,187,theory(equality)]) ).
cnf(518,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk10_2(X1,set_union2(X2,X3)),X2) ),
inference(spm,[status(thm)],[149,215,theory(equality)]) ).
cnf(831,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk10_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[149,234,theory(equality)]) ).
cnf(1110,plain,
( in(esk10_2(set_union2(X1,X2),X3),X2)
| in(esk10_2(set_union2(X1,X2),X3),X1)
| subset(set_union2(X1,X2),X3) ),
inference(spm,[status(thm)],[261,150,theory(equality)]) ).
cnf(2315,negated_conjecture,
( in(X1,set_union2(esk3_0,X2))
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[404,57,theory(equality)]) ).
cnf(2316,negated_conjecture,
( in(X1,set_union2(esk3_0,X2))
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[404,56,theory(equality)]) ).
cnf(8235,negated_conjecture,
( subset(X1,set_union2(X2,set_union2(esk3_0,X3)))
| ~ in(esk10_2(X1,set_union2(X2,set_union2(esk3_0,X3))),esk2_0) ),
inference(spm,[status(thm)],[831,2315,theory(equality)]) ).
cnf(10383,negated_conjecture,
( subset(X1,set_union2(esk3_0,X2))
| ~ in(esk10_2(X1,set_union2(esk3_0,X2)),esk4_0) ),
inference(spm,[status(thm)],[149,2316,theory(equality)]) ).
cnf(10898,plain,
( subset(set_union2(X1,X2),X1)
| in(esk10_2(set_union2(X1,X2),X1),X2) ),
inference(spm,[status(thm)],[149,1110,theory(equality)]) ).
cnf(10916,plain,
( subset(set_union2(X1,X2),set_union2(X1,X3))
| in(esk10_2(set_union2(X1,X2),set_union2(X1,X3)),X2) ),
inference(spm,[status(thm)],[518,1110,theory(equality)]) ).
cnf(461920,negated_conjecture,
subset(set_union2(set_union2(esk3_0,X1),esk4_0),set_union2(esk3_0,X1)),
inference(spm,[status(thm)],[10383,10898,theory(equality)]) ).
cnf(461961,negated_conjecture,
subset(set_union2(esk4_0,set_union2(esk3_0,X1)),set_union2(esk3_0,X1)),
inference(rw,[status(thm)],[461920,87,theory(equality)]) ).
cnf(466579,negated_conjecture,
( set_union2(esk3_0,X1) = set_union2(esk4_0,set_union2(esk3_0,X1))
| ~ subset(set_union2(esk3_0,X1),set_union2(esk4_0,set_union2(esk3_0,X1))) ),
inference(spm,[status(thm)],[130,461961,theory(equality)]) ).
cnf(466710,negated_conjecture,
( set_union2(esk3_0,X1) = set_union2(esk4_0,set_union2(esk3_0,X1))
| $false ),
inference(rw,[status(thm)],[466579,173,theory(equality)]) ).
cnf(466711,negated_conjecture,
set_union2(esk3_0,X1) = set_union2(esk4_0,set_union2(esk3_0,X1)),
inference(cn,[status(thm)],[466710,theory(equality)]) ).
cnf(473241,plain,
subset(set_union2(X1,esk2_0),set_union2(X1,set_union2(esk3_0,X2))),
inference(spm,[status(thm)],[8235,10916,theory(equality)]) ).
cnf(473293,negated_conjecture,
subset(set_union2(esk4_0,esk2_0),set_union2(esk3_0,X1)),
inference(spm,[status(thm)],[473241,466711,theory(equality)]) ).
cnf(473491,negated_conjecture,
subset(set_union2(esk2_0,esk4_0),set_union2(esk3_0,X1)),
inference(rw,[status(thm)],[473293,87,theory(equality)]) ).
cnf(473586,negated_conjecture,
subset(set_union2(esk2_0,esk4_0),esk3_0),
inference(spm,[status(thm)],[473491,42,theory(equality)]) ).
cnf(473697,negated_conjecture,
$false,
inference(sr,[status(thm)],[473586,55,theory(equality)]) ).
cnf(473698,negated_conjecture,
$false,
473697,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU125+2.p
% --creating new selector for []
% -running prover on /tmp/tmpYL2COf/sel_SEU125+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU125+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU125+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU125+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
%
%------------------------------------------------------------------------------