TSTP Solution File: SEU141+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU141+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 04:50:58 EST 2010
% Result : Theorem 5.58s
% Output : CNFRefutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 13 unt; 0 def)
% Number of atoms : 285 ( 62 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 356 ( 136 ~; 146 |; 66 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 159 ( 8 sgn 80 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',t3_boole) ).
fof(10,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',d4_xboole_0) ).
fof(12,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',d3_xboole_0) ).
fof(14,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',commutativity_k3_xboole_0) ).
fof(23,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',t4_xboole_0) ).
fof(24,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',t83_xboole_1) ).
fof(25,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[24]) ).
fof(28,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(29,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[23,theory(equality)]) ).
fof(37,plain,
! [X2] : set_difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(38,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[37]) ).
fof(49,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)],[28]) ).
fof(50,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)],[49]) ).
fof(51,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(esk2_3(X5,X6,X7),X7)
| ~ in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) )
& ( in(esk2_3(X5,X6,X7),X7)
| ( in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(skolemize,[status(esa)],[50]) ).
fof(52,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(esk2_3(X5,X6,X7),X7)
| ~ in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) )
& ( in(esk2_3(X5,X6,X7),X7)
| ( in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[51]) ).
fof(53,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(esk2_3(X5,X6,X7),X7)
| ~ in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6)
| X7 = set_difference(X5,X6) )
& ( in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X6)
| in(esk2_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) ) ),
inference(distribute,[status(thm)],[52]) ).
cnf(55,plain,
( X1 = set_difference(X2,X3)
| in(esk2_3(X2,X3,X1),X1)
| in(esk2_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,plain,
( X1 = set_difference(X2,X3)
| in(esk2_3(X2,X3,X1),X3)
| ~ in(esk2_3(X2,X3,X1),X2)
| ~ in(esk2_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(58,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(59,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(64,plain,
! [X1,X2,X3] :
( ( X3 != set_intersection2(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_intersection2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(65,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(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_intersection2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[64]) ).
fof(66,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(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_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[65]) ).
fof(67,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_intersection2(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_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[66]) ).
fof(68,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7)
| X7 != set_intersection2(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_intersection2(X5,X6) )
& ( in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk3_3(X5,X6,X7),X6)
| in(esk3_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[67]) ).
cnf(72,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[68]) ).
cnf(73,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(78,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[14]) ).
cnf(79,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[78]) ).
fof(107,plain,
! [X1,X2] :
( ( disjoint(X1,X2)
| ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(108,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| ? [X6] : in(X6,set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(variable_rename,[status(thm)],[107]) ).
fof(109,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| in(esk6_2(X4,X5),set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(skolemize,[status(esa)],[108]) ).
fof(110,plain,
! [X4,X5,X7] :
( ( ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) )
& ( disjoint(X4,X5)
| in(esk6_2(X4,X5),set_intersection2(X4,X5)) ) ),
inference(shift_quantors,[status(thm)],[109]) ).
cnf(111,plain,
( in(esk6_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[110]) ).
cnf(112,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[110]) ).
fof(113,negated_conjecture,
? [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_difference(X1,X2) != X1 )
& ( disjoint(X1,X2)
| set_difference(X1,X2) = X1 ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(114,negated_conjecture,
? [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) != X3 )
& ( disjoint(X3,X4)
| set_difference(X3,X4) = X3 ) ),
inference(variable_rename,[status(thm)],[113]) ).
fof(115,negated_conjecture,
( ( ~ disjoint(esk7_0,esk8_0)
| set_difference(esk7_0,esk8_0) != esk7_0 )
& ( disjoint(esk7_0,esk8_0)
| set_difference(esk7_0,esk8_0) = esk7_0 ) ),
inference(skolemize,[status(esa)],[114]) ).
cnf(116,negated_conjecture,
( set_difference(esk7_0,esk8_0) = esk7_0
| disjoint(esk7_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[115]) ).
cnf(117,negated_conjecture,
( set_difference(esk7_0,esk8_0) != esk7_0
| ~ disjoint(esk7_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[115]) ).
cnf(146,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[59,theory(equality)]) ).
cnf(151,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[73,theory(equality)]) ).
cnf(163,plain,
( disjoint(X1,X2)
| in(esk6_2(X1,X2),set_intersection2(X2,X1)) ),
inference(spm,[status(thm)],[111,79,theory(equality)]) ).
cnf(178,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[72,theory(equality)]) ).
cnf(184,plain,
( set_difference(X4,X5) = X4
| in(esk2_3(X4,X5,X4),X4) ),
inference(ef,[status(thm)],[55,theory(equality)]) ).
cnf(421,plain,
( in(esk6_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[151,111,theory(equality)]) ).
cnf(443,plain,
( in(esk6_2(X1,set_difference(X2,X3)),X2)
| disjoint(X1,set_difference(X2,X3)) ),
inference(spm,[status(thm)],[146,421,theory(equality)]) ).
cnf(657,plain,
( in(esk6_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[151,163,theory(equality)]) ).
cnf(842,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[112,178,theory(equality)]) ).
cnf(959,plain,
( set_difference(X1,X2) = X1
| in(esk2_3(X1,X2,X1),X2)
| ~ in(esk2_3(X1,X2,X1),X1) ),
inference(spm,[status(thm)],[56,184,theory(equality)]) ).
cnf(3424,negated_conjecture,
( set_difference(esk7_0,esk8_0) = esk7_0
| ~ in(X1,esk8_0)
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[842,116,theory(equality)]) ).
cnf(3581,negated_conjecture,
( ~ in(X1,esk8_0)
| ~ in(X1,esk7_0) ),
inference(csr,[status(thm)],[3424,58]) ).
cnf(3590,negated_conjecture,
( disjoint(X1,esk8_0)
| ~ in(esk6_2(X1,esk8_0),esk7_0) ),
inference(spm,[status(thm)],[3581,421,theory(equality)]) ).
cnf(3591,negated_conjecture,
( disjoint(esk8_0,X1)
| ~ in(esk6_2(esk8_0,X1),esk7_0) ),
inference(spm,[status(thm)],[3581,657,theory(equality)]) ).
cnf(3636,negated_conjecture,
disjoint(esk7_0,esk8_0),
inference(spm,[status(thm)],[3590,657,theory(equality)]) ).
cnf(3642,negated_conjecture,
( set_difference(esk7_0,esk8_0) != esk7_0
| $false ),
inference(rw,[status(thm)],[117,3636,theory(equality)]) ).
cnf(3643,negated_conjecture,
set_difference(esk7_0,esk8_0) != esk7_0,
inference(cn,[status(thm)],[3642,theory(equality)]) ).
cnf(3903,negated_conjecture,
disjoint(esk8_0,set_difference(esk7_0,X1)),
inference(spm,[status(thm)],[3591,443,theory(equality)]) ).
cnf(3915,negated_conjecture,
( ~ in(X2,set_difference(esk7_0,X1))
| ~ in(X2,esk8_0) ),
inference(spm,[status(thm)],[842,3903,theory(equality)]) ).
cnf(4160,negated_conjecture,
( set_difference(set_difference(esk7_0,X1),X2) = set_difference(esk7_0,X1)
| ~ in(esk2_3(set_difference(esk7_0,X1),X2,set_difference(esk7_0,X1)),esk8_0) ),
inference(spm,[status(thm)],[3915,184,theory(equality)]) ).
cnf(22796,plain,
( set_difference(X1,X2) = X1
| in(esk2_3(X1,X2,X1),X2) ),
inference(csr,[status(thm)],[959,184]) ).
cnf(160143,negated_conjecture,
set_difference(set_difference(esk7_0,X1),esk8_0) = set_difference(esk7_0,X1),
inference(spm,[status(thm)],[4160,22796,theory(equality)]) ).
cnf(160165,negated_conjecture,
set_difference(esk7_0,esk8_0) = esk7_0,
inference(spm,[status(thm)],[160143,38,theory(equality)]) ).
cnf(160666,negated_conjecture,
$false,
inference(sr,[status(thm)],[160165,3643,theory(equality)]) ).
cnf(160667,negated_conjecture,
$false,
160666,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU141+1.p
% --creating new selector for []
% -running prover on /tmp/tmpjRMtxD/sel_SEU141+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU141+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU141+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU141+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
%
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