TSTP Solution File: SEU119+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU119+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 04:42:15 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 73 ( 11 unt; 0 def)
% Number of atoms : 273 ( 61 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 341 ( 141 ~; 129 |; 64 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 137 ( 17 sgn 58 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,conjecture,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/tmp/tmpj_VOPc/sel_SEU119+1.p_1',t3_xboole_0) ).
fof(8,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/tmp/tmpj_VOPc/sel_SEU119+1.p_1',d7_xboole_0) ).
fof(10,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpj_VOPc/sel_SEU119+1.p_1',d3_xboole_0) ).
fof(12,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpj_VOPc/sel_SEU119+1.p_1',d1_xboole_0) ).
fof(14,negated_conjecture,
~ ! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(15,negated_conjecture,
~ ! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(18,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(27,negated_conjecture,
? [X1,X2] :
( ( ~ disjoint(X1,X2)
& ! [X3] :
( ~ in(X3,X1)
| ~ in(X3,X2) ) )
| ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(28,negated_conjecture,
? [X4,X5] :
( ( ~ disjoint(X4,X5)
& ! [X6] :
( ~ in(X6,X4)
| ~ in(X6,X5) ) )
| ( ? [X7] :
( in(X7,X4)
& in(X7,X5) )
& disjoint(X4,X5) ) ),
inference(variable_rename,[status(thm)],[27]) ).
fof(29,negated_conjecture,
( ( ~ disjoint(esk1_0,esk2_0)
& ! [X6] :
( ~ in(X6,esk1_0)
| ~ in(X6,esk2_0) ) )
| ( in(esk3_0,esk1_0)
& in(esk3_0,esk2_0)
& disjoint(esk1_0,esk2_0) ) ),
inference(skolemize,[status(esa)],[28]) ).
fof(30,negated_conjecture,
! [X6] :
( ( ( ~ in(X6,esk1_0)
| ~ in(X6,esk2_0) )
& ~ disjoint(esk1_0,esk2_0) )
| ( in(esk3_0,esk1_0)
& in(esk3_0,esk2_0)
& disjoint(esk1_0,esk2_0) ) ),
inference(shift_quantors,[status(thm)],[29]) ).
fof(31,negated_conjecture,
! [X6] :
( ( in(esk3_0,esk1_0)
| ~ in(X6,esk1_0)
| ~ in(X6,esk2_0) )
& ( in(esk3_0,esk2_0)
| ~ in(X6,esk1_0)
| ~ in(X6,esk2_0) )
& ( disjoint(esk1_0,esk2_0)
| ~ in(X6,esk1_0)
| ~ in(X6,esk2_0) )
& ( in(esk3_0,esk1_0)
| ~ disjoint(esk1_0,esk2_0) )
& ( in(esk3_0,esk2_0)
| ~ disjoint(esk1_0,esk2_0) )
& ( disjoint(esk1_0,esk2_0)
| ~ disjoint(esk1_0,esk2_0) ) ),
inference(distribute,[status(thm)],[30]) ).
cnf(33,negated_conjecture,
( in(esk3_0,esk2_0)
| ~ disjoint(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(34,negated_conjecture,
( in(esk3_0,esk1_0)
| ~ disjoint(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[31]) ).
cnf(35,negated_conjecture,
( disjoint(esk1_0,esk2_0)
| ~ in(X1,esk2_0)
| ~ in(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(42,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set )
& ( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(43,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X3,X4) != empty_set
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[42]) ).
cnf(44,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(49,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)],[10]) ).
fof(50,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)],[49]) ).
fof(51,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(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(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_intersection2(X5,X6) )
& ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[51]) ).
fof(53,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(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X6)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[52]) ).
cnf(54,plain,
( X1 = set_intersection2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| in(esk6_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,plain,
( X1 = set_intersection2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| in(esk6_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(57,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(58,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(59,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(63,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(64,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[64]) ).
fof(66,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[65]) ).
cnf(68,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(75,negated_conjecture,
( in(esk3_0,esk1_0)
| set_intersection2(esk1_0,esk2_0) != empty_set ),
inference(spm,[status(thm)],[34,44,theory(equality)]) ).
cnf(76,negated_conjecture,
( in(esk3_0,esk2_0)
| set_intersection2(esk1_0,esk2_0) != empty_set ),
inference(spm,[status(thm)],[33,44,theory(equality)]) ).
cnf(83,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[58,theory(equality)]) ).
cnf(88,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[59,theory(equality)]) ).
cnf(93,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[57,theory(equality)]) ).
cnf(101,negated_conjecture,
( disjoint(esk1_0,esk2_0)
| set_intersection2(X1,esk2_0) = X2
| in(esk6_3(X1,esk2_0,X2),X2)
| ~ in(esk6_3(X1,esk2_0,X2),esk1_0) ),
inference(spm,[status(thm)],[35,54,theory(equality)]) ).
cnf(104,plain,
( set_intersection2(X2,X3) = X1
| in(esk6_3(X2,X3,X1),X3)
| empty_set != X1 ),
inference(spm,[status(thm)],[68,54,theory(equality)]) ).
cnf(128,plain,
( set_intersection2(X2,X1) = X3
| empty_set != X1
| empty_set != X3 ),
inference(spm,[status(thm)],[68,104,theory(equality)]) ).
cnf(132,plain,
( set_intersection2(X1,X2) = empty_set
| empty_set != X2 ),
inference(er,[status(thm)],[128,theory(equality)]) ).
cnf(160,plain,
( in(X1,X2)
| ~ in(X1,empty_set)
| empty_set != X2 ),
inference(spm,[status(thm)],[83,132,theory(equality)]) ).
cnf(182,plain,
( empty_set != X2
| ~ in(X1,empty_set) ),
inference(csr,[status(thm)],[160,68]) ).
fof(183,plain,
( ~ epred1_0
<=> ! [X2] : empty_set != X2 ),
introduced(definition),
[split] ).
cnf(184,plain,
( epred1_0
| empty_set != X2 ),
inference(split_equiv,[status(thm)],[183]) ).
fof(185,plain,
( ~ epred2_0
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(definition),
[split] ).
cnf(186,plain,
( epred2_0
| ~ in(X1,empty_set) ),
inference(split_equiv,[status(thm)],[185]) ).
cnf(187,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[182,183,theory(equality)]),185,theory(equality)]),
[split] ).
cnf(188,plain,
epred1_0,
inference(er,[status(thm)],[184,theory(equality)]) ).
cnf(195,plain,
( epred2_0
| set_intersection2(X1,empty_set) = X2
| empty_set != X2 ),
inference(spm,[status(thm)],[186,104,theory(equality)]) ).
cnf(196,plain,
( ~ epred2_0
| $false ),
inference(rw,[status(thm)],[187,188,theory(equality)]) ).
cnf(197,plain,
~ epred2_0,
inference(cn,[status(thm)],[196,theory(equality)]) ).
cnf(228,plain,
( set_intersection2(X1,empty_set) = X2
| empty_set != X2 ),
inference(sr,[status(thm)],[195,197,theory(equality)]) ).
cnf(229,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(er,[status(thm)],[228,theory(equality)]) ).
cnf(236,plain,
( in(X1,X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[88,229,theory(equality)]) ).
cnf(264,plain,
( empty_set != set_intersection2(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[68,93,theory(equality)]) ).
cnf(302,plain,
( ~ in(X2,empty_set)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[264,229,theory(equality)]) ).
cnf(325,plain,
~ in(X2,empty_set),
inference(csr,[status(thm)],[302,236]) ).
cnf(441,negated_conjecture,
( set_intersection2(esk1_0,esk2_0) = X1
| in(esk6_3(esk1_0,esk2_0,X1),X1)
| disjoint(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[101,55,theory(equality)]) ).
cnf(461,negated_conjecture,
( set_intersection2(esk1_0,esk2_0) = empty_set
| disjoint(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[325,441,theory(equality)]) ).
cnf(476,negated_conjecture,
set_intersection2(esk1_0,esk2_0) = empty_set,
inference(csr,[status(thm)],[461,45]) ).
cnf(482,negated_conjecture,
( in(X1,empty_set)
| ~ in(X1,esk2_0)
| ~ in(X1,esk1_0) ),
inference(spm,[status(thm)],[93,476,theory(equality)]) ).
cnf(489,negated_conjecture,
( in(esk3_0,esk2_0)
| $false ),
inference(rw,[status(thm)],[76,476,theory(equality)]) ).
cnf(490,negated_conjecture,
in(esk3_0,esk2_0),
inference(cn,[status(thm)],[489,theory(equality)]) ).
cnf(491,negated_conjecture,
( in(esk3_0,esk1_0)
| $false ),
inference(rw,[status(thm)],[75,476,theory(equality)]) ).
cnf(492,negated_conjecture,
in(esk3_0,esk1_0),
inference(cn,[status(thm)],[491,theory(equality)]) ).
cnf(493,negated_conjecture,
( ~ in(X1,esk2_0)
| ~ in(X1,esk1_0) ),
inference(sr,[status(thm)],[482,325,theory(equality)]) ).
cnf(548,negated_conjecture,
~ in(esk3_0,esk1_0),
inference(spm,[status(thm)],[493,490,theory(equality)]) ).
cnf(559,negated_conjecture,
$false,
inference(rw,[status(thm)],[548,492,theory(equality)]) ).
cnf(560,negated_conjecture,
$false,
inference(cn,[status(thm)],[559,theory(equality)]) ).
cnf(561,negated_conjecture,
$false,
560,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU119+1.p
% --creating new selector for []
% -running prover on /tmp/tmpj_VOPc/sel_SEU119+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU119+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU119+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU119+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
%
%------------------------------------------------------------------------------