TSTP Solution File: SET918+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET918+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:47:13 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 273 ( 139 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 351 ( 127 ~; 142 |; 76 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 120 ( 4 sgn 80 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmpwTbgwo/sel_SET918+1.p_1',commutativity_k3_xboole_0) ).
fof(4,conjecture,
! [X1,X2,X3] :
~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
& in(X2,X3)
& X1 != X2 ),
file('/tmp/tmpwTbgwo/sel_SET918+1.p_1',t59_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpwTbgwo/sel_SET918+1.p_1',commutativity_k2_tarski) ).
fof(6,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpwTbgwo/sel_SET918+1.p_1',d1_tarski) ).
fof(8,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpwTbgwo/sel_SET918+1.p_1',d3_xboole_0) ).
fof(10,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpwTbgwo/sel_SET918+1.p_1',d2_tarski) ).
fof(11,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
& in(X2,X3)
& X1 != X2 ),
inference(assume_negation,[status(cth)],[4]) ).
fof(14,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(15,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[14]) ).
fof(21,negated_conjecture,
? [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = singleton(X1)
& in(X2,X3)
& X1 != X2 ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(22,negated_conjecture,
? [X4,X5,X6] :
( set_intersection2(unordered_pair(X4,X5),X6) = singleton(X4)
& in(X5,X6)
& X4 != X5 ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,negated_conjecture,
( set_intersection2(unordered_pair(esk2_0,esk3_0),esk4_0) = singleton(esk2_0)
& in(esk3_0,esk4_0)
& esk2_0 != esk3_0 ),
inference(skolemize,[status(esa)],[22]) ).
cnf(24,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,negated_conjecture,
in(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(26,negated_conjecture,
set_intersection2(unordered_pair(esk2_0,esk3_0),esk4_0) = singleton(esk2_0),
inference(split_conjunct,[status(thm)],[23]) ).
fof(27,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(28,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(30,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[29]) ).
fof(31,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4 )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[30]) ).
fof(32,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4 )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[32]) ).
cnf(37,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(41,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)],[8]) ).
fof(42,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)],[41]) ).
fof(43,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(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_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[42]) ).
fof(44,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(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_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[43]) ).
fof(45,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(esk7_3(X5,X6,X7),X7)
| ~ in(esk7_3(X5,X6,X7),X5)
| ~ in(esk7_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X5)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X6)
| in(esk7_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[44]) ).
cnf(49,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[45]) ).
fof(55,plain,
! [X1,X2,X3] :
( ( X3 != unordered_pair(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| X4 = X1
| X4 = X2 )
& ( ( X4 != X1
& X4 != X2 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( X4 != X1
& X4 != X2 ) )
& ( in(X4,X3)
| X4 = X1
| X4 = X2 ) )
| X3 = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(56,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( X9 != X5
& X9 != X6 ) )
& ( in(X9,X7)
| X9 = X5
| X9 = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[56]) ).
fof(58,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) )
| X7 != unordered_pair(X5,X6) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[57]) ).
fof(59,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X5
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X6
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[58]) ).
cnf(63,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(68,negated_conjecture,
set_intersection2(esk4_0,unordered_pair(esk2_0,esk3_0)) = singleton(esk2_0),
inference(rw,[status(thm)],[26,15,theory(equality)]) ).
cnf(74,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[63,theory(equality)]) ).
cnf(117,negated_conjecture,
set_intersection2(esk4_0,unordered_pair(esk3_0,esk2_0)) = singleton(esk2_0),
inference(rw,[status(thm)],[68,28,theory(equality)]) ).
cnf(120,negated_conjecture,
( in(X1,X2)
| singleton(esk2_0) != X2
| ~ in(X1,unordered_pair(esk3_0,esk2_0))
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[49,117,theory(equality)]) ).
cnf(125,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[74,theory(equality)]) ).
cnf(128,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[125,28,theory(equality)]) ).
cnf(259,negated_conjecture,
( in(esk3_0,X1)
| singleton(esk2_0) != X1
| ~ in(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[120,128,theory(equality)]) ).
cnf(270,negated_conjecture,
( in(esk3_0,X1)
| singleton(esk2_0) != X1
| $false ),
inference(rw,[status(thm)],[259,25,theory(equality)]) ).
cnf(271,negated_conjecture,
( in(esk3_0,X1)
| singleton(esk2_0) != X1 ),
inference(cn,[status(thm)],[270,theory(equality)]) ).
cnf(272,negated_conjecture,
in(esk3_0,singleton(esk2_0)),
inference(er,[status(thm)],[271,theory(equality)]) ).
cnf(274,negated_conjecture,
( X1 = esk3_0
| singleton(X1) != singleton(esk2_0) ),
inference(spm,[status(thm)],[37,272,theory(equality)]) ).
cnf(279,negated_conjecture,
esk2_0 = esk3_0,
inference(er,[status(thm)],[274,theory(equality)]) ).
cnf(280,negated_conjecture,
$false,
inference(sr,[status(thm)],[279,24,theory(equality)]) ).
cnf(281,negated_conjecture,
$false,
280,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET918+1.p
% --creating new selector for []
% -running prover on /tmp/tmpwTbgwo/sel_SET918+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET918+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET918+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET918+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
%
%------------------------------------------------------------------------------