%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU234+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 06:04:35 EST 2010
% Result : Theorem 0.34s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 7 unt; 0 def)
% Number of atoms : 255 ( 29 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 305 ( 108 ~; 118 |; 66 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 81 ( 0 sgn 56 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
file('/tmp/tmpmoZsLH/sel_SEU234+1.p_1',d3_ordinal1) ).
fof(10,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/tmp/tmpmoZsLH/sel_SEU234+1.p_1',d4_ordinal1) ).
fof(17,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/tmp/tmpmoZsLH/sel_SEU234+1.p_1',d2_ordinal1) ).
fof(23,conjecture,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
file('/tmp/tmpmoZsLH/sel_SEU234+1.p_1',t31_ordinal1) ).
fof(25,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/tmp/tmpmoZsLH/sel_SEU234+1.p_1',t24_ordinal1) ).
fof(42,negated_conjecture,
~ ! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( ordinal(X2)
& subset(X2,X1) ) )
=> ordinal(X1) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(43,plain,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(47,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(49,plain,
! [X1] :
( ( ~ epsilon_connected(X1)
| ! [X2,X3] :
( ~ in(X2,X1)
| ~ in(X3,X1)
| in(X2,X3)
| X2 = X3
| in(X3,X2) ) )
& ( ? [X2,X3] :
( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) )
| epsilon_connected(X1) ) ),
inference(fof_nnf,[status(thm)],[43]) ).
fof(50,plain,
! [X4] :
( ( ~ epsilon_connected(X4)
| ! [X5,X6] :
( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| X5 = X6
| in(X6,X5) ) )
& ( ? [X7,X8] :
( in(X7,X4)
& in(X8,X4)
& ~ in(X7,X8)
& X7 != X8
& ~ in(X8,X7) )
| epsilon_connected(X4) ) ),
inference(variable_rename,[status(thm)],[49]) ).
fof(51,plain,
! [X4] :
( ( ~ epsilon_connected(X4)
| ! [X5,X6] :
( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| X5 = X6
| in(X6,X5) ) )
& ( ( in(esk1_1(X4),X4)
& in(esk2_1(X4),X4)
& ~ in(esk1_1(X4),esk2_1(X4))
& esk1_1(X4) != esk2_1(X4)
& ~ in(esk2_1(X4),esk1_1(X4)) )
| epsilon_connected(X4) ) ),
inference(skolemize,[status(esa)],[50]) ).
fof(52,plain,
! [X4,X5,X6] :
( ( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| X5 = X6
| in(X6,X5)
| ~ epsilon_connected(X4) )
& ( ( in(esk1_1(X4),X4)
& in(esk2_1(X4),X4)
& ~ in(esk1_1(X4),esk2_1(X4))
& esk1_1(X4) != esk2_1(X4)
& ~ in(esk2_1(X4),esk1_1(X4)) )
| epsilon_connected(X4) ) ),
inference(shift_quantors,[status(thm)],[51]) ).
fof(53,plain,
! [X4,X5,X6] :
( ( ~ in(X5,X4)
| ~ in(X6,X4)
| in(X5,X6)
| X5 = X6
| in(X6,X5)
| ~ epsilon_connected(X4) )
& ( in(esk1_1(X4),X4)
| epsilon_connected(X4) )
& ( in(esk2_1(X4),X4)
| epsilon_connected(X4) )
& ( ~ in(esk1_1(X4),esk2_1(X4))
| epsilon_connected(X4) )
& ( esk1_1(X4) != esk2_1(X4)
| epsilon_connected(X4) )
& ( ~ in(esk2_1(X4),esk1_1(X4))
| epsilon_connected(X4) ) ),
inference(distribute,[status(thm)],[52]) ).
cnf(54,plain,
( epsilon_connected(X1)
| ~ in(esk2_1(X1),esk1_1(X1)) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,plain,
( epsilon_connected(X1)
| esk1_1(X1) != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,plain,
( epsilon_connected(X1)
| ~ in(esk1_1(X1),esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(57,plain,
( epsilon_connected(X1)
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(58,plain,
( epsilon_connected(X1)
| in(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
fof(95,plain,
! [X1] :
( ( ~ ordinal(X1)
| ( epsilon_transitive(X1)
& epsilon_connected(X1) ) )
& ( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(96,plain,
! [X2] :
( ( ~ ordinal(X2)
| ( epsilon_transitive(X2)
& epsilon_connected(X2) ) )
& ( ~ epsilon_transitive(X2)
| ~ epsilon_connected(X2)
| ordinal(X2) ) ),
inference(variable_rename,[status(thm)],[95]) ).
fof(97,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ ordinal(X2) )
& ( ~ epsilon_transitive(X2)
| ~ epsilon_connected(X2)
| ordinal(X2) ) ),
inference(distribute,[status(thm)],[96]) ).
cnf(98,plain,
( ordinal(X1)
| ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[97]) ).
fof(128,plain,
! [X1] :
( ( ~ epsilon_transitive(X1)
| ! [X2] :
( ~ in(X2,X1)
| subset(X2,X1) ) )
& ( ? [X2] :
( in(X2,X1)
& ~ subset(X2,X1) )
| epsilon_transitive(X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(129,plain,
! [X3] :
( ( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ in(X4,X3)
| subset(X4,X3) ) )
& ( ? [X5] :
( in(X5,X3)
& ~ subset(X5,X3) )
| epsilon_transitive(X3) ) ),
inference(variable_rename,[status(thm)],[128]) ).
fof(130,plain,
! [X3] :
( ( ~ epsilon_transitive(X3)
| ! [X4] :
( ~ in(X4,X3)
| subset(X4,X3) ) )
& ( ( in(esk9_1(X3),X3)
& ~ subset(esk9_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(skolemize,[status(esa)],[129]) ).
fof(131,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( ( in(esk9_1(X3),X3)
& ~ subset(esk9_1(X3),X3) )
| epsilon_transitive(X3) ) ),
inference(shift_quantors,[status(thm)],[130]) ).
fof(132,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| subset(X4,X3)
| ~ epsilon_transitive(X3) )
& ( in(esk9_1(X3),X3)
| epsilon_transitive(X3) )
& ( ~ subset(esk9_1(X3),X3)
| epsilon_transitive(X3) ) ),
inference(distribute,[status(thm)],[131]) ).
cnf(133,plain,
( epsilon_transitive(X1)
| ~ subset(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[132]) ).
cnf(134,plain,
( epsilon_transitive(X1)
| in(esk9_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(151,negated_conjecture,
? [X1] :
( ! [X2] :
( ~ in(X2,X1)
| ( ordinal(X2)
& subset(X2,X1) ) )
& ~ ordinal(X1) ),
inference(fof_nnf,[status(thm)],[42]) ).
fof(152,negated_conjecture,
? [X3] :
( ! [X4] :
( ~ in(X4,X3)
| ( ordinal(X4)
& subset(X4,X3) ) )
& ~ ordinal(X3) ),
inference(variable_rename,[status(thm)],[151]) ).
fof(153,negated_conjecture,
( ! [X4] :
( ~ in(X4,esk10_0)
| ( ordinal(X4)
& subset(X4,esk10_0) ) )
& ~ ordinal(esk10_0) ),
inference(skolemize,[status(esa)],[152]) ).
fof(154,negated_conjecture,
! [X4] :
( ( ~ in(X4,esk10_0)
| ( ordinal(X4)
& subset(X4,esk10_0) ) )
& ~ ordinal(esk10_0) ),
inference(shift_quantors,[status(thm)],[153]) ).
fof(155,negated_conjecture,
! [X4] :
( ( ordinal(X4)
| ~ in(X4,esk10_0) )
& ( subset(X4,esk10_0)
| ~ in(X4,esk10_0) )
& ~ ordinal(esk10_0) ),
inference(distribute,[status(thm)],[154]) ).
cnf(156,negated_conjecture,
~ ordinal(esk10_0),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(157,negated_conjecture,
( subset(X1,esk10_0)
| ~ in(X1,esk10_0) ),
inference(split_conjunct,[status(thm)],[155]) ).
cnf(158,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk10_0) ),
inference(split_conjunct,[status(thm)],[155]) ).
fof(165,plain,
! [X1] :
( ~ ordinal(X1)
| ! [X2] :
( ~ ordinal(X2)
| in(X1,X2)
| X1 = X2
| in(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[47]) ).
fof(166,plain,
! [X3] :
( ~ ordinal(X3)
| ! [X4] :
( ~ ordinal(X4)
| in(X3,X4)
| X3 = X4
| in(X4,X3) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,plain,
! [X3,X4] :
( ~ ordinal(X4)
| in(X3,X4)
| X3 = X4
| in(X4,X3)
| ~ ordinal(X3) ),
inference(shift_quantors,[status(thm)],[166]) ).
cnf(168,plain,
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[167]) ).
cnf(247,negated_conjecture,
( epsilon_transitive(esk10_0)
| ~ in(esk9_1(esk10_0),esk10_0) ),
inference(spm,[status(thm)],[133,157,theory(equality)]) ).
cnf(279,negated_conjecture,
( X1 = X2
| in(X1,X2)
| in(X2,X1)
| ~ ordinal(X1)
| ~ in(X2,esk10_0) ),
inference(spm,[status(thm)],[168,158,theory(equality)]) ).
cnf(329,negated_conjecture,
epsilon_transitive(esk10_0),
inference(csr,[status(thm)],[247,134]) ).
cnf(330,negated_conjecture,
( ordinal(esk10_0)
| ~ epsilon_connected(esk10_0) ),
inference(spm,[status(thm)],[98,329,theory(equality)]) ).
cnf(331,negated_conjecture,
~ epsilon_connected(esk10_0),
inference(sr,[status(thm)],[330,156,theory(equality)]) ).
cnf(406,negated_conjecture,
( X1 = esk1_1(esk10_0)
| in(esk1_1(esk10_0),X1)
| in(X1,esk1_1(esk10_0))
| epsilon_connected(esk10_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[279,58,theory(equality)]) ).
cnf(410,negated_conjecture,
( X1 = esk1_1(esk10_0)
| in(esk1_1(esk10_0),X1)
| in(X1,esk1_1(esk10_0))
| ~ ordinal(X1) ),
inference(sr,[status(thm)],[406,331,theory(equality)]) ).
cnf(1185,negated_conjecture,
( X1 = esk1_1(esk10_0)
| in(X1,esk1_1(esk10_0))
| in(esk1_1(esk10_0),X1)
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[410,158,theory(equality)]) ).
cnf(2212,negated_conjecture,
( esk2_1(esk10_0) = esk1_1(esk10_0)
| in(esk1_1(esk10_0),esk2_1(esk10_0))
| in(esk2_1(esk10_0),esk1_1(esk10_0))
| epsilon_connected(esk10_0) ),
inference(spm,[status(thm)],[1185,57,theory(equality)]) ).
cnf(2229,negated_conjecture,
( esk2_1(esk10_0) = esk1_1(esk10_0)
| in(esk1_1(esk10_0),esk2_1(esk10_0))
| in(esk2_1(esk10_0),esk1_1(esk10_0)) ),
inference(sr,[status(thm)],[2212,331,theory(equality)]) ).
cnf(2235,negated_conjecture,
( epsilon_connected(esk10_0)
| esk2_1(esk10_0) = esk1_1(esk10_0)
| in(esk1_1(esk10_0),esk2_1(esk10_0)) ),
inference(spm,[status(thm)],[54,2229,theory(equality)]) ).
cnf(2242,negated_conjecture,
( esk2_1(esk10_0) = esk1_1(esk10_0)
| in(esk1_1(esk10_0),esk2_1(esk10_0)) ),
inference(sr,[status(thm)],[2235,331,theory(equality)]) ).
cnf(2245,negated_conjecture,
( epsilon_connected(esk10_0)
| esk2_1(esk10_0) = esk1_1(esk10_0) ),
inference(spm,[status(thm)],[56,2242,theory(equality)]) ).
cnf(2252,negated_conjecture,
esk2_1(esk10_0) = esk1_1(esk10_0),
inference(sr,[status(thm)],[2245,331,theory(equality)]) ).
cnf(2254,negated_conjecture,
epsilon_connected(esk10_0),
inference(spm,[status(thm)],[55,2252,theory(equality)]) ).
cnf(2324,negated_conjecture,
$false,
inference(sr,[status(thm)],[2254,331,theory(equality)]) ).
cnf(2325,negated_conjecture,
$false,
2324,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU234+1.p
% --creating new selector for []
% -running prover on /tmp/tmpmoZsLH/sel_SEU234+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU234+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU234+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU234+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
%
%------------------------------------------------------------------------------