%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU124+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 04:43:26 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 139 ( 19 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 170 ( 62 ~; 69 |; 35 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 78 ( 5 sgn 50 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(7,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmpM15-NL/sel_SEU124+1.p_1',d2_xboole_0) ).
fof(9,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpM15-NL/sel_SEU124+1.p_1',commutativity_k2_xboole_0) ).
fof(15,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpM15-NL/sel_SEU124+1.p_1',d3_tarski) ).
fof(16,conjecture,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpM15-NL/sel_SEU124+1.p_1',t7_xboole_1) ).
fof(19,negated_conjecture,
~ ! [X1,X2] : subset(X1,set_union2(X1,X2)),
inference(assume_negation,[status(cth)],[16]) ).
fof(37,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)],[7]) ).
fof(38,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)],[37]) ).
fof(39,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(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_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,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(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_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,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(esk2_3(X5,X6,X7),X5)
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X6)
| ~ in(esk2_3(X5,X6,X7),X7)
| X7 = set_union2(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_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(45,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(51,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[9]) ).
cnf(52,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[51]) ).
fof(67,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)],[15]) ).
fof(68,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)],[67]) ).
fof(69,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk4_2(X4,X5),X4)
& ~ in(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[68]) ).
fof(70,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk4_2(X4,X5),X4)
& ~ in(esk4_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[69]) ).
fof(71,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk4_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[70]) ).
cnf(72,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(73,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[71]) ).
fof(75,negated_conjecture,
? [X1,X2] : ~ subset(X1,set_union2(X1,X2)),
inference(fof_nnf,[status(thm)],[19]) ).
fof(76,negated_conjecture,
? [X3,X4] : ~ subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[75]) ).
fof(77,negated_conjecture,
~ subset(esk5_0,set_union2(esk5_0,esk6_0)),
inference(skolemize,[status(esa)],[76]) ).
cnf(78,negated_conjecture,
~ subset(esk5_0,set_union2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[77]) ).
cnf(127,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[45,theory(equality)]) ).
cnf(324,plain,
( in(esk4_2(X1,X2),set_union2(X3,X1))
| subset(X1,X2) ),
inference(spm,[status(thm)],[127,73,theory(equality)]) ).
cnf(343,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[72,324,theory(equality)]) ).
cnf(352,plain,
subset(X1,set_union2(X1,X2)),
inference(spm,[status(thm)],[343,52,theory(equality)]) ).
cnf(372,negated_conjecture,
$false,
inference(rw,[status(thm)],[78,352,theory(equality)]) ).
cnf(373,negated_conjecture,
$false,
inference(cn,[status(thm)],[372,theory(equality)]) ).
cnf(374,negated_conjecture,
$false,
373,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU124+1.p
% --creating new selector for []
% -running prover on /tmp/tmpM15-NL/sel_SEU124+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU124+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU124+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU124+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
%
%------------------------------------------------------------------------------