TSTP Solution File: SET814+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET814+4 : TPTP v5.0.0. Released v3.2.0.
% 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 03:41:38 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 5 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 212 ( 80 ~; 79 |; 46 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 49 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpBtbbl-/sel_SET814+4.p_1',subset) ).
fof(2,axiom,
! [X1] :
( member(X1,on)
<=> ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( member(X3,X1)
=> subset(X3,X1) ) ) ),
file('/tmp/tmpBtbbl-/sel_SET814+4.p_1',ordinal_number) ).
fof(3,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X4] :
( member(X4,X1)
& member(X3,X4) ) ),
file('/tmp/tmpBtbbl-/sel_SET814+4.p_1',sum) ).
fof(10,conjecture,
! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
file('/tmp/tmpBtbbl-/sel_SET814+4.p_1',thV14) ).
fof(11,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
inference(assume_negation,[status(cth)],[10]) ).
fof(12,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(13,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[12]) ).
fof(14,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[13]) ).
fof(15,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[15]) ).
cnf(17,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(19,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(20,plain,
! [X1] :
( ( ~ member(X1,on)
| ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( ~ member(X3,X1)
| subset(X3,X1) ) ) )
& ( ~ set(X1)
| ~ strict_well_order(member_predicate,X1)
| ? [X3] :
( member(X3,X1)
& ~ subset(X3,X1) )
| member(X1,on) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(21,plain,
! [X4] :
( ( ~ member(X4,on)
| ( set(X4)
& strict_well_order(member_predicate,X4)
& ! [X5] :
( ~ member(X5,X4)
| subset(X5,X4) ) ) )
& ( ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| ? [X6] :
( member(X6,X4)
& ~ subset(X6,X4) )
| member(X4,on) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X4] :
( ( ~ member(X4,on)
| ( set(X4)
& strict_well_order(member_predicate,X4)
& ! [X5] :
( ~ member(X5,X4)
| subset(X5,X4) ) ) )
& ( ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| ( member(esk2_1(X4),X4)
& ~ subset(esk2_1(X4),X4) )
| member(X4,on) ) ),
inference(skolemize,[status(esa)],[21]) ).
fof(23,plain,
! [X4,X5] :
( ( ( ( ~ member(X5,X4)
| subset(X5,X4) )
& set(X4)
& strict_well_order(member_predicate,X4) )
| ~ member(X4,on) )
& ( ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| ( member(esk2_1(X4),X4)
& ~ subset(esk2_1(X4),X4) )
| member(X4,on) ) ),
inference(shift_quantors,[status(thm)],[22]) ).
fof(24,plain,
! [X4,X5] :
( ( ~ member(X5,X4)
| subset(X5,X4)
| ~ member(X4,on) )
& ( set(X4)
| ~ member(X4,on) )
& ( strict_well_order(member_predicate,X4)
| ~ member(X4,on) )
& ( member(esk2_1(X4),X4)
| ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| member(X4,on) )
& ( ~ subset(esk2_1(X4),X4)
| ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| member(X4,on) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(29,plain,
( subset(X2,X1)
| ~ member(X1,on)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(30,plain,
! [X3,X1] :
( ( ~ member(X3,sum(X1))
| ? [X4] :
( member(X4,X1)
& member(X3,X4) ) )
& ( ! [X4] :
( ~ member(X4,X1)
| ~ member(X3,X4) )
| member(X3,sum(X1)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(31,plain,
! [X5,X6] :
( ( ~ member(X5,sum(X6))
| ? [X7] :
( member(X7,X6)
& member(X5,X7) ) )
& ( ! [X8] :
( ~ member(X8,X6)
| ~ member(X5,X8) )
| member(X5,sum(X6)) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X5,X6] :
( ( ~ member(X5,sum(X6))
| ( member(esk3_2(X5,X6),X6)
& member(X5,esk3_2(X5,X6)) ) )
& ( ! [X8] :
( ~ member(X8,X6)
| ~ member(X5,X8) )
| member(X5,sum(X6)) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X5,X6,X8] :
( ( ~ member(X8,X6)
| ~ member(X5,X8)
| member(X5,sum(X6)) )
& ( ~ member(X5,sum(X6))
| ( member(esk3_2(X5,X6),X6)
& member(X5,esk3_2(X5,X6)) ) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X5,X6,X8] :
( ( ~ member(X8,X6)
| ~ member(X5,X8)
| member(X5,sum(X6)) )
& ( member(esk3_2(X5,X6),X6)
| ~ member(X5,sum(X6)) )
& ( member(X5,esk3_2(X5,X6))
| ~ member(X5,sum(X6)) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( member(X1,esk3_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( member(esk3_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(100,negated_conjecture,
? [X1] :
( member(X1,on)
& ~ subset(sum(X1),X1) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(101,negated_conjecture,
? [X2] :
( member(X2,on)
& ~ subset(sum(X2),X2) ),
inference(variable_rename,[status(thm)],[100]) ).
fof(102,negated_conjecture,
( member(esk13_0,on)
& ~ subset(sum(esk13_0),esk13_0) ),
inference(skolemize,[status(esa)],[101]) ).
cnf(103,negated_conjecture,
~ subset(sum(esk13_0),esk13_0),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(104,negated_conjecture,
member(esk13_0,on),
inference(split_conjunct,[status(thm)],[102]) ).
cnf(109,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ member(X2,on)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[19,29,theory(equality)]) ).
cnf(242,negated_conjecture,
( member(X1,esk13_0)
| ~ member(X1,X2)
| ~ member(X2,esk13_0) ),
inference(spm,[status(thm)],[109,104,theory(equality)]) ).
cnf(254,negated_conjecture,
( member(X1,esk13_0)
| ~ member(X1,esk3_2(X2,esk13_0))
| ~ member(X2,sum(esk13_0)) ),
inference(spm,[status(thm)],[242,36,theory(equality)]) ).
cnf(352,negated_conjecture,
( member(X1,esk13_0)
| ~ member(X1,sum(esk13_0)) ),
inference(spm,[status(thm)],[254,35,theory(equality)]) ).
cnf(362,negated_conjecture,
( member(esk1_2(sum(esk13_0),X1),esk13_0)
| subset(sum(esk13_0),X1) ),
inference(spm,[status(thm)],[352,18,theory(equality)]) ).
cnf(372,negated_conjecture,
subset(sum(esk13_0),esk13_0),
inference(spm,[status(thm)],[17,362,theory(equality)]) ).
cnf(381,negated_conjecture,
$false,
inference(sr,[status(thm)],[372,103,theory(equality)]) ).
cnf(382,negated_conjecture,
$false,
381,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET814+4.p
% --creating new selector for [SET006+0.ax, SET006+4.ax]
% -running prover on /tmp/tmpBtbbl-/sel_SET814+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET814+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET814+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET814+4.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
%
%------------------------------------------------------------------------------