TSTP Solution File: SET811+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET811+4 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:41:14 EST 2010
% Result : Theorem 3.54s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 66 ( 11 unt; 0 def)
% Number of atoms : 237 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 278 ( 107 ~; 106 |; 54 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 137 ( 6 sgn 64 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpNV_Zb-/sel_SET811+4.p_1',subset) ).
fof(2,axiom,
! [X3,X4,X1,X5] :
( member(X5,initial_segment(X3,X4,X1))
<=> ( member(X5,X1)
& apply(X4,X5,X3) ) ),
file('/tmp/tmpNV_Zb-/sel_SET811+4.p_1',initial_segment) ).
fof(3,axiom,
! [X1] :
( member(X1,on)
<=> ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( member(X3,X1)
=> subset(X3,X1) ) ) ),
file('/tmp/tmpNV_Zb-/sel_SET811+4.p_1',ordinal_number) ).
fof(6,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpNV_Zb-/sel_SET811+4.p_1',equal_set) ).
fof(8,axiom,
! [X3,X5] :
( apply(member_predicate,X3,X5)
<=> member(X3,X5) ),
file('/tmp/tmpNV_Zb-/sel_SET811+4.p_1',rel_member) ).
fof(10,conjecture,
! [X1] :
( member(X1,on)
=> ! [X3] :
( member(X3,X1)
=> equal_set(X3,initial_segment(X3,member_predicate,X1)) ) ),
file('/tmp/tmpNV_Zb-/sel_SET811+4.p_1',thV5) ).
fof(11,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> ! [X3] :
( member(X3,X1)
=> equal_set(X3,initial_segment(X3,member_predicate,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,
! [X3,X4,X1,X5] :
( ( ~ member(X5,initial_segment(X3,X4,X1))
| ( member(X5,X1)
& apply(X4,X5,X3) ) )
& ( ~ member(X5,X1)
| ~ apply(X4,X5,X3)
| member(X5,initial_segment(X3,X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(21,plain,
! [X6,X7,X8,X9] :
( ( ~ member(X9,initial_segment(X6,X7,X8))
| ( member(X9,X8)
& apply(X7,X9,X6) ) )
& ( ~ member(X9,X8)
| ~ apply(X7,X9,X6)
| member(X9,initial_segment(X6,X7,X8)) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X6,X7,X8,X9] :
( ( member(X9,X8)
| ~ member(X9,initial_segment(X6,X7,X8)) )
& ( apply(X7,X9,X6)
| ~ member(X9,initial_segment(X6,X7,X8)) )
& ( ~ member(X9,X8)
| ~ apply(X7,X9,X6)
| member(X9,initial_segment(X6,X7,X8)) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(23,plain,
( member(X1,initial_segment(X2,X3,X4))
| ~ apply(X3,X1,X2)
| ~ member(X1,X4) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(24,plain,
( apply(X3,X1,X2)
| ~ member(X1,initial_segment(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(26,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)],[3]) ).
fof(27,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)],[26]) ).
fof(28,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)],[27]) ).
fof(29,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)],[28]) ).
fof(30,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)],[29]) ).
cnf(35,plain,
( subset(X2,X1)
| ~ member(X1,on)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(50,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(51,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(53,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(66,plain,
! [X3,X5] :
( ( ~ apply(member_predicate,X3,X5)
| member(X3,X5) )
& ( ~ member(X3,X5)
| apply(member_predicate,X3,X5) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(67,plain,
! [X6,X7] :
( ( ~ apply(member_predicate,X6,X7)
| member(X6,X7) )
& ( ~ member(X6,X7)
| apply(member_predicate,X6,X7) ) ),
inference(variable_rename,[status(thm)],[66]) ).
cnf(68,plain,
( apply(member_predicate,X1,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
cnf(69,plain,
( member(X1,X2)
| ~ apply(member_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[67]) ).
fof(101,negated_conjecture,
? [X1] :
( member(X1,on)
& ? [X3] :
( member(X3,X1)
& ~ equal_set(X3,initial_segment(X3,member_predicate,X1)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(102,negated_conjecture,
? [X4] :
( member(X4,on)
& ? [X5] :
( member(X5,X4)
& ~ equal_set(X5,initial_segment(X5,member_predicate,X4)) ) ),
inference(variable_rename,[status(thm)],[101]) ).
fof(103,negated_conjecture,
( member(esk12_0,on)
& member(esk13_0,esk12_0)
& ~ equal_set(esk13_0,initial_segment(esk13_0,member_predicate,esk12_0)) ),
inference(skolemize,[status(esa)],[102]) ).
cnf(104,negated_conjecture,
~ equal_set(esk13_0,initial_segment(esk13_0,member_predicate,esk12_0)),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(105,negated_conjecture,
member(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(106,negated_conjecture,
member(esk12_0,on),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(113,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ member(X2,on)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[19,35,theory(equality)]) ).
cnf(115,plain,
( apply(X1,esk1_2(initial_segment(X2,X1,X3),X4),X2)
| subset(initial_segment(X2,X1,X3),X4) ),
inference(spm,[status(thm)],[24,18,theory(equality)]) ).
cnf(116,negated_conjecture,
( ~ subset(initial_segment(esk13_0,member_predicate,esk12_0),esk13_0)
| ~ subset(esk13_0,initial_segment(esk13_0,member_predicate,esk12_0)) ),
inference(spm,[status(thm)],[104,53,theory(equality)]) ).
cnf(121,plain,
( subset(X1,initial_segment(X2,X3,X4))
| ~ apply(X3,esk1_2(X1,initial_segment(X2,X3,X4)),X2)
| ~ member(esk1_2(X1,initial_segment(X2,X3,X4)),X4) ),
inference(spm,[status(thm)],[17,23,theory(equality)]) ).
cnf(220,negated_conjecture,
( member(X1,esk12_0)
| ~ member(X1,X2)
| ~ member(X2,esk12_0) ),
inference(spm,[status(thm)],[113,106,theory(equality)]) ).
cnf(230,negated_conjecture,
( member(X1,esk12_0)
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[220,105,theory(equality)]) ).
cnf(242,negated_conjecture,
( subset(X1,esk12_0)
| ~ member(esk1_2(X1,esk12_0),esk13_0) ),
inference(spm,[status(thm)],[17,230,theory(equality)]) ).
cnf(315,plain,
( member(esk1_2(initial_segment(X1,member_predicate,X2),X3),X1)
| subset(initial_segment(X1,member_predicate,X2),X3) ),
inference(spm,[status(thm)],[69,115,theory(equality)]) ).
cnf(325,plain,
subset(initial_segment(X1,member_predicate,X2),X1),
inference(spm,[status(thm)],[17,315,theory(equality)]) ).
cnf(331,negated_conjecture,
subset(initial_segment(esk13_0,member_predicate,X1),esk12_0),
inference(spm,[status(thm)],[242,315,theory(equality)]) ).
cnf(337,negated_conjecture,
( $false
| ~ subset(esk13_0,initial_segment(esk13_0,member_predicate,esk12_0)) ),
inference(rw,[status(thm)],[116,325,theory(equality)]) ).
cnf(338,negated_conjecture,
~ subset(esk13_0,initial_segment(esk13_0,member_predicate,esk12_0)),
inference(cn,[status(thm)],[337,theory(equality)]) ).
cnf(340,negated_conjecture,
( member(X1,esk12_0)
| ~ member(X1,initial_segment(esk13_0,member_predicate,X2)) ),
inference(spm,[status(thm)],[19,331,theory(equality)]) ).
cnf(353,negated_conjecture,
( member(esk1_2(initial_segment(esk13_0,member_predicate,X1),X2),esk12_0)
| subset(initial_segment(esk13_0,member_predicate,X1),X2) ),
inference(spm,[status(thm)],[340,18,theory(equality)]) ).
cnf(390,plain,
( subset(X1,initial_segment(X2,member_predicate,X3))
| ~ member(esk1_2(X1,initial_segment(X2,member_predicate,X3)),X3)
| ~ member(esk1_2(X1,initial_segment(X2,member_predicate,X3)),X2) ),
inference(spm,[status(thm)],[121,68,theory(equality)]) ).
cnf(391,plain,
( subset(initial_segment(X1,X2,X3),initial_segment(X1,X2,X4))
| ~ member(esk1_2(initial_segment(X1,X2,X3),initial_segment(X1,X2,X4)),X4) ),
inference(spm,[status(thm)],[121,115,theory(equality)]) ).
cnf(23916,negated_conjecture,
subset(initial_segment(esk13_0,member_predicate,X1),initial_segment(esk13_0,member_predicate,esk12_0)),
inference(spm,[status(thm)],[391,353,theory(equality)]) ).
cnf(23936,negated_conjecture,
( member(X1,initial_segment(esk13_0,member_predicate,esk12_0))
| ~ member(X1,initial_segment(esk13_0,member_predicate,X2)) ),
inference(spm,[status(thm)],[19,23916,theory(equality)]) ).
cnf(24799,plain,
( subset(X1,initial_segment(X2,member_predicate,X1))
| ~ member(esk1_2(X1,initial_segment(X2,member_predicate,X1)),X2) ),
inference(spm,[status(thm)],[390,18,theory(equality)]) ).
cnf(26936,plain,
subset(X1,initial_segment(X1,member_predicate,X1)),
inference(spm,[status(thm)],[24799,18,theory(equality)]) ).
cnf(26988,plain,
( member(X1,initial_segment(X2,member_predicate,X2))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[19,26936,theory(equality)]) ).
cnf(27075,negated_conjecture,
( member(X1,initial_segment(esk13_0,member_predicate,esk12_0))
| ~ member(X1,esk13_0) ),
inference(spm,[status(thm)],[23936,26988,theory(equality)]) ).
cnf(27094,negated_conjecture,
( subset(X1,initial_segment(esk13_0,member_predicate,esk12_0))
| ~ member(esk1_2(X1,initial_segment(esk13_0,member_predicate,esk12_0)),esk13_0) ),
inference(spm,[status(thm)],[17,27075,theory(equality)]) ).
cnf(40582,negated_conjecture,
subset(esk13_0,initial_segment(esk13_0,member_predicate,esk12_0)),
inference(spm,[status(thm)],[27094,18,theory(equality)]) ).
cnf(40592,negated_conjecture,
$false,
inference(sr,[status(thm)],[40582,338,theory(equality)]) ).
cnf(40593,negated_conjecture,
$false,
40592,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET811+4.p
% --creating new selector for [SET006+0.ax, SET006+4.ax]
% -running prover on /tmp/tmpNV_Zb-/sel_SET811+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET811+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET811+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET811+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
%
%------------------------------------------------------------------------------