TSTP Solution File: SET807+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET807+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 03:40:48 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 229 ( 0 equ)
% Maximal formula atoms : 46 ( 4 avg)
% Number of connectives : 271 ( 88 ~; 115 |; 61 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 1 sgn 62 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpk0U4Cr/sel_SET807+4.p_1',subset) ).
fof(3,axiom,
! [X4,X5] :
( pre_order(X4,X5)
<=> ( ! [X3] :
( member(X3,X5)
=> apply(X4,X3,X3) )
& ! [X3,X6,X7] :
( ( member(X3,X5)
& member(X6,X5)
& member(X7,X5) )
=> ( ( apply(X4,X3,X6)
& apply(X4,X6,X7) )
=> apply(X4,X3,X7) ) ) ) ),
file('/tmp/tmpk0U4Cr/sel_SET807+4.p_1',pre_order) ).
fof(4,conjecture,
! [X5] : pre_order(subset_predicate,power_set(X5)),
file('/tmp/tmpk0U4Cr/sel_SET807+4.p_1',thIV18a) ).
fof(5,axiom,
! [X3,X6] :
( apply(subset_predicate,X3,X6)
<=> subset(X3,X6) ),
file('/tmp/tmpk0U4Cr/sel_SET807+4.p_1',rel_subset) ).
fof(6,negated_conjecture,
~ ! [X5] : pre_order(subset_predicate,power_set(X5)),
inference(assume_negation,[status(cth)],[4]) ).
fof(7,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(8,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)],[7]) ).
fof(9,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)],[8]) ).
fof(10,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)],[9]) ).
fof(11,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)],[10]) ).
cnf(12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(13,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[11]) ).
cnf(14,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[11]) ).
fof(19,plain,
! [X4,X5] :
( ( ~ pre_order(X4,X5)
| ( ! [X3] :
( ~ member(X3,X5)
| apply(X4,X3,X3) )
& ! [X3,X6,X7] :
( ~ member(X3,X5)
| ~ member(X6,X5)
| ~ member(X7,X5)
| ~ apply(X4,X3,X6)
| ~ apply(X4,X6,X7)
| apply(X4,X3,X7) ) ) )
& ( ? [X3] :
( member(X3,X5)
& ~ apply(X4,X3,X3) )
| ? [X3,X6,X7] :
( member(X3,X5)
& member(X6,X5)
& member(X7,X5)
& apply(X4,X3,X6)
& apply(X4,X6,X7)
& ~ apply(X4,X3,X7) )
| pre_order(X4,X5) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(20,plain,
! [X8,X9] :
( ( ~ pre_order(X8,X9)
| ( ! [X10] :
( ~ member(X10,X9)
| apply(X8,X10,X10) )
& ! [X11,X12,X13] :
( ~ member(X11,X9)
| ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X8,X11,X12)
| ~ apply(X8,X12,X13)
| apply(X8,X11,X13) ) ) )
& ( ? [X14] :
( member(X14,X9)
& ~ apply(X8,X14,X14) )
| ? [X15,X16,X17] :
( member(X15,X9)
& member(X16,X9)
& member(X17,X9)
& apply(X8,X15,X16)
& apply(X8,X16,X17)
& ~ apply(X8,X15,X17) )
| pre_order(X8,X9) ) ),
inference(variable_rename,[status(thm)],[19]) ).
fof(21,plain,
! [X8,X9] :
( ( ~ pre_order(X8,X9)
| ( ! [X10] :
( ~ member(X10,X9)
| apply(X8,X10,X10) )
& ! [X11,X12,X13] :
( ~ member(X11,X9)
| ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X8,X11,X12)
| ~ apply(X8,X12,X13)
| apply(X8,X11,X13) ) ) )
& ( ( member(esk2_2(X8,X9),X9)
& ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9)) )
| ( member(esk3_2(X8,X9),X9)
& member(esk4_2(X8,X9),X9)
& member(esk5_2(X8,X9),X9)
& apply(X8,esk3_2(X8,X9),esk4_2(X8,X9))
& apply(X8,esk4_2(X8,X9),esk5_2(X8,X9))
& ~ apply(X8,esk3_2(X8,X9),esk5_2(X8,X9)) )
| pre_order(X8,X9) ) ),
inference(skolemize,[status(esa)],[20]) ).
fof(22,plain,
! [X8,X9,X10,X11,X12,X13] :
( ( ( ( ~ member(X11,X9)
| ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X8,X11,X12)
| ~ apply(X8,X12,X13)
| apply(X8,X11,X13) )
& ( ~ member(X10,X9)
| apply(X8,X10,X10) ) )
| ~ pre_order(X8,X9) )
& ( ( member(esk2_2(X8,X9),X9)
& ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9)) )
| ( member(esk3_2(X8,X9),X9)
& member(esk4_2(X8,X9),X9)
& member(esk5_2(X8,X9),X9)
& apply(X8,esk3_2(X8,X9),esk4_2(X8,X9))
& apply(X8,esk4_2(X8,X9),esk5_2(X8,X9))
& ~ apply(X8,esk3_2(X8,X9),esk5_2(X8,X9)) )
| pre_order(X8,X9) ) ),
inference(shift_quantors,[status(thm)],[21]) ).
fof(23,plain,
! [X8,X9,X10,X11,X12,X13] :
( ( ~ member(X11,X9)
| ~ member(X12,X9)
| ~ member(X13,X9)
| ~ apply(X8,X11,X12)
| ~ apply(X8,X12,X13)
| apply(X8,X11,X13)
| ~ pre_order(X8,X9) )
& ( ~ member(X10,X9)
| apply(X8,X10,X10)
| ~ pre_order(X8,X9) )
& ( member(esk3_2(X8,X9),X9)
| member(esk2_2(X8,X9),X9)
| pre_order(X8,X9) )
& ( member(esk4_2(X8,X9),X9)
| member(esk2_2(X8,X9),X9)
| pre_order(X8,X9) )
& ( member(esk5_2(X8,X9),X9)
| member(esk2_2(X8,X9),X9)
| pre_order(X8,X9) )
& ( apply(X8,esk3_2(X8,X9),esk4_2(X8,X9))
| member(esk2_2(X8,X9),X9)
| pre_order(X8,X9) )
& ( apply(X8,esk4_2(X8,X9),esk5_2(X8,X9))
| member(esk2_2(X8,X9),X9)
| pre_order(X8,X9) )
& ( ~ apply(X8,esk3_2(X8,X9),esk5_2(X8,X9))
| member(esk2_2(X8,X9),X9)
| pre_order(X8,X9) )
& ( member(esk3_2(X8,X9),X9)
| ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9))
| pre_order(X8,X9) )
& ( member(esk4_2(X8,X9),X9)
| ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9))
| pre_order(X8,X9) )
& ( member(esk5_2(X8,X9),X9)
| ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9))
| pre_order(X8,X9) )
& ( apply(X8,esk3_2(X8,X9),esk4_2(X8,X9))
| ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9))
| pre_order(X8,X9) )
& ( apply(X8,esk4_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9))
| pre_order(X8,X9) )
& ( ~ apply(X8,esk3_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X8,esk2_2(X8,X9),esk2_2(X8,X9))
| pre_order(X8,X9) ) ),
inference(distribute,[status(thm)],[22]) ).
cnf(24,plain,
( pre_order(X1,X2)
| ~ apply(X1,esk2_2(X1,X2),esk2_2(X1,X2))
| ~ apply(X1,esk3_2(X1,X2),esk5_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(25,plain,
( pre_order(X1,X2)
| apply(X1,esk4_2(X1,X2),esk5_2(X1,X2))
| ~ apply(X1,esk2_2(X1,X2),esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[23]) ).
cnf(26,plain,
( pre_order(X1,X2)
| apply(X1,esk3_2(X1,X2),esk4_2(X1,X2))
| ~ apply(X1,esk2_2(X1,X2),esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(38,negated_conjecture,
? [X5] : ~ pre_order(subset_predicate,power_set(X5)),
inference(fof_nnf,[status(thm)],[6]) ).
fof(39,negated_conjecture,
? [X6] : ~ pre_order(subset_predicate,power_set(X6)),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,negated_conjecture,
~ pre_order(subset_predicate,power_set(esk6_0)),
inference(skolemize,[status(esa)],[39]) ).
cnf(41,negated_conjecture,
~ pre_order(subset_predicate,power_set(esk6_0)),
inference(split_conjunct,[status(thm)],[40]) ).
fof(42,plain,
! [X3,X6] :
( ( ~ apply(subset_predicate,X3,X6)
| subset(X3,X6) )
& ( ~ subset(X3,X6)
| apply(subset_predicate,X3,X6) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(43,plain,
! [X7,X8] :
( ( ~ apply(subset_predicate,X7,X8)
| subset(X7,X8) )
& ( ~ subset(X7,X8)
| apply(subset_predicate,X7,X8) ) ),
inference(variable_rename,[status(thm)],[42]) ).
cnf(44,plain,
( apply(subset_predicate,X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,plain,
( subset(X1,X2)
| ~ apply(subset_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(47,plain,
subset(X1,X1),
inference(spm,[status(thm)],[12,13,theory(equality)]) ).
cnf(56,plain,
apply(subset_predicate,X1,X1),
inference(spm,[status(thm)],[44,47,theory(equality)]) ).
cnf(64,plain,
( apply(subset_predicate,esk3_2(subset_predicate,X1),esk4_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[26,56,theory(equality)]) ).
cnf(65,plain,
( apply(subset_predicate,esk4_2(subset_predicate,X1),esk5_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[25,56,theory(equality)]) ).
cnf(66,plain,
( pre_order(subset_predicate,X1)
| ~ apply(subset_predicate,esk3_2(subset_predicate,X1),esk5_2(subset_predicate,X1)) ),
inference(spm,[status(thm)],[24,56,theory(equality)]) ).
cnf(93,plain,
( subset(esk3_2(subset_predicate,X1),esk4_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[45,64,theory(equality)]) ).
cnf(97,plain,
( member(X1,esk4_2(subset_predicate,X2))
| pre_order(subset_predicate,X2)
| ~ member(X1,esk3_2(subset_predicate,X2)) ),
inference(spm,[status(thm)],[14,93,theory(equality)]) ).
cnf(101,plain,
( subset(esk4_2(subset_predicate,X1),esk5_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[45,65,theory(equality)]) ).
cnf(105,plain,
( member(X1,esk5_2(subset_predicate,X2))
| pre_order(subset_predicate,X2)
| ~ member(X1,esk4_2(subset_predicate,X2)) ),
inference(spm,[status(thm)],[14,101,theory(equality)]) ).
cnf(149,plain,
( pre_order(subset_predicate,X1)
| member(esk1_2(esk3_2(subset_predicate,X1),X2),esk4_2(subset_predicate,X1))
| subset(esk3_2(subset_predicate,X1),X2) ),
inference(spm,[status(thm)],[97,13,theory(equality)]) ).
cnf(187,plain,
( pre_order(subset_predicate,X1)
| member(esk1_2(esk3_2(subset_predicate,X1),X2),esk5_2(subset_predicate,X1))
| subset(esk3_2(subset_predicate,X1),X2) ),
inference(spm,[status(thm)],[105,149,theory(equality)]) ).
cnf(261,plain,
( subset(esk3_2(subset_predicate,X1),esk5_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[12,187,theory(equality)]) ).
cnf(265,plain,
( apply(subset_predicate,esk3_2(subset_predicate,X1),esk5_2(subset_predicate,X1))
| pre_order(subset_predicate,X1) ),
inference(spm,[status(thm)],[44,261,theory(equality)]) ).
cnf(269,plain,
pre_order(subset_predicate,X1),
inference(csr,[status(thm)],[265,66]) ).
cnf(271,negated_conjecture,
$false,
inference(rw,[status(thm)],[41,269,theory(equality)]) ).
cnf(272,negated_conjecture,
$false,
inference(cn,[status(thm)],[271,theory(equality)]) ).
cnf(273,negated_conjecture,
$false,
272,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET807+4.p
% --creating new selector for [SET006+0.ax, SET006+2.ax]
% -running prover on /tmp/tmpk0U4Cr/sel_SET807+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET807+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET807+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET807+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
%
%------------------------------------------------------------------------------