TSTP Solution File: SWV403+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV403+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 12:38:59 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 69 ( 11 unt; 0 def)
% Number of atoms : 202 ( 45 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 217 ( 84 ~; 88 |; 34 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 148 ( 7 sgn 88 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2,X3,X4] :
( less_than(X3,X4)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',ax30) ).
fof(4,axiom,
! [X1,X2,X3,X4] :
( strictly_less_than(X4,X3)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',ax29) ).
fof(6,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',totality) ).
fof(7,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',stricly_smaller_definition) ).
fof(10,axiom,
! [X1,X2,X3,X4,X5] :
( pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
<=> ( pair_in_list(X1,X3,X5)
| ( X2 = X3
& X4 = X5 ) ) ),
file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',ax23) ).
fof(12,conjecture,
! [X1] :
( ! [X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) )
=> ! [X5,X6,X7,X8,X9] :
( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
& strictly_less_than(X6,X7) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',l39_co) ).
fof(13,negated_conjecture,
~ ! [X1] :
( ! [X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) )
=> ! [X5,X6,X7,X8,X9] :
( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
& strictly_less_than(X6,X7) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(14,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(22,plain,
! [X1,X2,X3,X4] :
( ~ less_than(X3,X4)
| update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(23,plain,
! [X5,X6,X7,X8] :
( ~ less_than(X7,X8)
| update_slb(insert_slb(X5,pair(X6,X8)),X7) = insert_slb(update_slb(X5,X7),pair(X6,X8)) ),
inference(variable_rename,[status(thm)],[22]) ).
cnf(24,plain,
( update_slb(insert_slb(X1,pair(X2,X3)),X4) = insert_slb(update_slb(X1,X4),pair(X2,X3))
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[23]) ).
fof(25,plain,
! [X1,X2,X3,X4] :
( ~ strictly_less_than(X4,X3)
| update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(26,plain,
! [X5,X6,X7,X8] :
( ~ strictly_less_than(X8,X7)
| update_slb(insert_slb(X5,pair(X6,X8)),X7) = insert_slb(update_slb(X5,X7),pair(X6,X7)) ),
inference(variable_rename,[status(thm)],[25]) ).
cnf(27,plain,
( update_slb(insert_slb(X1,pair(X2,X3)),X4) = insert_slb(update_slb(X1,X4),pair(X2,X4))
| ~ strictly_less_than(X3,X4) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(30,plain,
! [X3,X4] :
( less_than(X3,X4)
| less_than(X4,X3) ),
inference(variable_rename,[status(thm)],[6]) ).
cnf(31,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X1,X2] :
( ( ~ strictly_less_than(X1,X2)
| ( less_than(X1,X2)
& ~ less_than(X2,X1) ) )
& ( ~ less_than(X1,X2)
| less_than(X2,X1)
| strictly_less_than(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(33,plain,
! [X3,X4] :
( ( ~ strictly_less_than(X3,X4)
| ( less_than(X3,X4)
& ~ less_than(X4,X3) ) )
& ( ~ less_than(X3,X4)
| less_than(X4,X3)
| strictly_less_than(X3,X4) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X3,X4] :
( ( less_than(X3,X4)
| ~ strictly_less_than(X3,X4) )
& ( ~ less_than(X4,X3)
| ~ strictly_less_than(X3,X4) )
& ( ~ less_than(X3,X4)
| less_than(X4,X3)
| strictly_less_than(X3,X4) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( ~ strictly_less_than(X1,X2)
| ~ less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(46,plain,
! [X1,X2,X3,X4,X5] :
( ( ~ pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
| pair_in_list(X1,X3,X5)
| ( X2 = X3
& X4 = X5 ) )
& ( ( ~ pair_in_list(X1,X3,X5)
& ( X2 != X3
| X4 != X5 ) )
| pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(47,plain,
! [X6,X7,X8,X9,X10] :
( ( ~ pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10)
| pair_in_list(X6,X8,X10)
| ( X7 = X8
& X9 = X10 ) )
& ( ( ~ pair_in_list(X6,X8,X10)
& ( X7 != X8
| X9 != X10 ) )
| pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) ) ),
inference(variable_rename,[status(thm)],[46]) ).
fof(48,plain,
! [X6,X7,X8,X9,X10] :
( ( X7 = X8
| pair_in_list(X6,X8,X10)
| ~ pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) )
& ( X9 = X10
| pair_in_list(X6,X8,X10)
| ~ pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) )
& ( ~ pair_in_list(X6,X8,X10)
| pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) )
& ( X7 != X8
| X9 != X10
| pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(49,plain,
( pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5)
| X3 != X5
| X2 != X4 ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,plain,
( pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5)
| ~ pair_in_list(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(51,plain,
( pair_in_list(X1,X4,X5)
| X3 = X5
| ~ pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(52,plain,
( pair_in_list(X1,X4,X5)
| X2 = X4
| ~ pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(55,negated_conjecture,
? [X1] :
( ! [X2,X3,X4] :
( ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X3,X4)
| pair_in_list(update_slb(X1,X4),X2,X4) )
& ? [X5,X6,X7,X8,X9] :
( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
& strictly_less_than(X6,X7)
& ~ pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(56,negated_conjecture,
? [X10] :
( ! [X11,X12,X13] :
( ~ pair_in_list(X10,X11,X12)
| ~ strictly_less_than(X12,X13)
| pair_in_list(update_slb(X10,X13),X11,X13) )
& ? [X14,X15,X16,X17,X18] :
( pair_in_list(insert_slb(X10,pair(X17,X18)),X14,X15)
& strictly_less_than(X15,X16)
& ~ pair_in_list(update_slb(insert_slb(X10,pair(X17,X18)),X16),X14,X16) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,negated_conjecture,
( ! [X11,X12,X13] :
( ~ pair_in_list(esk1_0,X11,X12)
| ~ strictly_less_than(X12,X13)
| pair_in_list(update_slb(esk1_0,X13),X11,X13) )
& pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0)
& strictly_less_than(esk3_0,esk4_0)
& ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[56]) ).
fof(58,negated_conjecture,
! [X11,X12,X13] :
( ( ~ pair_in_list(esk1_0,X11,X12)
| ~ strictly_less_than(X12,X13)
| pair_in_list(update_slb(esk1_0,X13),X11,X13) )
& pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0)
& strictly_less_than(esk3_0,esk4_0)
& ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0) ),
inference(shift_quantors,[status(thm)],[57]) ).
cnf(59,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,negated_conjecture,
strictly_less_than(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(61,negated_conjecture,
pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(62,negated_conjecture,
( pair_in_list(update_slb(esk1_0,X1),X2,X1)
| ~ strictly_less_than(X3,X1)
| ~ pair_in_list(esk1_0,X2,X3) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(68,negated_conjecture,
~ less_than(esk4_0,esk3_0),
inference(spm,[status(thm)],[36,60,theory(equality)]) ).
cnf(69,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[35,31]) ).
cnf(76,plain,
( pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X3)
| X2 != X4 ),
inference(er,[status(thm)],[49,theory(equality)]) ).
cnf(77,plain,
pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
inference(er,[status(thm)],[76,theory(equality)]) ).
cnf(79,negated_conjecture,
( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk6_0)),esk2_0,esk4_0)
| ~ less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[59,24,theory(equality)]) ).
cnf(80,negated_conjecture,
( esk6_0 = esk3_0
| pair_in_list(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[51,61,theory(equality)]) ).
cnf(82,negated_conjecture,
( esk5_0 = esk2_0
| pair_in_list(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[52,61,theory(equality)]) ).
cnf(85,negated_conjecture,
( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk2_0,esk4_0)
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[59,27,theory(equality)]) ).
cnf(100,negated_conjecture,
( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| esk6_0 = esk3_0
| ~ strictly_less_than(esk3_0,X1) ),
inference(spm,[status(thm)],[62,80,theory(equality)]) ).
cnf(101,negated_conjecture,
( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| esk2_0 = esk5_0
| ~ strictly_less_than(esk3_0,X1) ),
inference(spm,[status(thm)],[62,82,theory(equality)]) ).
cnf(118,negated_conjecture,
( ~ strictly_less_than(esk6_0,esk4_0)
| ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[85,50,theory(equality)]) ).
cnf(119,negated_conjecture,
( esk6_0 = esk3_0
| ~ strictly_less_than(esk6_0,esk4_0)
| ~ strictly_less_than(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[118,100,theory(equality)]) ).
cnf(120,negated_conjecture,
( esk2_0 = esk5_0
| ~ strictly_less_than(esk6_0,esk4_0)
| ~ strictly_less_than(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[118,101,theory(equality)]) ).
cnf(121,negated_conjecture,
( esk6_0 = esk3_0
| ~ strictly_less_than(esk6_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[119,60,theory(equality)]) ).
cnf(122,negated_conjecture,
( esk6_0 = esk3_0
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(cn,[status(thm)],[121,theory(equality)]) ).
cnf(123,negated_conjecture,
( esk2_0 = esk5_0
| ~ strictly_less_than(esk6_0,esk4_0)
| $false ),
inference(rw,[status(thm)],[120,60,theory(equality)]) ).
cnf(124,negated_conjecture,
( esk2_0 = esk5_0
| ~ strictly_less_than(esk6_0,esk4_0) ),
inference(cn,[status(thm)],[123,theory(equality)]) ).
cnf(125,negated_conjecture,
( esk6_0 = esk3_0
| less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[122,69,theory(equality)]) ).
cnf(126,negated_conjecture,
( esk2_0 = esk5_0
| less_than(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[124,69,theory(equality)]) ).
cnf(143,negated_conjecture,
( ~ less_than(esk4_0,esk6_0)
| ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[79,50,theory(equality)]) ).
cnf(144,negated_conjecture,
( esk6_0 = esk3_0
| ~ less_than(esk4_0,esk6_0)
| ~ strictly_less_than(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[143,100,theory(equality)]) ).
cnf(146,negated_conjecture,
( esk6_0 = esk3_0
| ~ less_than(esk4_0,esk6_0)
| $false ),
inference(rw,[status(thm)],[144,60,theory(equality)]) ).
cnf(147,negated_conjecture,
( esk6_0 = esk3_0
| ~ less_than(esk4_0,esk6_0) ),
inference(cn,[status(thm)],[146,theory(equality)]) ).
cnf(150,negated_conjecture,
esk6_0 = esk3_0,
inference(csr,[status(thm)],[147,125]) ).
cnf(152,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk3_0)),esk4_0),esk2_0,esk4_0),
inference(rw,[status(thm)],[59,150,theory(equality)]) ).
cnf(162,negated_conjecture,
( esk2_0 = esk5_0
| less_than(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[126,150,theory(equality)]) ).
cnf(163,negated_conjecture,
esk2_0 = esk5_0,
inference(sr,[status(thm)],[162,68,theory(equality)]) ).
cnf(186,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk3_0)),esk4_0),esk5_0,esk4_0),
inference(rw,[status(thm)],[152,163,theory(equality)]) ).
cnf(188,negated_conjecture,
( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk5_0,esk4_0)
| ~ strictly_less_than(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[186,27,theory(equality)]) ).
cnf(189,negated_conjecture,
( $false
| ~ strictly_less_than(esk3_0,esk4_0) ),
inference(rw,[status(thm)],[188,77,theory(equality)]) ).
cnf(190,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[189,60,theory(equality)]) ).
cnf(191,negated_conjecture,
$false,
inference(cn,[status(thm)],[190,theory(equality)]) ).
cnf(192,negated_conjecture,
$false,
191,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV403+1.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax]
% -running prover on /tmp/tmpop_l-_/sel_SWV403+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV403+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV403+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV403+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
%
%------------------------------------------------------------------------------