TSTP Solution File: SWV182+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWV182+1 : TPTP v5.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 12:22:15 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 30 unt; 0 def)
% Number of atoms : 299 ( 66 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 353 ( 124 ~; 115 |; 76 &)
% ( 1 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-3 aty)
% Number of variables : 102 ( 0 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2,X3] :
( ( leq(X1,X2)
& leq(X2,X3) )
=> leq(X1,X3) ),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',transitivity_leq) ).
fof(4,axiom,
! [X1,X2] :
( ( leq(X1,X2)
& X1 != X2 )
=> gt(X2,X1) ),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',leq_gt2) ).
fof(5,axiom,
! [X1,X2] :
( gt(X2,X1)
=> leq(X1,X2) ),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',leq_gt1) ).
fof(6,axiom,
! [X1] : plus(n1,X1) = succ(X1),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',succ_plus_1_l) ).
fof(14,axiom,
! [X1] : plus(X1,n1) = succ(X1),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',succ_plus_1_r) ).
fof(15,axiom,
! [X1] : ~ gt(X1,X1),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',irreflexivity_gt) ).
fof(21,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> gt(succ(X2),X1) ),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',leq_succ_gt_equiv) ).
fof(36,axiom,
gt(n1,n0),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',gt_1_0) ).
fof(39,conjecture,
( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n135299) )
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select3(q_init,X4,X5) = init ) )
& ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select3(center_init,X6,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,n4) )
=> a_select2(mu_init,X7) = init ) )
& ( gt(loopcounter,n0)
=> ! [X8] :
( ( leq(n0,X8)
& leq(X8,n4) )
=> a_select2(rho_init,X8) = init ) )
& ( gt(loopcounter,n0)
=> ! [X9] :
( ( leq(n0,X9)
& leq(X9,n4) )
=> a_select2(sigma_init,X9) = init ) ) )
=> ! [X10] :
( ( leq(n0,X10)
& leq(X10,n4) )
=> a_select2(rho_init,X10) = init ) ),
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',cl5_nebula_init_0086) ).
fof(59,axiom,
succ(n0) = n1,
file('/tmp/tmpAz6Y5m/sel_SWV182+1.p_1',successor_1) ).
fof(64,negated_conjecture,
~ ( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n135299) )
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select3(q_init,X4,X5) = init ) )
& ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select3(center_init,X6,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,n4) )
=> a_select2(mu_init,X7) = init ) )
& ( gt(loopcounter,n0)
=> ! [X8] :
( ( leq(n0,X8)
& leq(X8,n4) )
=> a_select2(rho_init,X8) = init ) )
& ( gt(loopcounter,n0)
=> ! [X9] :
( ( leq(n0,X9)
& leq(X9,n4) )
=> a_select2(sigma_init,X9) = init ) ) )
=> ! [X10] :
( ( leq(n0,X10)
& leq(X10,n4) )
=> a_select2(rho_init,X10) = init ) ),
inference(assume_negation,[status(cth)],[39]) ).
fof(65,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[15,theory(equality)]) ).
fof(66,plain,
( epred1_0
=> ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& ! [X4] :
( ( leq(n0,X4)
& leq(X4,n135299) )
=> ! [X5] :
( ( leq(n0,X5)
& leq(X5,n4) )
=> a_select3(q_init,X4,X5) = init ) )
& ! [X6] :
( ( leq(n0,X6)
& leq(X6,n4) )
=> a_select3(center_init,X6,n0) = init )
& ( gt(loopcounter,n0)
=> ! [X7] :
( ( leq(n0,X7)
& leq(X7,n4) )
=> a_select2(mu_init,X7) = init ) )
& ( gt(loopcounter,n0)
=> ! [X8] :
( ( leq(n0,X8)
& leq(X8,n4) )
=> a_select2(rho_init,X8) = init ) )
& ( gt(loopcounter,n0)
=> ! [X9] :
( ( leq(n0,X9)
& leq(X9,n4) )
=> a_select2(sigma_init,X9) = init ) ) ) ),
introduced(definition) ).
fof(67,negated_conjecture,
~ ( epred1_0
=> ! [X10] :
( ( leq(n0,X10)
& leq(X10,n4) )
=> a_select2(rho_init,X10) = init ) ),
inference(apply_def,[status(esa)],[64,66,theory(equality)]) ).
fof(73,plain,
! [X1,X2,X3] :
( ~ leq(X1,X2)
| ~ leq(X2,X3)
| leq(X1,X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(74,plain,
! [X4,X5,X6] :
( ~ leq(X4,X5)
| ~ leq(X5,X6)
| leq(X4,X6) ),
inference(variable_rename,[status(thm)],[73]) ).
cnf(75,plain,
( leq(X1,X2)
| ~ leq(X3,X2)
| ~ leq(X1,X3) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(76,plain,
! [X1,X2] :
( ~ leq(X1,X2)
| X1 = X2
| gt(X2,X1) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(77,plain,
! [X3,X4] :
( ~ leq(X3,X4)
| X3 = X4
| gt(X4,X3) ),
inference(variable_rename,[status(thm)],[76]) ).
cnf(78,plain,
( gt(X1,X2)
| X2 = X1
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(79,plain,
! [X1,X2] :
( ~ gt(X2,X1)
| leq(X1,X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(80,plain,
! [X3,X4] :
( ~ gt(X4,X3)
| leq(X3,X4) ),
inference(variable_rename,[status(thm)],[79]) ).
cnf(81,plain,
( leq(X1,X2)
| ~ gt(X2,X1) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(82,plain,
! [X2] : plus(n1,X2) = succ(X2),
inference(variable_rename,[status(thm)],[6]) ).
cnf(83,plain,
plus(n1,X1) = succ(X1),
inference(split_conjunct,[status(thm)],[82]) ).
fof(99,plain,
! [X2] : plus(X2,n1) = succ(X2),
inference(variable_rename,[status(thm)],[14]) ).
cnf(100,plain,
plus(X1,n1) = succ(X1),
inference(split_conjunct,[status(thm)],[99]) ).
fof(101,plain,
! [X2] : ~ gt(X2,X2),
inference(variable_rename,[status(thm)],[65]) ).
cnf(102,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[101]) ).
fof(113,plain,
! [X1,X2] :
( ( ~ leq(X1,X2)
| gt(succ(X2),X1) )
& ( ~ gt(succ(X2),X1)
| leq(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(114,plain,
! [X3,X4] :
( ( ~ leq(X3,X4)
| gt(succ(X4),X3) )
& ( ~ gt(succ(X4),X3)
| leq(X3,X4) ) ),
inference(variable_rename,[status(thm)],[113]) ).
cnf(116,plain,
( gt(succ(X1),X2)
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[114]) ).
cnf(135,plain,
gt(n1,n0),
inference(split_conjunct,[status(thm)],[36]) ).
fof(138,negated_conjecture,
( epred1_0
& ? [X10] :
( leq(n0,X10)
& leq(X10,n4)
& a_select2(rho_init,X10) != init ) ),
inference(fof_nnf,[status(thm)],[67]) ).
fof(139,negated_conjecture,
( epred1_0
& ? [X11] :
( leq(n0,X11)
& leq(X11,n4)
& a_select2(rho_init,X11) != init ) ),
inference(variable_rename,[status(thm)],[138]) ).
fof(140,negated_conjecture,
( epred1_0
& leq(n0,esk1_0)
& leq(esk1_0,n4)
& a_select2(rho_init,esk1_0) != init ),
inference(skolemize,[status(esa)],[139]) ).
cnf(141,negated_conjecture,
a_select2(rho_init,esk1_0) != init,
inference(split_conjunct,[status(thm)],[140]) ).
cnf(142,negated_conjecture,
leq(esk1_0,n4),
inference(split_conjunct,[status(thm)],[140]) ).
cnf(143,negated_conjecture,
leq(n0,esk1_0),
inference(split_conjunct,[status(thm)],[140]) ).
cnf(144,negated_conjecture,
epred1_0,
inference(split_conjunct,[status(thm)],[140]) ).
cnf(176,plain,
succ(n0) = n1,
inference(split_conjunct,[status(thm)],[59]) ).
fof(181,plain,
( ~ epred1_0
| ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& ! [X4] :
( ~ leq(n0,X4)
| ~ leq(X4,n135299)
| ! [X5] :
( ~ leq(n0,X5)
| ~ leq(X5,n4)
| a_select3(q_init,X4,X5) = init ) )
& ! [X6] :
( ~ leq(n0,X6)
| ~ leq(X6,n4)
| a_select3(center_init,X6,n0) = init )
& ( ~ gt(loopcounter,n0)
| ! [X7] :
( ~ leq(n0,X7)
| ~ leq(X7,n4)
| a_select2(mu_init,X7) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X8] :
( ~ leq(n0,X8)
| ~ leq(X8,n4)
| a_select2(rho_init,X8) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X9] :
( ~ leq(n0,X9)
| ~ leq(X9,n4)
| a_select2(sigma_init,X9) = init ) ) ) ),
inference(fof_nnf,[status(thm)],[66]) ).
fof(182,plain,
( ~ epred1_0
| ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& ! [X10] :
( ~ leq(n0,X10)
| ~ leq(X10,n135299)
| ! [X11] :
( ~ leq(n0,X11)
| ~ leq(X11,n4)
| a_select3(q_init,X10,X11) = init ) )
& ! [X12] :
( ~ leq(n0,X12)
| ~ leq(X12,n4)
| a_select3(center_init,X12,n0) = init )
& ( ~ gt(loopcounter,n0)
| ! [X13] :
( ~ leq(n0,X13)
| ~ leq(X13,n4)
| a_select2(mu_init,X13) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X14] :
( ~ leq(n0,X14)
| ~ leq(X14,n4)
| a_select2(rho_init,X14) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X15] :
( ~ leq(n0,X15)
| ~ leq(X15,n4)
| a_select2(sigma_init,X15) = init ) ) ) ),
inference(variable_rename,[status(thm)],[181]) ).
fof(183,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( ( ~ leq(n0,X15)
| ~ leq(X15,n4)
| a_select2(sigma_init,X15) = init
| ~ gt(loopcounter,n0) )
& ( ~ leq(n0,X14)
| ~ leq(X14,n4)
| a_select2(rho_init,X14) = init
| ~ gt(loopcounter,n0) )
& ( ~ leq(n0,X13)
| ~ leq(X13,n4)
| a_select2(mu_init,X13) = init
| ~ gt(loopcounter,n0) )
& ( ~ leq(n0,X12)
| ~ leq(X12,n4)
| a_select3(center_init,X12,n0) = init )
& ( ~ leq(n0,X11)
| ~ leq(X11,n4)
| a_select3(q_init,X10,X11) = init
| ~ leq(n0,X10)
| ~ leq(X10,n135299) )
& leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter) )
| ~ epred1_0 ),
inference(shift_quantors,[status(thm)],[182]) ).
fof(184,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( ~ leq(n0,X15)
| ~ leq(X15,n4)
| a_select2(sigma_init,X15) = init
| ~ gt(loopcounter,n0)
| ~ epred1_0 )
& ( ~ leq(n0,X14)
| ~ leq(X14,n4)
| a_select2(rho_init,X14) = init
| ~ gt(loopcounter,n0)
| ~ epred1_0 )
& ( ~ leq(n0,X13)
| ~ leq(X13,n4)
| a_select2(mu_init,X13) = init
| ~ gt(loopcounter,n0)
| ~ epred1_0 )
& ( ~ leq(n0,X12)
| ~ leq(X12,n4)
| a_select3(center_init,X12,n0) = init
| ~ epred1_0 )
& ( ~ leq(n0,X11)
| ~ leq(X11,n4)
| a_select3(q_init,X10,X11) = init
| ~ leq(n0,X10)
| ~ leq(X10,n135299)
| ~ epred1_0 )
& ( leq(tptp_float_0_001,pv76)
| ~ epred1_0 )
& ( leq(n1,loopcounter)
| ~ epred1_0 ) ),
inference(distribute,[status(thm)],[183]) ).
cnf(185,plain,
( leq(n1,loopcounter)
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[184]) ).
cnf(190,plain,
( a_select2(rho_init,X1) = init
| ~ epred1_0
| ~ gt(loopcounter,n0)
| ~ leq(X1,n4)
| ~ leq(n0,X1) ),
inference(split_conjunct,[status(thm)],[184]) ).
cnf(193,plain,
plus(n0,n1) = n1,
inference(rw,[status(thm)],[176,100,theory(equality)]),
[unfolding] ).
cnf(194,plain,
plus(n1,X1) = plus(X1,n1),
inference(rw,[status(thm)],[83,100,theory(equality)]),
[unfolding] ).
cnf(211,plain,
( gt(plus(X1,n1),X2)
| ~ leq(X2,X1) ),
inference(rw,[status(thm)],[116,100,theory(equality)]),
[unfolding] ).
cnf(214,plain,
( leq(n1,loopcounter)
| $false ),
inference(rw,[status(thm)],[185,144,theory(equality)]) ).
cnf(215,plain,
leq(n1,loopcounter),
inference(cn,[status(thm)],[214,theory(equality)]) ).
cnf(223,plain,
leq(n0,n1),
inference(spm,[status(thm)],[81,135,theory(equality)]) ).
cnf(249,plain,
( leq(X1,loopcounter)
| ~ leq(X1,n1) ),
inference(spm,[status(thm)],[75,215,theory(equality)]) ).
cnf(258,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[193,194,theory(equality)]) ).
cnf(271,plain,
~ leq(plus(X1,n1),X1),
inference(spm,[status(thm)],[102,211,theory(equality)]) ).
cnf(348,plain,
( a_select2(rho_init,X1) = init
| $false
| ~ leq(X1,n4)
| ~ leq(n0,X1)
| ~ gt(loopcounter,n0) ),
inference(rw,[status(thm)],[190,144,theory(equality)]) ).
cnf(349,plain,
( a_select2(rho_init,X1) = init
| ~ leq(X1,n4)
| ~ leq(n0,X1)
| ~ gt(loopcounter,n0) ),
inference(cn,[status(thm)],[348,theory(equality)]) ).
cnf(350,plain,
( ~ gt(loopcounter,n0)
| ~ leq(esk1_0,n4)
| ~ leq(n0,esk1_0) ),
inference(spm,[status(thm)],[141,349,theory(equality)]) ).
cnf(420,plain,
~ leq(plus(n1,X1),X1),
inference(spm,[status(thm)],[271,194,theory(equality)]) ).
cnf(442,plain,
~ leq(n1,n0),
inference(spm,[status(thm)],[420,258,theory(equality)]) ).
cnf(514,plain,
( loopcounter = n0
| ~ leq(esk1_0,n4)
| ~ leq(n0,esk1_0)
| ~ leq(n0,loopcounter) ),
inference(spm,[status(thm)],[350,78,theory(equality)]) ).
cnf(515,negated_conjecture,
( loopcounter = n0
| ~ leq(n0,esk1_0)
| ~ leq(n0,loopcounter) ),
inference(spm,[status(thm)],[514,142,theory(equality)]) ).
cnf(516,negated_conjecture,
( loopcounter = n0
| ~ leq(n0,loopcounter) ),
inference(spm,[status(thm)],[515,143,theory(equality)]) ).
cnf(553,plain,
( loopcounter = n0
| ~ leq(n0,n1) ),
inference(spm,[status(thm)],[516,249,theory(equality)]) ).
cnf(556,plain,
( loopcounter = n0
| $false ),
inference(rw,[status(thm)],[553,223,theory(equality)]) ).
cnf(557,plain,
loopcounter = n0,
inference(cn,[status(thm)],[556,theory(equality)]) ).
cnf(558,plain,
leq(n1,n0),
inference(rw,[status(thm)],[215,557,theory(equality)]) ).
cnf(559,plain,
$false,
inference(sr,[status(thm)],[558,442,theory(equality)]) ).
cnf(560,plain,
$false,
559,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV182+1.p
% --creating new selector for [SWV003+0.ax]
% -running prover on /tmp/tmpAz6Y5m/sel_SWV182+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV182+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV182+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV182+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
%
%------------------------------------------------------------------------------