TSTP Solution File: MSC010+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MSC010+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 05:34:04 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 55
% Syntax : Number of formulae : 144 ( 19 unt; 20 typ; 0 def)
% Number of atoms : 4859 ( 932 equ)
% Maximal formula atoms : 136 ( 39 avg)
% Number of connectives : 5341 ( 758 ~; 596 |;3540 &)
% ( 168 <=>; 279 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 13 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 152 ( 152 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-3 aty)
% Number of variables : 1258 (1236 !; 0 ?;1258 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(pv64_type,type,
pv64: $i ).
tff(pv63_type,type,
pv63: $i ).
tff(n5_type,type,
n5: $i ).
tff(n0_type,type,
n0: $i ).
tff(init_type,type,
init: $i ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(id_ds1_filter_init_type,type,
id_ds1_filter_init: $i ).
tff(pred_type,type,
pred: $i > $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(pminus_ds1_filter_init_type,type,
pminus_ds1_filter_init: $i ).
tff(xhatmin_ds1_filter_init_type,type,
xhatmin_ds1_filter_init: $i ).
tff(r_ds1_filter_init_type,type,
r_ds1_filter_init: $i ).
tff(n2_type,type,
n2: $i ).
tff(q_ds1_filter_init_type,type,
q_ds1_filter_init: $i ).
tff(dv_ds1_filter_init_type,type,
dv_ds1_filter_init: $i ).
tff(phi_ds1_filter_init_type,type,
phi_ds1_filter_init: $i ).
tff(h_ds1_filter_init_type,type,
h_ds1_filter_init: $i ).
tff(n998_type,type,
n998: $i ).
tff(pv5_type,type,
pv5: $i ).
tff(1,plain,
( ( $false
| $false )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) )
<=> ~ ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ~ ~ ~ ( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
& ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
=> ! [X21: $i,X22: $i] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) )
<=> ~ ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
~ ~ ~ ( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
& ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
=> ! [X21: $i,X22: $i] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n91) ).
tff(5,plain,
~ ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
~ ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ),
inference(or_elim,[status(thm)],[5]) ).
tff(7,plain,
~ ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) )
<=> $false ),
inference(iff_false,[status(thm)],[7]) ).
tff(9,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ( $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) ),
inference(or_elim,[status(thm)],[5]) ).
tff(12,plain,
! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
( ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
<=> $true ),
inference(iff_true,[status(thm)],[12]) ).
tff(14,plain,
! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ),
inference(and_elim,[status(thm)],[11]) ).
tff(15,plain,
( ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(17,plain,
( ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
<=> $true ),
inference(iff_true,[status(thm)],[16]) ).
tff(18,plain,
! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(19,plain,
( ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
<=> $true ),
inference(iff_true,[status(thm)],[18]) ).
tff(20,plain,
! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(21,plain,
( ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
<=> $true ),
inference(iff_true,[status(thm)],[20]) ).
tff(22,plain,
! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(23,plain,
( ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
<=> $true ),
inference(iff_true,[status(thm)],[22]) ).
tff(24,plain,
! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(25,plain,
( ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
<=> $true ),
inference(iff_true,[status(thm)],[24]) ).
tff(26,plain,
! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(27,plain,
( ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
<=> $true ),
inference(iff_true,[status(thm)],[26]) ).
tff(28,plain,
! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(29,plain,
( ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
<=> $true ),
inference(iff_true,[status(thm)],[28]) ).
tff(30,plain,
! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(31,plain,
( ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
<=> $true ),
inference(iff_true,[status(thm)],[30]) ).
tff(32,plain,
leq(pv64,n5),
inference(and_elim,[status(thm)],[11]) ).
tff(33,plain,
( leq(pv64,n5)
<=> $true ),
inference(iff_true,[status(thm)],[32]) ).
tff(34,plain,
leq(pv63,n5),
inference(and_elim,[status(thm)],[11]) ).
tff(35,plain,
( leq(pv63,n5)
<=> $true ),
inference(iff_true,[status(thm)],[34]) ).
tff(36,plain,
leq(pv5,n998),
inference(and_elim,[status(thm)],[11]) ).
tff(37,plain,
( leq(pv5,n998)
<=> $true ),
inference(iff_true,[status(thm)],[36]) ).
tff(38,plain,
leq(n0,pv64),
inference(and_elim,[status(thm)],[11]) ).
tff(39,plain,
( leq(n0,pv64)
<=> $true ),
inference(iff_true,[status(thm)],[38]) ).
tff(40,plain,
leq(n0,pv63),
inference(and_elim,[status(thm)],[11]) ).
tff(41,plain,
( leq(n0,pv63)
<=> $true ),
inference(iff_true,[status(thm)],[40]) ).
tff(42,plain,
leq(n0,pv5),
inference(and_elim,[status(thm)],[11]) ).
tff(43,plain,
( leq(n0,pv5)
<=> $true ),
inference(iff_true,[status(thm)],[42]) ).
tff(44,plain,
pv63 != pv64,
inference(and_elim,[status(thm)],[11]) ).
tff(45,plain,
( ( pv63 != pv64 )
<=> $true ),
inference(iff_true,[status(thm)],[44]) ).
tff(46,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
<=> ( $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true
& $true ) ),
inference(monotonicity,[status(thm)],[45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13]) ).
tff(47,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[46,10]) ).
tff(48,plain,
( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[48,9]) ).
tff(50,plain,
( ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) )
<=> ( $false
| $false ) ),
inference(monotonicity,[status(thm)],[49,8]) ).
tff(51,plain,
( ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[50,1]) ).
tff(52,plain,
( ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) )
<=> ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
=> ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) )
<=> ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
^ [X21: $i,X22: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5) )
<=> ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5) ) )),
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
<=> ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) ) )),
rewrite(
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
<=> ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) ) )),
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
<=> ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) ) )),
trans(
monotonicity(
rewrite(
( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
<=> ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) )),
( ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) )
<=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) )),
rewrite(
( ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) )
<=> ( ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
| ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) )),
( ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) )
<=> ( ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
| ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) )),
( ( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) )
<=> ( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
| ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) )),
rewrite(
( ( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
| ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) )
<=> ( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) )),
( ( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) )
<=> ( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X21: $i,X22: $i] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) )
<=> ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
^ [X19: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [X20: $i] :
rewrite(
( ( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) )
<=> ( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ))),
( ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) )
<=> ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) )),
( ( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
<=> ( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )),
rewrite(
( ( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
<=> ( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )),
( ( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
<=> ( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
<=> ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
^ [X17: $i,X18: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5) )
<=> ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5) ) )),
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
<=> ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) ) )),
rewrite(
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
<=> ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) ) )),
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
<=> ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) ) )),
rewrite(
( ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) )
<=> ( ~ gt(pv63,X17)
| ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )),
( ( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
<=> ( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( ~ gt(pv63,X17)
| ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) ) )),
rewrite(
( ( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( ~ gt(pv63,X17)
| ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
<=> ( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ) )),
( ( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
<=> ( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
<=> ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [X15: $i,X16: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5) )
<=> ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5) ) )),
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
<=> ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) ) )),
rewrite(
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
<=> ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) ) )),
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
<=> ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) ) )),
rewrite(
( ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) )
<=> ( ~ ( ( X15 = pv63 )
& gt(pv64,X16) )
| ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )),
( ( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
<=> ( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ~ ( ( X15 = pv63 )
& gt(pv64,X16) )
| ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) ) )),
rewrite(
( ( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ~ ( ( X15 = pv63 )
& gt(pv64,X16) )
| ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
<=> ( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ) )),
( ( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
<=> ( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
<=> ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [X13: $i,X14: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5) )
<=> ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5) ) )),
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
<=> ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) ) )),
rewrite(
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
<=> ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) ) )),
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
<=> ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) ) )),
( ( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
<=> ( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) )),
rewrite(
( ( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
<=> ( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) )),
( ( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
<=> ( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
<=> ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [X11: $i,X12: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5) )
<=> ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5) ) )),
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
<=> ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) ) )),
rewrite(
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
<=> ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) ) )),
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
<=> ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) ) )),
( ( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
<=> ( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) )),
rewrite(
( ( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
<=> ( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) )),
( ( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
<=> ( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
<=> ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [X9: $i,X10: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2) )
<=> ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2) ) )),
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
<=> ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) ) )),
rewrite(
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
<=> ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) ) )),
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
<=> ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) ) )),
( ( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
<=> ( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) )),
rewrite(
( ( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
<=> ( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) )),
( ( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
<=> ( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
<=> ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
^ [X7: $i,X8: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5) )
<=> ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5) ) )),
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
<=> ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) ) )),
rewrite(
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
<=> ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) ) )),
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
<=> ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) ) )),
( ( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
<=> ( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) )),
rewrite(
( ( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
<=> ( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) )),
( ( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
<=> ( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
<=> ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
^ [X5: $i,X6: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5) )
<=> ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5) ) )),
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
<=> ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) ) )),
rewrite(
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
<=> ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) ) )),
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
<=> ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) ) )),
( ( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
<=> ( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) )),
rewrite(
( ( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
<=> ( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) )),
( ( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
<=> ( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
<=> ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [X3: $i,X4: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5) )
<=> ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5) ) )),
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
<=> ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) ) )),
rewrite(
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
<=> ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) ) )),
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
<=> ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) ) )),
( ( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
<=> ( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) )),
rewrite(
( ( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
<=> ( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) )),
( ( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
<=> ( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
<=> ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [X1: $i,X2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2) )
<=> ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2) ) )),
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
<=> ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) ) )),
rewrite(
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
<=> ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) ) )),
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
<=> ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) ) )),
( ( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
<=> ( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) )),
rewrite(
( ( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
<=> ( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) )),
( ( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
<=> ( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
<=> ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64) ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998) ) ),
inference(transitivity,[status(thm)],[93,88]) ).
tff(95,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5) ) ),
inference(transitivity,[status(thm)],[95,87]) ).
tff(97,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5) ) ),
inference(transitivity,[status(thm)],[97,86]) ).
tff(99,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) ) ),
inference(monotonicity,[status(thm)],[98,85]) ).
tff(100,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) ) ) ),
inference(transitivity,[status(thm)],[99,83]) ).
tff(101,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) ) ),
inference(monotonicity,[status(thm)],[100,82]) ).
tff(102,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) ) ) ),
inference(transitivity,[status(thm)],[101,80]) ).
tff(103,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) ) ),
inference(monotonicity,[status(thm)],[102,79]) ).
tff(104,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) ) ) ),
inference(transitivity,[status(thm)],[103,77]) ).
tff(105,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) ) ),
inference(monotonicity,[status(thm)],[104,76]) ).
tff(106,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) ) ) ),
inference(transitivity,[status(thm)],[105,74]) ).
tff(107,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) ) ),
inference(monotonicity,[status(thm)],[106,73]) ).
tff(108,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) ) ) ),
inference(transitivity,[status(thm)],[107,71]) ).
tff(109,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) ) ),
inference(monotonicity,[status(thm)],[108,70]) ).
tff(110,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) ) ),
inference(transitivity,[status(thm)],[109,68]) ).
tff(111,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) ) ),
inference(monotonicity,[status(thm)],[110,67]) ).
tff(112,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) ) ),
inference(transitivity,[status(thm)],[111,65]) ).
tff(113,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ) ) ),
inference(monotonicity,[status(thm)],[112,64]) ).
tff(114,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) ) ) ),
inference(transitivity,[status(thm)],[113,62]) ).
tff(115,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ) ) ),
inference(monotonicity,[status(thm)],[114,61]) ).
tff(116,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) ) ) ),
inference(transitivity,[status(thm)],[115,59]) ).
tff(117,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
& ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) ) ),
inference(monotonicity,[status(thm)],[116,58]) ).
tff(118,plain,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
& ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
<=> ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) ) ),
inference(transitivity,[status(thm)],[117,56]) ).
tff(119,plain,
( ( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
& ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
=> ! [X21: $i,X22: $i] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) )
<=> ( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
=> ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ) ),
inference(monotonicity,[status(thm)],[118,55]) ).
tff(120,plain,
( ( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
& ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
=> ! [X21: $i,X22: $i] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) )
<=> ( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ) ),
inference(transitivity,[status(thm)],[119,53]) ).
tff(121,axiom,
( ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( ( X15 = pv63 )
& gt(pv64,X16) )
=> ( a_select3(id_ds1_filter_init,X15,X16) = init ) ) )
& ! [X17: $i,X18: $i] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> ( a_select3(id_ds1_filter_init,X17,X18) = init ) ) )
& ! [X19: $i] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20: $i] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
=> ! [X21: $i,X22: $i] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) )
=> ( a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n1) ).
tff(122,plain,
( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ~ ( ( pv63 != pv64 )
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1: $i,X2: $i] :
( ~ ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
| ( a_select3(h_ds1_filter_init,X1,X2) = init ) )
& ! [X3: $i,X4: $i] :
( ~ ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
| ( a_select3(phi_ds1_filter_init,X3,X4) = init ) )
& ! [X5: $i,X6: $i] :
( ~ ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
| ( a_select3(dv_ds1_filter_init,X5,X6) = init ) )
& ! [X7: $i,X8: $i] :
( ~ ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
| ( a_select3(q_ds1_filter_init,X7,X8) = init ) )
& ! [X9: $i,X10: $i] :
( ~ ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
| ( a_select3(r_ds1_filter_init,X9,X10) = init ) )
& ! [X11: $i,X12: $i] :
( ~ ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
| ( a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) )
& ! [X13: $i,X14: $i] :
( ~ ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
| ( a_select3(pminus_ds1_filter_init,X13,X14) = init ) )
& ! [X15: $i,X16: $i] :
( ( a_select3(id_ds1_filter_init,X15,X16) = init )
| ~ ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
| ~ ( ( X15 = pv63 )
& gt(pv64,X16) ) )
& ! [X17: $i,X18: $i] :
( ( a_select3(id_ds1_filter_init,X17,X18) = init )
| ~ ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
| ~ gt(pv63,X17) )
& ! [X19: $i] :
( ~ ( leq(n0,X19)
& leq(X19,pred(pv63)) )
| ! [X20: $i] :
( ~ ( leq(n0,X20)
& leq(X20,n5) )
| ( a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) )
| ! [X21: $i,X22: $i] :
( ( a_select3(id_ds1_filter_init,X21,X22) = init )
| ~ ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
| ~ ( ( pv64 != X22 )
& ( X21 = pv63 )
& leq(X22,pv64) ) ) ),
inference(modus_ponens,[status(thm)],[122,52]) ).
tff(124,plain,
$false,
inference(modus_ponens,[status(thm)],[123,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MSC010+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 03:22:19 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------