%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV475+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:59:33 AM UTC 2026
% Result : Theorem 87.03s 24.79s
% Output : Refutation 89.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 85
% Syntax : Number of formulae : 715 ( 351 unt; 0 typ; 18 def)
% Number of atoms : 3018 (1652 equ; 0 cnn)
% Maximal formula atoms : 177 ( 4 avg)
% Number of connectives : 11880 (1496 ~; 916 |; 895 &;8243 @)
% ( 13 <=>; 317 =>; 0 <=; 0 <~>)
% Maximal formula depth : 89 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 28 con; 0-4 aty)
% Number of variables : 1546 ( 9 ^;1410 !; 109 ?;1546 :)
% ( 0 !>; 0 ?*; 0 @-; 18 @+)
% Comments :
%------------------------------------------------------------------------------
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Ldr_decl,type,
m_Ldr: $i > $i ).
thf(queue_decl,type,
queue: $i > $i ).
thf(host_decl,type,
host: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(setIn_decl,type,
setIn: $i > $i > $o ).
thf(alive_decl,type,
alive: $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(status_decl,type,
status: $i ).
thf(elec_1_decl,type,
elec_1: $i ).
thf(elec_2_decl,type,
elec_2: $i ).
thf(elid_decl,type,
elid: $i ).
thf(down_decl,type,
down: $i ).
thf(pendack_decl,type,
pendack: $i ).
thf(norm_decl,type,
norm: $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(wait_decl,type,
wait: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(nbr_proc_decl,type,
nbr_proc: $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(acks_decl,type,
acks: $i ).
thf(snoc_decl,type,
snoc: $i > $i > $i ).
thf(m_NotNorm_decl,type,
m_NotNorm: $i > $i ).
thf(m_Halt_decl,type,
m_Halt: $i > $i ).
thf(m_NormQ_decl,type,
m_NormQ: $i > $i ).
thf(pidMsg_decl,type,
pidMsg: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $o ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(nil_decl,type,
nil: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(last_decl,type,
last: $i > $i ).
thf(init_decl,type,
init: $i > $i ).
thf(setEmpty_decl,type,
setEmpty: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(pidElem_decl,type,
pidElem: $i > $o ).
thf(pids_decl,type,
pids: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ ( B @ m_Ack ) @ cons ) ) )
& ( ? [E: $i,F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( G @ host @ s ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ? [G: $i,H: $i] :
( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( H @ host ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( E @ host @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ? [G: $i] :
( ( ( G @ host @ ( elid @ index ) @ host )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= wait )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ? [G: $i] :
( ( ( G @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i] :
( ? [F: $i,G: $i] :
( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( G @ host @ ( F @ host @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i] :
( ? [G: $i] :
( ( ( G @ host @ ( ldr @ index ) )
= ( G @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( G @ host ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( elid @ index ) )
= B ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
| ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( I @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) )
& ! [J: $i] :
( ( ( J @ ( zero @ s @ leq ) )
& ~ ( J @ ( I @ host @ leq ) ) )
=> ( ( J
= ( H @ host ) )
| ( I @ host @ ( down @ index ) @ ( J @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( sk1 @ ( C @ ( A @ m_Ack ) @ cons ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host )
= ( F @ host @ s ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( F @ setIn ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( G @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( D @ host @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( elid @ index ) @ host )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= wait )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( E = D ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( elid @ index ) )
= A ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
| ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( A @ host @ queue )
= ( sk1 @ ( B @ ( sk2 @ m_Ack ) @ cons ) ) )
& ( ? [C: $i,D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( C @ host )
= ( E @ host @ s ) )
& ( E @ host @ queue @ ( C @ m_Down @ elem ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( E @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ? [C: $i] :
( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( F @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ ( C @ host @ leq ) )
& ( alive @ ( C @ setIn ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( C @ host @ queue @ ( D @ ( C @ m_Ack ) @ elem ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( elid @ index ) @ host )
= ( D @ host ) )
& ( ( E @ host @ ( status @ index ) )
= wait )
& ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ( ( E @ host )
!= ( D @ host ) ) )
=> ~ ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( alive @ ( D @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ( ( E @ host )
!= ( D @ host ) ) )
=> ~ ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( alive @ ( D @ setIn ) ) ) )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( ( E @ host )
!= ( C @ host ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( ( E @ host )
!= ( C @ host ) ) )
=> ~ ( ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i] :
( ? [D: $i,E: $i] :
( ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( D = C ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( C @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( C @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( C @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i] :
( ( ( alive @ ( C @ setIn ) )
& ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
| ( ( C @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( C @ host @ ( elid @ index ) )
= C ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ( ( D @ host )
!= ( C @ host ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Ldr @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ( ( ( ( B @ host )
= ( A @ host @ ( pendack @ index ) ) )
& ( ( A @ host @ ( status @ index ) )
= elec_2 )
& ( ( A @ host @ ( elid @ index ) )
= sk2 ) )
=> ( ( A @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
| ( A @ host @ ( acks @ index ) @ ( C @ host @ setIn ) ) )
=> ! [D: $i] :
( ( ( A @ host )
= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( A @ host )
!= ( G @ host ) )
=> ( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( G @ host @ s ) )
& ( A @ m_Ldr @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( A @ m_Ldr @ ( G @ host @ queue @ snoc ) @ ( E @ m_Down @ elem ) )
& ( G @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( ( A @ host )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( ( sk3 @ host @ queue )
= ( sk1 @ ( A @ ( sk2 @ m_Ack ) @ cons ) ) )
& ( ? [B: $i,C: $i,D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_1 )
& ( ( B @ host )
= ( D @ host @ s ) )
& ( D @ host @ queue @ ( B @ m_Down @ elem ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( D @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( D @ host @ leq ) ) )
=> ( ( E
= ( C @ host ) )
| ( D @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ~ ? [B: $i] :
( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host )
= ( E @ host ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( E @ host @ ( B @ host @ leq ) )
& ( alive @ ( B @ setIn ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ( B @ host @ queue @ ( C @ ( B @ m_Ack ) @ elem ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( elid @ index ) @ host )
= ( C @ host ) )
& ( ( D @ host @ ( status @ index ) )
= wait )
& ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( B @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ( ( D @ host )
!= ( C @ host ) ) )
=> ~ ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( alive @ ( C @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( B @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ( ( D @ host )
!= ( C @ host ) ) )
=> ~ ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( alive @ ( C @ setIn ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ( ( D @ host )
!= ( B @ host ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ( ( D @ host )
!= ( B @ host ) ) )
=> ~ ( ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i] :
( ? [C: $i,D: $i] :
( ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( C = B ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( C @ host )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( B @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( B @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( ( B @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( B @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i] :
( ( ( alive @ ( B @ setIn ) )
& ( ( ( B @ host @ ( status @ index ) )
= elec_2 )
| ( ( B @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( B @ host @ ( elid @ index ) )
= B ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ( ( C @ host )
!= ( B @ host ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Ldr @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) ) )
=> ( ( alive @ ( sk3 @ setIn ) )
=> ( ( ( ( A @ host )
= ( sk3 @ host @ ( pendack @ index ) ) )
& ( ( sk3 @ host @ ( status @ index ) )
= elec_2 )
& ( ( sk3 @ host @ ( elid @ index ) )
= sk2 ) )
=> ( ( sk3 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [B: $i] :
( ( ( ( B @ host )
= ( A @ host ) )
| ( sk3 @ host @ ( acks @ index ) @ ( B @ host @ setIn ) ) )
=> ! [C: $i] :
( ( ( sk3 @ host )
= ( C @ host ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( B @ host )
= ( F @ host ) )
=> ( ( ( sk3 @ host )
!= ( F @ host ) )
=> ( ( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host )
= ( F @ host @ s ) )
& ( sk3 @ m_Ldr @ ( F @ host @ queue @ snoc ) @ ( E @ m_Down @ elem ) )
& ( sk3 @ m_Ldr @ ( F @ host @ queue @ snoc ) @ ( D @ m_Down @ elem ) )
& ( F @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( F @ setIn ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( ( ( sk3 @ host )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( A @ host @ leq ) ) )
=> ( ( E
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( A @ host @ leq ) ) )
=> ( ( D
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( ( A @ host )
= ( sk4 @ host ) )
| ( sk3 @ host @ ( acks @ index ) @ ( A @ host @ setIn ) ) )
=> ! [B: $i] :
( ( ( sk3 @ host )
= ( B @ host ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ host )
= ( E @ host ) )
=> ( ( ( sk3 @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( C @ host )
= ( E @ host @ s ) )
& ( sk3 @ m_Ldr @ ( E @ host @ queue @ snoc ) @ ( D @ m_Down @ elem ) )
& ( sk3 @ m_Ldr @ ( E @ host @ queue @ snoc ) @ ( C @ m_Down @ elem ) )
& ( E @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ( ( ( sk3 @ host )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( ( sk3 @ host )
= ( A @ host ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( sk7 @ host )
= ( D @ host ) )
=> ( ( ( sk3 @ host )
!= ( D @ host ) )
=> ( ( ( ( D @ host @ ( status @ index ) )
= elec_1 )
& ( ( B @ host )
= ( D @ host @ s ) )
& ( sk3 @ m_Ldr @ ( D @ host @ queue @ snoc ) @ ( C @ m_Down @ elem ) )
& ( sk3 @ m_Ldr @ ( D @ host @ queue @ snoc ) @ ( B @ m_Down @ elem ) )
& ( D @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( D @ host @ leq ) ) )
=> ( ( E
= ( C @ host ) )
| ( D @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ~ ( ( ( sk3 @ host )
= ( A @ host ) )
& ( alive @ ( A @ setIn ) ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk7 @ host )
= ( C @ host ) )
=> ( ( ( sk3 @ host )
!= ( C @ host ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ( ( A @ host )
= ( C @ host @ s ) )
& ( sk3 @ m_Ldr @ ( C @ host @ queue @ snoc ) @ ( B @ m_Down @ elem ) )
& ( sk3 @ m_Ldr @ ( C @ host @ queue @ snoc ) @ ( A @ m_Down @ elem ) )
& ( C @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( C @ setIn ) )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( C @ host @ leq ) ) )
=> ( ( D
= ( B @ host ) )
| ( C @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ~ ( ( ( sk3 @ host )
= ( sk8 @ host ) )
& ( alive @ ( sk8 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk7 @ host )
= ( B @ host ) )
=> ( ( ( sk3 @ host )
!= ( B @ host ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk9 @ host )
= ( B @ host @ s ) )
& ( sk3 @ m_Ldr @ ( B @ host @ queue @ snoc ) @ ( A @ m_Down @ elem ) )
& ( sk3 @ m_Ldr @ ( B @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ) )
& ( B @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( B @ setIn ) )
& ! [C: $i] :
( ( ( C @ ( zero @ s @ leq ) )
& ~ ( C @ ( B @ host @ leq ) ) )
=> ( ( C
= ( A @ host ) )
| ( B @ host @ ( down @ index ) @ ( C @ setIn ) ) ) ) )
=> ~ ( ( ( sk3 @ host )
= ( sk8 @ host ) )
& ( alive @ ( sk8 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( ( ( sk7 @ host )
= ( A @ host ) )
=> ( ( ( sk3 @ host )
!= ( A @ host ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk9 @ host )
= ( A @ host @ s ) )
& ( sk3 @ m_Ldr @ ( A @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ) )
& ( sk3 @ m_Ldr @ ( A @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ) )
& ( A @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( A @ setIn ) )
& ! [B: $i] :
( ( ( B @ ( zero @ s @ leq ) )
& ~ ( B @ ( A @ host @ leq ) ) )
=> ( ( B
= ( sk10 @ host ) )
| ( A @ host @ ( down @ index ) @ ( B @ setIn ) ) ) ) )
=> ~ ( ( ( sk3 @ host )
= ( sk8 @ host ) )
& ( alive @ ( sk8 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ ( B @ m_Ack ) @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( H @ host @ queue @ ( F @ m_Down @ elem ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( H @ host ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( E @ host @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( elid @ index ) @ host )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= wait )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( G @ host @ ( F @ host @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( G @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( G @ host ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( elid @ index ) )
= B ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
| ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( I @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) )
& ! [J: $i] :
( ( ( J @ ( zero @ s @ leq ) )
& ~ ( J @ ( I @ host @ leq ) ) )
=> ( ( J
= ( H @ host ) )
| ( I @ host @ ( down @ index ) @ ( J @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ ( B @ m_Ack ) @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( H @ host @ queue @ ( F @ m_Down @ elem ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( H @ host ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( E @ host @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( elid @ index ) @ host )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= wait )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( G @ host @ ( F @ host @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( G @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( G @ host ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( elid @ index ) )
= B ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
| ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( I @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) )
& ! [J: $i] :
( ( ( J @ ( zero @ s @ leq ) )
& ~ ( J @ ( I @ host @ leq ) ) )
=> ( ( J
= ( H @ host ) )
| ( I @ host @ ( down @ index ) @ ( J @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ ( B @ m_Ack ) @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( H @ host @ queue @ ( F @ m_Down @ elem ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( H @ host ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( E @ host @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( elid @ index ) @ host )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= wait )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( G @ host @ ( F @ host @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( G @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( G @ host ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( elid @ index ) )
= B ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
| ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( I @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) )
& ! [J: $i] :
( ( ( J @ ( zero @ s @ leq ) )
& ~ ( J @ ( I @ host @ leq ) ) )
=> ( ( J
= ( H @ host ) )
| ( I @ host @ ( down @ index ) @ ( J @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[226]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[227]) ).
thf(70,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ ( B @ m_Ack ) @ cons ) ) )
& ( ? [E: $i,F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( G @ host @ s ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ? [G: $i,H: $i] :
( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( H @ host ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( E @ host @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ? [G: $i] :
( ( ( G @ host @ ( elid @ index ) @ host )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= wait )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ? [G: $i] :
( ( ( G @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i] :
( ? [F: $i,G: $i] :
( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( G @ host @ ( F @ host @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i] :
( ? [G: $i] :
( ( ( G @ host @ ( ldr @ index ) )
= ( G @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( G @ host ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( elid @ index ) )
= B ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
| ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( I @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) )
& ! [J: $i] :
( ( ( J @ ( zero @ s @ leq ) )
& ~ ( J @ ( I @ host @ leq ) ) )
=> ( ( J
= ( H @ host ) )
| ( I @ host @ ( down @ index ) @ ( J @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(71,plain,
! [ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ host )
= ( sk8 @ host ) )
& ( alive @ ( sk8 @ setIn ) )
& ( ( sk11 @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk9 @ host )
= ( sk11 @ host @ s ) )
& ( sk3 @ m_Ldr @ ( sk11 @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ) )
& ( sk3 @ m_Ldr @ ( sk11 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ) )
& ( sk11 @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( sk11 @ setIn ) )
& ( ( ZS
= ( sk10 @ host ) )
| ( sk11 @ host @ ( down @ index ) @ ( ZS @ setIn ) )
| ~ ( ZS @ ( zero @ s @ leq ) )
| ( ZS @ ( sk11 @ host @ leq ) ) )
& ( ( sk3 @ host )
!= ( sk11 @ host ) )
& ( ( sk7 @ host )
= ( sk11 @ host ) )
& ( ( sk3 @ host )
= ( sk8 @ host ) )
& ( ( ( sk7 @ host )
= ( sk4 @ host ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) )
& ( sk3 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
& ( ( sk4 @ host )
= ( sk3 @ host @ ( pendack @ index ) ) )
& ( ( sk3 @ host @ ( status @ index ) )
= elec_2 )
& ( ( sk3 @ host @ ( elid @ index ) )
= sk2 )
& ( alive @ ( sk3 @ setIn ) )
& ( ( sk3 @ host @ queue )
= ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ( ( ZO @ ( ZP @ ( ZQ @ sk6 ) ) )
!= ( ZP @ host ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ~ ( ZQ @ host @ ( down @ index ) @ ( ZO @ ( ZP @ ( ZQ @ sk6 ) ) @ setIn ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ( ZO @ ( ZP @ ( ZQ @ sk6 ) ) @ ( zero @ s @ leq ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ~ ( ZO @ ( ZP @ ( ZQ @ sk6 ) ) @ ( ZQ @ host @ leq ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ( ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk5 ) ) ) )
!= ( ZM @ host ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ~ ( ZN @ host @ ( down @ index ) @ ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk5 ) ) ) @ setIn ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk5 ) ) ) @ ( zero @ s @ leq ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ~ ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk5 ) ) ) @ ( ZN @ host @ leq ) ) )
& ( ( ( ZI @ host @ ( ldr @ index ) )
!= ( ZI @ host ) )
| ( ( ZI @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( ZI @ setIn ) )
| ( ( ZJ @ host @ ( elid @ index ) @ host )
!= ( ZI @ host ) )
| ( ( ZJ @ host @ ( status @ index ) )
!= wait )
| ( ( ZI @ host )
!= ( ZH @ host ) )
| ~ ( ZJ @ host @ queue @ ( ZH @ m_Down @ elem ) )
| ~ ( alive @ ( ZJ @ setIn ) )
| ( ( ZJ @ host )
= ( ZI @ host ) ) )
& ( ( ( ZF @ host @ ( ldr @ index ) )
!= ( ZF @ host ) )
| ( ( ZF @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( ZF @ setIn ) )
| ( ( ZG @ host @ ( ldr @ index ) )
!= ( ZF @ host ) )
| ( ( ZG @ host @ ( status @ index ) )
!= norm )
| ( ( ZF @ host )
!= ( ZE @ host ) )
| ~ ( ZG @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZG @ setIn ) )
| ( ( ZG @ host )
= ( ZF @ host ) ) )
& ( ~ ( ZC @ host @ ( down @ index ) @ ( ZB @ host @ setIn ) )
| ~ ( ZA @ host @ queue @ ( ZD @ m_Down @ elem ) )
| ( ( ZD @ host )
!= ( ZC @ host ) )
| ( ( ZB @ host )
!= ( ZA @ host ) )
| ~ ( alive @ ( ZC @ setIn ) )
| ~ ( alive @ ( ZA @ setIn ) )
| ( ( ZC @ host )
= ( ZA @ host ) ) )
& ( ~ ( Y @ host @ queue @ ( X @ m_Down @ elem ) )
| ~ ( W @ host @ queue @ ( Z @ m_Down @ elem ) )
| ( ( Z @ host )
!= ( Y @ host ) )
| ( ( X @ host )
!= ( W @ host ) )
| ~ ( alive @ ( Y @ setIn ) )
| ~ ( alive @ ( W @ setIn ) )
| ( ( Y @ host )
= ( W @ host ) ) )
& ( ( ( T @ host @ ( status @ index ) )
!= norm )
| ( ( T @ host @ ( ldr @ index ) )
!= ( T @ host ) )
| ~ ( alive @ ( T @ setIn ) )
| ( ( U @ host )
!= ( T @ host ) )
| ~ ( V @ host @ queue @ ( U @ m_Down @ elem ) )
| ~ ( alive @ ( V @ setIn ) )
| ( V @ host @ ( U @ host @ leq ) ) )
& ( ( S = R )
| ( ( S @ host @ ( ldr @ index ) )
!= ( S @ host ) )
| ( ( S @ host @ ( status @ index ) )
!= norm )
| ( ( R @ host @ ( status @ index ) )
!= norm )
| ( ( R @ host @ ( ldr @ index ) )
!= ( R @ host ) )
| ~ ( alive @ ( S @ setIn ) )
| ~ ( alive @ ( R @ setIn ) ) )
& ( ~ ( O @ host @ queue @ ( P @ m_Down @ elem ) )
| ~ ( alive @ ( O @ setIn ) )
| ( ( Q @ host @ ( ldr @ index ) )
!= ( Q @ host ) )
| ( ( Q @ host @ ( status @ index ) )
!= norm )
| ( ( P @ host )
!= ( Q @ host ) )
| ~ ( alive @ ( Q @ setIn ) ) )
& ( ( L @ host @ ( N @ host @ ( pendack @ index ) @ leq ) )
| ( ( N @ host @ ( status @ index ) )
!= elec_2 )
| ( ( N @ host )
!= ( M @ host ) )
| ~ ( L @ host @ queue @ ( M @ m_Down @ elem ) )
| ~ ( alive @ ( N @ setIn ) )
| ~ ( alive @ ( L @ setIn ) ) )
& ( ~ ( J @ host @ ( down @ index ) @ ( K @ host @ setIn ) )
| ~ ( alive @ ( J @ setIn ) )
| ( ( K @ host @ ( ldr @ index ) )
!= ( K @ host ) )
| ( ( K @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( K @ setIn ) ) )
& ( ( H @ host @ ( I @ host @ ( pendack @ index ) @ leq ) )
| ( ( I @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( H @ host @ ( down @ index ) @ ( I @ host @ setIn ) )
| ~ ( alive @ ( I @ setIn ) )
| ~ ( alive @ ( H @ setIn ) ) )
& ( ( ( G @ host @ ( elid @ index ) )
= G )
| ~ ( alive @ ( G @ setIn ) )
| ( ( G @ host @ ( status @ index ) )
!= elec_2 ) )
& ( ( ( G @ host @ ( elid @ index ) )
= G )
| ~ ( alive @ ( G @ setIn ) )
| ( ( G @ host @ ( status @ index ) )
!= elec_1 ) )
& ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) )
| ( ( F @ host )
!= ( E @ host ) )
| ( F = E ) )
& ( ( ( D @ host )
!= ( C @ host ) )
| ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(77,plain,
( ( sk3 @ host @ queue )
= ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(138,plain,
( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
= ( sk3 @ host @ queue ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(7351,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk3 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[138,228]) ).
thf(7352,plain,
( ( sk4 @ ( sk2 @ m_Ack ) )
= ( sk3 @ host @ queue @ head ) ),
inference(pattern_uni,[status(thm)],[7351:[bind(A,$thf( sk4 @ ( sk2 @ m_Ack ) )),bind(B,$thf( sk1 ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(232,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(233,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[232]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(10351,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( B @ ( A @ m_Ack ) ) )
| ( ( sk3 @ host @ queue @ head )
!= ( C @ m_NotNorm ) ) ),
inference(paramod_ordered,[status(thm)],[7352,235]) ).
thf(10352,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NotNorm ) ),
inference(pattern_uni,[status(thm)],[10351:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(10353,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NotNorm ) ),
inference(simp,[status(thm)],[10352]) ).
thf(10360,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ head )
!= ( sk3 @ host @ queue @ head ) )
| ( A
!= ( C @ m_NotNorm ) ) ),
inference(paramod_ordered,[status(thm)],[228,10353]) ).
thf(10391,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NotNorm @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[10360]) ).
thf(10399,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NotNorm @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[10391]) ).
thf(104,plain,
( ( sk3 @ host @ ( elid @ index ) )
= sk2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(160,plain,
( ( sk3 @ host @ ( elid @ index ) )
= sk2 ),
inference(lifteq,[status(thm)],[104]) ).
thf(107,plain,
sk3 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(618,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( elid @ index ) ) )
| ( sk2 @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[160,107]) ).
thf(623,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != elid )
| ( sk2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[618]) ).
thf(628,plain,
( ( pendack != elid )
| ( sk2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[623]) ).
thf(74,plain,
( ( sk9 @ host )
= ( sk11 @ host @ s ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(133,plain,
( ( sk11 @ host @ s )
= ( sk9 @ host ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(76,plain,
( ( sk7 @ host )
= ( sk11 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(147,plain,
( ( sk11 @ host )
= ( sk7 @ host ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(555,plain,
( ( sk7 @ host @ s )
= ( sk9 @ host ) ),
inference(rewrite,[status(thm)],[133,147]) ).
thf(18,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_02) ).
thf(236,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(237,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[236]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).
thf(423,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(424,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[423]) ).
thf(425,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[424]) ).
thf(2855,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[237,425]) ).
thf(2856,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2855]) ).
thf(2875,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2856]) ).
thf(2896,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2875]) ).
thf(4829,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( A @ host @ s ) )
| ( ( zero @ s )
!= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[555,2896]) ).
thf(4830,plain,
( ( zero @ s )
!= ( sk9 @ host ) ),
inference(pattern_uni,[status(thm)],[4829:[bind(A,$thf( sk7 ))]]) ).
thf(4848,plain,
( ( ( sk7 @ host @ s )
!= ( zero @ s ) )
| ( ( sk9 @ host )
!= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[555,4830]) ).
thf(4849,plain,
( ( sk7 @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[4848]) ).
thf(4852,plain,
( ( sk7 @ host )
!= zero ),
inference(simp,[status(thm)],[4849]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(365,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(109,plain,
sk11 @ host @ s @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(542,plain,
sk7 @ host @ s @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[109,147]) ).
thf(556,plain,
sk9 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[542,555]) ).
thf(2865,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk9 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,425]) ).
thf(2866,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk9 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2865]) ).
thf(2883,plain,
! [A: $i] :
( ( A
!= ( sk9 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2866]) ).
thf(2889,plain,
( ( sk9 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2883]) ).
thf(82,plain,
( ( sk3 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(162,plain,
( ( sk3 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[82]) ).
thf(90,plain,
( ( sk4 @ host )
= ( sk3 @ host @ ( pendack @ index ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(167,plain,
( ( sk3 @ host @ ( pendack @ index ) )
= ( sk4 @ host ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(767,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ( ( sk4 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[162,167]) ).
thf(784,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != status )
| ( ( sk4 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[767]) ).
thf(793,plain,
( ( pendack != status )
| ( ( sk4 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[784]) ).
thf(4822,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[2896]) ).
thf(5443,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( zero != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,4822]) ).
thf(5444,plain,
( ( zero != elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[5443:[bind(A,$thf( sk4 ))]]) ).
thf(53,axiom,
norm != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(406,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(407,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[406]) ).
thf(408,plain,
wait != norm,
inference(lifteq,[status(thm)],[407]) ).
thf(95,plain,
sk3 @ m_Ldr @ ( sk11 @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(521,plain,
sk3 @ m_Ldr @ ( sk7 @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ),
inference(rewrite,[status(thm)],[95,147]) ).
thf(63,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_45) ).
thf(440,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(441,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[440]) ).
thf(442,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[441]) ).
thf(756,plain,
! [A: $i] :
( ( ( sk3 @ m_Ldr @ ( sk7 @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[521,442]) ).
thf(757,plain,
! [A: $i] :
( ( sk3 @ m_Ldr @ ( sk7 @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[756]) ).
thf(760,plain,
! [A: $i] :
( ( ( sk3 @ m_Ldr @ ( sk7 @ host @ queue @ snoc ) )
!= q_nil )
| ( ( sk10 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[757]) ).
thf(762,plain,
( ( sk3 @ m_Ldr @ ( sk7 @ host @ queue @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[760]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).
thf(388,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[388]) ).
thf(2843,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk9 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[555,425]) ).
thf(2844,plain,
~ ( sk7 @ host @ ( sk9 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[2843:[bind(A,$thf( sk7 @ host ))]]) ).
thf(19392,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk9 @ host @ leq ) ) )
| ~ $true
| ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[389,2844]) ).
thf(19393,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk9 @ host @ leq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[19392]) ).
thf(19394,plain,
sk9 @ host @ ( sk7 @ host @ leq ),
inference(pattern_uni,[status(thm)],[19393:[bind(A,$thf( sk9 @ host )),bind(B,$thf( sk7 @ host ))]]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(19531,plain,
! [B: $i,A: $i] :
( ( ( sk9 @ host @ ( sk7 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[19394,94]) ).
thf(19532,plain,
! [B: $i,A: $i] :
( ( ( sk9 @ host @ ( sk7 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[19531]) ).
thf(19533,plain,
~ ( sk7 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[19532:[bind(A,$thf( sk7 )),bind(B,$thf( sk9 ))]]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(244,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(245,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[244]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[245]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[246]) ).
thf(1268,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,237]) ).
thf(1269,plain,
( ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[1268:[bind(A,$thf( sk4 ))]]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) )
!= ( C @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(111,plain,
( ( sk3 @ host )
= ( sk8 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(168,plain,
( ( sk8 @ host )
= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(2784,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( B ))]]) ).
thf(2825,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(simp,[status(thm)],[2784]) ).
thf(6943,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk3 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[168,2825]) ).
thf(6944,plain,
~ ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[6943:[bind(A,$thf( sk8 ))]]) ).
thf(11,axiom,
elec_1 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_06) ).
thf(215,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(216,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[215]) ).
thf(217,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[216]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(273,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(274,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[273]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).
thf(304,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) ) )
& ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(305,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) ) )
& ! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[304]) ).
thf(306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ leq ) )
| ( C != D ) )
& ( ( D @ ( C @ leq ) )
| ( C != D ) )
& ( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[305]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[306]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(312,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[311]) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[312,94]) ).
thf(1701,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ ( B @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[1700]) ).
thf(1702,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[1701:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(1705,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(simp,[status(thm)],[1702]) ).
thf(106,plain,
( ( sk11 @ host @ ( status @ index ) )
= elec_1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(128,plain,
( ( sk11 @ host @ ( status @ index ) )
= elec_1 ),
inference(lifteq,[status(thm)],[106]) ).
thf(550,plain,
( ( sk7 @ host @ ( status @ index ) )
= elec_1 ),
inference(rewrite,[status(thm)],[128,147]) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ ( B @ ( C @ sk6 ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(110,plain,
( ( sk3 @ host )
!= ( sk11 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(113,plain,
( ( sk11 @ host )
!= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(500,plain,
( ( sk7 @ host )
!= ( sk3 @ host ) ),
inference(rewrite,[status(thm)],[113,147]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( D @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(38,axiom,
elec_2 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_08) ).
thf(338,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(339,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[338]) ).
thf(340,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[339]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_62) ).
thf(404,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
thf(332,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(333,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[332]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[334]) ).
thf(971,plain,
! [A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk3 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[138,335]) ).
thf(972,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk4 @ ( sk2 @ m_Ack ) )
!= A )
| ( sk3 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[971]) ).
thf(973,plain,
( ( sk1 != q_nil )
| ( sk3 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[972]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
thf(470,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(471,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ) ),
inference(miniscope,[status(thm)],[470]) ).
thf(472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Ldr )
= ( D @ m_Ldr ) ) )
& ( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[471]) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[472]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[473]) ).
thf(476,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[475]) ).
thf(477,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk22 )
= A ),
inference(cnf,[status(esa)],[476]) ).
thf(6009,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk22 )
= A ),
inference(lifteq,[status(thm)],[477]) ).
thf(75,plain,
( ( ( sk7 @ host )
= ( sk4 @ host ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(161,plain,
( ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) )
| ( ( sk7 @ host )
= ( sk4 @ host ) ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(1385,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( sk3 @ m_Ldr @ ( sk4 @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[161,521]) ).
thf(1386,plain,
( ( sk3 @ m_Ldr @ ( sk4 @ host @ queue @ snoc ) @ ( sk10 @ m_Down @ elem ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(pattern_uni,[status(thm)],[1385:[]]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(436,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).
thf(255,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[256]) ).
thf(55,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(413,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(414,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[413]) ).
thf(415,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[414]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).
thf(378,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( B @ ( C @ snoc ) @ ( A @ elem ) ) )
& ( ( B @ ( C @ snoc ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(379,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( B @ ( C @ snoc ) @ ( A @ elem ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[378]) ).
thf(380,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( F @ snoc ) @ ( D @ elem ) )
| ~ ( F @ ( D @ elem ) ) )
& ( ( E @ ( F @ snoc ) @ ( D @ elem ) )
| ( D != E ) )
& ( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( B @ ( C @ snoc ) @ ( A @ elem ) ) ) ),
inference(cnf,[status(esa)],[379]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[380]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[382]) ).
thf(386,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[385]) ).
thf(6490,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk3 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[168,1705]) ).
thf(6491,plain,
~ ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[6490:[bind(A,$thf( sk8 ))]]) ).
thf(13275,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,6491]) ).
thf(13276,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13275]) ).
thf(13345,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13276]) ).
thf(13404,plain,
! [A: $i] :
( ( sk8 @ m_Ldr @ ( A @ snoc ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[13345]) ).
thf(16397,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[415,13404]) ).
thf(16398,plain,
( ( q_nil @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[16397:[bind(A,$thf( sk8 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ pidElem )
<=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).
thf(293,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) )
=> ( A @ pidElem ) )
& ( ( A @ pidElem )
=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(294,plain,
( ! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ m_Down ) )
| ? [B: $i] :
( A
= ( B @ m_Halt ) ) )
=> ( A @ pidElem ) )
& ! [A: $i] :
( ( A @ pidElem )
=> ( ? [B: $i] :
( A
= ( B @ m_Down ) )
| ? [B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ),
inference(miniscope,[status(thm)],[293]) ).
thf(295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk18 @ m_Down ) )
| ( A
= ( A @ sk17 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[294]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[295]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(301,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[300]) ).
thf(774,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( elid @ index ) ) )
| ( ( sk4 @ host )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[160,167]) ).
thf(786,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != elid )
| ( ( sk4 @ host )
= sk2 ) ),
inference(simp,[status(thm)],[774]) ).
thf(795,plain,
( ( pendack != elid )
| ( ( sk4 @ host )
= sk2 ) ),
inference(simp,[status(thm)],[786]) ).
thf(1528,plain,
( ( ( sk4 @ host )
!= ( sk4 @ host ) )
| ( pendack != status )
| ( sk2 = elec_2 )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,793]) ).
thf(1529,plain,
( ( pendack != status )
| ( sk2 = elec_2 )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[1528:[]]) ).
thf(102,plain,
! [A: $i] :
( ( A
= ( sk10 @ host ) )
| ( sk11 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk11 @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(134,plain,
! [A: $i] :
( ( sk11 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk11 @ host @ leq ) )
| ( A
= ( sk10 @ host ) ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(135,plain,
! [A: $i] :
( ( sk11 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk11 @ host @ leq ) )
| ( A
= ( sk10 @ host ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(3668,plain,
! [A: $i] :
( ( sk7 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk7 @ host @ leq ) )
| ( A
= ( sk10 @ host ) ) ),
inference(rewrite,[status(thm)],[135,147]) ).
thf(3936,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk7 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk7 @ host @ leq ) )
| ( B
= ( sk10 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[312,3668]) ).
thf(3937,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk7 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk7 @ host @ leq ) )
| ( B
= ( sk10 @ host ) ) ),
inference(simp,[status(thm)],[3936]) ).
thf(3938,plain,
( ( sk7 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk7 @ host @ leq ) )
| ( ( zero @ s )
= ( sk10 @ host ) ) ),
inference(pattern_uni,[status(thm)],[3937:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s ))]]) ).
thf(2841,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[628,425]) ).
thf(2842,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( nbr_proc @ leq ) ) )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2841]) ).
thf(2876,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= nbr_proc )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2842]) ).
thf(2897,plain,
( ( ( sk2 @ s )
!= nbr_proc )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2876]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(251,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(252,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[251]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(11046,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( B @ ( A @ m_Ack ) ) )
| ( ( sk3 @ host @ queue @ head )
!= ( C @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[7352,254]) ).
thf(11047,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Down ) ),
inference(pattern_uni,[status(thm)],[11046:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(11051,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Down ) ),
inference(simp,[status(thm)],[11047]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( C @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( C @ host ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( C @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( C @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(341,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(342,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[341]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[342]) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[343]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ leq ) )
<=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_64) ).
thf(460,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) )
=> ( B @ s @ ( A @ leq ) ) )
& ( ( B @ s @ ( A @ leq ) )
=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(156,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(157,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[156]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).
thf(238,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(239,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[238]) ).
thf(240,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[239]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[240]) ).
thf(6454,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[415,241]) ).
thf(6455,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[6454:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
thf(261,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(56,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_05) ).
thf(416,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(13,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_03) ).
thf(220,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2851,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[220,425]) ).
thf(2852,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[2851]) ).
thf(2872,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[2852]) ).
thf(2893,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2872]) ).
thf(2929,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[2893]) ).
thf(35,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).
thf(325,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[163]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ ordered )
<=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_54) ).
thf(443,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( A @ ( B @ snoc ) @ ordered ) )
& ( ( A @ ( B @ snoc ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(211,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(72,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(120,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(121,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[120]) ).
thf(1008,plain,
( ( ( sk7 @ host )
!= ( sk4 @ host ) )
| ( ( sk3 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,500]) ).
thf(1040,plain,
( ( sk7 != sk4 )
| ( ( sk3 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1008]) ).
thf(13259,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,6944]) ).
thf(13260,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[13259]) ).
thf(13324,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[13260]) ).
thf(13383,plain,
! [A: $i] :
( ( sk8 @ m_Down @ ( A @ snoc ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[13324]) ).
thf(15892,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[415,13383]) ).
thf(15893,plain,
( ( q_nil @ ( sk8 @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[15892:[bind(A,$thf( sk8 @ m_Down )),bind(B,$thf( q_nil ))]]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_01) ).
thf(480,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_50) ).
thf(397,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(4841,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[168,2896]) ).
thf(4842,plain,
( ( sk3 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[4841:[bind(A,$thf( sk8 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( A @ ( B @ ( C @ sk6 ) ) @ ( C @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(393,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(394,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[393]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[395]) ).
thf(20,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_04) ).
thf(242,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(243,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[242]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(206,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5447,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( sk2 != zero )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,4822]) ).
thf(5448,plain,
( ( sk2 != zero )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[5447:[bind(A,$thf( sk4 ))]]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
thf(280,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(22,axiom,
elec_1 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_07) ).
thf(248,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(437,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Ldr ) ),
inference(miniscope,[status(thm)],[436]) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(cnf,[status(esa)],[437]) ).
thf(439,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(lifteq,[status(thm)],[438]) ).
thf(2940,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk9 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[312,2844]) ).
thf(2941,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk9 @ host @ leq ) ) ),
inference(simp,[status(thm)],[2940]) ).
thf(2983,plain,
! [A: $i] :
( ( A
!= ( sk7 @ host ) )
| ( A
!= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[2941]) ).
thf(2995,plain,
( ( sk9 @ host )
!= ( sk7 @ host ) ),
inference(simp,[status(thm)],[2983]) ).
thf(3251,plain,
( ( ( sk11 @ host )
!= ( sk9 @ host ) )
| ( ( sk7 @ host )
!= ( sk7 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[147,2995]) ).
thf(3252,plain,
( ( sk11 @ host )
!= ( sk9 @ host ) ),
inference(simp,[status(thm)],[3251]) ).
thf(3265,plain,
sk11 != sk9,
inference(simp,[status(thm)],[3252]) ).
thf(85,plain,
alive @ ( sk8 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(197,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ) ),
inference(miniscope,[status(thm)],[196]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Halt )
= ( D @ m_Halt ) ) )
& ( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[197]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[198]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(25,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).
thf(258,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(259,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[258]) ).
thf(260,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[259]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(429,plain,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(587,plain,
( ( ( sk3 @ host @ ( elid @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ( sk2 = elec_2 ) ),
inference(paramod_ordered,[status(thm)],[162,160]) ).
thf(592,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( elid != status )
| ( sk2 = elec_2 ) ),
inference(simp,[status(thm)],[587]) ).
thf(598,plain,
( ( elid != status )
| ( sk2 = elec_2 ) ),
inference(simp,[status(thm)],[592]) ).
thf(764,plain,
sk4 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[107,167]) ).
thf(2859,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk4 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[764,425]) ).
thf(2860,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk4 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2859]) ).
thf(2884,plain,
! [A: $i] :
( ( A
!= ( sk4 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2860]) ).
thf(2890,plain,
( ( sk4 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2884]) ).
thf(3250,plain,
sk9 != sk7,
inference(simp,[status(thm)],[2995]) ).
thf(92,plain,
alive @ ( sk11 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(229,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6470,plain,
! [A: $i] :
( ( ( sk11 @ host )
!= ( A @ host ) )
| ~ ( sk7 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[147,1705]) ).
thf(6471,plain,
~ ( sk7 @ host @ queue @ ( sk11 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[6470:[bind(A,$thf( sk11 ))]]) ).
thf(13317,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,6471]) ).
thf(13318,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13317]) ).
thf(13339,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk11 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13318]) ).
thf(13398,plain,
! [A: $i] :
( ( sk11 @ m_Ldr @ ( A @ snoc ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[13339]) ).
thf(16359,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk11 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[415,13398]) ).
thf(16360,plain,
( ( q_nil @ ( sk11 @ m_Ldr @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[16359:[bind(A,$thf( sk11 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(13319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,442]) ).
thf(13320,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[13319]) ).
thf(13332,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[13320]) ).
thf(13391,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[13332]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).
thf(283,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(284,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[283]) ).
thf(285,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ cons ) @ ( D @ elem ) )
| ~ ( F @ ( D @ elem ) ) )
& ( ( F @ ( E @ cons ) @ ( D @ elem ) )
| ( D != E ) )
& ( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[287]) ).
thf(291,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[290]) ).
thf(12217,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,6471]) ).
thf(12218,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[12217]) ).
thf(12245,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk11 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[12218]) ).
thf(12304,plain,
! [A: $i] :
( ( A @ ( sk11 @ m_Ldr @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[12245]) ).
thf(1011,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,243]) ).
thf(1012,plain,
( ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[1011:[bind(A,$thf( sk4 ))]]) ).
thf(572,plain,
( ( ( sk9 @ host )
!= ( sk8 @ host ) )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[168,556]) ).
thf(576,plain,
( ( sk9 != sk8 )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(2861,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk9 != sk8 ) ),
inference(paramod_ordered,[status(thm)],[576,425]) ).
thf(2862,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2861]) ).
thf(2874,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= nbr_proc )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2862]) ).
thf(2895,plain,
( ( ( sk3 @ host @ s )
!= nbr_proc )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2874]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(400,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(401,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[400]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[401]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[402]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).
thf(183,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(184,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ) ),
inference(miniscope,[status(thm)],[183]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_NormQ )
= ( D @ m_NormQ ) ) )
& ( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[184]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[185]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(169,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(499,plain,
sk11 != sk3,
inference(simp,[status(thm)],[113]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(2845,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[243,425]) ).
thf(2846,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2845]) ).
thf(2877,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2846]) ).
thf(2898,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2877]) ).
thf(3621,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[168,2898]) ).
thf(3622,plain,
( ( nbr_proc @ s )
!= ( sk3 @ host ) ),
inference(pattern_uni,[status(thm)],[3621:[bind(A,$thf( sk8 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(193,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(509,plain,
( ( ( sk11 @ host )
!= ( sk8 @ host ) )
| ( ( sk7 @ host )
= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[168,147]) ).
thf(517,plain,
( ( sk11 != sk8 )
| ( ( sk7 @ host )
= ( sk3 @ host ) ) ),
inference(simp,[status(thm)],[509]) ).
thf(2240,plain,
sk11 != sk8,
inference(simplifyReflect,[status(thm)],[517,500]) ).
thf(5387,plain,
( ( sk3 @ host )
!= zero ),
inference(simp,[status(thm)],[4842]) ).
thf(6923,plain,
! [A: $i] :
( ( ( sk11 @ host )
!= ( A @ host ) )
| ~ ( sk7 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[147,2825]) ).
thf(6924,plain,
~ ( sk7 @ host @ queue @ ( sk11 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[6923:[bind(A,$thf( sk11 ))]]) ).
thf(13311,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,6924]) ).
thf(13312,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[13311]) ).
thf(13356,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk11 @ m_Down ) ) ),
inference(simp,[status(thm)],[13312]) ).
thf(13415,plain,
! [A: $i] :
( ( sk11 @ m_Down @ ( A @ snoc ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[13356]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
thf(173,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).
thf(371,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7359,plain,
( ( sk1 @ ( sk3 @ host @ queue @ head @ cons ) )
= ( sk3 @ host @ queue ) ),
inference(rewrite,[status(thm)],[138,7352]) ).
thf(12207,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ host @ queue @ head @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk3 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[7359,291]) ).
thf(12208,plain,
sk3 @ host @ queue @ ( sk3 @ host @ queue @ head @ elem ),
inference(pattern_uni,[status(thm)],[12207:[bind(A,$thf( sk3 @ host @ queue @ head )),bind(B,$thf( sk1 ))]]) ).
thf(12986,plain,
( ( ( sk3 @ host @ queue @ ( sk3 @ host @ queue @ head @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12208,6491]) ).
thf(12987,plain,
( ( sk3 @ host @ queue @ ( sk3 @ host @ queue @ head @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[12986]) ).
thf(13086,plain,
( ( ( sk3 @ host @ queue )
!= ( sk3 @ host @ queue ) )
| ( ( sk3 @ host @ queue @ head )
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[12987]) ).
thf(13137,plain,
( ( sk3 @ host @ queue @ head )
!= ( sk8 @ m_Ldr ) ),
inference(simp,[status(thm)],[13086]) ).
thf(1514,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( sk2 @ leq ) )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,243]) ).
thf(1515,plain,
( ( nbr_proc @ ( sk2 @ leq ) )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[1514:[bind(A,$thf( sk4 ))]]) ).
thf(12213,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,6924]) ).
thf(12214,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk11 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[12213]) ).
thf(12259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk11 @ m_Down ) ) ),
inference(simp,[status(thm)],[12214]) ).
thf(12318,plain,
! [A: $i] :
( ( A @ ( sk11 @ m_Down @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[12259]) ).
thf(3611,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( nbr_proc @ s ) )
| ( ( sk9 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[555,2898]) ).
thf(3625,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= nbr_proc )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[3611]) ).
thf(3630,plain,
( ( sk7 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[3625]) ).
thf(3634,plain,
( ( ( sk7 @ host )
!= ( sk4 @ host ) )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,3630]) ).
thf(3639,plain,
( ( sk7 != sk4 )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[3634]) ).
thf(12071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) @ init )
= C ) ),
inference(paramod_ordered,[status(thm)],[415,257]) ).
thf(12072,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[12071:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).
thf(277,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[278]) ).
thf(18650,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( B @ ( A @ m_Ack ) ) )
| ( ( sk3 @ host @ queue @ head )
!= ( C @ m_NormQ ) ) ),
inference(paramod_ordered,[status(thm)],[7352,344]) ).
thf(18651,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NormQ ) ),
inference(pattern_uni,[status(thm)],[18650:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(18657,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NormQ ) ),
inference(simp,[status(thm)],[18651]) ).
thf(18659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ head )
!= ( sk3 @ host @ queue @ head ) )
| ( A
!= ( C @ m_NormQ ) ) ),
inference(paramod_ordered,[status(thm)],[228,18657]) ).
thf(18695,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NormQ @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[18659]) ).
thf(18704,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NormQ @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[18695]) ).
thf(2857,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( sk2 @ leq ) ) )
| ~ $true
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[1515,425]) ).
thf(2858,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( sk2 @ leq ) ) )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2857]) ).
thf(2873,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= sk2 )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2858]) ).
thf(2894,plain,
( ( ( nbr_proc @ s )
!= sk2 )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2873]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B = A )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B = A )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
thf(315,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Down )
!= ( B @ m_Down ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(316,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ) ),
inference(miniscope,[status(thm)],[315]) ).
thf(317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Down )
= ( D @ m_Down ) ) )
& ( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[316]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[317]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[318]) ).
thf(321,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[320]) ).
thf(322,plain,
! [A: $i] :
( ( A @ m_Down @ sk19 )
= A ),
inference(cnf,[status(esa)],[321]) ).
thf(6001,plain,
! [A: $i] :
( ( A @ m_Down @ sk19 )
= A ),
inference(lifteq,[status(thm)],[322]) ).
thf(101,plain,
sk3 @ m_Ldr @ ( sk11 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(563,plain,
sk3 @ m_Ldr @ ( sk7 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ),
inference(rewrite,[status(thm)],[101,147]) ).
thf(1387,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( sk3 @ m_Ldr @ ( sk4 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[161,563]) ).
thf(1388,plain,
( ( sk3 @ m_Ldr @ ( sk4 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(pattern_uni,[status(thm)],[1387:[]]) ).
thf(19415,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ~ $true
| ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[389,425]) ).
thf(19416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[19415]) ).
thf(19417,plain,
! [A: $i] : ( A @ s @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[19416:[bind(A,$thf( A )),bind(B,$thf( A @ s )),bind(C,$thf( A ))]]) ).
thf(2847,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[312,425]) ).
thf(2848,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2847]) ).
thf(2885,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2848]) ).
thf(2891,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[2885]) ).
thf(602,plain,
! [A: $i] :
( ( ( alive @ ( sk11 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,260]) ).
thf(603,plain,
! [A: $i] :
( ( alive @ ( sk11 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[602]) ).
thf(608,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk11 != A ) ),
inference(simp,[status(thm)],[603]) ).
thf(611,plain,
setEmpty != alive,
inference(simp,[status(thm)],[608]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(83,plain,
alive @ ( sk3 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(12,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
thf(218,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(219,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[218]) ).
thf(491,plain,
( ( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,219]) ).
thf(492,plain,
( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[491]) ).
thf(495,plain,
( ( alive != alive )
| ( sk3 != nil ) ),
inference(simp,[status(thm)],[492]) ).
thf(498,plain,
sk3 != nil,
inference(simp,[status(thm)],[495]) ).
thf(801,plain,
( ( ( sk11 @ host )
!= ( sk4 @ host ) )
| ( sk7 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[147,764]) ).
thf(807,plain,
( ( sk11 != sk4 )
| ( sk7 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[801]) ).
thf(7784,plain,
( ( ( sk7 @ host @ ( sk9 @ host @ leq ) )
!= ( sk7 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk11 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[807,2844]) ).
thf(7785,plain,
( ( ( sk7 @ host @ ( sk9 @ host @ leq ) )
!= ( sk7 @ host @ ( nbr_proc @ leq ) ) )
| ( sk11 != sk4 ) ),
inference(simp,[status(thm)],[7784]) ).
thf(7825,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( ( sk9 @ host )
!= nbr_proc )
| ( sk11 != sk4 ) ),
inference(simp,[status(thm)],[7785]) ).
thf(7843,plain,
( ( ( sk9 @ host )
!= nbr_proc )
| ( sk11 != sk4 ) ),
inference(simp,[status(thm)],[7825]) ).
thf(189,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[188]) ).
thf(190,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk13 )
= A ),
inference(cnf,[status(esa)],[189]) ).
thf(4887,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk13 )
= A ),
inference(lifteq,[status(thm)],[190]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(170,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[170]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
thf(419,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(11055,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ head )
!= ( sk3 @ host @ queue @ head ) )
| ( A
!= ( C @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[228,11051]) ).
thf(11085,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[11055]) ).
thf(11092,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[11085]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(374,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(375,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[374]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[375]) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(41,axiom,
elec_2 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_09) ).
thf(362,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[295]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[298]) ).
thf(303,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[302]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ ordered )
<=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_53) ).
thf(345,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ( A @ cons ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(483,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(420,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[419]) ).
thf(421,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[420]) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[421]) ).
thf(2583,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk3 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[138,422]) ).
thf(2584,plain,
( ( sk3 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2583:[bind(A,$thf( sk4 @ ( sk2 @ m_Ack ) )),bind(B,$thf( sk1 ))]]) ).
thf(2588,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ queue )
!= q_nil )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,2584]) ).
thf(2593,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ queue )
!= q_nil )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2588]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( B @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(202,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[201]) ).
thf(203,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(cnf,[status(esa)],[202]) ).
thf(5459,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(lifteq,[status(thm)],[203]) ).
thf(398,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[397]) ).
thf(399,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[398]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_63) ).
thf(267,plain,
! [A: $i,B: $i] :
( ( ( B @ s @ ( A @ s @ leq ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( B @ s @ ( A @ s @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(10455,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( zero @ s ) )
| ( A @ host @ ( sk10 @ host @ leq ) )
| ( sk7 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk7 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[3938,237]) ).
thf(10456,plain,
! [A: $i] :
( ( A @ host @ ( sk10 @ host @ leq ) )
| ( sk7 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk7 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[10455:[]]) ).
thf(12119,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ host @ queue @ head @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk3 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[7359,279]) ).
thf(12120,plain,
( ( sk3 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[12119:[bind(A,$thf( sk3 @ host @ queue @ head )),bind(B,$thf( sk1 ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_39) ).
thf(426,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1466,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( sk2 @ ( zero @ s @ leq ) )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,237]) ).
thf(1467,plain,
( ( sk2 @ ( zero @ s @ leq ) )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[1466:[bind(A,$thf( sk4 ))]]) ).
thf(207,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[206]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[207]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[208]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( B @ setIn ) )
| ( ( C @ host @ ( elid @ index ) @ host )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= wait )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( elid @ index ) @ host )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= wait )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( elid @ index ) @ host )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= wait )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(3623,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( nbr_proc @ s ) )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[3611]) ).
thf(3629,plain,
( ( sk7 @ host @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[3623]) ).
thf(4812,plain,
( ( nbr_proc @ s )
!= ( sk9 @ host ) ),
inference(rewrite,[status(thm)],[3629,555]) ).
thf(19363,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( B @ ( A @ m_Ack ) ) )
| ( ( sk3 @ host @ queue @ head )
!= ( C @ m_Ldr ) ) ),
inference(paramod_ordered,[status(thm)],[7352,439]) ).
thf(19364,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Ldr ) ),
inference(pattern_uni,[status(thm)],[19363:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(19367,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Ldr ) ),
inference(simp,[status(thm)],[19364]) ).
thf(2924,plain,
( ( ( sk8 @ host )
!= ( sk4 @ host ) )
| ( ( sk3 @ host @ s )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[168,2890]) ).
thf(2927,plain,
( ( sk8 != sk4 )
| ( ( sk3 @ host @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2924]) ).
thf(12219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,442]) ).
thf(12220,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[12219]) ).
thf(12273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[12220]) ).
thf(12332,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[12273]) ).
thf(174,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ) ),
inference(miniscope,[status(thm)],[173]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_NotNorm )
= ( D @ m_NotNorm ) ) )
& ( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[174]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[175]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(179,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[178]) ).
thf(180,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk12 )
= A ),
inference(cnf,[status(esa)],[179]) ).
thf(3659,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk12 )
= A ),
inference(lifteq,[status(thm)],[180]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
thf(409,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(615,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[162,107]) ).
thf(622,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[615]) ).
thf(627,plain,
( ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[622]) ).
thf(2863,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[627,425]) ).
thf(2864,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2863]) ).
thf(2882,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2864]) ).
thf(2888,plain,
( ( ( elec_2 @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2882]) ).
thf(3637,plain,
( ( ( sk7 @ host )
!= ( sk4 @ host ) )
| ( sk2 != nbr_proc )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,3630]) ).
thf(3642,plain,
( ( sk7 != sk4 )
| ( sk2 != nbr_proc )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[3637]) ).
thf(329,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[328]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[329]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[330]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm ) ),
inference(simp,[status(thm)],[126]) ).
thf(802,plain,
( ( ( sk8 @ host )
!= ( sk4 @ host ) )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[168,764]) ).
thf(808,plain,
( ( sk8 != sk4 )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[802]) ).
thf(366,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[365]) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[366]) ).
thf(368,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[367]) ).
thf(19268,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( B @ ( A @ m_Ack ) ) )
| ( ( sk3 @ host @ queue @ head )
!= ( C @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[7352,368]) ).
thf(19269,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Halt ) ),
inference(pattern_uni,[status(thm)],[19268:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(19272,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Halt ) ),
inference(simp,[status(thm)],[19269]) ).
thf(19277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ head )
!= ( sk3 @ host @ queue @ head ) )
| ( A
!= ( C @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[228,19272]) ).
thf(19313,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Halt @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[19277]) ).
thf(19325,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Halt @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[19313]) ).
thf(18587,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk11 @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[415,13415]) ).
thf(18588,plain,
( ( q_nil @ ( sk11 @ m_Down @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[18587:[bind(A,$thf( sk11 @ m_Down )),bind(B,$thf( q_nil ))]]) ).
thf(1511,plain,
( ( ( sk7 @ host )
!= ( sk4 @ host ) )
| ( ( sk3 @ host )
!= sk2 )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,500]) ).
thf(1546,plain,
( ( sk7 != sk4 )
| ( ( sk3 @ host )
!= sk2 )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[1511]) ).
thf(1710,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ( sk7 != sk4 )
| ( sk2 != sk2 )
| ( pendack != elid )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,1546]) ).
thf(1711,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ( sk7 != sk4 )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[1710]) ).
thf(1717,plain,
( ( sk4 != sk3 )
| ( sk7 != sk4 )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[1711]) ).
thf(489,plain,
( ( ( alive @ ( sk11 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[92,219]) ).
thf(490,plain,
( ( alive @ ( sk11 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(494,plain,
( ( alive != alive )
| ( sk11 != nil ) ),
inference(simp,[status(thm)],[490]) ).
thf(497,plain,
sk11 != nil,
inference(simp,[status(thm)],[494]) ).
thf(4837,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk2 @ s )
!= ( zero @ s ) )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[795,2896]) ).
thf(4838,plain,
( ( ( sk2 @ s )
!= ( zero @ s ) )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[4837:[bind(A,$thf( sk4 ))]]) ).
thf(2853,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[1012,425]) ).
thf(2854,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2853]) ).
thf(2871,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2854]) ).
thf(2892,plain,
( ( ( nbr_proc @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2871]) ).
thf(534,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( ( sk3 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[168,500]) ).
thf(535,plain,
( ( sk8 @ host )
!= ( sk7 @ host ) ),
inference(simp,[status(thm)],[534]) ).
thf(539,plain,
sk8 != sk7,
inference(simp,[status(thm)],[535]) ).
thf(249,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[248]) ).
thf(250,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[249]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[229]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[230]) ).
thf(1325,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( ( sk4 @ host @ s )
= ( sk9 @ host ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[161,555]) ).
thf(1326,plain,
( ( ( sk4 @ host @ s )
= ( sk9 @ host ) )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(pattern_uni,[status(thm)],[1325:[]]) ).
thf(3612,plain,
! [A: $i] :
( ( ( sk11 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk7 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[147,2898]) ).
thf(3613,plain,
( ( nbr_proc @ s )
!= ( sk7 @ host ) ),
inference(pattern_uni,[status(thm)],[3612:[bind(A,$thf( sk11 ))]]) ).
thf(2587,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ( ( elec_2 @ queue )
!= q_nil )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,2584]) ).
thf(2594,plain,
( ( sk4 != sk3 )
| ( ( elec_2 @ queue )
!= q_nil )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2587]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).
thf(390,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(417,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[416]) ).
thf(418,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[417]) ).
thf(4833,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,2896]) ).
thf(4834,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[4833:[bind(A,$thf( sk4 ))]]) ).
thf(19482,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk9 @ host @ ( sk7 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19394,425]) ).
thf(19483,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk9 @ host @ ( sk7 @ host @ leq ) ) ),
inference(simp,[status(thm)],[19482]) ).
thf(19536,plain,
! [A: $i] :
( ( A
!= ( sk9 @ host ) )
| ( ( A @ s )
!= ( sk7 @ host ) ) ),
inference(simp,[status(thm)],[19483]) ).
thf(19559,plain,
( ( sk9 @ host @ s )
!= ( sk7 @ host ) ),
inference(simp,[status(thm)],[19536]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m_Down @ elem ) )
& ( ( B @ host )
= ( C @ host ) )
& ( A @ ( B @ m_Halt @ cons ) @ ordered ) )
=> ( C @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_57) ).
thf(433,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m_Down @ elem ) )
& ( ( B @ host )
= ( C @ host ) )
& ( A @ ( B @ m_Halt @ cons ) @ ordered ) )
=> ( C @ ( B @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(212,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[211]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[212]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk6 ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk6 ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(lifteq,[status(thm)],[112]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk6 ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(1347,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( ( sk4 @ host @ ( status @ index ) )
= elec_1 )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[161,550]) ).
thf(1348,plain,
( ( ( sk4 @ host @ ( status @ index ) )
= elec_1 )
| ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ) ),
inference(pattern_uni,[status(thm)],[1347:[]]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[150]) ).
thf(9,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
thf(210,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(194,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[194]) ).
thf(532,plain,
sk7 != sk3,
inference(simp,[status(thm)],[500]) ).
thf(12177,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,6491]) ).
thf(12178,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[12177]) ).
thf(12261,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[12178]) ).
thf(12320,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[12261]) ).
thf(1284,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ( sk7 != sk4 )
| ( elec_2 != elec_2 )
| ( pendack != status )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[793,1040]) ).
thf(1285,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ( sk7 != sk4 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1284]) ).
thf(1288,plain,
( ( sk4 != sk3 )
| ( sk7 != sk4 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1285]) ).
thf(10303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) @ last )
= B ) ),
inference(paramod_ordered,[status(thm)],[415,231]) ).
thf(10304,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[10303:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(43,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).
thf(369,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(484,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[483]) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[484]) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[485]) ).
thf(487,plain,
( ( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,219]) ).
thf(488,plain,
( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(493,plain,
( ( alive != alive )
| ( sk8 != nil ) ),
inference(simp,[status(thm)],[488]) ).
thf(496,plain,
sk8 != nil,
inference(simp,[status(thm)],[493]) ).
thf(363,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[362]) ).
thf(364,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[363]) ).
thf(5457,plain,
( ( sk2 != sk2 )
| ( zero != elec_2 )
| ( pendack != elid )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[598,5448]) ).
thf(5458,plain,
( ( zero != elec_2 )
| ( pendack != elid )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[5457:[]]) ).
thf(12967,plain,
( ( ( sk3 @ host @ queue @ ( sk3 @ host @ queue @ head @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12208,6944]) ).
thf(12968,plain,
( ( sk3 @ host @ queue @ ( sk3 @ host @ queue @ head @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[12967]) ).
thf(13116,plain,
( ( ( sk3 @ host @ queue )
!= ( sk3 @ host @ queue ) )
| ( ( sk3 @ host @ queue @ head )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[12968]) ).
thf(13156,plain,
( ( sk3 @ host @ queue @ head )
!= ( sk8 @ m_Down ) ),
inference(simp,[status(thm)],[13116]) ).
thf(12161,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,6944]) ).
thf(12162,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[12161]) ).
thf(12272,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[12162]) ).
thf(12331,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[12272]) ).
thf(24077,plain,
$false,
inference(e,[status(thm)],[69,10399,628,4852,555,365,2889,5444,408,762,19533,247,1269,440,115,6944,217,276,1705,550,142,500,153,2844,340,404,973,6009,1386,436,257,16398,301,2825,1529,389,3938,2897,11051,196,125,344,460,157,6455,228,261,4830,416,2929,325,164,443,211,238,121,1040,2893,15893,480,147,397,4842,221,132,396,243,312,206,5448,280,293,6491,248,117,439,793,3265,220,85,201,260,429,137,598,160,2890,3250,92,229,16360,13391,12304,1012,2895,403,188,388,169,499,328,3622,193,2240,10353,5387,393,13415,173,371,13398,237,244,13404,13137,1515,2995,12318,13383,3639,12072,425,166,279,18704,2894,149,161,6001,423,1388,291,413,19417,2891,611,144,498,4822,335,236,7843,4887,159,764,406,172,219,419,11092,377,362,303,2896,345,3668,140,483,251,2593,155,5459,521,130,399,563,226,267,241,167,10456,12120,426,162,1467,795,374,255,209,123,4812,19367,2927,12332,18657,3659,409,2888,3642,331,127,338,808,19325,470,576,18588,386,1717,497,2584,4838,2892,627,556,539,218,368,250,231,1326,3613,2594,7359,304,258,390,3630,418,4834,19394,19559,235,433,214,119,378,1348,315,168,1546,12208,183,422,6924,151,19272,273,210,242,341,807,195,532,12320,94,283,415,1288,400,332,7352,2898,6471,10304,178,277,442,369,254,486,83,496,364,232,5458,13156,12331,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/5.42 % Computer : n011.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Sat Sep 26 13:56:34 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/5.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/5.85 % [INFO] Parsing done (149ms).
% 0.18/5.86 % [INFO] Running in sequential loop mode.
% 1.78/6.05 % [INFO] eprover registered as external prover.
% 1.78/6.06 % [INFO] Scanning for conjecture ...
% 2.08/6.19 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.29/6.27 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.63/6.30 % [INFO] Problem is first-order (TPTP FOF).
% 2.63/6.31 % [INFO] Type checking passed.
% 2.63/6.31 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 87.03/24.79 % External prover 'e' found a proof!
% 87.03/24.79 % [INFO] Killing All external provers ...
% 87.03/24.79 % Time passed: 19282ms (effective reasoning time: 18926ms)
% 87.03/24.79 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 87.03/24.79 % Axioms used in derivation (66): axiom_44, axiom_09, axiom_54, axiom_64, axiom_20, axiom_57, axiom_53, axiom_17, axiom_14, axiom_37, axiom_26, axiom_55, axiom_08, axiom_33, axiom_10, axiom_40, axiom_22, axiom_59, axiom_49, axiom_15, axiom_51, axiom_04, axiom_21, axiom_19, axiom_63, axiom_38, axiom_43, axiom_27, axiom_32, axiom_60, axiom_16, axiom_50, axiom_05, axiom_46, axiom_42, axiom_31, axiom_24, axiom_61, axiom_06, axiom_35, axiom_28, axiom, axiom_65, axiom_36, axiom_02, axiom_39, axiom_47, axiom_13, axiom_41, axiom_25, axiom_52, axiom_34, axiom_58, axiom_62, axiom_45, axiom_29, axiom_11, axiom_56, axiom_07, axiom_30, axiom_23, axiom_01, axiom_18, axiom_12, axiom_03, axiom_48
% 87.03/24.79 % No. of inferences in proof: 697
% 87.03/24.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19282 ms resp. 18926 ms w/o parsing
% 89.83/25.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 89.83/25.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------