%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV477+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 87.43s 20.58s
% Output : Refutation 89.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 85
% Syntax : Number of formulae : 714 ( 340 unt; 0 typ; 18 def)
% Number of atoms : 3031 (1642 equ; 0 cnn)
% Maximal formula atoms : 176 ( 4 avg)
% Number of connectives : 11702 (1535 ~; 928 |; 887 &;8040 @)
% ( 13 <=>; 299 =>; 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 : 1515 ( 9 ^;1382 !; 106 ?;1515 :)
% ( 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(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(last_decl,type,
last: $i > $i ).
thf(snoc_decl,type,
snoc: $i > $i > $i ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(init_decl,type,
init: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $o ).
thf(nil_decl,type,
nil: $i ).
thf(setEmpty_decl,type,
setEmpty: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(pidElem_decl,type,
pidElem: $i > $o ).
thf(head_decl,type,
head: $i > $i ).
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 ) ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( C @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ queue @ ( 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 ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( E @ host ) )
& ( alive @ ( E @ 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 ) ) )
=> ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( G @ host @ s ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ queue @ ( 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 ) ) ) ) )
=> ~ ( ( ( B @ host )
= ( D @ host ) )
& ( alive @ ( D @ 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 ) ) )
=> ! [C: $i] :
( ( ( A @ host )
= ( C @ host ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( A @ host )
!= ( F @ host ) )
=> ( ( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host )
= ( F @ host @ s ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ queue @ ( 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 ) ) ) ) )
=> ~ ( ( ( A @ host )
= ( C @ host ) )
& ( alive @ ( C @ 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 ) ) )
=> ! [B: $i] :
( ( ( sk3 @ host )
= ( B @ host ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( sk3 @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( C @ host )
= ( E @ host @ s ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( E @ host @ queue @ ( 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(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 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( ( sk3 @ host )
= ( A @ host ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( sk3 @ host )
!= ( D @ host ) )
=> ( ( ( ( D @ host @ ( status @ index ) )
= elec_1 )
& ( ( B @ host )
= ( D @ host @ s ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( D @ host @ queue @ ( 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] :
( ( ( sk3 @ host )
!= ( C @ host ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ( ( A @ host )
= ( C @ host @ s ) )
& ( C @ host @ queue @ ( B @ m_Down @ elem ) )
& ( C @ host @ queue @ ( 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] :
( ( ( sk3 @ host )
!= ( B @ host ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk9 @ host )
= ( B @ host @ s ) )
& ( B @ host @ queue @ ( A @ m_Down @ elem ) )
& ( B @ host @ queue @ ( 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] :
~ ( ( ( sk3 @ host )
!= ( A @ host ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk9 @ host )
= ( A @ host @ s ) )
& ( A @ host @ queue @ ( sk10 @ m_Down @ elem ) )
& ( A @ host @ queue @ ( 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(5,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(182,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(183,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)],[182]) ).
thf(184,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)],[183]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[184]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[185]) ).
thf(188,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[187]) ).
thf(189,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk13 )
= A ),
inference(cnf,[status(esa)],[188]) ).
thf(2199,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk13 )
= A ),
inference(lifteq,[status(thm)],[189]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_01) ).
thf(479,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(17,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(232,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(57,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(419,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(420,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[419]) ).
thf(421,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[420]) ).
thf(2395,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[232,421]) ).
thf(2396,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[2395]) ).
thf(2401,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[2396]) ).
thf(2412,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2401]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(246,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(247,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[246]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[247]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[248]) ).
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] :
( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( I @ host @ queue @ ( H @ m_Down @ elem ) )
& ( I @ host @ queue @ ( 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/sandbox/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] :
( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( I @ host @ queue @ ( H @ m_Down @ elem ) )
& ( I @ host @ queue @ ( 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] :
( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( I @ host @ queue @ ( H @ m_Down @ elem ) )
& ( I @ host @ queue @ ( 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(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 ) ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( C @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ queue @ ( 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 ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( E @ host ) )
& ( alive @ ( E @ 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 ) )
& ( sk11 @ host @ queue @ ( sk10 @ m_Down @ elem ) )
& ( sk11 @ host @ queue @ ( 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 ) )
& ( ( 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,
sk11 @ host @ queue @ ( sk9 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(74,plain,
( ( sk9 @ host )
= ( sk11 @ host @ s ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(131,plain,
( ( sk11 @ host @ s )
= ( sk9 @ host ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(384,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[384]) ).
thf(14130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ~ $true
| ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[385,421]) ).
thf(14131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[14130]) ).
thf(14132,plain,
! [A: $i] : ( A @ s @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[14131:[bind(A,$thf( A )),bind(B,$thf( A @ s )),bind(C,$thf( A ))]]) ).
thf(14587,plain,
! [A: $i] :
( ( ( sk11 @ host @ s )
!= ( A @ s ) )
| ( sk9 @ host @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[131,14132]) ).
thf(14588,plain,
sk9 @ host @ ( sk11 @ host @ leq ),
inference(pattern_uni,[status(thm)],[14587:[bind(A,$thf( sk11 @ host ))]]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(14684,plain,
! [B: $i,A: $i] :
( ( ( sk9 @ host @ ( sk11 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[14588,95]) ).
thf(14685,plain,
! [B: $i,A: $i] :
( ( ( sk9 @ host @ ( sk11 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[14684]) ).
thf(14686,plain,
~ ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[14685:[bind(A,$thf( sk11 )),bind(B,$thf( sk9 ))]]) ).
thf(14791,plain,
( ( ( sk11 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[77,14686]) ).
thf(14792,plain,
( ( sk11 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[14791]) ).
thf(14816,plain,
( ( ( sk11 @ host @ queue )
!= ( sk11 @ host @ queue ) )
| ( ( sk9 @ m_Down )
!= ( sk9 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[14792]) ).
thf(14822,plain,
( ( sk9 @ m_Down )
!= ( sk9 @ m_Ldr ) ),
inference(simp,[status(thm)],[14816]) ).
thf(88,plain,
sk11 @ host @ queue @ ( sk10 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(91,plain,
( ( sk4 @ host )
= ( sk3 @ host @ ( pendack @ index ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(150,plain,
( ( sk3 @ host @ ( pendack @ index ) )
= ( sk4 @ host ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(104,plain,
( ( sk3 @ host @ ( elid @ index ) )
= sk2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(157,plain,
( ( sk3 @ host @ ( elid @ index ) )
= sk2 ),
inference(lifteq,[status(thm)],[104]) ).
thf(629,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( elid @ index ) ) )
| ( ( sk4 @ host )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[150,157]) ).
thf(642,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != elid )
| ( ( sk4 @ host )
= sk2 ) ),
inference(simp,[status(thm)],[629]) ).
thf(645,plain,
( ( pendack != elid )
| ( ( sk4 @ host )
= sk2 ) ),
inference(simp,[status(thm)],[642]) ).
thf(42,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(365,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(96,plain,
( ( sk7 @ host )
!= ( sk4 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(138,plain,
( ( sk7 @ host )
!= ( sk4 @ host ) ),
inference(lifteq,[status(thm)],[96]) ).
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(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(276,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(242,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(243,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[242]) ).
thf(2375,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[243,421]) ).
thf(2376,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2375]) ).
thf(2402,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2376]) ).
thf(2413,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2402]) ).
thf(4230,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[2413]) ).
thf(4806,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( sk2 != zero )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[645,4230]) ).
thf(4807,plain,
( ( sk2 != zero )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[4806:[bind(A,$thf( sk4 ))]]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(202,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,plain,
( ( sk3 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(158,plain,
( ( sk3 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[82]) ).
thf(632,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ( ( sk4 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[150,158]) ).
thf(640,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != status )
| ( ( sk4 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[632]) ).
thf(644,plain,
( ( pendack != status )
| ( ( sk4 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[640]) ).
thf(21,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(244,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(245,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[244]) ).
thf(2383,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[245,421]) ).
thf(2384,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2383]) ).
thf(2408,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2384]) ).
thf(2419,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2408]) ).
thf(3034,plain,
! [A: $i] :
( ( ( sk11 @ host @ s )
!= ( nbr_proc @ s ) )
| ( ( sk9 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[131,2419]) ).
thf(3037,plain,
! [A: $i] :
( ( ( sk11 @ host )
!= nbr_proc )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[3034]) ).
thf(3039,plain,
( ( sk11 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[3037]) ).
thf(3046,plain,
( ( ( sk11 @ host )
!= ( sk4 @ host ) )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[644,3039]) ).
thf(3049,plain,
( ( sk11 != sk4 )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[3046]) ).
thf(109,plain,
sk11 @ host @ s @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(533,plain,
sk9 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[109,131]) ).
thf(75,plain,
~ ( sk3 @ host @ ( acks @ index ) @ ( sk7 @ host @ setIn ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(542,plain,
( ( ( sk3 @ host @ ( acks @ index ) )
!= ( sk3 @ host @ ( elid @ index ) ) )
| ~ ( sk2 @ ( sk7 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[157,75]) ).
thf(546,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( acks != elid )
| ~ ( sk2 @ ( sk7 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[542]) ).
thf(550,plain,
( ( acks != elid )
| ~ ( sk2 @ ( sk7 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[546]) ).
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(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 ) )
| ( ( 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(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 ) )
| ( ( 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)],[141]) ).
thf(14775,plain,
( ( ( sk11 @ host @ queue @ ( sk10 @ m_Down @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,14686]) ).
thf(14776,plain,
( ( sk11 @ host @ queue @ ( sk10 @ m_Down @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[14775]) ).
thf(14815,plain,
( ( ( sk11 @ host @ queue )
!= ( sk11 @ host @ queue ) )
| ( ( sk10 @ m_Down )
!= ( sk9 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[14776]) ).
thf(14829,plain,
( ( sk10 @ m_Down )
!= ( sk9 @ m_Ldr ) ),
inference(simp,[status(thm)],[14815]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(337,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(338,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[337]) ).
thf(339,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[338]) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(52,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(402,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(403,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[402]) ).
thf(404,plain,
wait != norm,
inference(lifteq,[status(thm)],[403]) ).
thf(76,plain,
( ( sk3 @ host @ queue )
= ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(145,plain,
( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
= ( sk3 @ host @ queue ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(282,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(283,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)],[282]) ).
thf(284,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)],[283]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[284]) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[286]) ).
thf(290,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[289]) ).
thf(7175,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk3 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[145,290]) ).
thf(7176,plain,
sk3 @ host @ queue @ ( sk4 @ ( sk2 @ m_Ack ) @ elem ),
inference(pattern_uni,[status(thm)],[7175:[bind(A,$thf( sk4 @ ( sk2 @ m_Ack ) )),bind(B,$thf( sk1 ))]]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(429,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(430,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[429]) ).
thf(431,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[430]) ).
thf(8441,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk3 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[145,431]) ).
thf(8442,plain,
( ( sk4 @ ( sk2 @ m_Ack ) )
= ( sk3 @ host @ queue @ head ) ),
inference(pattern_uni,[status(thm)],[8441:[bind(A,$thf( sk4 @ ( sk2 @ m_Ack ) )),bind(B,$thf( sk1 ))]]) ).
thf(8851,plain,
sk3 @ host @ queue @ ( sk3 @ host @ queue @ head @ elem ),
inference(rewrite,[status(thm)],[7176,8442]) ).
thf(63,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(439,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(440,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[439]) ).
thf(441,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[440]) ).
thf(613,plain,
! [A: $i] :
( ( ( sk11 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[77,441]) ).
thf(614,plain,
! [A: $i] :
( ( sk11 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[613]) ).
thf(617,plain,
! [A: $i] :
( ( ( sk11 @ host @ queue )
!= q_nil )
| ( ( sk9 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[614]) ).
thf(619,plain,
( ( sk11 @ host @ queue )
!= q_nil ),
inference(simp,[status(thm)],[617]) ).
thf(998,plain,
( ( ( sk11 @ host )
!= ( sk4 @ host ) )
| ( ( elec_2 @ queue )
!= q_nil )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[644,619]) ).
thf(1046,plain,
( ( sk11 != sk4 )
| ( ( elec_2 @ queue )
!= q_nil )
| ( pendack != status ) ),
inference(simp,[status(thm)],[998]) ).
thf(25,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(257,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(111,plain,
( ( sk3 @ host )
= ( sk8 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(167,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(127,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(2522,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( B != A ) ),
inference(simp,[status(thm)],[128]) ).
thf(2568,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(simp,[status(thm)],[2522]) ).
thf(5362,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk3 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[167,2568]) ).
thf(5363,plain,
~ ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[5362:[bind(A,$thf( sk8 ))]]) ).
thf(7323,plain,
( ( ( sk3 @ host @ queue @ ( sk4 @ ( sk2 @ m_Ack ) @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,5363]) ).
thf(7324,plain,
( ( sk3 @ host @ queue @ ( sk4 @ ( sk2 @ m_Ack ) @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7323]) ).
thf(7405,plain,
( ( ( sk3 @ host @ queue )
!= ( sk3 @ host @ queue ) )
| ( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[7324]) ).
thf(7444,plain,
( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( sk8 @ m_Down ) ),
inference(simp,[status(thm)],[7405]) ).
thf(8848,plain,
( ( sk3 @ host @ queue @ head )
!= ( sk8 @ m_Down ) ),
inference(rewrite,[status(thm)],[7444,8442]) ).
thf(1000,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[644,243]) ).
thf(1001,plain,
( ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[1000:[bind(A,$thf( sk4 ))]]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(389,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(93,plain,
alive @ ( sk11 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(16,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(230,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(231,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[230]) ).
thf(495,plain,
( ( ( alive @ ( sk11 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,231]) ).
thf(496,plain,
( ( alive @ ( sk11 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(501,plain,
( ( alive != alive )
| ( sk11 != nil ) ),
inference(simp,[status(thm)],[496]) ).
thf(504,plain,
sk11 != nil,
inference(simp,[status(thm)],[501]) ).
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(124,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(125,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)],[124]) ).
thf(4239,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[167,2413]) ).
thf(4240,plain,
( ( sk3 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[4239:[bind(A,$thf( sk8 ))]]) ).
thf(4275,plain,
( ( sk3 @ host )
!= zero ),
inference(simp,[status(thm)],[4240]) ).
thf(54,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(409,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(410,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[409]) ).
thf(411,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[410]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[202]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[203]) ).
thf(6642,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)],[411,204]) ).
thf(6643,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[6642:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
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(151,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(152,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)],[151]) ).
thf(8849,plain,
( ( sk1 @ ( sk3 @ host @ queue @ head @ cons ) )
= ( sk3 @ host @ queue ) ),
inference(rewrite,[status(thm)],[145,8442]) ).
thf(2373,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk9 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[533,421]) ).
thf(2374,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk9 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2373]) ).
thf(2409,plain,
! [A: $i] :
( ( A
!= ( sk9 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2374]) ).
thf(2420,plain,
( ( sk9 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2409]) ).
thf(100,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(163,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(164,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[163]) ).
thf(83,plain,
alive @ ( sk3 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(785,plain,
( ( ( sk2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk3 @ setIn ) ) )
| ( acks != elid )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,550]) ).
thf(786,plain,
( ( ( sk2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk3 @ setIn ) ) )
| ( acks != elid ) ),
inference(simp,[status(thm)],[785]) ).
thf(789,plain,
( ( sk2 != alive )
| ( ( sk7 @ host )
!= sk3 )
| ( acks != elid ) ),
inference(simp,[status(thm)],[786]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(482,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(483,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[482]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[483]) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[484]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(238,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
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(33,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(303,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(304,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)],[303]) ).
thf(305,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)],[304]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[305]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[307]) ).
thf(311,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[310]) ).
thf(954,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)],[311,95]) ).
thf(955,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)],[954]) ).
thf(956,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[955:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(958,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(simp,[status(thm)],[956]) ).
thf(5310,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk3 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[167,958]) ).
thf(5311,plain,
~ ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[5310:[bind(A,$thf( sk8 ))]]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(328,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(329,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[328]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[329]) ).
thf(331,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[330]) ).
thf(804,plain,
! [A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk3 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[145,331]) ).
thf(805,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk4 @ ( sk2 @ m_Ack ) )
!= A )
| ( sk3 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[804]) ).
thf(806,plain,
( ( sk1 != q_nil )
| ( sk3 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[805]) ).
thf(628,plain,
( ( ( sk3 @ host @ ( acks @ index ) )
!= ( sk3 @ host @ ( pendack @ index ) ) )
| ~ ( sk4 @ host @ ( sk7 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[150,75]) ).
thf(643,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( acks != pendack )
| ~ ( sk4 @ host @ ( sk7 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[628]) ).
thf(646,plain,
( ( acks != pendack )
| ~ ( sk4 @ host @ ( sk7 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[643]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(253,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
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(132,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(133,plain,
! [A: $i] :
( ( sk11 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk11 @ host @ leq ) )
| ( A
= ( sk10 @ host ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(3387,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk11 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk11 @ host @ leq ) )
| ( B
= ( sk10 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[311,133]) ).
thf(3388,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk11 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk11 @ host @ leq ) )
| ( B
= ( sk10 @ host ) ) ),
inference(simp,[status(thm)],[3387]) ).
thf(3389,plain,
( ( sk11 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk11 @ host @ leq ) )
| ( ( zero @ s )
= ( sk10 @ host ) ) ),
inference(pattern_uni,[status(thm)],[3388:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s ))]]) ).
thf(98,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(146,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)],[98]) ).
thf(147,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)],[146]) ).
thf(107,plain,
sk3 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(580,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( elid @ index ) ) )
| ( sk2 @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[157,107]) ).
thf(584,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != elid )
| ( sk2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[580]) ).
thf(588,plain,
( ( pendack != elid )
| ( sk2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[584]) ).
thf(2391,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[588,421]) ).
thf(2392,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( nbr_proc @ leq ) ) )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2391]) ).
thf(2399,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= nbr_proc )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2392]) ).
thf(2424,plain,
( ( ( sk2 @ s )
!= nbr_proc )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2399]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(396,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[276]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[277]) ).
thf(6699,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk3 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[145,278]) ).
thf(6700,plain,
( ( sk3 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[6699:[bind(A,$thf( sk4 @ ( sk2 @ m_Ack ) )),bind(B,$thf( sk1 ))]]) ).
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(507,plain,
sk11 != sk3,
inference(simp,[status(thm)],[113]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(233,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)],[18]) ).
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(627,plain,
sk4 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[107,150]) ).
thf(755,plain,
( ( ( sk8 @ host )
!= ( sk4 @ host ) )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[167,627]) ).
thf(761,plain,
( ( sk8 != sk4 )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(551,plain,
( ( ( sk3 @ host @ ( acks @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ~ ( elec_2 @ ( sk7 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[158,75]) ).
thf(558,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( acks != status )
| ~ ( elec_2 @ ( sk7 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(567,plain,
( ( acks != status )
| ~ ( elec_2 @ ( sk7 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[558]) ).
thf(791,plain,
( ( ( elec_2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk11 @ setIn ) ) )
| ( acks != status )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,567]) ).
thf(792,plain,
( ( ( elec_2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk11 @ setIn ) ) )
| ( acks != status ) ),
inference(simp,[status(thm)],[791]) ).
thf(798,plain,
( ( elec_2 != alive )
| ( ( sk7 @ host )
!= sk11 )
| ( acks != status ) ),
inference(simp,[status(thm)],[792]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ pidElem )
<=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(292,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(508,plain,
( ( ( sk11 @ host )
!= ( sk8 @ host ) )
| ( ( sk3 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[167,113]) ).
thf(509,plain,
( ( sk11 @ host )
!= ( sk8 @ host ) ),
inference(simp,[status(thm)],[508]) ).
thf(512,plain,
sk11 != sk8,
inference(simp,[status(thm)],[509]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(469,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(470,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)],[469]) ).
thf(471,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)],[470]) ).
thf(472,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[471]) ).
thf(474,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[472]) ).
thf(475,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[474]) ).
thf(476,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk22 )
= A ),
inference(cnf,[status(esa)],[475]) ).
thf(4323,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk22 )
= A ),
inference(lifteq,[status(thm)],[476]) ).
thf(85,plain,
alive @ ( sk8 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(198,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(199,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[199]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[200]) ).
thf(37,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(334,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(293,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)],[292]) ).
thf(294,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)],[293]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[294]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(302,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[301]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(260,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(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(159,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(160,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)],[159]) ).
thf(390,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[389]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[390]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[391]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(192,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(272,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(273,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[272]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[273]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[274]) ).
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 ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ setIn ) ) ),
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 ) )
| ~ ( 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)],[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 ) )
| ~ ( 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)],[136]) ).
thf(15,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(227,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(228,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[227]) ).
thf(229,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[228]) ).
thf(23,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(250,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(251,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[250]) ).
thf(252,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[251]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[196]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(361,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(435,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(324,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1016,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[644,245]) ).
thf(1017,plain,
( ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[1016:[bind(A,$thf( sk4 ))]]) ).
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(155,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(156,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)],[155]) ).
thf(4247,plain,
! [A: $i] :
( ( ( sk11 @ host @ s )
!= ( A @ host @ s ) )
| ( ( zero @ s )
!= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[131,2413]) ).
thf(4248,plain,
( ( zero @ s )
!= ( sk9 @ host ) ),
inference(pattern_uni,[status(thm)],[4247:[bind(A,$thf( sk11 ))]]) ).
thf(362,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[362]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[363]) ).
thf(16230,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)],[8442,364]) ).
thf(16231,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Halt ) ),
inference(pattern_uni,[status(thm)],[16230:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(16242,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Halt ) ),
inference(simp,[status(thm)],[16231]) ).
thf(14558,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14132,421]) ).
thf(14559,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[14558]) ).
thf(14595,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[14559]) ).
thf(14613,plain,
! [A: $i] :
( ( A @ s @ s )
!= A ),
inference(simp,[status(thm)],[14595]) ).
thf(14564,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk11 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk11 @ host @ leq ) )
| ( B
= ( sk10 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[14132,133]) ).
thf(14565,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk11 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk11 @ host @ leq ) )
| ( B
= ( sk10 @ host ) ) ),
inference(simp,[status(thm)],[14564]) ).
thf(14566,plain,
( ( sk11 @ host @ ( down @ index ) @ ( zero @ s @ s @ setIn ) )
| ( zero @ s @ s @ ( sk11 @ host @ leq ) )
| ( ( zero @ s @ s )
= ( sk10 @ host ) ) ),
inference(pattern_uni,[status(thm)],[14565:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s @ s ))]]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(374,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)],[45]) ).
thf(375,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)],[374]) ).
thf(376,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)],[375]) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[376]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[378]) ).
thf(382,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[381]) ).
thf(7468,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,5311]) ).
thf(7469,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7468]) ).
thf(7561,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7469]) ).
thf(7572,plain,
! [A: $i] :
( ( sk8 @ m_Ldr @ ( A @ snoc ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[7561]) ).
thf(14560,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( A @ s ) )
| ( sk10 @ host @ ( A @ leq ) )
| ( sk11 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk11 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[3389,14132]) ).
thf(14561,plain,
( ( sk10 @ host @ ( zero @ leq ) )
| ( sk11 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk11 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[14560:[bind(A,$thf( zero ))]]) ).
thf(254,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[253]) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[254]) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(393,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(14793,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,14686]) ).
thf(14794,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[14793]) ).
thf(14819,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk11 @ host @ queue ) )
| ( A
!= ( sk9 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[14794]) ).
thf(14824,plain,
! [A: $i] :
( ( sk9 @ m_Ldr @ ( A @ snoc ) )
!= ( sk11 @ host @ queue ) ),
inference(simp,[status(thm)],[14819]) ).
thf(15316,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk9 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk11 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[411,14824]) ).
thf(15317,plain,
( ( q_nil @ ( sk9 @ m_Ldr @ cons ) )
!= ( sk11 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[15316:[bind(A,$thf( sk9 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(266,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(40,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_09) ).
thf(358,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(359,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[358]) ).
thf(360,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[359]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(205,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)],[10]) ).
thf(239,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[238]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[239]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(8864,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)],[8442,241]) ).
thf(8865,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NotNorm ) ),
inference(pattern_uni,[status(thm)],[8864:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(8872,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NotNorm ) ),
inference(simp,[status(thm)],[8865]) ).
thf(11941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ head )
!= ( sk3 @ host @ queue @ head ) )
| ( A
!= ( C @ m_NotNorm ) ) ),
inference(paramod_ordered,[status(thm)],[431,8872]) ).
thf(11962,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NotNorm @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[11941]) ).
thf(11972,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NotNorm @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[11962]) ).
thf(540,plain,
( ( ( sk9 @ host )
!= ( sk8 @ host ) )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[167,533]) ).
thf(541,plain,
( ( sk9 != sk8 )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[540]) ).
thf(5416,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( zero @ s ) )
| ( A @ host @ ( sk10 @ host @ leq ) )
| ( sk11 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk11 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[3389,243]) ).
thf(5417,plain,
! [A: $i] :
( ( A @ host @ ( sk10 @ host @ leq ) )
| ( sk11 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk11 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[5416:[]]) ).
thf(2387,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk4 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[627,421]) ).
thf(2388,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk4 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2387]) ).
thf(2398,plain,
! [A: $i] :
( ( A
!= ( sk4 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2388]) ).
thf(2423,plain,
( ( sk4 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2398]) ).
thf(55,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(412,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(425,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)],[59]) ).
thf(90,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(165,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)],[90]) ).
thf(166,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)],[165]) ).
thf(4254,plain,
( ( ( sk11 @ host @ s )
!= ( zero @ s ) )
| ( ( sk9 @ host )
!= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[131,4248]) ).
thf(4255,plain,
( ( sk11 @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[4254]) ).
thf(4256,plain,
( ( sk11 @ host )
!= zero ),
inference(simp,[status(thm)],[4255]) ).
thf(7504,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,441]) ).
thf(7505,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[7504]) ).
thf(7534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[7505]) ).
thf(7599,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[7534]) ).
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(148,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[148]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(279,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
thf(314,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(315,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)],[314]) ).
thf(316,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)],[315]) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[316]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[317]) ).
thf(320,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[319]) ).
thf(321,plain,
! [A: $i] :
( ( A @ m_Down @ sk19 )
= A ),
inference(cnf,[status(esa)],[320]) ).
thf(2602,plain,
! [A: $i] :
( ( A @ m_Down @ sk19 )
= A ),
inference(lifteq,[status(thm)],[321]) ).
thf(8403,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[411,7572]) ).
thf(8404,plain,
( ( q_nil @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[8403:[bind(A,$thf( sk8 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(258,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[257]) ).
thf(259,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[258]) ).
thf(572,plain,
! [A: $i] :
( ( ( alive @ ( sk3 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,259]) ).
thf(573,plain,
! [A: $i] :
( ( alive @ ( sk3 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(576,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[573]) ).
thf(577,plain,
setEmpty != alive,
inference(simp,[status(thm)],[576]) ).
thf(778,plain,
( ( ( sk2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk11 @ setIn ) ) )
| ( acks != elid )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,550]) ).
thf(779,plain,
( ( ( sk2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk11 @ setIn ) ) )
| ( acks != elid ) ),
inference(simp,[status(thm)],[778]) ).
thf(787,plain,
( ( sk2 != alive )
| ( ( sk7 @ host )
!= sk11 )
| ( acks != elid ) ),
inference(simp,[status(thm)],[779]) ).
thf(8862,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)],[8442,256]) ).
thf(8863,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Down ) ),
inference(pattern_uni,[status(thm)],[8862:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(8877,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_Down ) ),
inference(simp,[status(thm)],[8863]) ).
thf(206,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)],[205]) ).
thf(207,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)],[206]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[207]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[208]) ).
thf(211,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[210]) ).
thf(212,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(cnf,[status(esa)],[211]) ).
thf(2442,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(lifteq,[status(thm)],[212]) ).
thf(1091,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( sk2 @ ( zero @ s @ leq ) )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[645,243]) ).
thf(1092,plain,
( ( sk2 @ ( zero @ s @ leq ) )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[1091:[bind(A,$thf( sk4 ))]]) ).
thf(2425,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[2412]) ).
thf(7486,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[382,5363]) ).
thf(7487,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7486]) ).
thf(7557,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[7487]) ).
thf(7568,plain,
! [A: $i] :
( ( sk8 @ m_Down @ ( A @ snoc ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[7557]) ).
thf(8386,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[411,7568]) ).
thf(8387,plain,
( ( q_nil @ ( sk8 @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[8386:[bind(A,$thf( sk8 @ m_Down )),bind(B,$thf( q_nil ))]]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(415,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(416,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[415]) ).
thf(417,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[416]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[417]) ).
thf(2357,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ ( sk2 @ m_Ack ) @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk3 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[145,418]) ).
thf(2358,plain,
( ( sk3 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2357:[bind(A,$thf( sk4 @ ( sk2 @ m_Ack ) )),bind(B,$thf( sk1 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(172,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(12,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(219,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2379,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[311,421]) ).
thf(2380,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2379]) ).
thf(2397,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2380]) ).
thf(2422,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[2397]) ).
thf(3026,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[167,2419]) ).
thf(3027,plain,
( ( nbr_proc @ s )
!= ( sk3 @ host ) ),
inference(pattern_uni,[status(thm)],[3026:[bind(A,$thf( sk8 ))]]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(367,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
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(139,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(140,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)],[139]) ).
thf(793,plain,
( ( ( elec_2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk8 @ setIn ) ) )
| ( acks != status )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,567]) ).
thf(794,plain,
( ( ( elec_2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk8 @ setIn ) ) )
| ( acks != status ) ),
inference(simp,[status(thm)],[793]) ).
thf(799,plain,
( ( elec_2 != alive )
| ( ( sk7 @ host )
!= sk8 )
| ( acks != status ) ),
inference(simp,[status(thm)],[794]) ).
thf(518,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( ( sk4 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[167,138]) ).
thf(520,plain,
( ( sk8 != sk7 )
| ( ( sk4 @ host )
!= ( sk3 @ host ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(624,plain,
( ( ( sk8 @ host )
!= ( sk4 @ host ) )
| ( sk8 != sk7 )
| ( ( sk3 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[167,520]) ).
thf(625,plain,
( ( ( sk8 @ host )
!= ( sk4 @ host ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[624]) ).
thf(626,plain,
( ( sk8 != sk4 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[625]) ).
thf(7159,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,5363]) ).
thf(7160,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7159]) ).
thf(7197,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[7160]) ).
thf(7250,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[7197]) ).
thf(521,plain,
( ( sk8 != sk7 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[518]) ).
thf(582,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[158,107]) ).
thf(586,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[582]) ).
thf(589,plain,
( ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[586]) ).
thf(2385,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[589,421]) ).
thf(2386,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2385]) ).
thf(2407,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2386]) ).
thf(2418,plain,
( ( ( elec_2 @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2407]) ).
thf(89,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(129,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)],[89]) ).
thf(130,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)],[129]) ).
thf(397,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[396]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[397]) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[398]) ).
thf(4231,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk2 @ s )
!= ( zero @ s ) )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[645,2413]) ).
thf(4232,plain,
( ( ( sk2 @ s )
!= ( zero @ s ) )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[4231:[bind(A,$thf( sk4 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(223,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(224,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[223]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[224]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[225]) ).
thf(497,plain,
( ( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,231]) ).
thf(498,plain,
( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[497]) ).
thf(502,plain,
( ( alive != alive )
| ( sk8 != nil ) ),
inference(simp,[status(thm)],[498]) ).
thf(505,plain,
sk8 != nil,
inference(simp,[status(thm)],[502]) ).
thf(92,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(134,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)],[92]) ).
thf(135,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)],[134]) ).
thf(552,plain,
( ( ( sk3 @ host @ ( elid @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ( sk2 = elec_2 ) ),
inference(paramod_ordered,[status(thm)],[158,157]) ).
thf(560,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( elid != status )
| ( sk2 = elec_2 ) ),
inference(simp,[status(thm)],[552]) ).
thf(563,plain,
( ( elid != status )
| ( sk2 = elec_2 ) ),
inference(simp,[status(thm)],[560]) ).
thf(2533,plain,
! [B: $i,A: $i] :
( ( ( sk11 @ host @ queue @ ( sk10 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[88,128]) ).
thf(2534,plain,
! [B: $i,A: $i] :
( ( ( sk11 @ host @ queue @ ( sk10 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[2533]) ).
thf(2535,plain,
( ( sk11 @ host )
!= ( sk10 @ host ) ),
inference(pattern_uni,[status(thm)],[2534:[bind(A,$thf( sk11 )),bind(B,$thf( sk10 ))]]) ).
thf(2393,plain,
! [A: $i] :
( ( ( sk11 @ host @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk9 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[131,421]) ).
thf(2394,plain,
~ ( sk11 @ host @ ( sk9 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[2393:[bind(A,$thf( sk11 @ host ))]]) ).
thf(14583,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( sk11 @ host @ ( sk9 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14132,2394]) ).
thf(14584,plain,
! [A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( sk11 @ host @ ( sk9 @ host @ leq ) ) ),
inference(simp,[status(thm)],[14583]) ).
thf(14596,plain,
! [A: $i] :
( ( ( A @ s )
!= ( sk11 @ host ) )
| ( A
!= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[14584]) ).
thf(14614,plain,
( ( sk9 @ host @ s )
!= ( sk11 @ host ) ),
inference(simp,[status(thm)],[14596]) ).
thf(94,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(161,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)],[94]) ).
thf(162,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)],[161]) ).
thf(101,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(122,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)],[101]) ).
thf(123,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)],[122]) ).
thf(193,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[193]) ).
thf(519,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[518]) ).
thf(524,plain,
( ( ( sk7 @ host )
!= ( sk3 @ host ) )
| ( sk4 != sk3 ) ),
inference(rewrite,[status(thm)],[519,167]) ).
thf(525,plain,
( ( sk7 != sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[524]) ).
thf(325,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[324]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[325]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[326]) ).
thf(413,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[412]) ).
thf(414,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[413]) ).
thf(2445,plain,
( ( ( sk8 @ host )
!= ( sk4 @ host ) )
| ( ( sk3 @ host @ s )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[167,2423]) ).
thf(2454,plain,
( ( sk8 != sk4 )
| ( ( sk3 @ host @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2445]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(2381,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk9 != sk8 ) ),
inference(paramod_ordered,[status(thm)],[541,421]) ).
thf(2382,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2381]) ).
thf(2400,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= nbr_proc )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2382]) ).
thf(2411,plain,
( ( ( sk3 @ host @ s )
!= nbr_proc )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[2400]) ).
thf(335,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[334]) ).
thf(336,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[335]) ).
thf(4245,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[644,2413]) ).
thf(4246,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[4245:[bind(A,$thf( sk4 ))]]) ).
thf(99,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(153,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)],[99]) ).
thf(154,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)],[153]) ).
thf(173,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)],[172]) ).
thf(174,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)],[173]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[174]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(178,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[177]) ).
thf(179,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk12 )
= A ),
inference(cnf,[status(esa)],[178]) ).
thf(1504,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk12 )
= A ),
inference(lifteq,[status(thm)],[179]) ).
thf(4837,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)],[411,201]) ).
thf(4838,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[4837:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(4818,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( zero != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[644,4230]) ).
thf(4819,plain,
( ( zero != elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[4818:[bind(A,$thf( sk4 ))]]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(386,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)],[47]) ).
thf(7301,plain,
( ( ( sk3 @ host @ queue @ ( sk4 @ ( sk2 @ m_Ack ) @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,5311]) ).
thf(7302,plain,
( ( sk3 @ host @ queue @ ( sk4 @ ( sk2 @ m_Ack ) @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7301]) ).
thf(7404,plain,
( ( ( sk3 @ host @ queue )
!= ( sk3 @ host @ queue ) )
| ( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7302]) ).
thf(7443,plain,
( ( sk4 @ ( sk2 @ m_Ack ) )
!= ( sk8 @ m_Ldr ) ),
inference(simp,[status(thm)],[7404]) ).
thf(8850,plain,
( ( sk3 @ host @ queue @ head )
!= ( sk8 @ m_Ldr ) ),
inference(rewrite,[status(thm)],[7443,8442]) ).
thf(7143,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,5311]) ).
thf(7144,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7143]) ).
thf(7186,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7144]) ).
thf(7239,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[7186]) ).
thf(3035,plain,
! [A: $i] :
( ( ( sk11 @ host @ s )
!= ( nbr_proc @ s ) )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[3034]) ).
thf(3038,plain,
( ( sk11 @ host @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[3035]) ).
thf(3056,plain,
( ( nbr_proc @ s )
!= ( sk9 @ host ) ),
inference(rewrite,[status(thm)],[3038,131]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(215,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(216,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[215]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[216]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(1125,plain,
( ( ( sk4 @ host )
!= ( sk4 @ host ) )
| ( pendack != status )
| ( sk2 = elec_2 )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[645,644]) ).
thf(1126,plain,
( ( pendack != status )
| ( sk2 = elec_2 )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[1125:[]]) ).
thf(1107,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( sk2 @ leq ) )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[645,245]) ).
thf(1108,plain,
( ( nbr_proc @ ( sk2 @ leq ) )
| ( pendack != elid ) ),
inference(pattern_uni,[status(thm)],[1107:[bind(A,$thf( sk4 ))]]) ).
thf(11983,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ head )
!= ( sk3 @ host @ queue @ head ) )
| ( A
!= ( C @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[431,8877]) ).
thf(12004,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[11983]) ).
thf(12010,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[12004]) ).
thf(517,plain,
sk7 != sk4,
inference(simp,[status(thm)],[138]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(168,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(169,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[168]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(14810,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,14686]) ).
thf(14811,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk11 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[14810]) ).
thf(14818,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk11 @ host @ queue ) )
| ( A
!= ( sk9 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[14811]) ).
thf(14823,plain,
! [A: $i] :
( ( A @ ( sk9 @ m_Ldr @ cons ) )
!= ( sk11 @ host @ queue ) ),
inference(simp,[status(thm)],[14818]) ).
thf(2371,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[1017,421]) ).
thf(2372,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2371]) ).
thf(2410,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2372]) ).
thf(2421,plain,
( ( ( nbr_proc @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2410]) ).
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(296,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[294]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(300,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[299]) ).
thf(2467,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk11 @ host @ ( sk9 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[311,2394]) ).
thf(2468,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk11 @ host @ ( sk9 @ host @ leq ) ) ),
inference(simp,[status(thm)],[2467]) ).
thf(2510,plain,
! [A: $i] :
( ( A
!= ( sk11 @ host ) )
| ( A
!= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[2468]) ).
thf(2517,plain,
( ( sk11 @ host )
!= ( sk9 @ host ) ),
inference(simp,[status(thm)],[2510]) ).
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/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(432,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(53,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(405,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(4842,plain,
( ( sk2 != sk2 )
| ( zero != elec_2 )
| ( pendack != elid )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[563,4807]) ).
thf(4843,plain,
( ( zero != elec_2 )
| ( pendack != elid )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[4842:[]]) ).
thf(371,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[370]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[371]) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[372]) ).
thf(2587,plain,
sk11 != sk10,
inference(simp,[status(thm)],[2535]) ).
thf(58,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(422,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(780,plain,
( ( ( sk2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk8 @ setIn ) ) )
| ( acks != elid )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,550]) ).
thf(781,plain,
( ( ( sk2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk8 @ setIn ) ) )
| ( acks != elid ) ),
inference(simp,[status(thm)],[780]) ).
thf(790,plain,
( ( sk2 != alive )
| ( ( sk7 @ host )
!= sk8 )
| ( acks != elid ) ),
inference(simp,[status(thm)],[781]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',axiom_53) ).
thf(341,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)],[39]) ).
thf(499,plain,
( ( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,231]) ).
thf(500,plain,
( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[499]) ).
thf(503,plain,
( ( alive != alive )
| ( sk3 != nil ) ),
inference(simp,[status(thm)],[500]) ).
thf(506,plain,
sk3 != nil,
inference(simp,[status(thm)],[503]) ).
thf(2572,plain,
sk11 != sk9,
inference(simp,[status(thm)],[2517]) ).
thf(2389,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( sk2 @ leq ) ) )
| ~ $true
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[1108,421]) ).
thf(2390,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( sk2 @ leq ) ) )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2389]) ).
thf(2406,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= sk2 )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2390]) ).
thf(2417,plain,
( ( ( nbr_proc @ s )
!= sk2 )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[2406]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(400,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(106,plain,
( ( sk11 @ host @ ( status @ index ) )
= elec_1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(126,plain,
( ( sk11 @ host @ ( status @ index ) )
= elec_1 ),
inference(lifteq,[status(thm)],[106]) ).
thf(796,plain,
( ( ( elec_2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk3 @ setIn ) ) )
| ( acks != status )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,567]) ).
thf(797,plain,
( ( ( elec_2 @ ( sk7 @ host @ setIn ) )
!= ( alive @ ( sk3 @ setIn ) ) )
| ( acks != status ) ),
inference(simp,[status(thm)],[796]) ).
thf(801,plain,
( ( elec_2 != alive )
| ( ( sk7 @ host )
!= sk3 )
| ( acks != status ) ),
inference(simp,[status(thm)],[797]) ).
thf(1018,plain,
( ( ( sk4 @ host )
!= ( sk4 @ host ) )
| ( sk8 != sk7 )
| ( ( sk3 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[644,520]) ).
thf(1019,plain,
( ( sk8 != sk7 )
| ( ( sk3 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[1018:[]]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ leq ) )
<=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(459,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(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/sandbox/benchmark/theBenchmark.p',axiom_54) ).
thf(442,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(14048,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)],[8442,340]) ).
thf(14049,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NormQ ) ),
inference(pattern_uni,[status(thm)],[14048:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(14062,plain,
! [A: $i] :
( ( sk3 @ host @ queue @ head )
!= ( A @ m_NormQ ) ),
inference(simp,[status(thm)],[14049]) ).
thf(14082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ head )
!= ( sk3 @ host @ queue @ head ) )
| ( A
!= ( C @ m_NormQ ) ) ),
inference(paramod_ordered,[status(thm)],[431,14062]) ).
thf(14104,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NormQ @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[14082]) ).
thf(14114,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_NormQ @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[14104]) ).
thf(394,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[393]) ).
thf(395,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[394]) ).
thf(15232,plain,
! [A: $i] :
( ( ( A @ s @ s )
!= ( sk11 @ host @ s ) )
| ( ( sk9 @ host )
!= A ) ),
inference(paramod_ordered,[status(thm)],[131,14613]) ).
thf(15237,plain,
( ( sk9 @ host @ s @ s )
!= ( sk11 @ host @ s ) ),
inference(simp,[status(thm)],[15232]) ).
thf(15245,plain,
( ( sk9 @ host @ s @ s )
!= ( sk9 @ host ) ),
inference(rewrite,[status(thm)],[15237,131]) ).
thf(13,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(222,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3040,plain,
( ( ( sk11 @ host )
!= ( sk4 @ host ) )
| ( sk2 != nbr_proc )
| ( pendack != elid ) ),
inference(paramod_ordered,[status(thm)],[645,3039]) ).
thf(3047,plain,
( ( sk11 != sk4 )
| ( sk2 != nbr_proc )
| ( pendack != elid ) ),
inference(simp,[status(thm)],[3040]) ).
thf(6157,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)],[411,197]) ).
thf(6158,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[6157:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(7179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,441]) ).
thf(7180,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[7179]) ).
thf(7231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[7180]) ).
thf(7284,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[7231]) ).
thf(19065,plain,
$false,
inference(e,[status(thm)],[2199,479,2412,249,14822,88,645,69,365,138,115,276,4807,202,385,384,3049,533,550,142,14829,340,404,8851,1046,257,8848,1001,389,504,619,125,4275,6643,157,421,93,152,8849,2420,14686,164,789,14132,485,238,121,5311,806,646,253,3389,147,4230,2424,396,133,6700,411,243,507,233,117,761,798,14588,292,512,439,4323,85,201,334,302,260,160,392,192,429,275,137,229,252,197,361,435,324,1017,156,4248,16242,14613,14566,77,2419,7572,14561,328,256,393,8442,15317,128,244,266,360,205,11972,311,541,5417,2423,412,2413,425,166,4256,7599,149,279,2602,402,8404,2568,577,958,204,259,8872,382,5363,787,8877,2442,1092,2425,8387,2358,172,113,219,2422,419,230,567,245,303,3027,367,140,799,520,626,7250,14824,198,521,2418,130,399,4232,278,223,226,505,431,241,167,135,563,2535,14614,589,162,374,123,194,525,282,150,327,409,414,95,4240,2454,182,331,441,7568,370,2411,336,4246,154,1504,314,4838,4819,386,8850,7239,627,482,524,3056,250,231,218,1126,1108,3039,588,12010,517,158,171,418,2394,75,246,14823,272,2421,290,119,300,2517,432,405,4843,373,168,2587,422,790,242,341,506,358,195,2572,2417,400,415,126,801,1019,644,459,131,442,14114,395,15245,14062,227,337,469,222,3047,364,232,6158,83,7284,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV477+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.22/0.49 % Computer : n020.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 13:57:06 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.42/1.34 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.96/1.68 % [INFO] Parsing done (331ms).
% 1.96/1.69 % [INFO] Running in sequential loop mode.
% 3.06/2.16 % [INFO] eprover registered as external prover.
% 3.06/2.17 % [INFO] Scanning for conjecture ...
% 3.63/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 4.24/2.51 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 4.24/2.56 % [INFO] Problem is first-order (TPTP FOF).
% 4.24/2.57 % [INFO] Type checking passed.
% 4.24/2.58 % [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 ...
% 87.43/20.57 % External prover 'e' found a proof!
% 87.43/20.57 % [INFO] Killing All external provers ...
% 87.43/20.57 % Time passed: 19872ms (effective reasoning time: 18877ms)
% 87.43/20.57 % 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)>
% 87.43/20.58 % 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
% 87.43/20.58 % No. of inferences in proof: 696
% 87.43/20.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19872 ms resp. 18877 ms w/o parsing
% 89.85/21.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 89.85/21.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------