%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV479+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 : n018.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 08:59:34 AM UTC 2026
% Result : Theorem 84.81s 21.20s
% Output : Refutation 86.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 86
% Syntax : Number of formulae : 811 ( 391 unt; 0 typ; 19 def)
% Number of atoms : 3112 (1715 equ; 0 cnn)
% Maximal formula atoms : 176 ( 3 avg)
% Number of connectives : 12140 (1634 ~; 964 |; 796 &;8436 @)
% ( 13 <=>; 297 =>; 0 <=; 0 <~>)
% Maximal formula depth : 89 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 58 usr; 27 con; 0-4 aty)
% Number of variables : 1647 ( 9 ^;1517 !; 102 ?;1647 :)
% ( 0 !>; 0 ?*; 0 @-; 19 @+)
% 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 > $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $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 > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ 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 @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
!= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( 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 ) ) ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( A @ host @ queue )
= ( sk1 @ ( B @ m_Down @ 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 @ leq ) )
=> ( ( ( ( B @ host )
= ( A @ host @ ( pendack @ index ) ) )
& ( ( A @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( A @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [C: $i] :
( ( A @ host @ ( acks @ index ) @ ( C @ host @ setIn ) )
=> ! [D: $i] :
( ( ( A @ host )
= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
!= ( G @ host ) )
=> ( ( ( A @ host )
!= ( G @ host ) )
=> ( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( G @ host @ s ) )
& ( 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 ) ) ) ) )
=> ~ ( ( ( A @ host )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( ( sk2 @ host @ queue )
= ( sk1 @ ( A @ m_Down @ 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 @ ( sk2 @ setIn ) )
=> ( ( A @ host @ ( sk2 @ host @ leq ) )
=> ( ( ( ( A @ host )
= ( sk2 @ host @ ( pendack @ index ) ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [B: $i] :
( ( sk2 @ host @ ( acks @ index ) @ ( B @ host @ setIn ) )
=> ! [C: $i] :
( ( ( sk2 @ host )
= ( C @ host ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( B @ host )
!= ( F @ host ) )
=> ( ( ( sk2 @ 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 ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [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(sk5_def,definition,
( sk5
= ( ^ [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(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( sk2 @ host @ ( acks @ index ) @ ( A @ host @ setIn ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
= ( B @ host ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ host )
!= ( E @ host ) )
=> ( ( ( sk2 @ 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 ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
= ( A @ host ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( sk6 @ host )
!= ( D @ host ) )
=> ( ( ( sk2 @ 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 ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( A @ host ) )
& ( alive @ ( A @ setIn ) ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk6 @ host )
!= ( C @ host ) )
=> ( ( ( sk2 @ 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 ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk6 @ host )
!= ( B @ host ) )
=> ( ( ( sk2 @ host )
!= ( B @ host ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk8 @ host )
= ( B @ host @ s ) )
& ( B @ host @ queue @ ( A @ m_Down @ elem ) )
& ( B @ host @ queue @ ( sk8 @ 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 ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( ( sk6 @ host )
!= ( A @ host ) )
=> ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk8 @ host )
= ( A @ host @ s ) )
& ( A @ host @ queue @ ( sk9 @ m_Down @ elem ) )
& ( A @ host @ queue @ ( sk8 @ m_Down @ elem ) )
& ( A @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( A @ setIn ) )
& ! [B: $i] :
( ( ( B @ ( zero @ s @ leq ) )
& ~ ( B @ ( A @ host @ leq ) ) )
=> ( ( B
= ( sk9 @ host ) )
| ( A @ host @ ( down @ index ) @ ( B @ setIn ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ 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 @ leq ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
!= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( 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 @ m_Down @ 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 @ leq ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
!= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( 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] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ! [D: $i,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 ) ) ) ) )
=> ~ ( ( ( 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 @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
!= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( 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 ) ) ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ 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 @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
!= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( 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 ) ) ) ) )
=> ~ ( ( ( B @ 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] :
( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) )
& ( ( sk10 @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk8 @ host )
= ( sk10 @ host @ s ) )
& ( sk10 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
& ( sk10 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
& ( sk10 @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( sk10 @ setIn ) )
& ( ( ZS
= ( sk9 @ host ) )
| ( sk10 @ host @ ( down @ index ) @ ( ZS @ setIn ) )
| ~ ( ZS @ ( zero @ s @ leq ) )
| ( ZS @ ( sk10 @ host @ leq ) ) )
& ( ( sk2 @ host )
!= ( sk10 @ host ) )
& ( ( sk6 @ host )
!= ( sk10 @ host ) )
& ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ) )
& ( sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
& ( ( sk3 @ host )
= ( sk2 @ host @ ( pendack @ index ) ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_2 )
& ( sk3 @ host @ ( sk2 @ host @ leq ) )
& ( alive @ ( sk2 @ setIn ) )
& ( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ 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 @ sk5 ) ) )
!= ( 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 @ sk5 ) ) @ 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 @ sk5 ) ) @ ( 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 @ sk5 ) ) @ ( 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 @ sk4 ) ) ) )
!= ( 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 @ sk4 ) ) ) @ 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 @ sk4 ) ) ) @ ( 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 @ sk4 ) ) ) @ ( 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(97,plain,
( ( sk2 @ host )
= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(133,plain,
( ( sk7 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(5431,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( B != A ) ),
inference(simp,[status(thm)],[139]) ).
thf(5509,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(simp,[status(thm)],[5431]) ).
thf(6345,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[133,5509]) ).
thf(6346,plain,
~ ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[6345:[bind(A,$thf( sk7 ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(218,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(219,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[218]) ).
thf(220,plain,
! [A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[219]) ).
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(373,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(374,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)],[373]) ).
thf(375,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)],[374]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[375]) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[377]) ).
thf(381,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[380]) ).
thf(18006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( A @ ( B @ elem ) )
| ( A = q_nil ) ),
inference(paramod_ordered,[status(thm)],[220,381]) ).
thf(18007,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(pattern_uni,[status(thm)],[18006:[bind(A,$thf( E )),bind(B,$thf( E @ last )),bind(C,$thf( E @ init ))]]) ).
thf(18110,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(simp,[status(thm)],[18007]) ).
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(302,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(303,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)],[302]) ).
thf(304,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)],[303]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[304]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(310,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[309]) ).
thf(57,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(418,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(419,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[418]) ).
thf(420,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[419]) ).
thf(2897,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[310,420]) ).
thf(2898,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2897]) ).
thf(2939,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2898]) ).
thf(2960,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[2939]) ).
thf(19917,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ( q_nil != B )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[18110,2960]) ).
thf(19918,plain,
! [A: $i] :
( ( q_nil != A )
| ( A @ s @ ( A @ s @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[19917:[bind(A,$thf( C @ s )),bind(B,$thf( C ))]]) ).
thf(20697,plain,
q_nil @ s @ ( q_nil @ s @ last @ elem ),
inference(simp,[status(thm)],[19918]) ).
thf(63,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(438,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(439,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[438]) ).
thf(440,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[439]) ).
thf(20962,plain,
! [A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20697,440]) ).
thf(20963,plain,
! [A: $i] :
( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[20962]) ).
thf(21086,plain,
! [A: $i] :
( ( ( q_nil @ s )
!= q_nil )
| ( ( q_nil @ s @ last )
!= A ) ),
inference(simp,[status(thm)],[20963]) ).
thf(21164,plain,
( ( q_nil @ s )
!= q_nil ),
inference(simp,[status(thm)],[21086]) ).
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(468,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(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(232,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(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[232]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(481,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(98,plain,
( ( sk3 @ host )
= ( sk2 @ host @ ( pendack @ index ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(145,plain,
( ( sk2 @ host @ ( pendack @ index ) )
= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(112,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(115,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[112]) ).
thf(554,plain,
( ( ( sk2 @ host @ ( pendack @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[145,115]) ).
thf(560,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( pendack != status )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[554]) ).
thf(564,plain,
( ( pendack != status )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[560]) ).
thf(86,plain,
sk3 @ host @ ( sk2 @ host @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(644,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( elec_2 @ ( sk2 @ host @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,86]) ).
thf(645,plain,
( ( elec_2 @ ( sk2 @ host @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[644:[]]) ).
thf(37,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(333,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(23,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(249,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(580,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[86,93]) ).
thf(581,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[580]) ).
thf(582,plain,
~ ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
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(281,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(282,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)],[281]) ).
thf(283,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)],[282]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[283]) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[285]) ).
thf(289,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[288]) ).
thf(901,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)],[310,93]) ).
thf(902,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)],[901]) ).
thf(903,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[902:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(904,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(simp,[status(thm)],[903]) ).
thf(5561,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[133,904]) ).
thf(5562,plain,
~ ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[5561:[bind(A,$thf( sk7 ))]]) ).
thf(7038,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,5562]) ).
thf(7039,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7038]) ).
thf(7105,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7039]) ).
thf(7164,plain,
! [A: $i] :
( ( A @ ( sk7 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7105]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(214,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(215,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[214]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[215]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[216]) ).
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(119,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(120,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)],[119]) ).
thf(54,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(408,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(168,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[167]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[168]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(94,plain,
sk10 @ host @ s @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(84,plain,
( ( sk8 @ host )
= ( sk10 @ host @ s ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(124,plain,
( ( sk10 @ host @ s )
= ( sk8 @ host ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(519,plain,
sk8 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[94,124]) ).
thf(2901,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[519,420]) ).
thf(2902,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2901]) ).
thf(2945,plain,
! [A: $i] :
( ( A
!= ( sk8 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2902]) ).
thf(2947,plain,
( ( sk8 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2945]) ).
thf(409,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[408]) ).
thf(410,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[409]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(194,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[194]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[195]) ).
thf(6795,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)],[410,196]) ).
thf(6796,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[6795:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
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(385,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(46,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(383,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[383]) ).
thf(110,plain,
alive @ ( sk10 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(25,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(256,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(257,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[256]) ).
thf(258,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[257]) ).
thf(541,plain,
! [A: $i] :
( ( ( alive @ ( sk10 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,258]) ).
thf(542,plain,
! [A: $i] :
( ( alive @ ( sk10 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(547,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk10 != A ) ),
inference(simp,[status(thm)],[542]) ).
thf(550,plain,
setEmpty != alive,
inference(simp,[status(thm)],[547]) ).
thf(21,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(243,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(244,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[243]) ).
thf(2905,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,420]) ).
thf(2906,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2905]) ).
thf(2942,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2906]) ).
thf(2963,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2942]) ).
thf(4551,plain,
! [A: $i] :
( ( ( sk10 @ host @ s )
!= ( nbr_proc @ s ) )
| ( ( sk8 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[124,2963]) ).
thf(4560,plain,
! [A: $i] :
( ( ( sk10 @ host )
!= nbr_proc )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[4551]) ).
thf(4564,plain,
( ( sk10 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[4560]) ).
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(340,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(87,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(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 @ ( elid @ index ) @ host )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= wait )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(153,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)],[152]) ).
thf(96,plain,
sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(611,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( sk6 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[115,96]) ).
thf(617,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != status )
| ( elec_2 @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[611]) ).
thf(623,plain,
( ( acks != status )
| ( elec_2 @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[617]) ).
thf(16,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(229,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(230,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[229]) ).
thf(1467,plain,
( ( ( elec_2 @ ( sk6 @ host @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true
| ( acks != status ) ),
inference(paramod_ordered,[status(thm)],[623,230]) ).
thf(1468,plain,
( ( ( elec_2 @ ( sk6 @ host @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ( acks != status ) ),
inference(simp,[status(thm)],[1467]) ).
thf(1507,plain,
( ( elec_2 != alive )
| ( ( sk6 @ host )
!= nil )
| ( acks != status ) ),
inference(simp,[status(thm)],[1468]) ).
thf(107,plain,
( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(158,plain,
( ( sk1 @ ( sk3 @ m_Down @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[385]) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[386]) ).
thf(17190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( C @ ( A @ cons ) ) )
| ( ( B @ ( sk2 @ host @ queue @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ) ),
inference(paramod_ordered,[status(thm)],[158,387]) ).
thf(17191,plain,
! [A: $i] :
( ( A @ ( sk2 @ host @ queue @ snoc ) )
= ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) ) ),
inference(pattern_uni,[status(thm)],[17190:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(17209,plain,
! [A: $i] :
( ( A @ ( sk2 @ host @ queue @ snoc ) )
= ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[17191]) ).
thf(7338,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,582]) ).
thf(7339,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7338]) ).
thf(7442,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7339]) ).
thf(7461,plain,
! [A: $i] :
( ( sk3 @ m_Ldr @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7442]) ).
thf(17284,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk3 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17209,7461]) ).
thf(17285,plain,
( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17284:[bind(A,$thf( sk3 @ m_Ldr )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(17257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ last )
= B ) ),
inference(paramod_ordered,[status(thm)],[17209,196]) ).
thf(17258,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[17257:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(404,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(92,plain,
! [A: $i] :
( ( A
= ( sk9 @ host ) )
| ( sk10 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk10 @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(131,plain,
! [A: $i] :
( ( sk10 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk10 @ host @ leq ) )
| ( A
= ( sk9 @ host ) ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(132,plain,
! [A: $i] :
( ( sk10 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk10 @ host @ leq ) )
| ( A
= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(3451,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk10 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk10 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[310,132]) ).
thf(3452,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk10 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk10 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[3451]) ).
thf(3453,plain,
( ( sk10 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk10 @ host @ leq ) )
| ( ( zero @ s )
= ( sk9 @ host ) ) ),
inference(pattern_uni,[status(thm)],[3452:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s ))]]) ).
thf(12420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ~ $true
| ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[384,420]) ).
thf(12421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[12420]) ).
thf(12422,plain,
! [A: $i] : ( A @ s @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[12421:[bind(A,$thf( A )),bind(B,$thf( A @ s )),bind(C,$thf( A ))]]) ).
thf(13237,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( A @ s ) )
| ( sk9 @ host @ ( A @ leq ) )
| ( sk10 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk10 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[3453,12422]) ).
thf(13238,plain,
( ( sk9 @ host @ ( zero @ leq ) )
| ( sk10 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk10 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[13237:[bind(A,$thf( zero ))]]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(414,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(415,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[414]) ).
thf(416,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[415]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[416]) ).
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(291,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(292,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)],[291]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk17 @ m_Down ) )
| ( A
= ( A @ sk16 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[292]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(301,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[300]) ).
thf(7334,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,6346]) ).
thf(7335,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7334]) ).
thf(7415,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Down ) ) ),
inference(simp,[status(thm)],[7335]) ).
thf(7494,plain,
! [A: $i] :
( ( sk7 @ m_Down @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7415]) ).
thf(12338,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk7 @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[410,7494]) ).
thf(12339,plain,
( ( q_nil @ ( sk7 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[12338:[bind(A,$thf( sk7 @ m_Down )),bind(B,$thf( q_nil ))]]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(259,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(260,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( C @ ( A @ m_Ack ) )
= ( D @ ( B @ m_Ack ) ) ) ),
inference(miniscope,[status(thm)],[259]) ).
thf(261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(263,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[262]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk15 ) )
= A ),
inference(cnf,[status(esa)],[263]) ).
thf(17036,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk15 ) )
= A ),
inference(lifteq,[status(thm)],[264]) ).
thf(7064,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[158,289]) ).
thf(7065,plain,
sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[7064:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(7260,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[7065,139]) ).
thf(7261,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[7260]) ).
thf(7262,plain,
( ( sk3 @ host )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[7261:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(369,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(370,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[369]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[370]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[371]) ).
thf(17184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ cons ) @ snoc ) )
!= ( sk3 @ m_Ldr @ ( D @ snoc ) ) )
| ( ( B @ ( C @ snoc ) @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[387,7461]) ).
thf(17185,plain,
! [B: $i,A: $i] :
( ( sk3 @ m_Ldr @ ( B @ snoc ) @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17184:[bind(A,$thf( E )),bind(B,$thf( sk3 @ m_Ldr )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ cons ) ))]]) ).
thf(17206,plain,
! [B: $i,A: $i] :
( ( sk3 @ m_Ldr @ ( B @ snoc ) @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[17185]) ).
thf(18427,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( sk3 @ m_Ldr @ ( B @ snoc ) @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[158,17206]) ).
thf(18428,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( sk3 @ m_Ldr @ ( B @ snoc ) @ ( A @ cons ) ) ),
inference(simp,[status(thm)],[18427]) ).
thf(18443,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ m_Ldr @ ( B @ snoc ) )
!= sk1 )
| ( ( sk3 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[18428]) ).
thf(18453,plain,
! [A: $i] :
( ( sk3 @ m_Ldr @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[18443]) ).
thf(20880,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk3 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[410,18453]) ).
thf(20881,plain,
( ( q_nil @ ( sk3 @ m_Ldr @ cons ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[20880:[bind(A,$thf( sk3 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(13239,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk10 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk10 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[12422,132]) ).
thf(13240,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk10 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk10 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[13239]) ).
thf(13241,plain,
( ( sk10 @ host @ ( down @ index ) @ ( zero @ s @ s @ setIn ) )
| ( zero @ s @ s @ ( sk10 @ host @ leq ) )
| ( ( zero @ s @ s )
= ( sk9 @ host ) ) ),
inference(pattern_uni,[status(thm)],[13240:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s @ s ))]]) ).
thf(801,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,244]) ).
thf(802,plain,
( ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[801:[bind(A,$thf( sk3 ))]]) ).
thf(40,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_09) ).
thf(357,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(75,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 @ sk4 ) ) ) @ ( D @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(156,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 @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(157,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 @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(235,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[234]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk14 ) )
= B ),
inference(cnf,[status(esa)],[235]) ).
thf(17017,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk14 ) )
= B ),
inference(lifteq,[status(thm)],[236]) ).
thf(7032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,440]) ).
thf(7033,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[7032]) ).
thf(7097,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[7033]) ).
thf(7156,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[7097]) ).
thf(58,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(421,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(15,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(226,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(227,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[226]) ).
thf(228,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[227]) ).
thf(78,plain,
sk10 @ host @ queue @ ( sk8 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(7342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,440]) ).
thf(7343,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[7342]) ).
thf(7385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[7343]) ).
thf(7464,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[7385]) ).
thf(4558,plain,
! [A: $i] :
( ( ( sk10 @ host @ s )
!= ( nbr_proc @ s ) )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[4551]) ).
thf(4563,plain,
( ( sk10 @ host @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[4558]) ).
thf(4595,plain,
( ( nbr_proc @ s )
!= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[4563,124]) ).
thf(91,plain,
sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(553,plain,
sk3 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[91,145]) ).
thf(2915,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[553,420]) ).
thf(2916,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2915]) ).
thf(2929,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2916]) ).
thf(2950,plain,
( ( sk3 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2929]) ).
thf(90,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(163,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)],[90]) ).
thf(164,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)],[163]) ).
thf(4579,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,4564]) ).
thf(4583,plain,
( ( sk10 != sk3 )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[4579]) ).
thf(609,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[96,258]) ).
thf(610,plain,
! [A: $i] :
( ( sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[609]) ).
thf(620,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( acks @ index ) )
!= setEmpty )
| ( ( sk6 @ host )
!= A ) ),
inference(simp,[status(thm)],[610]) ).
thf(625,plain,
( ( sk2 @ host @ ( acks @ index ) )
!= setEmpty ),
inference(simp,[status(thm)],[620]) ).
thf(783,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( pendack @ index ) ) )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(paramod_ordered,[status(thm)],[145,625]) ).
thf(785,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != pendack )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[783]) ).
thf(789,plain,
( ( acks != pendack )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[785]) ).
thf(7348,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,5562]) ).
thf(7349,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7348]) ).
thf(7386,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7349]) ).
thf(7465,plain,
! [A: $i] :
( ( sk7 @ m_Ldr @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7386]) ).
thf(17278,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk7 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17209,7465]) ).
thf(17279,plain,
( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17278:[bind(A,$thf( sk7 @ m_Ldr )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(17604,plain,
( ( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[158,17279]) ).
thf(17605,plain,
( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[17604]) ).
thf(17628,plain,
( ( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[17605]) ).
thf(17635,plain,
( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17628]) ).
thf(2903,plain,
! [A: $i] :
( ( ( sk10 @ host @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk8 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[124,420]) ).
thf(2904,plain,
~ ( sk10 @ host @ ( sk8 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[2903:[bind(A,$thf( sk10 @ host ))]]) ).
thf(3020,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ~ ( sk10 @ host @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[133,2904]) ).
thf(3067,plain,
( ( sk8 != sk7 )
| ~ ( sk10 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[3020]) ).
thf(17376,plain,
( ( ( sk10 @ host @ ( sk2 @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ( sk8 != sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,3067]) ).
thf(17377,plain,
( ( ( sk10 @ host @ ( sk2 @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[17376]) ).
thf(17413,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[17377]) ).
thf(17438,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[17413]) ).
thf(17453,plain,
( ( sk10 != sk3 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[17438]) ).
thf(7358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,904]) ).
thf(7359,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7358]) ).
thf(7407,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( C @ host @ queue ) )
| ( A
!= ( C @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7359]) ).
thf(7486,plain,
! [B: $i,A: $i] :
( ( B @ m_Ldr @ ( A @ snoc ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[7407]) ).
thf(16983,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( C @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( C @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[410,7486]) ).
thf(16984,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Ldr @ cons ) )
!= ( A @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[16983:[bind(A,$thf( D @ m_Ldr )),bind(B,$thf( q_nil )),bind(C,$thf( D ))]]) ).
thf(16989,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Ldr @ cons ) )
!= ( A @ host @ queue ) ),
inference(simp,[status(thm)],[16984]) ).
thf(20,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(241,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(242,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[241]) ).
thf(2921,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,420]) ).
thf(2922,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2921]) ).
thf(2940,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2922]) ).
thf(2961,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2940]) ).
thf(5032,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[2961]) ).
thf(88,plain,
( ( sk6 @ host )
!= ( sk10 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(121,plain,
( ( sk10 @ host )
!= ( sk6 @ host ) ),
inference(lifteq,[status(thm)],[88]) ).
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(146,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[146]) ).
thf(13,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(221,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(597,plain,
! [A: $i] :
( ( ( sk10 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,440]) ).
thf(598,plain,
! [A: $i] :
( ( sk10 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[597]) ).
thf(601,plain,
! [A: $i] :
( ( ( sk10 @ host @ queue )
!= q_nil )
| ( ( sk8 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[598]) ).
thf(603,plain,
( ( sk10 @ host @ queue )
!= q_nil ),
inference(simp,[status(thm)],[601]) ).
thf(627,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( ( elec_2 @ queue )
!= q_nil )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,603]) ).
thf(660,plain,
( ( sk10 != sk3 )
| ( ( elec_2 @ queue )
!= q_nil )
| ( pendack != status ) ),
inference(simp,[status(thm)],[627]) ).
thf(55,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(411,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(428,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(469,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)],[468]) ).
thf(470,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)],[469]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[470]) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[471]) ).
thf(474,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[473]) ).
thf(475,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk21 )
= A ),
inference(cnf,[status(esa)],[474]) ).
thf(5137,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk21 )
= A ),
inference(lifteq,[status(thm)],[475]) ).
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(265,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(74,plain,
alive @ ( sk2 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(3007,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk10 @ host @ ( sk8 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[310,2904]) ).
thf(3008,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk10 @ host @ ( sk8 @ host @ leq ) ) ),
inference(simp,[status(thm)],[3007]) ).
thf(3055,plain,
! [A: $i] :
( ( A
!= ( sk10 @ host ) )
| ( A
!= ( sk8 @ host ) ) ),
inference(simp,[status(thm)],[3008]) ).
thf(3086,plain,
( ( sk10 @ host )
!= ( sk8 @ host ) ),
inference(simp,[status(thm)],[3055]) ).
thf(3389,plain,
sk10 != sk8,
inference(simp,[status(thm)],[3086]) ).
thf(2895,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( sk2 @ host @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[645,420]) ).
thf(2896,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( sk2 @ host @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2895]) ).
thf(2943,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= ( sk2 @ host ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2896]) ).
thf(2964,plain,
( ( ( elec_2 @ s )
!= ( sk2 @ host ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2943]) ).
thf(95,plain,
( ( sk2 @ host )
!= ( sk10 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(116,plain,
( ( sk10 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(246,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[245]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[246]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(809,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( acks != pendack )
| ( setEmpty != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,789]) ).
thf(810,plain,
( ( acks != pendack )
| ( setEmpty != elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[809:[]]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[201]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[202]) ).
thf(17288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ init )
= C ) ),
inference(paramod_ordered,[status(thm)],[17209,203]) ).
thf(17289,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ init )
= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17288:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
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(366,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(5043,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[133,2961]) ).
thf(5044,plain,
( ( sk2 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[5043:[bind(A,$thf( sk7 ))]]) ).
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(49,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(392,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
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(424,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(10,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(204,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(205,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)],[204]) ).
thf(206,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)],[205]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[206]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[207]) ).
thf(210,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[209]) ).
thf(211,plain,
! [A: $i] :
( ( A @ m_Halt @ sk13 )
= A ),
inference(cnf,[status(esa)],[210]) ).
thf(2986,plain,
! [A: $i] :
( ( A @ m_Halt @ sk13 )
= A ),
inference(lifteq,[status(thm)],[211]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(275,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(77,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(136,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)],[77]) ).
thf(137,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)],[136]) ).
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(252,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(197,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11248,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk7 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[410,7465]) ).
thf(11249,plain,
( ( q_nil @ ( sk7 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[11248:[bind(A,$thf( sk7 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(2909,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,420]) ).
thf(2910,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[2909]) ).
thf(2941,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[2910]) ).
thf(2962,plain,
( ( sk3 @ host @ s )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[2941]) ).
thf(3413,plain,
( ( ( sk10 @ host @ s )
!= ( sk3 @ host @ s ) )
| ( ( sk8 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[124,2962]) ).
thf(3422,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[3413]) ).
thf(6392,plain,
( ( sk10 != sk3 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[3422]) ).
thf(482,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[481]) ).
thf(483,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(7324,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,7262]) ).
thf(7325,plain,
( ( ( sk2 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[7324:[]]) ).
thf(52,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(401,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(402,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[401]) ).
thf(403,plain,
wait != norm,
inference(lifteq,[status(thm)],[402]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(388,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(18568,plain,
! [A: $i] :
( ( A != setEmpty )
| ( q_nil != alive )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[18110,550]) ).
thf(18569,plain,
( ( q_nil != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[18568:[bind(A,$thf( setEmpty ))]]) ).
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 @ sk5 ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
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 @ sk5 ) ) @ ( 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)],[105]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( 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)],[140]) ).
thf(13248,plain,
! [A: $i] :
( ( ( sk10 @ host @ s )
!= ( A @ s ) )
| ( sk8 @ host @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[124,12422]) ).
thf(13249,plain,
sk8 @ host @ ( sk10 @ host @ leq ),
inference(pattern_uni,[status(thm)],[13248:[bind(A,$thf( sk10 @ host ))]]) ).
thf(13328,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk10 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[13249,93]) ).
thf(13329,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk10 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13328]) ).
thf(13330,plain,
~ ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[13329:[bind(A,$thf( sk10 )),bind(B,$thf( sk8 ))]]) ).
thf(13469,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,13330]) ).
thf(13470,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13469]) ).
thf(13493,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk10 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13470]) ).
thf(13504,plain,
! [A: $i] :
( ( sk8 @ m_Ldr @ ( A @ snoc ) )
!= ( sk10 @ host @ queue ) ),
inference(simp,[status(thm)],[13493]) ).
thf(2992,plain,
( ( ( sk10 @ host @ s )
!= ( sk3 @ host @ s ) )
| ( ( sk8 @ host )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[124,2950]) ).
thf(3000,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( ( sk8 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2992]) ).
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(336,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(337,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[336]) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[337]) ).
thf(339,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[338]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(191,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(192,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[191]) ).
thf(193,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[192]) ).
thf(3399,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( ( sk8 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,3086]) ).
thf(3400,plain,
( ( sk10 != sk3 )
| ( ( sk8 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[3399]) ).
thf(17910,plain,
( ( ( sk8 @ host )
!= ( sk3 @ host ) )
| ( sk10 != sk3 )
| ( elec_2 != elec_2 )
| ( pendack != status )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,3400]) ).
thf(17911,plain,
( ( ( sk8 @ host )
!= ( sk3 @ host ) )
| ( sk10 != sk3 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[17910]) ).
thf(17912,plain,
( ( sk8 != sk3 )
| ( sk10 != sk3 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[17911]) ).
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(171,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(172,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)],[171]) ).
thf(173,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)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(177,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[176]) ).
thf(178,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk11 )
= A ),
inference(cnf,[status(esa)],[177]) ).
thf(1842,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk11 )
= A ),
inference(lifteq,[status(thm)],[178]) ).
thf(13250,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( sk10 @ host @ ( sk8 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12422,2904]) ).
thf(13251,plain,
! [A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( sk10 @ host @ ( sk8 @ host @ leq ) ) ),
inference(simp,[status(thm)],[13250]) ).
thf(13285,plain,
! [A: $i] :
( ( ( A @ s )
!= ( sk10 @ host ) )
| ( A
!= ( sk8 @ host ) ) ),
inference(simp,[status(thm)],[13251]) ).
thf(13309,plain,
( ( sk8 @ host @ s )
!= ( sk10 @ host ) ),
inference(simp,[status(thm)],[13285]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(222,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(223,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[222]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[223]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[224]) ).
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(360,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(2877,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[158,417]) ).
thf(2878,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2877:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(19796,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[18110,2878]) ).
thf(19797,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[19796]) ).
thf(19798,plain,
sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ),
inference(pattern_uni,[status(thm)],[19797:[bind(A,$thf( sk2 @ host @ queue ))]]) ).
thf(21221,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19798,582]) ).
thf(21222,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[21221]) ).
thf(21351,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[21222]) ).
thf(21441,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Ldr ) ),
inference(simp,[status(thm)],[21351]) ).
thf(529,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[133,519]) ).
thf(530,plain,
( ( sk8 != sk7 )
| ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[529]) ).
thf(4549,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[133,2963]) ).
thf(4550,plain,
( ( nbr_proc @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[4549:[bind(A,$thf( sk7 ))]]) ).
thf(85,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(127,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)],[85]) ).
thf(128,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)],[127]) ).
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(237,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(395,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(396,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[395]) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[396]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(83,plain,
sk10 @ host @ queue @ ( sk9 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(5488,plain,
! [B: $i,A: $i] :
( ( ( sk10 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[83,139]) ).
thf(5489,plain,
! [B: $i,A: $i] :
( ( ( sk10 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[5488]) ).
thf(5490,plain,
( ( sk10 @ host )
!= ( sk9 @ host ) ),
inference(pattern_uni,[status(thm)],[5489:[bind(A,$thf( sk10 )),bind(B,$thf( sk9 ))]]) ).
thf(5513,plain,
sk10 != sk9,
inference(simp,[status(thm)],[5490]) ).
thf(21202,plain,
( ( ( sk10 @ host @ s )
!= ( q_nil @ s ) )
| ( ( sk8 @ host )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[124,21164]) ).
thf(21214,plain,
( ( ( sk10 @ host )
!= q_nil )
| ( ( sk8 @ host )
!= q_nil ) ),
inference(simp,[status(thm)],[21202]) ).
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(181,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(182,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)],[181]) ).
thf(183,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)],[182]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(187,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk12 )
= A ),
inference(cnf,[status(esa)],[187]) ).
thf(2235,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk12 )
= A ),
inference(lifteq,[status(thm)],[188]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[428]) ).
thf(430,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[429]) ).
thf(111,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 @ sk5 ) ) @ setIn ) ) ),
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 ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk5 ) ) @ 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)],[111]) ).
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 ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk5 ) ) @ 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)],[165]) ).
thf(7028,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,582]) ).
thf(7029,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7028]) ).
thf(7106,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7029]) ).
thf(7165,plain,
! [A: $i] :
( ( A @ ( sk3 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7106]) ).
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(148,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(149,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)],[148]) ).
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(117,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(118,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[117]) ).
thf(17272,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk8 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk10 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17209,13504]) ).
thf(17273,plain,
( ( sk8 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk10 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17272:[bind(A,$thf( sk8 @ m_Ldr )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(896,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,242]) ).
thf(897,plain,
( ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( sk3 ))]]) ).
thf(2923,plain,
! [A: $i] :
( ( ( elec_2 @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[897,420]) ).
thf(2924,plain,
! [A: $i] :
( ( ( elec_2 @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2923]) ).
thf(2938,plain,
! [A: $i] :
( ( elec_2 != A )
| ( ( zero @ s )
!= ( A @ s ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2924]) ).
thf(2959,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2938]) ).
thf(412,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[411]) ).
thf(413,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[412]) ).
thf(389,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[388]) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[389]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[390]) ).
thf(7024,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,6346]) ).
thf(7025,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7024]) ).
thf(7132,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Down ) ) ),
inference(simp,[status(thm)],[7025]) ).
thf(7191,plain,
! [A: $i] :
( ( A @ ( sk7 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7132]) ).
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(313,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(13458,plain,
( ( ( sk10 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,13330]) ).
thf(13459,plain,
( ( sk10 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13458]) ).
thf(13492,plain,
( ( ( sk10 @ host @ queue )
!= ( sk10 @ host @ queue ) )
| ( ( sk8 @ m_Down )
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13459]) ).
thf(13503,plain,
( ( sk8 @ m_Down )
!= ( sk8 @ m_Ldr ) ),
inference(simp,[status(thm)],[13492]) ).
thf(76,plain,
( ( sk10 @ host @ ( status @ index ) )
= elec_1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(144,plain,
( ( sk10 @ host @ ( status @ index ) )
= elec_1 ),
inference(lifteq,[status(thm)],[76]) ).
thf(17259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( C @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[17209,7464]) ).
thf(17260,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[17259:[bind(A,$thf( A )),bind(B,$thf( sk2 @ host @ queue )),bind(C,$thf( A ))]]) ).
thf(334,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[333]) ).
thf(335,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[334]) ).
thf(7376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ~ $true
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(paramod_ordered,[status(thm)],[381,139]) ).
thf(7377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[7376]) ).
thf(7427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( C @ host @ queue ) )
| ( A
!= ( D @ m_Down ) )
| ( D != C ) ),
inference(simp,[status(thm)],[7377]) ).
thf(7446,plain,
! [B: $i,A: $i] :
( ( B @ m_Down @ ( A @ snoc ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[7427]) ).
thf(16224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( C @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( C @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[410,7446]) ).
thf(16225,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Down @ cons ) )
!= ( A @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[16224:[bind(A,$thf( D @ m_Down )),bind(B,$thf( q_nil )),bind(C,$thf( D ))]]) ).
thf(16226,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Down @ cons ) )
!= ( A @ host @ queue ) ),
inference(simp,[status(thm)],[16225]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(271,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(272,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[271]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[272]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(7318,plain,
( ( ( sk7 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[133,7262]) ).
thf(7319,plain,
( ( sk7 @ host )
!= ( sk3 @ host ) ),
inference(simp,[status(thm)],[7318]) ).
thf(7328,plain,
sk7 != sk3,
inference(simp,[status(thm)],[7319]) ).
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(434,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
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(327,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(328,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[327]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[328]) ).
thf(330,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[329]) ).
thf(888,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[158,330]) ).
thf(889,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Down )
!= A )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
( ( sk1 != q_nil )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[889]) ).
thf(485,plain,
( ( ( alive @ ( sk10 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,230]) ).
thf(486,plain,
( ( alive @ ( sk10 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(491,plain,
( ( alive != alive )
| ( sk10 != nil ) ),
inference(simp,[status(thm)],[486]) ).
thf(494,plain,
sk10 != nil,
inference(simp,[status(thm)],[491]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(323,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(7197,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7065,582]) ).
thf(7198,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7197]) ).
thf(7280,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7198]) ).
thf(7302,plain,
( ( sk3 @ m_Down )
!= ( sk3 @ m_Ldr ) ),
inference(simp,[status(thm)],[7280]) ).
thf(17168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ cons ) @ snoc ) )
!= ( E @ ( D @ snoc ) ) )
| ( ( B @ ( C @ snoc ) @ ( A @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[387,7464]) ).
thf(17169,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ snoc ) @ ( B @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[17168:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ cons ) )),bind(E,$thf( B ))]]) ).
thf(17215,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ snoc ) @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[17169]) ).
thf(17241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( D @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) @ ( C @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[410,17215]) ).
thf(17242,plain,
! [B: $i,A: $i] :
( ( q_nil @ ( A @ cons ) @ ( B @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[17241:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( q_nil ))]]) ).
thf(17248,plain,
! [B: $i,A: $i] :
( ( q_nil @ ( A @ cons ) @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[17242]) ).
thf(13246,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12422,420]) ).
thf(13247,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[13246]) ).
thf(13280,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[13247]) ).
thf(13304,plain,
! [A: $i] :
( ( A @ s @ s )
!= A ),
inference(simp,[status(thm)],[13280]) ).
thf(104,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 @ sk5 ) ) @ ( C @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(154,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 @ sk5 ) ) @ ( 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)],[104]) ).
thf(155,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 @ sk5 ) ) @ ( 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)],[154]) ).
thf(5366,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( zero != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,5032]) ).
thf(5367,plain,
( ( zero != elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[5366:[bind(A,$thf( sk3 ))]]) ).
thf(238,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[237]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[238]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[239]) ).
thf(250,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[249]) ).
thf(251,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[250]) ).
thf(102,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 @ sk5 ) ) )
!= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(129,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 @ sk5 ) ) )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(130,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 @ sk5 ) ) )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[129]) ).
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(278,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(393,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[392]) ).
thf(394,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[393]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[295]) ).
thf(299,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[298]) ).
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(399,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(109,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 @ sk4 ) ) ) )
!= ( C @ host ) ) ),
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 ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[109]) ).
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 ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(10406,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk3 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[410,7461]) ).
thf(10407,plain,
( ( q_nil @ ( sk3 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[10406:[bind(A,$thf( sk3 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(505,plain,
sk10 != sk6,
inference(simp,[status(thm)],[121]) ).
thf(7068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ~ $true
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(paramod_ordered,[status(thm)],[289,139]) ).
thf(7069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[7068]) ).
thf(7112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( C @ host @ queue ) )
| ( A
!= ( D @ m_Down ) )
| ( D != C ) ),
inference(simp,[status(thm)],[7069]) ).
thf(7171,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Down @ cons ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[7112]) ).
thf(14897,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( A @ ( B @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( B @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[158,7171]) ).
thf(14898,plain,
( ( sk3 @ host @ queue )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[14897:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
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(431,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(10416,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[158,430]) ).
thf(10417,plain,
( ( sk2 @ host @ queue @ head )
= ( sk3 @ m_Down ) ),
inference(pattern_uni,[status(thm)],[10416:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(524,plain,
( ( ( sk2 @ host @ ( pendack @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[115,91]) ).
thf(526,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[524]) ).
thf(528,plain,
( ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[526]) ).
thf(2925,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[528,420]) ).
thf(2926,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2925]) ).
thf(2931,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2926]) ).
thf(2952,plain,
( ( ( elec_2 @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2931]) ).
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(161,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(162,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[161]) ).
thf(7193,plain,
( ( ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7065,6346]) ).
thf(7194,plain,
( ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7193]) ).
thf(7273,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk7 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[7194]) ).
thf(7298,plain,
( ( sk7 @ m_Down )
!= ( sk3 @ m_Down ) ),
inference(simp,[status(thm)],[7273]) ).
thf(106,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 @ sk4 ) ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(122,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 @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(123,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 @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[275]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[276]) ).
thf(6842,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[158,277]) ).
thf(6843,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[6842:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
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(458,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(253,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[252]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[253]) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[254]) ).
thf(17055,plain,
( ( sk10 != sk3 )
| ( ( sk8 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[3000]) ).
thf(13895,plain,
! [A: $i] :
( ( ( A @ s @ s )
!= ( sk10 @ host @ s ) )
| ( ( sk8 @ host )
!= A ) ),
inference(paramod_ordered,[status(thm)],[124,13304]) ).
thf(13906,plain,
( ( sk8 @ host @ s @ s )
!= ( sk10 @ host @ s ) ),
inference(simp,[status(thm)],[13895]) ).
thf(13916,plain,
( ( sk8 @ host @ s @ s )
!= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[13906,124]) ).
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(441,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(499,plain,
( ( ( sk10 @ host )
!= ( sk7 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[133,116]) ).
thf(500,plain,
( ( sk10 @ host )
!= ( sk7 @ host ) ),
inference(simp,[status(thm)],[499]) ).
thf(502,plain,
sk10 != sk7,
inference(simp,[status(thm)],[500]) ).
thf(17282,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk7 @ m_Down @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17209,7494]) ).
thf(17283,plain,
( ( sk7 @ m_Down @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17282:[bind(A,$thf( sk7 @ m_Down )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(17759,plain,
( ( ( sk7 @ m_Down @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[158,17283]) ).
thf(17760,plain,
( ( sk7 @ m_Down @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[17759]) ).
thf(17783,plain,
( ( ( sk7 @ m_Down @ ( sk1 @ snoc ) )
!= sk1 )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[17760]) ).
thf(17790,plain,
( ( sk7 @ m_Down @ ( sk1 @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17783]) ).
thf(358,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[357]) ).
thf(359,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[358]) ).
thf(2907,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk8 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[530,420]) ).
thf(2908,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[2907]) ).
thf(2927,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host ) )
| ( ( A @ s )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[2908]) ).
thf(2948,plain,
( ( ( sk2 @ host @ s )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[2927]) ).
thf(17,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(231,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2917,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,420]) ).
thf(2918,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[2917]) ).
thf(2928,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[2918]) ).
thf(2949,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2928]) ).
thf(497,plain,
sk10 != sk2,
inference(simp,[status(thm)],[116]) ).
thf(13993,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk10 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[410,13504]) ).
thf(13994,plain,
( ( q_nil @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk10 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[13993:[bind(A,$thf( sk8 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(626,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( ( sk6 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,121]) ).
thf(656,plain,
( ( sk10 != sk3 )
| ( ( sk6 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[626]) ).
thf(5083,plain,
( ( sk2 @ host )
!= zero ),
inference(simp,[status(thm)],[5044]) ).
thf(361,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[360]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[362]) ).
thf(198,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[197]) ).
thf(199,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[199]) ).
thf(5385,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)],[410,200]) ).
thf(5386,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[5385:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(82,plain,
alive @ ( sk7 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(487,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,230]) ).
thf(488,plain,
( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(492,plain,
( ( alive != alive )
| ( sk7 != nil ) ),
inference(simp,[status(thm)],[488]) ).
thf(495,plain,
sk7 != nil,
inference(simp,[status(thm)],[492]) ).
thf(1836,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( sk10 != sk3 )
| ( elec_2 != elec_2 )
| ( pendack != status )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[564,656]) ).
thf(1837,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( sk10 != sk3 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1839,plain,
( ( sk6 != sk3 )
| ( sk10 != sk3 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1837]) ).
thf(17268,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ ( B @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[17209,381]) ).
thf(17269,plain,
! [A: $i] : ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ ( A @ elem ) ),
inference(pattern_uni,[status(thm)],[17268:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(6817,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)],[410,203]) ).
thf(6818,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[6817:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
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(113,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(114,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)],[113]) ).
thf(13456,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,13330]) ).
thf(13457,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13456]) ).
thf(13490,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk10 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13457]) ).
thf(13502,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk10 @ host @ queue ) ),
inference(simp,[status(thm)],[13490]) ).
thf(314,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)],[313]) ).
thf(315,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)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[315]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[316]) ).
thf(319,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[318]) ).
thf(320,plain,
! [A: $i] :
( ( A @ m_Down @ sk18 )
= A ),
inference(cnf,[status(esa)],[319]) ).
thf(3430,plain,
! [A: $i] :
( ( A @ m_Down @ sk18 )
= A ),
inference(lifteq,[status(thm)],[320]) ).
thf(21615,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( q_nil != alive ) ),
inference(paramod_ordered,[status(thm)],[18569,440]) ).
thf(21616,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[21615]) ).
thf(21766,plain,
! [A: $i] :
( ( setEmpty != q_nil )
| ( ( setEmpty @ last )
!= A )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[21616]) ).
thf(21782,plain,
( ( setEmpty != q_nil )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[21766]) ).
thf(5671,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( zero @ s ) )
| ( A @ host @ ( sk9 @ host @ leq ) )
| ( sk10 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk10 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[3453,242]) ).
thf(5672,plain,
! [A: $i] :
( ( A @ host @ ( sk9 @ host @ leq ) )
| ( sk10 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk10 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[5671:[]]) ).
thf(7048,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,904]) ).
thf(7049,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7048]) ).
thf(7098,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( C @ host @ queue ) )
| ( A
!= ( C @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7049]) ).
thf(7157,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Ldr @ cons ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[7098]) ).
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(478,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
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(150,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(151,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)],[150]) ).
thf(2899,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[802,420]) ).
thf(2900,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2899]) ).
thf(2930,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2900]) ).
thf(2951,plain,
( ( ( nbr_proc @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2930]) ).
thf(780,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( setEmpty != elec_2 ) ),
inference(paramod_ordered,[status(thm)],[115,625]) ).
thf(787,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != status )
| ( setEmpty != elec_2 ) ),
inference(simp,[status(thm)],[780]) ).
thf(790,plain,
( ( acks != status )
| ( setEmpty != elec_2 ) ),
inference(simp,[status(thm)],[787]) ).
thf(2983,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[2949]) ).
thf(324,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[323]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[324]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(89,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 @ sk4 ) ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(125,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 @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(126,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 @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(435,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Ldr ) ),
inference(miniscope,[status(thm)],[434]) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(cnf,[status(esa)],[435]) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(lifteq,[status(thm)],[436]) ).
thf(5045,plain,
! [A: $i] :
( ( ( sk10 @ host @ s )
!= ( A @ host @ s ) )
| ( ( zero @ s )
!= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[124,2961]) ).
thf(5046,plain,
( ( zero @ s )
!= ( sk8 @ host ) ),
inference(pattern_uni,[status(thm)],[5045:[bind(A,$thf( sk10 ))]]) ).
thf(5058,plain,
( ( ( sk10 @ host @ s )
!= ( zero @ s ) )
| ( ( sk8 @ host )
!= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[124,5046]) ).
thf(5059,plain,
( ( sk10 @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[5058]) ).
thf(5060,plain,
( ( sk10 @ host )
!= zero ),
inference(simp,[status(thm)],[5059]) ).
thf(7218,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7065,5562]) ).
thf(7219,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7218]) ).
thf(7276,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7219]) ).
thf(7299,plain,
( ( sk3 @ m_Down )
!= ( sk7 @ m_Ldr ) ),
inference(simp,[status(thm)],[7276]) ).
thf(615,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( pendack @ index ) ) )
| ( sk3 @ host @ ( sk6 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[145,96]) ).
thf(619,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != pendack )
| ( sk3 @ host @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[615]) ).
thf(624,plain,
( ( acks != pendack )
| ( sk3 @ host @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[619]) ).
thf(13488,plain,
( ( ( sk10 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,13330]) ).
thf(13489,plain,
( ( sk10 @ host @ queue @ ( sk9 @ m_Down @ elem ) )
!= ( sk10 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13488]) ).
thf(13494,plain,
( ( ( sk10 @ host @ queue )
!= ( sk10 @ host @ queue ) )
| ( ( sk9 @ m_Down )
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13489]) ).
thf(13505,plain,
( ( sk9 @ m_Down )
!= ( sk8 @ m_Ldr ) ),
inference(simp,[status(thm)],[13494]) ).
thf(489,plain,
( ( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,230]) ).
thf(490,plain,
( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(493,plain,
( ( alive != alive )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[490]) ).
thf(496,plain,
sk2 != nil,
inference(simp,[status(thm)],[493]) ).
thf(42,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(364,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17830,plain,
( ( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[158,17285]) ).
thf(17831,plain,
( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[17830]) ).
thf(17854,plain,
( ( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[17831]) ).
thf(17861,plain,
( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17854]) ).
thf(7310,plain,
sk3 != sk2,
inference(simp,[status(thm)],[7262]) ).
thf(33062,plain,
$false,
inference(e,[status(thm)],[6346,5509,21164,468,234,481,645,69,333,249,582,115,7164,217,120,440,408,170,2947,6796,385,384,550,4564,340,153,1507,17285,17258,404,13238,417,301,12339,17036,7262,372,20881,13241,802,357,196,157,17017,110,7156,20697,421,93,228,289,78,7464,4595,2950,164,4583,789,17635,17453,16989,3453,623,5032,121,147,17206,221,132,133,660,411,428,5137,265,74,3389,2964,116,243,248,201,810,381,5562,17289,220,366,302,5044,160,392,424,2986,275,137,252,197,625,11249,6392,229,484,7325,519,7065,403,388,420,7486,12422,18569,141,13504,256,3000,339,193,17912,1842,13309,96,124,225,244,360,21441,530,4550,128,237,2963,398,3422,5513,21214,2235,430,2904,166,7165,149,904,176,191,13249,3086,291,118,17273,259,281,204,2959,413,391,7191,313,13503,144,17209,181,17260,86,335,7465,16226,274,7328,230,245,434,271,890,494,323,7302,17248,13304,155,330,387,5367,240,251,130,278,394,299,226,241,167,399,2962,135,10407,13330,505,438,14898,431,10417,2952,162,7298,209,123,6843,553,458,255,2878,194,145,414,327,17055,13916,310,7494,441,502,17283,17790,359,2948,336,7461,2949,497,13994,17215,656,17438,5083,3067,363,203,2960,5386,495,218,7446,19798,3400,231,1839,5490,17269,6818,258,158,186,114,401,171,139,13502,418,3430,21782,383,5672,214,7157,478,17279,82,151,7171,2951,790,18453,410,2983,373,603,564,326,242,126,437,897,2961,18110,528,5060,5046,200,277,7299,369,395,624,13505,83,222,496,364,232,17861,7310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV479+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 13:59:36 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.70/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.93/0.87 % [INFO] Parsing done (157ms).
% 0.93/0.88 % [INFO] Running in sequential loop mode.
% 1.78/1.09 % [INFO] eprover registered as external prover.
% 1.78/1.09 % [INFO] Scanning for conjecture ...
% 2.42/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.69/1.45 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.93/1.50 % [INFO] Problem is first-order (TPTP FOF).
% 2.93/1.52 % [INFO] Type checking passed.
% 2.93/1.52 % [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 ...
% 84.64/21.20 % External prover 'e' found a proof!
% 84.81/21.20 % [INFO] Killing All external provers ...
% 84.81/21.20 % Time passed: 20699ms (effective reasoning time: 20316ms)
% 84.81/21.20 % 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)>
% 84.81/21.20 % 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
% 84.81/21.20 % No. of inferences in proof: 792
% 84.81/21.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20699 ms resp. 20316 ms w/o parsing
% 86.72/21.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 86.72/21.60 % [INFO] Killing All external provers ...
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