%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV468+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 : n012.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 08:59:32 AM UTC 2026
% Result : Theorem 177.73s 56.82s
% Output : Refutation 174.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 81
% Syntax : Number of formulae : 519 ( 279 unt; 0 typ; 14 def)
% Number of atoms : 2059 (1085 equ; 0 cnn)
% Maximal formula atoms : 129 ( 3 avg)
% Number of connectives : 7796 ( 974 ~; 508 |; 643 &;5388 @)
% ( 13 <=>; 270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 77 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 24 con; 0-3 aty)
% Number of variables : 1160 ( 5 ^;1047 !; 94 ?;1160 :)
% ( 0 !>; 0 ?*; 0 @-; 14 @+)
% 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(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_2_decl,type,
elec_2: $i ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(elec_1_decl,type,
elec_1: $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(m_Down_decl,type,
m_Down: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(wait_decl,type,
wait: $i ).
thf(nbr_proc_decl,type,
nbr_proc: $i ).
thf(setEmpty_decl,type,
setEmpty: $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(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 ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk18_decl,type,
sk18: $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 )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ~ ( D @ host @ ( F @ host @ leq ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ~ ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [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] :
( ( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ ( F @ m_Ack ) @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( F @ host @ leq ) ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) )
& ! [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 @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [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_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ~ ( C @ host @ ( B @ host @ leq ) )
=> ( ~ ( ( ( ( C @ host )
= ( B @ host @ ( elid @ index ) @ host ) )
& ( ( B @ host @ ( status @ index ) )
= wait ) )
| ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( C @ host ) ) ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( B @ host @ leq ) ) )
=> ( ( D
= ( C @ host ) )
| ( B @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ( ( B @ host @ ( nbr_proc @ leq ) )
=> ( ~ ! [D: $i] : ( setEmpty @ ( D @ host @ setIn ) )
=> ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ! [E: $i] :
( ( ( B @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ~ ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( B @ host )
= ( D @ host ) )
& ( alive @ ( D @ 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 )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ~ ( C @ host @ ( E @ host @ leq ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i] :
( ? [D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ~ ( D @ host @ ( pendack @ index ) @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ~ ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [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] :
( ( ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) ) )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( C @ host @ queue @ ( D @ ( C @ m_Ack ) @ elem ) ) )
& ! [C: $i] :
( ? [D: $i,E: $i] :
( ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( C @ host @ ( E @ host @ leq ) ) )
=> ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ! [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 @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( C @ host @ queue @ ( D @ ( C @ m_Ack ) @ elem ) ) )
& ! [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_Ldr @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ( ~ ( B @ host @ ( A @ host @ leq ) )
=> ( ~ ( ( ( ( B @ host )
= ( A @ host @ ( elid @ index ) @ host ) )
& ( ( A @ host @ ( status @ index ) )
= wait ) )
| ( ( ( A @ host @ ( status @ index ) )
= norm )
& ( ( A @ host @ ( ldr @ index ) )
= ( B @ host ) ) ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_1 )
& ! [C: $i] :
( ( ( C @ ( zero @ s @ leq ) )
& ~ ( C @ ( A @ host @ leq ) ) )
=> ( ( C
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( C @ setIn ) ) ) ) )
=> ( ( A @ host @ ( nbr_proc @ leq ) )
=> ( ~ ! [C: $i] : ( setEmpty @ ( C @ host @ setIn ) )
=> ! [C: $i] :
( ( ( A @ host )
= ( C @ host ) )
=> ! [D: $i] :
( ( ( A @ host )
!= ( D @ host ) )
=> ( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ~ ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( A @ host )
= ( C @ host ) )
& ( alive @ ( C @ 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 )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ~ ( B @ host @ ( D @ host @ leq ) )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( D @ host @ leq ) ) )
=> ( ( E
= ( C @ host ) )
| ( D @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i] :
( ? [C: $i,D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( C @ host @ ( B @ host @ leq ) ) )
=> ~ ( C @ host @ ( pendack @ index ) @ ( B @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i] :
( ? [C: $i] :
( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ~ ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [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] :
( ( ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( D @ setIn ) ) )
& ( alive @ ( B @ setIn ) ) )
=> ~ ( B @ host @ queue @ ( C @ ( B @ m_Ack ) @ elem ) ) )
& ! [B: $i] :
( ? [C: $i,D: $i] :
( ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( C @ ( D @ m_Ack ) @ elem ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( C @ host @ ( B @ host @ leq ) ) )
=> ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( B @ host @ ( D @ host @ leq ) ) )
=> ~ ( B @ host @ queue @ ( C @ m_Down @ elem ) ) )
& ! [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 @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( B @ host @ queue @ ( C @ ( B @ m_Ack ) @ elem ) ) )
& ! [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_Ldr @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) ) )
=> ( ( alive @ ( sk2 @ setIn ) )
=> ( ~ ( A @ host @ ( sk2 @ host @ leq ) )
=> ( ~ ( ( ( ( A @ host )
= ( sk2 @ host @ ( elid @ index ) @ host ) )
& ( ( sk2 @ host @ ( status @ index ) )
= wait ) )
| ( ( ( sk2 @ host @ ( status @ index ) )
= norm )
& ( ( sk2 @ host @ ( ldr @ index ) )
= ( A @ host ) ) ) )
=> ( ( ( ( sk2 @ host @ ( status @ index ) )
= elec_1 )
& ! [B: $i] :
( ( ( B @ ( zero @ s @ leq ) )
& ~ ( B @ ( sk2 @ host @ leq ) ) )
=> ( ( B
= ( A @ host ) )
| ( sk2 @ host @ ( down @ index ) @ ( B @ setIn ) ) ) ) )
=> ( ( sk2 @ host @ ( nbr_proc @ leq ) )
=> ( ~ ! [B: $i] : ( setEmpty @ ( B @ host @ setIn ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
= ( B @ host ) )
=> ! [C: $i] :
( ( ( sk2 @ host )
!= ( C @ host ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ~ ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( sk2 @ host )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [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(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( setEmpty @ ( A @ host @ setIn ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
= ( A @ host ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
!= ( B @ host ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( B @ setIn ) )
& ~ ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( sk2 @ host )
= ( A @ host ) )
& ( alive @ ( A @ setIn ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( A @ setIn ) )
& ~ ( sk6 @ host @ ( A @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk6 @ host ) )
& ( alive @ ( sk6 @ setIn ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[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] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ~ ( E @ host @ ( G @ host @ leq ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( F @ host @ ( pendack @ index ) @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ~ ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [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,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ ( G @ m_Ack ) @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( E @ host @ ( G @ host @ leq ) ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) )
& ! [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 @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [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_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ~ ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( C @ host @ leq ) ) )
=> ( ( E
= ( D @ host ) )
| ( C @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ( ( C @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ~ ( setEmpty @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i] :
( ( ( C @ host )
!= ( G @ host ) )
=> ( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( G @ setIn ) )
& ~ ( F @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ~ ( E @ host @ ( G @ host @ leq ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( F @ host @ ( pendack @ index ) @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ~ ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [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,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ ( G @ m_Ack ) @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( E @ host @ ( G @ host @ leq ) ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) )
& ! [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 @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [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_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ~ ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( C @ host @ leq ) ) )
=> ( ( E
= ( D @ host ) )
| ( C @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ( ( C @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ~ ( setEmpty @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i] :
( ( ( C @ host )
!= ( G @ host ) )
=> ( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( G @ setIn ) )
& ~ ( F @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ~ ( D @ host @ ( F @ host @ leq ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ~ ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [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,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ ( F @ m_Ack ) @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( F @ host @ leq ) ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) )
& ! [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 @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [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_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ~ ( C @ host @ ( B @ host @ leq ) )
=> ( ~ ( ( ( ( C @ host )
= ( B @ host @ ( elid @ index ) @ host ) )
& ( ( B @ host @ ( status @ index ) )
= wait ) )
| ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( C @ host ) ) ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( B @ host @ leq ) ) )
=> ( ( D
= ( C @ host ) )
| ( B @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ( ( B @ host @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ~ ( setEmpty @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i] :
( ( ( B @ host )
!= ( F @ host ) )
=> ( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ~ ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(268,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(269,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)],[268]) ).
thf(270,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)],[269]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[270]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[272]) ).
thf(276,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[275]) ).
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 )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ~ ( D @ host @ ( F @ host @ leq ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ~ ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [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] :
( ( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ ( F @ m_Ack ) @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( F @ host @ leq ) ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) )
& ! [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 @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [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_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ~ ( C @ host @ ( B @ host @ leq ) )
=> ( ~ ( ( ( ( C @ host )
= ( B @ host @ ( elid @ index ) @ host ) )
& ( ( B @ host @ ( status @ index ) )
= wait ) )
| ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( C @ host ) ) ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( B @ host @ leq ) ) )
=> ( ( D
= ( C @ host ) )
| ( B @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ( ( B @ host @ ( nbr_proc @ leq ) )
=> ( ~ ! [D: $i] : ( setEmpty @ ( D @ host @ setIn ) )
=> ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ! [E: $i] :
( ( ( B @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ~ ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( B @ host )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(71,plain,
! [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 )
= ( sk6 @ host ) )
& ( alive @ ( sk6 @ setIn ) )
& ( ( sk7 @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( sk7 @ setIn ) )
& ~ ( sk6 @ host @ ( sk7 @ host @ ( pendack @ index ) @ leq ) )
& ( ( sk2 @ host )
!= ( sk7 @ host ) )
& ( ( sk2 @ host )
= ( sk6 @ host ) )
& ~ ( setEmpty @ ( sk5 @ host @ setIn ) )
& ( sk2 @ host @ ( nbr_proc @ leq ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_1 )
& ( ( ZM
= ( sk3 @ host ) )
| ( sk2 @ host @ ( down @ index ) @ ( ZM @ setIn ) )
| ~ ( ZM @ ( zero @ s @ leq ) )
| ( ZM @ ( sk2 @ host @ leq ) ) )
& ( ( ( sk3 @ host )
!= ( sk2 @ host @ ( elid @ index ) @ host ) )
| ( ( sk2 @ host @ ( status @ index ) )
!= wait ) )
& ( ( ( sk2 @ host @ ( status @ index ) )
!= norm )
| ( ( sk2 @ host @ ( ldr @ index ) )
!= ( sk3 @ host ) ) )
& ~ ( sk3 @ host @ ( sk2 @ host @ leq ) )
& ( alive @ ( sk2 @ setIn ) )
& ( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
& ( ( ( ZJ @ host @ ( status @ index ) )
!= norm )
| ( ( ZJ @ host @ ( ldr @ index ) )
!= ( ZJ @ host ) )
| ~ ( alive @ ( ZJ @ setIn ) )
| ( ( ZL @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( ZL @ host @ queue @ ( ZK @ m_Down @ elem ) )
| ( ZJ @ host @ ( ZL @ host @ leq ) )
| ( ( ZJ @ ( ZK @ ( ZL @ sk4 ) ) )
!= ( ZK @ host ) ) )
& ( ( ( ZJ @ host @ ( status @ index ) )
!= norm )
| ( ( ZJ @ host @ ( ldr @ index ) )
!= ( ZJ @ host ) )
| ~ ( alive @ ( ZJ @ setIn ) )
| ( ( ZL @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( ZL @ host @ queue @ ( ZK @ m_Down @ elem ) )
| ( ZJ @ host @ ( ZL @ host @ leq ) )
| ~ ( ZL @ host @ ( down @ index ) @ ( ZJ @ ( ZK @ ( ZL @ sk4 ) ) @ setIn ) ) )
& ( ( ( ZJ @ host @ ( status @ index ) )
!= norm )
| ( ( ZJ @ host @ ( ldr @ index ) )
!= ( ZJ @ host ) )
| ~ ( alive @ ( ZJ @ setIn ) )
| ( ( ZL @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( ZL @ host @ queue @ ( ZK @ m_Down @ elem ) )
| ( ZJ @ host @ ( ZL @ host @ leq ) )
| ( ZJ @ ( ZK @ ( ZL @ sk4 ) ) @ ( zero @ s @ leq ) ) )
& ( ( ( ZJ @ host @ ( status @ index ) )
!= norm )
| ( ( ZJ @ host @ ( ldr @ index ) )
!= ( ZJ @ host ) )
| ~ ( alive @ ( ZJ @ setIn ) )
| ( ( ZL @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( ZL @ host @ queue @ ( ZK @ m_Down @ elem ) )
| ( ZJ @ host @ ( ZL @ host @ leq ) )
| ~ ( ZJ @ ( ZK @ ( ZL @ sk4 ) ) @ ( ZL @ host @ leq ) ) )
& ( ( ( ZG @ host @ ( status @ index ) )
!= norm )
| ( ( ZG @ host @ ( ldr @ index ) )
!= ( ZG @ host ) )
| ~ ( alive @ ( ZG @ setIn ) )
| ( ( ZI @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZH @ host )
!= ( ZG @ host ) )
| ~ ( ZI @ host @ queue @ ( ZH @ m_Down @ elem ) )
| ~ ( alive @ ( ZI @ setIn ) ) )
& ( ~ ( ZF @ host @ ( pendack @ index ) @ ( ZE @ host @ ( pendack @ index ) @ leq ) )
| ( ( ZF @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZE @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( ZF @ setIn ) )
| ~ ( alive @ ( ZE @ setIn ) )
| ( ZF @ host @ ( ZE @ host @ leq ) ) )
& ( ( ( ZC @ host @ ( status @ index ) )
!= norm )
| ( ( ZC @ host @ ( ldr @ index ) )
!= ( ZC @ host ) )
| ~ ( alive @ ( ZC @ setIn ) )
| ( ( ZD @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ZC @ host @ ( ZD @ host @ ( pendack @ index ) @ leq ) ) )
& ( ~ ( Z @ host @ queue @ ( ZA @ m_Down @ elem ) )
| ~ ( alive @ ( Z @ setIn ) )
| ( ( ZB @ host @ ( ldr @ index ) )
!= ( ZB @ host ) )
| ( ( ZB @ host @ ( status @ index ) )
!= norm )
| ( ( ZA @ host )
!= ( ZB @ host ) )
| ~ ( alive @ ( ZB @ setIn ) ) )
& ( ( W @ host @ ( Y @ host @ ( pendack @ index ) @ leq ) )
| ( ( Y @ host @ ( status @ index ) )
!= elec_2 )
| ( ( Y @ host )
!= ( X @ host ) )
| ~ ( W @ host @ queue @ ( X @ m_Down @ elem ) )
| ~ ( alive @ ( Y @ setIn ) )
| ~ ( alive @ ( W @ setIn ) ) )
& ( ~ ( T @ host @ queue @ ( U @ ( T @ m_Ack ) @ elem ) )
| ( ( V @ host @ ( status @ index ) )
!= elec_2 )
| ( ( T @ host @ ( status @ index ) )
!= elec_2 )
| ( ( V @ host )
!= ( U @ host ) )
| ~ ( alive @ ( V @ setIn ) )
| ~ ( alive @ ( T @ setIn ) ) )
& ( ( ( Q @ host @ ( status @ index ) )
!= norm )
| ( ( Q @ host @ ( ldr @ index ) )
!= ( Q @ host ) )
| ~ ( alive @ ( Q @ setIn ) )
| ( ( R @ host )
!= ( Q @ host ) )
| ~ ( S @ host @ queue @ ( R @ ( S @ m_Ack ) @ elem ) )
| ~ ( alive @ ( S @ setIn ) ) )
& ( ( O @ host @ ( P @ host @ ( pendack @ index ) @ leq ) )
| ( ( P @ host @ ( status @ index ) )
!= elec_2 )
| ( ( O @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( P @ setIn ) )
| ~ ( alive @ ( O @ setIn ) )
| ( P @ host @ ( O @ host @ leq ) ) )
& ( ~ ( L @ host @ queue @ ( M @ m_Down @ elem ) )
| ( ( N @ host @ ( status @ index ) )
!= elec_2 )
| ( ( N @ host )
!= ( M @ host ) )
| ~ ( alive @ ( N @ setIn ) )
| ~ ( alive @ ( L @ setIn ) )
| ( L @ host @ ( N @ host @ leq ) ) )
& ( ~ ( 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 ) )
& ( ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) )
| ( ( F @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( F @ setIn ) ) )
& ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( D = C ) )
& ( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(84,plain,
( ( sk2 @ host )
= ( sk6 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(120,plain,
( ( sk6 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[84]) ).
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(289,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(290,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)],[289]) ).
thf(291,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)],[290]) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[291]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[293]) ).
thf(297,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[296]) ).
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(750,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)],[297,93]) ).
thf(751,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)],[750]) ).
thf(752,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[751:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(762,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(simp,[status(thm)],[752]) ).
thf(1987,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[120,762]) ).
thf(1988,plain,
~ ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[1987:[bind(A,$thf( sk6 ))]]) ).
thf(2781,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[276,1988]) ).
thf(2782,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[2781]) ).
thf(2810,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[2782]) ).
thf(2822,plain,
! [A: $i] :
( ( A @ ( sk6 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2810]) ).
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(347,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(468,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(91,plain,
alive @ ( sk6 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(16,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(216,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(217,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[216]) ).
thf(476,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[91,217]) ).
thf(477,plain,
( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[476]) ).
thf(480,plain,
( ( alive != alive )
| ( sk6 != nil ) ),
inference(simp,[status(thm)],[477]) ).
thf(481,plain,
sk6 != nil,
inference(simp,[status(thm)],[480]) ).
thf(58,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(408,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(379,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
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(168,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(169,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)],[168]) ).
thf(170,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)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[170]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(174,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[173]) ).
thf(175,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk9 )
= A ),
inference(cnf,[status(esa)],[174]) ).
thf(1041,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk9 )
= A ),
inference(lifteq,[status(thm)],[175]) ).
thf(21,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(230,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(231,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[230]) ).
thf(57,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(405,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(406,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[405]) ).
thf(407,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[406]) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,407]) ).
thf(1586,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1585]) ).
thf(1593,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1586]) ).
thf(1599,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[1593]) ).
thf(1670,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,1599]) ).
thf(1671,plain,
( ( nbr_proc @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[1670:[bind(A,$thf( sk6 ))]]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(382,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(383,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[382]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[383]) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[384]) ).
thf(97,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(127,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_1 ),
inference(lifteq,[status(thm)],[97]) ).
thf(95,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(111,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(112,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[111]) ).
thf(796,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( status @ index ) )
!= ( A @ host @ ( status @ index ) ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( elec_1 != elec_1 ) ),
inference(paramod_ordered,[status(thm)],[127,112]) ).
thf(797,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( status @ index ) )
!= ( A @ host @ ( status @ index ) ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A ) ),
inference(simp,[status(thm)],[796]) ).
thf(798,plain,
( ~ ( alive @ ( sk2 @ setIn ) )
| ( ( sk2 @ host @ ( elid @ index ) )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[797:[bind(A,$thf( sk2 ))]]) ).
thf(85,plain,
alive @ ( sk2 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(2368,plain,
( ~ $true
| ( ( sk2 @ host @ ( elid @ index ) )
= sk2 ) ),
inference(rewrite,[status(thm)],[798,85]) ).
thf(2369,plain,
( ( sk2 @ host @ ( elid @ index ) )
= sk2 ),
inference(simp,[status(thm)],[2368]) ).
thf(2395,plain,
( ( ( sk2 @ host @ ( elid @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( sk2 = elec_1 ) ),
inference(paramod_ordered,[status(thm)],[2369,127]) ).
thf(2411,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( elid != status )
| ( sk2 = elec_1 ) ),
inference(simp,[status(thm)],[2395]) ).
thf(2445,plain,
( ( elid != status )
| ( sk2 = elec_1 ) ),
inference(simp,[status(thm)],[2411]) ).
thf(87,plain,
sk2 @ host @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(2579,plain,
( ( sk2 != sk2 )
| ( elec_1 @ host @ ( nbr_proc @ leq ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[2445,87]) ).
thf(2580,plain,
( ( elec_1 @ host @ ( nbr_proc @ leq ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[2579:[]]) ).
thf(100,plain,
( ( sk7 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(153,plain,
( ( sk7 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[100]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(401,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(402,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[401]) ).
thf(403,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[402]) ).
thf(404,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[403]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(415,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[415]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[416]) ).
thf(106,plain,
! [A: $i] :
( ( A
= ( sk3 @ host ) )
| ( sk2 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk2 @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(118,plain,
! [A: $i] :
( ( sk2 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk2 @ host @ leq ) )
| ( A
= ( sk3 @ host ) ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(119,plain,
! [A: $i] :
( ( sk2 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk2 @ host @ leq ) )
| ( A
= ( sk3 @ host ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk2 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk2 @ host @ leq ) )
| ( B
= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[297,119]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk2 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk2 @ host @ leq ) )
| ( B
= ( sk3 @ host ) ) ),
inference(simp,[status(thm)],[1044]) ).
thf(1046,plain,
( ( sk2 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk2 @ host @ leq ) )
| ( ( zero @ s )
= ( sk3 @ host ) ) ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s ))]]) ).
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(278,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(279,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)],[278]) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk14 @ m_Down ) )
| ( A
= ( A @ sk13 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[279]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[280]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(288,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[287]) ).
thf(1587,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[87,407]) ).
thf(1588,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[1587]) ).
thf(1595,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1588]) ).
thf(1601,plain,
( ( sk2 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[1595]) ).
thf(20,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(228,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(229,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[228]) ).
thf(1581,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[229,407]) ).
thf(1582,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1581]) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1582]) ).
thf(1603,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1597]) ).
thf(1686,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[120,1603]) ).
thf(1687,plain,
( ( sk2 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[1686:[bind(A,$thf( sk6 ))]]) ).
thf(1703,plain,
( ( sk2 @ host )
!= zero ),
inference(simp,[status(thm)],[1687]) ).
thf(37,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(320,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(99,plain,
~ ( sk6 @ host @ ( sk7 @ host @ ( pendack @ index ) @ leq ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(542,plain,
~ ( sk2 @ host @ ( sk7 @ host @ ( pendack @ index ) @ leq ) ),
inference(rewrite,[status(thm)],[99,120]) ).
thf(547,plain,
( ( ( sk2 @ host @ ( sk7 @ host @ ( pendack @ index ) @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[87,542]) ).
thf(548,plain,
( ( sk2 @ host @ ( sk7 @ host @ ( pendack @ index ) @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(554,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( ( sk7 @ host @ ( pendack @ index ) )
!= nbr_proc ) ),
inference(simp,[status(thm)],[548]) ).
thf(557,plain,
( ( sk7 @ host @ ( pendack @ index ) )
!= nbr_proc ),
inference(simp,[status(thm)],[554]) ).
thf(559,plain,
( ( ( sk7 @ host @ ( pendack @ index ) )
!= ( sk7 @ host @ ( status @ index ) ) )
| ( nbr_proc != elec_2 ) ),
inference(paramod_ordered,[status(thm)],[153,557]) ).
thf(562,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( pendack != status )
| ( nbr_proc != elec_2 ) ),
inference(simp,[status(thm)],[559]) ).
thf(565,plain,
( ( pendack != status )
| ( nbr_proc != elec_2 ) ),
inference(simp,[status(thm)],[562]) ).
thf(63,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(425,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(426,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[425]) ).
thf(427,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[426]) ).
thf(2797,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[276,427]) ).
thf(2798,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[2797]) ).
thf(2802,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[2798]) ).
thf(2814,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[2802]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(184,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(372,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(79,plain,
( ( sk2 @ host )
!= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(146,plain,
( ( sk7 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(504,plain,
sk7 != sk2,
inference(simp,[status(thm)],[146]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ( ( A @ ( B @ ( C @ sk4 ) ) )
!= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ ( B @ ( C @ sk4 ) ) )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ ( B @ ( C @ sk4 ) ) )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(40,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_09) ).
thf(344,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(2561,plain,
( ( sk2 != sk2 )
| ( alive @ ( elec_1 @ setIn ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[2445,85]) ).
thf(2562,plain,
( ( alive @ ( elec_1 @ setIn ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[2561:[]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(155,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[155]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[156]) ).
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(421,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(258,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(259,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[258]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(23,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(236,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(237,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[236]) ).
thf(238,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[237]) ).
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(353,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(72,plain,
~ ( sk3 @ host @ ( sk2 @ host @ leq ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(753,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,72]) ).
thf(754,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[753]) ).
thf(761,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( A
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[754]) ).
thf(765,plain,
( ( sk3 @ host )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[761]) ).
thf(766,plain,
sk3 != sk2,
inference(simp,[status(thm)],[765]) ).
thf(54,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(395,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(396,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[395]) ).
thf(397,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[396]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[132]) ).
thf(17,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(218,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(543,plain,
( ( ( sk7 @ host @ ( pendack @ index ) )
!= ( sk7 @ host @ ( status @ index ) ) )
| ~ ( sk2 @ host @ ( elec_2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[153,542]) ).
thf(556,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( pendack != status )
| ~ ( sk2 @ host @ ( elec_2 @ leq ) ) ),
inference(simp,[status(thm)],[543]) ).
thf(558,plain,
( ( pendack != status )
| ~ ( sk2 @ host @ ( elec_2 @ leq ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(655,plain,
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( sk2 @ host @ ( elec_2 @ leq ) ) )
| ( pendack != status )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,558]) ).
thf(656,plain,
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( sk2 @ host @ ( elec_2 @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[655]) ).
thf(660,plain,
( ( ( sk2 @ host )
!= nbr_proc )
| ( ( zero @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[656]) ).
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(411,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(25,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(243,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
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(428,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(1583,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,407]) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1583]) ).
thf(1594,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1584]) ).
thf(1600,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[1594]) ).
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(265,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(505,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,146]) ).
thf(506,plain,
( ( sk7 @ host )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[505]) ).
thf(507,plain,
sk7 != sk6,
inference(simp,[status(thm)],[506]) ).
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(300,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(301,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)],[300]) ).
thf(302,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)],[301]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[302]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[303]) ).
thf(306,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[305]) ).
thf(307,plain,
! [A: $i] :
( ( A @ m_Down @ sk15 )
= A ),
inference(cnf,[status(esa)],[306]) ).
thf(1696,plain,
! [A: $i] :
( ( A @ m_Down @ sk15 )
= A ),
inference(lifteq,[status(thm)],[307]) ).
thf(185,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[184]) ).
thf(186,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[186]) ).
thf(1974,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)],[397,187]) ).
thf(1975,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[1974:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
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(360,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(361,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)],[360]) ).
thf(362,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)],[361]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[362]) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(368,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[367]) ).
thf(2897,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[368,427]) ).
thf(2898,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[2897]) ).
thf(2910,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[2898]) ).
thf(2922,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[2910]) ).
thf(78,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(116,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(117,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[116]) ).
thf(102,plain,
( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(124,plain,
( ( sk1 @ ( sk3 @ m_Down @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[124,404]) ).
thf(1038,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[1037:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(2573,plain,
( ( sk2 != sk2 )
| ( ( elec_1 @ host @ queue )
!= q_nil )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[2445,1038]) ).
thf(2574,plain,
( ( ( elec_1 @ host @ queue )
!= q_nil )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[2573:[]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[181]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[182]) ).
thf(2163,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)],[397,183]) ).
thf(2164,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[2163:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(380,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[379]) ).
thf(381,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[380]) ).
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(314,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(315,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[315]) ).
thf(317,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[316]) ).
thf(712,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[124,317]) ).
thf(713,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Down )
!= A )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[712]) ).
thf(714,plain,
( ( sk1 != q_nil )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[713]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(422,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Ldr ) ),
inference(miniscope,[status(thm)],[421]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(cnf,[status(esa)],[422]) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(lifteq,[status(thm)],[423]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[136]) ).
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(224,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
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(252,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(1589,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,407]) ).
thf(1590,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[1589]) ).
thf(1596,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[1590]) ).
thf(1602,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1596]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(188,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(52,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(388,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(356,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(469,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[468]) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[469]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[470]) ).
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(158,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(159,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)],[158]) ).
thf(160,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)],[159]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(164,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[163]) ).
thf(165,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk8 )
= A ),
inference(cnf,[status(esa)],[164]) ).
thf(933,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk8 )
= A ),
inference(lifteq,[status(thm)],[165]) ).
thf(2787,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[124,276]) ).
thf(2788,plain,
sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[2787:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(2827,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2788,1988]) ).
thf(2828,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[2827]) ).
thf(2863,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk6 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[2828]) ).
thf(2868,plain,
( ( sk3 @ m_Down )
!= ( sk6 @ m_Ldr ) ),
inference(simp,[status(thm)],[2863]) ).
thf(1612,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[1602]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(210,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[210]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[211]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk4 ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk4 ) ) @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk4 ) ) @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[128]) ).
thf(641,plain,
! [A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,72]) ).
thf(642,plain,
! [A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[641]) ).
thf(648,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= nbr_proc )
| ( ( A @ host )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[642]) ).
thf(1625,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host )
!= nbr_proc )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,648]) ).
thf(1626,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1625]) ).
thf(1627,plain,
( ( sk3 @ host )
!= nbr_proc ),
inference(pattern_uni,[status(thm)],[1626:[bind(A,$thf( sk6 ))]]) ).
thf(2881,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[368,1988]) ).
thf(2882,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[2881]) ).
thf(2911,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[2882]) ).
thf(2923,plain,
! [A: $i] :
( ( sk6 @ m_Ldr @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2911]) ).
thf(3214,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk6 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[397,2923]) ).
thf(3215,plain,
( ( q_nil @ ( sk6 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[3214:[bind(A,$thf( sk6 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(205,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(398,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(262,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[262]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[263]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(178,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(179,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[178]) ).
thf(180,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[179]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
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(191,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(2524,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[124,264]) ).
thf(2525,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[2524:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[280]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(286,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[285]) ).
thf(202,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[201]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[202]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[203]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(391,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
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(445,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(35,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(310,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(311,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[310]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[311]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[312]) ).
thf(348,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[347]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(757,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk2 @ host @ ( elec_2 @ leq ) ) )
| ( pendack != status )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,558]) ).
thf(758,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk2 @ host @ ( elec_2 @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[757]) ).
thf(760,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host ) )
| ( A != elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[758]) ).
thf(764,plain,
( ( ( sk2 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[760]) ).
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(219,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(244,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[243]) ).
thf(245,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[244]) ).
thf(13,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(208,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(103,plain,
alive @ ( sk7 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
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(323,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(213,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(474,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,217]) ).
thf(475,plain,
( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[474]) ).
thf(479,plain,
( ( alive != alive )
| ( sk7 != nil ) ),
inference(simp,[status(thm)],[475]) ).
thf(483,plain,
sk7 != nil,
inference(simp,[status(thm)],[479]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( C @ host @ queue @ ( B @ ( C @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ ( C @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ ( C @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(3538,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[124,417]) ).
thf(3539,plain,
( ( sk2 @ host @ queue @ head )
= ( sk3 @ m_Down ) ),
inference(pattern_uni,[status(thm)],[3538:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
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(455,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(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ host @ ( C @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ host @ ( C @ host @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ host @ ( C @ host @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(2238,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( zero @ s ) )
| ( A @ host @ ( sk3 @ host @ leq ) )
| ( sk2 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[1046,229]) ).
thf(2239,plain,
! [A: $i] :
( ( A @ host @ ( sk3 @ host @ leq ) )
| ( sk2 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk2 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[2238:[]]) ).
thf(496,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ~ ( sk2 @ host @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[120,72]) ).
thf(500,plain,
( ( sk6 != sk3 )
| ~ ( sk2 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(748,plain,
( ( sk6 != sk3 )
| ~ $true ),
inference(rewrite,[status(thm)],[500,297]) ).
thf(749,plain,
sk6 != sk3,
inference(simp,[status(thm)],[748]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[122]) ).
thf(472,plain,
( ( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,217]) ).
thf(473,plain,
( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[472]) ).
thf(478,plain,
( ( alive != alive )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[473]) ).
thf(482,plain,
sk2 != nil,
inference(simp,[status(thm)],[478]) ).
thf(2581,plain,
( ( sk2 != sk2 )
| ( nil != elec_1 )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[2445,482]) ).
thf(2582,plain,
( ( nil != elec_1 )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[2581:[]]) ).
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(327,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(567,plain,
! [A: $i] :
( ( ( alive @ ( sk2 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,245]) ).
thf(568,plain,
! [A: $i] :
( ( alive @ ( sk2 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[567]) ).
thf(573,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[568]) ).
thf(576,plain,
setEmpty != alive,
inference(simp,[status(thm)],[573]) ).
thf(357,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[356]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[357]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
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(386,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(192,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)],[191]) ).
thf(193,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)],[192]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[193]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(197,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[196]) ).
thf(198,plain,
! [A: $i] :
( ( A @ m_Halt @ sk10 )
= A ),
inference(cnf,[status(esa)],[197]) ).
thf(1617,plain,
! [A: $i] :
( ( A @ m_Halt @ sk10 )
= A ),
inference(lifteq,[status(thm)],[198]) ).
thf(456,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)],[455]) ).
thf(457,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)],[456]) ).
thf(458,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[457]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[458]) ).
thf(461,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[460]) ).
thf(462,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk18 )
= A ),
inference(cnf,[status(esa)],[461]) ).
thf(1966,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk18 )
= A ),
inference(lifteq,[status(thm)],[462]) ).
thf(1685,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[1603]) ).
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(465,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(2553,plain,
( ( sk2 != sk2 )
| ( ( elec_1 @ host @ s )
!= nbr_proc )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[2445,1601]) ).
thf(2554,plain,
( ( ( elec_1 @ host @ s )
!= nbr_proc )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[2553:[]]) ).
thf(389,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[388]) ).
thf(390,plain,
wait != norm,
inference(lifteq,[status(thm)],[389]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ~ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ~ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ host @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ( A @ host @ ( C @ host @ leq ) )
| ~ ( A @ ( B @ ( C @ sk4 ) ) @ ( C @ host @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[113]) ).
thf(76,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(138,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)],[76]) ).
thf(139,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)],[138]) ).
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(418,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(42,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(351,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(755,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk2 @ host @ ( sk7 @ host @ ( pendack @ index ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,542]) ).
thf(756,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk2 @ host @ ( sk7 @ host @ ( pendack @ index ) @ leq ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(759,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host ) )
| ( A
!= ( sk7 @ host @ ( pendack @ index ) ) ) ),
inference(simp,[status(thm)],[756]) ).
thf(763,plain,
( ( sk7 @ host @ ( pendack @ index ) )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[759]) ).
thf(345,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[344]) ).
thf(346,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[345]) ).
thf(376,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[375]) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[376]) ).
thf(378,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[377]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(232,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(233,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[232]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[234]) ).
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(246,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(2779,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)],[276,762]) ).
thf(2780,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[2779]) ).
thf(2803,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( C @ host @ queue ) )
| ( A
!= ( C @ m_Ldr ) ) ),
inference(simp,[status(thm)],[2780]) ).
thf(2815,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Ldr @ cons ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[2803]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[189]) ).
thf(324,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[323]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[324]) ).
thf(326,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(92,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(125,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)],[92]) ).
thf(126,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)],[125]) ).
thf(2185,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)],[397,190]) ).
thf(2186,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[2185:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(2571,plain,
( ( sk2 != sk2 )
| ( ( elec_1 @ host )
!= elec_2 )
| ( pendack != status )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[2445,764]) ).
thf(2572,plain,
( ( ( elec_1 @ host )
!= elec_2 )
| ( pendack != status )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[2571:[]]) ).
thf(399,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[398]) ).
thf(400,plain,
elec_1 != elec_2,
inference(lifteq,[status(thm)],[399]) ).
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(239,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(240,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[239]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[240]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[241]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[130]) ).
thf(225,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[224]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[225]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(321,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[320]) ).
thf(322,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[321]) ).
thf(2193,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ init )
= q_nil ) ),
inference(paramod_ordered,[status(thm)],[124,2186]) ).
thf(2203,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Down )
!= A )
| ( ( sk2 @ host @ queue @ init )
= q_nil ) ),
inference(simp,[status(thm)],[2193]) ).
thf(2206,plain,
( ( sk1 != q_nil )
| ( ( sk2 @ host @ queue @ init )
= q_nil ) ),
inference(simp,[status(thm)],[2203]) ).
thf(214,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[213]) ).
thf(215,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[214]) ).
thf(219046,plain,
$false,
inference(e,[status(thm)],[69,2822,347,468,481,408,762,120,379,1041,217,276,1671,385,1988,2580,153,404,417,1046,288,1601,1703,320,565,2814,184,372,504,110,344,2562,542,157,421,93,228,289,261,216,238,353,766,397,133,660,411,243,428,1600,265,507,1696,1975,2922,117,2574,2164,381,714,85,201,297,424,407,137,2445,229,1687,224,252,1602,317,188,388,356,471,124,933,2868,1612,212,129,1599,1627,3215,2788,360,205,765,398,558,425,264,180,375,191,2525,286,204,391,445,382,313,236,181,350,764,187,219,1603,230,245,208,103,323,213,91,483,2923,108,3539,278,455,2369,135,2239,209,112,749,123,2582,557,327,310,127,576,359,1038,370,154,72,386,314,1617,1966,1685,87,482,218,368,465,231,2554,258,390,114,401,139,418,158,351,763,346,119,378,235,246,300,146,405,183,168,262,2815,190,326,126,2186,268,2572,400,415,239,242,395,427,131,178,227,322,2206,215,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV468+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.09/5.33 % Computer : n012.cluster.edu
% 0.09/5.33 % Model : x86_64 x86_64
% 0.09/5.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.33 % Memory : 8046.5625MB
% 0.09/5.33 % OS : Linux 6.8.0-71-generic
% 0.09/5.33 % CPULimit : 300
% 0.09/5.33 % WCLimit : 300
% 0.09/5.33 % DateTime : Sat Sep 26 13:55:43 UTC 2026
% 0.09/5.34 % CPUTime :
% 0.09/5.34 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
% 0.10/5.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.10/5.73 % [INFO] Parsing done (115ms).
% 0.10/5.74 % [INFO] Running in sequential loop mode.
% 0.10/5.92 % [INFO] eprover registered as external prover.
% 0.10/5.93 % [INFO] Scanning for conjecture ...
% 1.43/6.04 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 1.43/6.11 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 1.68/6.13 % [INFO] Problem is first-order (TPTP FOF).
% 1.68/6.14 % [INFO] Type checking passed.
% 1.68/6.14 % [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 ...
% 177.73/56.82 % External prover 'e' found a proof!
% 177.73/56.82 % [INFO] Killing All external provers ...
% 177.73/56.82 % Time passed: 51402ms (effective reasoning time: 51076ms)
% 177.73/56.82 % 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)>
% 177.73/56.82 % 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
% 177.73/56.82 % No. of inferences in proof: 505
% 177.73/56.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 51402 ms resp. 51076 ms w/o parsing
% 174.11/56.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 174.11/56.98 % [INFO] Killing All external provers ...
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