%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV466+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 104.02s 31.62s
% Output : Refutation 107.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 85
% Syntax : Number of formulae : 791 ( 373 unt; 0 typ; 18 def)
% Number of atoms : 2614 (1410 equ; 0 cnn)
% Maximal formula atoms : 112 ( 3 avg)
% Number of connectives : 9893 (1351 ~; 710 |; 586 &;6961 @)
% ( 13 <=>; 272 =>; 0 <=; 0 <~>)
% Maximal formula depth : 77 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 27 con; 0-4 aty)
% Number of variables : 1397 ( 6 ^;1280 !; 93 ?;1397 :)
% ( 0 !>; 0 ?*; 0 @-; 18 @+)
% Comments :
%------------------------------------------------------------------------------
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Ldr_decl,type,
m_Ldr: $i > $i ).
thf(queue_decl,type,
queue: $i > $i ).
thf(host_decl,type,
host: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(m_Halt_decl,type,
m_Halt: $i > $i ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(setIn_decl,type,
setIn: $i > $i > $o ).
thf(alive_decl,type,
alive: $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(pendack_decl,type,
pendack: $i ).
thf(status_decl,type,
status: $i ).
thf(elec_1_decl,type,
elec_1: $i ).
thf(elec_2_decl,type,
elec_2: $i ).
thf(elid_decl,type,
elid: $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(norm_decl,type,
norm: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(down_decl,type,
down: $i ).
thf(nbr_proc_decl,type,
nbr_proc: $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(acks_decl,type,
acks: $i ).
thf(snoc_decl,type,
snoc: $i > $i > $i ).
thf(m_NotNorm_decl,type,
m_NotNorm: $i > $i ).
thf(m_NormQ_decl,type,
m_NormQ: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $o ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(wait_decl,type,
wait: $i ).
thf(nil_decl,type,
nil: $i ).
thf(pids_decl,type,
pids: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(last_decl,type,
last: $i > $i ).
thf(init_decl,type,
init: $i > $i ).
thf(setEmpty_decl,type,
setEmpty: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(pidElem_decl,type,
pidElem: $i > $o ).
thf(pidMsg_decl,type,
pidMsg: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk20_decl,type,
sk20: $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] :
( ( ( E @ host )
= ( F @ host @ ( pendack @ index ) @ s ) )
& ( ( D @ host )
= ( F @ host @ ( pendack @ index ) ) )
& ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( F @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( F @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( E @ host ) )
& ( ( G @ host )
= nbr_proc )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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] :
( ( ? [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] :
( ( ( ( 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] :
( ( ( 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] :
( ( ( 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_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( C @ host @ ( B @ host @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( G @ host )
= ( H @ host @ ( pendack @ index ) @ s ) )
& ( ( F @ host )
= ( H @ host @ ( pendack @ index ) ) )
& ( ( H @ host @ ( status @ index ) )
= elec_2 )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( F @ ( H @ m_Ack ) @ elem ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( A @ host @ queue )
= ( sk1 @ ( B @ m_Down @ cons ) ) )
& ( ? [C: $i,D: $i,E: $i] :
( ( ( D @ host )
= ( E @ host @ ( pendack @ index ) @ s ) )
& ( ( C @ host )
= ( E @ host @ ( pendack @ index ) ) )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( E @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ? [C: $i] :
( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( D @ host ) )
& ( ( F @ host )
= nbr_proc )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i] :
( ? [D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
& ( alive @ ( E @ setIn ) )
& ~ ( C @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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] :
( ( ? [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] :
( ( ( ( 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] :
( ( ( 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] :
( ( ( 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_1 )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( C @ ( D @ m_Ack ) @ elem ) ) )
& ! [C: $i,D: $i] :
( ( ( D @ host @ queue @ ( C @ ( D @ m_Ack ) @ elem ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( pendack @ index ) @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
=> ~ ( E @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ( ( D @ host )
!= ( C @ host ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Ldr @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ( ( B @ host @ ( A @ host @ leq ) )
=> ( ( ( ( B @ host )
= ( A @ host @ ( pendack @ index ) ) )
& ( ( A @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( A @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [C: $i] :
( ( A @ host @ ( acks @ index ) @ ( C @ host @ setIn ) )
=> ! [D: $i] :
( ( ( A @ host )
= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( A @ host )
!= ( G @ host ) )
=> ( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( A @ m_Ldr @ ( G @ host @ queue @ snoc ) @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( A @ m_Ldr @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( A @ host )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( ( sk2 @ host @ queue )
= ( sk1 @ ( A @ m_Down @ cons ) ) )
& ( ? [B: $i,C: $i,D: $i] :
( ( ( C @ host )
= ( D @ host @ ( pendack @ index ) @ s ) )
& ( ( B @ host )
= ( D @ host @ ( pendack @ index ) ) )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( D @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ? [B: $i] :
( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( C @ host ) )
& ( ( E @ host )
= nbr_proc )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i] :
( ? [C: $i,D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
& ( alive @ ( D @ setIn ) )
& ~ ( B @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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] :
( ( ? [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] :
( ( ( ( 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] :
( ( ( 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] :
( ( ( 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_1 )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( C @ host @ queue @ ( B @ ( C @ m_Ack ) @ elem ) ) )
& ! [B: $i,C: $i] :
( ( ( C @ host @ queue @ ( B @ ( C @ m_Ack ) @ elem ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( pendack @ index ) @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
=> ~ ( D @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ( ( C @ host )
!= ( B @ host ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Ldr @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) ) )
=> ( ( alive @ ( sk2 @ setIn ) )
=> ( ( A @ host @ ( sk2 @ host @ leq ) )
=> ( ( ( ( A @ host )
= ( sk2 @ host @ ( pendack @ index ) ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [B: $i] :
( ( sk2 @ host @ ( acks @ index ) @ ( B @ host @ setIn ) )
=> ! [C: $i] :
( ( ( sk2 @ host )
= ( C @ host ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( B @ host )
= ( F @ host ) )
=> ( ( ( sk2 @ host )
!= ( F @ host ) )
=> ( ( ( ( E @ host )
= ( F @ host @ ( pendack @ index ) @ s ) )
& ( ( D @ host )
= ( F @ host @ ( pendack @ index ) ) )
& ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ m_Ldr @ ( F @ host @ queue @ snoc ) @ ( D @ ( F @ m_Ack ) @ elem ) )
& ( sk2 @ m_Ldr @ ( F @ host @ queue @ snoc ) @ ( E @ m_Down @ elem ) )
& ( F @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( sk2 @ host )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( A @ host @ leq ) ) )
=> ( ( E
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( sk2 @ host @ ( acks @ index ) @ ( A @ host @ setIn ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
= ( B @ host ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ host )
= ( E @ host ) )
=> ( ( ( sk2 @ host )
!= ( E @ host ) )
=> ( ( ( ( D @ host )
= ( E @ host @ ( pendack @ index ) @ s ) )
& ( ( C @ host )
= ( E @ host @ ( pendack @ index ) ) )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ m_Ldr @ ( E @ host @ queue @ snoc ) @ ( C @ ( E @ m_Ack ) @ elem ) )
& ( sk2 @ m_Ldr @ ( E @ host @ queue @ snoc ) @ ( D @ m_Down @ elem ) )
& ( E @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( ( sk2 @ host )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
= ( A @ host ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( sk5 @ host )
= ( D @ host ) )
=> ( ( ( sk2 @ host )
!= ( D @ host ) )
=> ( ( ( ( C @ host )
= ( D @ host @ ( pendack @ index ) @ s ) )
& ( ( B @ host )
= ( D @ host @ ( pendack @ index ) ) )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ m_Ldr @ ( D @ host @ queue @ snoc ) @ ( B @ ( D @ m_Ack ) @ elem ) )
& ( sk2 @ m_Ldr @ ( D @ host @ queue @ snoc ) @ ( C @ m_Down @ elem ) )
& ( D @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( ( sk2 @ host )
= ( A @ host ) )
& ( alive @ ( A @ setIn ) ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk5 @ host )
= ( C @ host ) )
=> ( ( ( sk2 @ host )
!= ( C @ host ) )
=> ( ( ( ( B @ host )
= ( C @ host @ ( pendack @ index ) @ s ) )
& ( ( A @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ m_Ldr @ ( C @ host @ queue @ snoc ) @ ( A @ ( C @ m_Ack ) @ elem ) )
& ( sk2 @ m_Ldr @ ( C @ host @ queue @ snoc ) @ ( B @ m_Down @ elem ) )
& ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk6 @ host ) )
& ( alive @ ( sk6 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk5 @ host )
= ( B @ host ) )
=> ( ( ( sk2 @ host )
!= ( B @ host ) )
=> ( ( ( ( A @ host )
= ( B @ host @ ( pendack @ index ) @ s ) )
& ( ( sk7 @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ m_Ldr @ ( B @ host @ queue @ snoc ) @ ( sk7 @ ( B @ m_Ack ) @ elem ) )
& ( sk2 @ m_Ldr @ ( B @ host @ queue @ snoc ) @ ( A @ m_Down @ elem ) )
& ( B @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( B @ setIn ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk6 @ host ) )
& ( alive @ ( sk6 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( ( sk5 @ host )
= ( A @ host ) )
=> ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ( ( ( ( sk8 @ host )
= ( A @ host @ ( pendack @ index ) @ s ) )
& ( ( sk7 @ host )
= ( A @ host @ ( pendack @ index ) ) )
& ( ( A @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ m_Ldr @ ( A @ host @ queue @ snoc ) @ ( sk7 @ ( A @ m_Ack ) @ elem ) )
& ( sk2 @ m_Ldr @ ( A @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
& ( A @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( A @ setIn ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk6 @ host ) )
& ( alive @ ( sk6 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( G @ host )
= ( H @ host @ ( pendack @ index ) @ s ) )
& ( ( F @ host )
= ( H @ host @ ( pendack @ index ) ) )
& ( ( H @ host @ ( status @ index ) )
= elec_2 )
& ( H @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( H @ host @ queue @ ( F @ ( H @ m_Ack ) @ elem ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( alive @ ( H @ setIn ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( H @ host )
= ( F @ host ) )
& ( ( H @ host )
= nbr_proc )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( F @ host @ queue @ ( G @ m_Halt @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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,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] :
( ( ( ( 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] :
( ( ( ( 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] :
( ( ( 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_1 )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( F @ host @ queue @ ( E @ ( F @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( F @ host @ queue @ ( E @ ( F @ m_Ack ) @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ( F @ host @ ( pendack @ index ) @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( H @ host )
= ( I @ host @ ( pendack @ index ) @ s ) )
& ( ( G @ host )
= ( I @ host @ ( pendack @ index ) ) )
& ( ( I @ host @ ( status @ index ) )
= elec_2 )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ ( I @ m_Ack ) @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( I @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( G @ host )
= ( H @ host @ ( pendack @ index ) @ s ) )
& ( ( F @ host )
= ( H @ host @ ( pendack @ index ) ) )
& ( ( H @ host @ ( status @ index ) )
= elec_2 )
& ( H @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( H @ host @ queue @ ( F @ ( H @ m_Ack ) @ elem ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( alive @ ( H @ setIn ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( H @ host )
= ( F @ host ) )
& ( ( H @ host )
= nbr_proc )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( F @ host @ queue @ ( G @ m_Halt @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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,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] :
( ( ( ( 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] :
( ( ( ( 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] :
( ( ( 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_1 )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( F @ host @ queue @ ( E @ ( F @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( F @ host @ queue @ ( E @ ( F @ m_Ack ) @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ( F @ host @ ( pendack @ index ) @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( H @ host )
= ( I @ host @ ( pendack @ index ) @ s ) )
& ( ( G @ host )
= ( I @ host @ ( pendack @ index ) ) )
& ( ( I @ host @ ( status @ index ) )
= elec_2 )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ ( I @ m_Ack ) @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( I @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( G @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( E @ host ) )
& ( ( G @ host )
= nbr_proc )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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,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] :
( ( ( ( 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] :
( ( ( ( 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] :
( ( ( 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_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( C @ host @ ( B @ host @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( G @ host )
= ( H @ host @ ( pendack @ index ) @ s ) )
& ( ( F @ host )
= ( H @ host @ ( pendack @ index ) ) )
& ( ( H @ host @ ( status @ index ) )
= elec_2 )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( F @ ( H @ m_Ack ) @ elem ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ( ( E @ host )
= ( F @ host @ ( pendack @ index ) @ s ) )
& ( ( D @ host )
= ( F @ host @ ( pendack @ index ) ) )
& ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( F @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( F @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( E @ host ) )
& ( ( G @ host )
= nbr_proc )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( 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] :
( ( ? [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] :
( ( ( ( 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] :
( ( ( 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] :
( ( ( 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_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( C @ host @ ( B @ host @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( G @ host )
= ( H @ host @ ( pendack @ index ) @ s ) )
& ( ( F @ host )
= ( H @ host @ ( pendack @ index ) ) )
& ( ( H @ host @ ( status @ index ) )
= elec_2 )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( F @ ( H @ m_Ack ) @ elem ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(71,plain,
! [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 ) )
& ( ( sk8 @ host )
= ( sk9 @ host @ ( pendack @ index ) @ s ) )
& ( ( sk7 @ host )
= ( sk9 @ host @ ( pendack @ index ) ) )
& ( ( sk9 @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ m_Ldr @ ( sk9 @ host @ queue @ snoc ) @ ( sk7 @ ( sk9 @ m_Ack ) @ elem ) )
& ( sk2 @ m_Ldr @ ( sk9 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
& ( sk9 @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( sk9 @ setIn ) )
& ( ( sk2 @ host )
!= ( sk9 @ host ) )
& ( ( sk5 @ host )
= ( sk9 @ host ) )
& ( ( sk2 @ host )
= ( sk6 @ host ) )
& ( sk2 @ host @ ( acks @ index ) @ ( sk5 @ host @ setIn ) )
& ( sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
& ( ( sk3 @ host )
= ( sk2 @ host @ ( pendack @ index ) ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_2 )
& ( sk3 @ host @ ( sk2 @ host @ leq ) )
& ( alive @ ( sk2 @ setIn ) )
& ( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
& ( ( ( ZK @ host @ ( status @ index ) )
!= norm )
| ( ( ZK @ host @ ( ldr @ index ) )
!= ( ZK @ host ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ( ( ZI @ host )
!= ( ZJ @ host @ ( pendack @ index ) @ s ) )
| ( ( ZH @ host )
!= ( ZJ @ host @ ( pendack @ index ) ) )
| ( ( ZJ @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( ZJ @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( ZJ @ host @ queue @ ( ZH @ ( ZJ @ m_Ack ) @ elem ) )
| ~ ( ZJ @ host @ queue @ ( ZI @ m_Down @ elem ) )
| ~ ( alive @ ( ZJ @ setIn ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ( ( ZG @ host )
!= nbr_proc )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ( ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) )
!= ( ZF @ host ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ( ( ZG @ host )
!= nbr_proc )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ~ ( ZG @ host @ ( down @ index ) @ ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) @ setIn ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ( ( ZG @ host )
!= nbr_proc )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) @ ( zero @ s @ leq ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ( ( ZG @ host )
!= nbr_proc )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ~ ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) @ ( ZG @ host @ leq ) ) )
& ( ( ( ZA @ host @ ( status @ index ) )
!= norm )
| ( ( ZA @ host @ ( ldr @ index ) )
!= ( ZA @ host ) )
| ~ ( alive @ ( ZA @ setIn ) )
| ( ( ZC @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( ZB @ host @ queue @ ( ZC @ m_Halt @ elem ) )
| ~ ( alive @ ( ZC @ setIn ) )
| ( ZA @ host @ ( ZC @ host @ ( pendack @ index ) @ leq ) ) )
& ( ~ ( Z @ host @ ( pendack @ index ) @ ( Y @ host @ ( pendack @ index ) @ leq ) )
| ( ( Z @ host @ ( status @ index ) )
!= elec_2 )
| ( ( Y @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( Z @ setIn ) )
| ~ ( alive @ ( Y @ setIn ) )
| ( Z @ host @ ( Y @ host @ leq ) ) )
& ( ~ ( V @ host @ queue @ ( W @ ( V @ m_Ack ) @ elem ) )
| ( ( X @ host @ ( status @ index ) )
!= elec_2 )
| ( ( V @ host @ ( status @ index ) )
!= elec_2 )
| ( ( X @ host )
!= ( W @ host ) )
| ~ ( alive @ ( X @ setIn ) )
| ~ ( alive @ ( V @ setIn ) ) )
& ( ( T @ host @ ( U @ host @ ( pendack @ index ) @ leq ) )
| ( ( U @ host @ ( status @ index ) )
!= elec_2 )
| ( ( T @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( U @ setIn ) )
| ~ ( alive @ ( T @ setIn ) )
| ( U @ host @ ( T @ host @ leq ) ) )
& ( ( ( Q @ host @ ( status @ index ) )
!= norm )
| ( ( Q @ host @ ( ldr @ index ) )
!= ( Q @ host ) )
| ~ ( alive @ ( Q @ setIn ) )
| ( ( R @ host )
!= ( Q @ host ) )
| ~ ( S @ host @ queue @ ( R @ m_Down @ elem ) )
| ~ ( alive @ ( S @ setIn ) ) )
& ( ( ( P @ host @ ( elid @ index ) )
= P )
| ~ ( alive @ ( P @ setIn ) )
| ( ( P @ host @ ( status @ index ) )
!= elec_2 ) )
& ( ( ( P @ host @ ( elid @ index ) )
= P )
| ~ ( alive @ ( P @ setIn ) )
| ( ( P @ host @ ( status @ index ) )
!= elec_1 ) )
& ( ~ ( O @ host @ queue @ ( N @ ( O @ m_Ack ) @ elem ) )
| ( ( O @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( alive @ ( O @ setIn ) ) )
& ( ( M @ host @ ( pendack @ index ) @ ( L @ host @ leq ) )
| ~ ( M @ host @ queue @ ( L @ ( M @ m_Ack ) @ elem ) )
| ~ ( alive @ ( M @ setIn ) ) )
& ( ~ ( alive @ ( K @ setIn ) )
| ~ ( alive @ ( J @ setIn ) )
| ( ( K @ host )
!= ( J @ host ) )
| ( K = J ) )
& ( ~ ( I @ host @ ( G @ host @ leq ) )
| ~ ( H @ host @ queue @ ( G @ ( I @ m_Ack ) @ elem ) ) )
& ( ~ ( F @ host @ ( E @ host @ leq ) )
| ~ ( E @ host @ queue @ ( F @ m_Halt @ elem ) ) )
& ( ( ( D @ host )
!= ( C @ host ) )
| ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(91,plain,
( ( sk2 @ host )
= ( sk6 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(135,plain,
( ( sk6 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).
thf(283,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)],[32]) ).
thf(284,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)],[283]) ).
thf(285,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)],[284]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[287]) ).
thf(291,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[290]) ).
thf(78,plain,
( ( sk7 @ host )
= ( sk9 @ host @ ( pendack @ index ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(118,plain,
( ( sk9 @ host @ ( pendack @ index ) )
= ( sk7 @ host ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(77,plain,
( ( sk5 @ host )
= ( sk9 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(126,plain,
( ( sk9 @ host )
= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(595,plain,
( ( sk5 @ host @ ( pendack @ index ) )
= ( sk7 @ host ) ),
inference(rewrite,[status(thm)],[118,126]) ).
thf(96,plain,
( ( sk8 @ host )
= ( sk9 @ host @ ( pendack @ index ) @ s ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(127,plain,
( ( sk9 @ host @ ( pendack @ index ) @ s )
= ( sk8 @ host ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(942,plain,
( ( sk5 @ host @ ( pendack @ index ) @ s )
= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[127,126]) ).
thf(952,plain,
( ( ( sk5 @ host @ ( pendack @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ( ( sk7 @ host @ s )
= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[595,942]) ).
thf(953,plain,
( ( sk7 @ host @ s )
= ( sk8 @ host ) ),
inference(pattern_uni,[status(thm)],[952:[]]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).
thf(406,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(407,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[406]) ).
thf(408,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[407]) ).
thf(2022,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk8 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[953,408]) ).
thf(2023,plain,
~ ( sk7 @ host @ ( sk8 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[2022:[bind(A,$thf( sk7 @ host ))]]) ).
thf(2382,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk8 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,2023]) ).
thf(2383,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk8 @ host @ leq ) ) ),
inference(simp,[status(thm)],[2382]) ).
thf(2413,plain,
! [A: $i] :
( ( A
!= ( sk7 @ host ) )
| ( A
!= ( sk8 @ host ) ) ),
inference(simp,[status(thm)],[2383]) ).
thf(2421,plain,
( ( sk8 @ host )
!= ( sk7 @ host ) ),
inference(simp,[status(thm)],[2413]) ).
thf(2425,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( ( sk7 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[135,2421]) ).
thf(2429,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[2425]) ).
thf(5437,plain,
( ( ( sk8 @ host )
!= ( sk2 @ host ) )
| ( sk7 != sk2 ) ),
inference(rewrite,[status(thm)],[2429,135]) ).
thf(74,plain,
sk3 @ host @ ( sk2 @ host @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[74,111]) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1022]) ).
thf(1024,plain,
~ ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).
thf(357,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(358,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)],[357]) ).
thf(359,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)],[358]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[359]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[361]) ).
thf(365,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[364]) ).
thf(101,plain,
alive @ ( sk2 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(34,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).
thf(304,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(305,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(5705,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( A @ ( B @ elem ) )
| ( A = q_nil ) ),
inference(paramod_ordered,[status(thm)],[306,365]) ).
thf(5706,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(pattern_uni,[status(thm)],[5705:[bind(A,$thf( E )),bind(B,$thf( E @ last )),bind(C,$thf( E @ init ))]]) ).
thf(5736,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(simp,[status(thm)],[5706]) ).
thf(99,plain,
( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(137,plain,
( ( sk1 @ ( sk3 @ m_Down @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
thf(402,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(403,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[402]) ).
thf(404,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[403]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[404]) ).
thf(1998,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[137,405]) ).
thf(1999,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(6077,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[5736,1999]) ).
thf(6078,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[6077]) ).
thf(6079,plain,
sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ),
inference(pattern_uni,[status(thm)],[6078:[bind(A,$thf( sk2 @ host @ queue ))]]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(495,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[74,76]) ).
thf(496,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(497,plain,
~ ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(8044,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6079,497]) ).
thf(8045,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[8044]) ).
thf(8097,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[8045]) ).
thf(8154,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Ldr ) ),
inference(simp,[status(thm)],[8097]) ).
thf(9,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_03) ).
thf(181,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2030,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[181,408]) ).
thf(2031,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[2030]) ).
thf(2042,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[2031]) ).
thf(2066,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2042]) ).
thf(2072,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[2066]) ).
thf(85,plain,
alive @ ( sk9 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(8,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
thf(179,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(180,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[179]) ).
thf(471,plain,
( ( ( alive @ ( sk9 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,180]) ).
thf(472,plain,
( ( alive @ ( sk9 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[471]) ).
thf(476,plain,
( ( alive != alive )
| ( sk9 != nil ) ),
inference(simp,[status(thm)],[472]) ).
thf(479,plain,
sk9 != nil,
inference(simp,[status(thm)],[476]) ).
thf(102,plain,
( ( sk9 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(123,plain,
( ( sk9 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[102]) ).
thf(533,plain,
( ( sk5 @ host @ ( status @ index ) )
= elec_2 ),
inference(rewrite,[status(thm)],[123,126]) ).
thf(596,plain,
( ( ( sk5 @ host @ ( status @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ( ( sk7 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[595,533]) ).
thf(611,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( status != pendack )
| ( ( sk7 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[596]) ).
thf(615,plain,
( ( status != pendack )
| ( ( sk7 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[611]) ).
thf(16,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_02) ).
thf(205,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(206,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[205]) ).
thf(2016,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[206,408]) ).
thf(2017,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2016]) ).
thf(2054,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2017]) ).
thf(2063,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2054]) ).
thf(2906,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( A @ host @ s ) )
| ( ( zero @ s )
!= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[953,2063]) ).
thf(2907,plain,
( ( zero @ s )
!= ( sk8 @ host ) ),
inference(pattern_uni,[status(thm)],[2906:[bind(A,$thf( sk7 ))]]) ).
thf(2915,plain,
( ( ( sk7 @ host @ s )
!= ( zero @ s ) )
| ( ( sk8 @ host )
!= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[953,2907]) ).
thf(2916,plain,
( ( sk7 @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2915]) ).
thf(2918,plain,
( ( sk7 @ host )
!= zero ),
inference(simp,[status(thm)],[2916]) ).
thf(2920,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( zero != elec_2 )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[615,2918]) ).
thf(2921,plain,
( ( zero != elec_2 )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[2920:[]]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(465,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(466,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[465]) ).
thf(467,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[466]) ).
thf(468,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[467]) ).
thf(105,plain,
( ( sk2 @ host )
!= ( sk9 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(130,plain,
( ( sk9 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(481,plain,
sk9 != sk2,
inference(simp,[status(thm)],[130]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).
thf(161,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)],[4]) ).
thf(162,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)],[161]) ).
thf(163,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)],[162]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[164]) ).
thf(167,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[166]) ).
thf(168,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk11 )
= A ),
inference(cnf,[status(esa)],[167]) ).
thf(2077,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk11 )
= A ),
inference(lifteq,[status(thm)],[168]) ).
thf(23,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).
thf(227,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(228,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[227]) ).
thf(229,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[228]) ).
thf(570,plain,
! [A: $i] :
( ( ( alive @ ( sk9 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,229]) ).
thf(571,plain,
! [A: $i] :
( ( alive @ ( sk9 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[570]) ).
thf(578,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk9 != A ) ),
inference(simp,[status(thm)],[571]) ).
thf(582,plain,
setEmpty != alive,
inference(simp,[status(thm)],[578]) ).
thf(88,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( B @ host )
!= ( C @ host @ ( pendack @ index ) @ s ) )
| ( ( A @ host )
!= ( C @ host @ ( pendack @ index ) ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( C @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( C @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( B @ host )
!= ( C @ host @ ( pendack @ index ) @ s ) )
| ( ( A @ host )
!= ( C @ host @ ( pendack @ index ) ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( C @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( B @ host )
!= ( C @ host @ ( pendack @ index ) @ s ) )
| ( ( A @ host )
!= ( C @ host @ ( pendack @ index ) ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[114]) ).
thf(20,axiom,
elec_1 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_07) ).
thf(217,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(84,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(120,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[84]) ).
thf(106,plain,
( ( sk3 @ host )
= ( sk2 @ host @ ( pendack @ index ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(119,plain,
( ( sk2 @ host @ ( pendack @ index ) )
= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(682,plain,
( ( ( sk2 @ host @ ( status @ index ) )
!= ( sk2 @ host @ ( pendack @ index ) ) )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[120,119]) ).
thf(688,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( status != pendack )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[682]) ).
thf(698,plain,
( ( status != pendack )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[688]) ).
thf(731,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( elec_2 @ ( sk2 @ host @ leq ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[698,74]) ).
thf(732,plain,
( ( elec_2 @ ( sk2 @ host @ leq ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[731:[]]) ).
thf(2026,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( sk2 @ host @ leq ) ) )
| ~ $true
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[732,408]) ).
thf(2027,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( sk2 @ host @ leq ) ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2026]) ).
thf(2053,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= ( sk2 @ host ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2027]) ).
thf(2062,plain,
( ( ( elec_2 @ s )
!= ( sk2 @ host ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2053]) ).
thf(87,plain,
sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(675,plain,
sk3 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[87,119]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_63) ).
thf(236,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)],[25]) ).
thf(237,plain,
( ! [A: $i,B: $i] :
( ( B @ s @ ( A @ s @ leq ) )
=> ( B @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ s @ ( A @ s @ leq ) ) ) ),
inference(miniscope,[status(thm)],[236]) ).
thf(238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ leq ) )
| ~ ( D @ s @ ( C @ s @ leq ) ) )
& ( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[238]) ).
thf(8268,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[675,239]) ).
thf(8269,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8268]) ).
thf(8270,plain,
sk3 @ host @ s @ ( nbr_proc @ s @ leq ),
inference(pattern_uni,[status(thm)],[8269:[bind(A,$thf( nbr_proc )),bind(B,$thf( sk3 @ host ))]]) ).
thf(8645,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8270,408]) ).
thf(8646,plain,
! [A: $i] :
( ( sk3 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8645]) ).
thf(8699,plain,
! [A: $i] :
( ( ( sk3 @ host @ s )
!= A )
| ( ( nbr_proc @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8646]) ).
thf(8709,plain,
( ( sk3 @ host @ s @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[8699]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(379,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1305,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)],[291,76]) ).
thf(1306,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)],[1305]) ).
thf(1307,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[1306:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(1309,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(simp,[status(thm)],[1307]) ).
thf(3779,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[135,1309]) ).
thf(3780,plain,
~ ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[3779:[bind(A,$thf( sk6 ))]]) ).
thf(4541,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,3780]) ).
thf(4542,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4541]) ).
thf(4575,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4542]) ).
thf(4623,plain,
! [A: $i] :
( ( sk6 @ m_Ldr @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[4575]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).
thf(367,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[367]) ).
thf(5068,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ~ $true
| ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[368,408]) ).
thf(5069,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[5068]) ).
thf(5070,plain,
! [A: $i] : ( A @ s @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[5069:[bind(A,$thf( A )),bind(B,$thf( A @ s )),bind(C,$thf( A ))]]) ).
thf(5231,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5070,408]) ).
thf(5232,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[5231]) ).
thf(5259,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[5232]) ).
thf(5269,plain,
! [A: $i] :
( ( A @ s @ s )
!= A ),
inference(simp,[status(thm)],[5259]) ).
thf(5305,plain,
! [A: $i] :
( ( ( A @ s @ s )
!= ( sk7 @ host @ s ) )
| ( ( sk8 @ host )
!= A ) ),
inference(paramod_ordered,[status(thm)],[953,5269]) ).
thf(5313,plain,
( ( sk8 @ host @ s @ s )
!= ( sk7 @ host @ s ) ),
inference(simp,[status(thm)],[5305]) ).
thf(5454,plain,
( ( sk8 @ host @ s @ s )
!= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[5313,953]) ).
thf(5966,plain,
! [A: $i] :
( ( A != sk2 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[5736,101]) ).
thf(5967,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5966:[bind(A,$thf( sk2 ))]]) ).
thf(52,axiom,
norm != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(385,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(2426,plain,
( ( ( sk9 @ host )
!= ( sk8 @ host ) )
| ( ( sk7 @ host )
!= ( sk5 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[126,2421]) ).
thf(2434,plain,
( ( sk9 != sk8 )
| ( sk7 != sk5 ) ),
inference(simp,[status(thm)],[2426]) ).
thf(55,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(396,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(397,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[396]) ).
thf(398,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).
thf(224,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[224]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[225]) ).
thf(3825,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)],[398,226]) ).
thf(3826,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[3825:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[141]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(172,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[171]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).
thf(262,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)],[30]) ).
thf(263,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)],[262]) ).
thf(264,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)],[263]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[264]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(270,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[269]) ).
thf(4277,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,497]) ).
thf(4278,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4277]) ).
thf(4323,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4278]) ).
thf(4371,plain,
! [A: $i] :
( ( A @ ( sk3 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[4323]) ).
thf(7991,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6079,1024]) ).
thf(7992,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[7991]) ).
thf(8130,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Halt ) ) ),
inference(simp,[status(thm)],[7992]) ).
thf(8165,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Halt ) ),
inference(simp,[status(thm)],[8130]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(320,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(2034,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[675,408]) ).
thf(2035,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2034]) ).
thf(2043,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2035]) ).
thf(2067,plain,
( ( sk3 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2043]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(198,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[199]) ).
thf(3643,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)],[398,200]) ).
thf(3644,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[3643:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(182,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)],[10]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(372,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5079,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk8 @ host @ leq ) ) )
| ~ $true
| ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[368,2023]) ).
thf(5080,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk7 @ host @ ( sk8 @ host @ leq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[5079]) ).
thf(5081,plain,
sk8 @ host @ ( sk7 @ host @ leq ),
inference(pattern_uni,[status(thm)],[5080:[bind(A,$thf( sk8 @ host )),bind(B,$thf( sk7 @ host ))]]) ).
thf(5148,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk7 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[5081,111]) ).
thf(5149,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk7 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[5148]) ).
thf(5150,plain,
~ ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[5149:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(2908,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[135,2063]) ).
thf(2909,plain,
( ( sk2 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[2908:[bind(A,$thf( sk6 ))]]) ).
thf(3116,plain,
( ( sk2 @ host )
!= zero ),
inference(simp,[status(thm)],[2909]) ).
thf(18,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_04) ).
thf(211,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(212,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[211]) ).
thf(2020,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[212,408]) ).
thf(2021,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2020]) ).
thf(2052,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2021]) ).
thf(2061,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2052]) ).
thf(2645,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( nbr_proc @ s ) )
| ( ( sk8 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[953,2061]) ).
thf(2652,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= nbr_proc )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[2645]) ).
thf(2657,plain,
( ( sk7 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[2652]) ).
thf(2664,plain,
( ( ( sk9 @ host )
!= ( sk7 @ host ) )
| ( ( sk5 @ host )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[126,2657]) ).
thf(2667,plain,
( ( sk9 != sk7 )
| ( ( sk5 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2664]) ).
thf(86,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(109,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)],[86]) ).
thf(110,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)],[109]) ).
thf(948,plain,
( ( ( sk5 @ host @ ( status @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ( ( elec_2 @ s )
= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[533,942]) ).
thf(957,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( status != pendack )
| ( ( elec_2 @ s )
= ( sk8 @ host ) ) ),
inference(simp,[status(thm)],[948]) ).
thf(965,plain,
( ( status != pendack )
| ( ( elec_2 @ s )
= ( sk8 @ host ) ) ),
inference(simp,[status(thm)],[957]) ).
thf(2028,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,408]) ).
thf(2029,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2028]) ).
thf(2048,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2029]) ).
thf(2057,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[2048]) ).
thf(3659,plain,
! [A: $i] :
( ( ( elec_2 @ s )
!= ( A @ s ) )
| ( ( sk8 @ host )
!= A )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[965,2057]) ).
thf(3660,plain,
( ( ( sk8 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[3659:[bind(A,$thf( elec_2 ))]]) ).
thf(3815,plain,
( ( ( sk8 @ host )
!= ( sk3 @ host ) )
| ( elec_2 != elec_2 )
| ( status != pendack )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[698,3660]) ).
thf(3816,plain,
( ( ( sk8 @ host )
!= ( sk3 @ host ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[3815]) ).
thf(3821,plain,
( ( sk8 != sk3 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[3816]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[124]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(344,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1302,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[291,111]) ).
thf(1303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1302]) ).
thf(1304,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[1303:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(1308,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(simp,[status(thm)],[1304]) ).
thf(3489,plain,
! [A: $i] :
( ( ( sk9 @ host )
!= ( A @ host ) )
| ~ ( sk5 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[126,1308]) ).
thf(3490,plain,
~ ( sk5 @ host @ queue @ ( sk9 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[3489:[bind(A,$thf( sk9 ))]]) ).
thf(4275,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk5 @ host @ queue @ ( sk9 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,3490]) ).
thf(4276,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk5 @ host @ queue @ ( sk9 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4275]) ).
thf(4305,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk5 @ host @ queue ) )
| ( A
!= ( sk9 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4276]) ).
thf(4353,plain,
! [A: $i] :
( ( A @ ( sk9 @ m_Halt @ cons ) )
!= ( sk5 @ host @ queue ) ),
inference(simp,[status(thm)],[4305]) ).
thf(63,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_45) ).
thf(422,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(423,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[422]) ).
thf(424,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[423]) ).
thf(4255,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,424]) ).
thf(4256,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[4255]) ).
thf(4310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[4256]) ).
thf(4358,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[4310]) ).
thf(8258,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[181,239]) ).
thf(8259,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8258]) ).
thf(8260,plain,
nbr_proc @ s @ ( zero @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[8259:[bind(A,$thf( zero @ s )),bind(B,$thf( nbr_proc ))]]) ).
thf(8410,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8260,408]) ).
thf(8411,plain,
! [A: $i] :
( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8410]) ).
thf(8462,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= A )
| ( ( zero @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8411]) ).
thf(8468,plain,
( ( nbr_proc @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[8462]) ).
thf(4257,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[137,270]) ).
thf(4258,plain,
sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[4257:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(3485,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[135,1308]) ).
thf(3486,plain,
~ ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[3485:[bind(A,$thf( sk6 ))]]) ).
thf(4421,plain,
( ( ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4258,3486]) ).
thf(4422,plain,
( ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[4421]) ).
thf(4464,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk6 @ m_Halt )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[4422]) ).
thf(4492,plain,
( ( sk6 @ m_Halt )
!= ( sk3 @ m_Down ) ),
inference(simp,[status(thm)],[4464]) ).
thf(2432,plain,
( ( ( sk9 @ host )
!= ( sk8 @ host ) )
| ( sk7 != sk5 ) ),
inference(simp,[status(thm)],[2426]) ).
thf(5492,plain,
( ( ( sk8 @ host )
!= ( sk5 @ host ) )
| ( sk7 != sk5 ) ),
inference(rewrite,[status(thm)],[2432,126]) ).
thf(5493,plain,
( ( sk8 != sk5 )
| ( sk7 != sk5 ) ),
inference(simp,[status(thm)],[5492]) ).
thf(8062,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6079,3780]) ).
thf(8063,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[8062]) ).
thf(8115,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[8063]) ).
thf(8161,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Ldr ) ),
inference(simp,[status(thm)],[8115]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(213,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(214,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[213]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[214]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(788,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( elec_2 @ leq ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[615,212]) ).
thf(789,plain,
( ( nbr_proc @ ( elec_2 @ leq ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[788:[bind(A,$thf( sk7 ))]]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_50) ).
thf(376,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(242,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)],[26]) ).
thf(243,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)],[242]) ).
thf(244,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)],[243]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[244]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[245]) ).
thf(248,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[247]) ).
thf(249,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(cnf,[status(esa)],[248]) ).
thf(2451,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(lifteq,[status(thm)],[249]) ).
thf(4497,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,1024]) ).
thf(4498,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4497]) ).
thf(4565,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4498]) ).
thf(4613,plain,
! [A: $i] :
( ( sk3 @ m_Halt @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[4565]) ).
thf(5913,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk3 @ m_Halt @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[398,4613]) ).
thf(5914,plain,
( ( q_nil @ ( sk3 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[5913:[bind(A,$thf( sk3 @ m_Halt )),bind(B,$thf( q_nil ))]]) ).
thf(42,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).
thf(348,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(353,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(81,plain,
alive @ ( sk6 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(473,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,180]) ).
thf(474,plain,
( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[473]) ).
thf(477,plain,
( ( alive != alive )
| ( sk6 != nil ) ),
inference(simp,[status(thm)],[474]) ).
thf(480,plain,
sk6 != nil,
inference(simp,[status(thm)],[477]) ).
thf(713,plain,
( ( ( sk9 @ host )
!= ( sk3 @ host ) )
| ( sk5 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[126,675]) ).
thf(718,plain,
( ( sk9 != sk3 )
| ( sk5 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[713]) ).
thf(2024,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk5 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk9 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[718,408]) ).
thf(2025,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk5 @ host @ ( nbr_proc @ leq ) ) )
| ( sk9 != sk3 ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2049,plain,
! [A: $i] :
( ( A
!= ( sk5 @ host ) )
| ( ( A @ s )
!= nbr_proc )
| ( sk9 != sk3 ) ),
inference(simp,[status(thm)],[2025]) ).
thf(2058,plain,
( ( ( sk5 @ host @ s )
!= nbr_proc )
| ( sk9 != sk3 ) ),
inference(simp,[status(thm)],[2049]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ pidElem )
<=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).
thf(272,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)],[31]) ).
thf(273,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)],[272]) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk16 @ m_Down ) )
| ( A
= ( A @ sk15 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[273]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[274]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[276]) ).
thf(280,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[279]) ).
thf(98,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 @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(131,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 ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(132,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 ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(307,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
thf(311,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(312,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[311]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[312]) ).
thf(314,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[313]) ).
thf(1072,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[137,314]) ).
thf(1073,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Down )
!= A )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[1072]) ).
thf(1074,plain,
( ( sk1 != q_nil )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[1073]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(5438,plain,
( ( sk8 != sk2 )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[5437]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
thf(230,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)],[24]) ).
thf(231,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( C @ ( A @ m_Ack ) )
= ( D @ ( B @ m_Ack ) ) ) ),
inference(miniscope,[status(thm)],[230]) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[231]) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[232]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
thf(452,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(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(201,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2430,plain,
( ( sk8 != sk6 )
| ( ( sk7 @ host )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[2425]) ).
thf(5483,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( sk8 != sk6 )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[135,2430]) ).
thf(5484,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( sk8 != sk6 ) ),
inference(simp,[status(thm)],[5483]) ).
thf(5487,plain,
( ( sk7 != sk6 )
| ( sk8 != sk6 ) ),
inference(simp,[status(thm)],[5484]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(220,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(4980,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[4258,150]) ).
thf(4981,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[4980]) ).
thf(4982,plain,
( ( sk3 @ host )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[4981:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(5043,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[135,4982]) ).
thf(5044,plain,
( ( sk6 @ host )
!= ( sk3 @ host ) ),
inference(simp,[status(thm)],[5043]) ).
thf(5049,plain,
sk6 != sk3,
inference(simp,[status(thm)],[5044]) ).
thf(82,plain,
sk2 @ host @ ( acks @ index ) @ ( sk5 @ host @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(576,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( acks @ index ) @ ( sk5 @ host @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,229]) ).
thf(577,plain,
! [A: $i] :
( ( sk2 @ host @ ( acks @ index ) @ ( sk5 @ host @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[576]) ).
thf(581,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( acks @ index ) )
!= setEmpty )
| ( ( sk5 @ host )
!= A ) ),
inference(simp,[status(thm)],[577]) ).
thf(585,plain,
( ( sk2 @ host @ ( acks @ index ) )
!= setEmpty ),
inference(simp,[status(thm)],[581]) ).
thf(679,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( pendack @ index ) ) )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(paramod_ordered,[status(thm)],[119,585]) ).
thf(696,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != pendack )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[679]) ).
thf(703,plain,
( ( acks != pendack )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[696]) ).
thf(745,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( acks != pendack )
| ( setEmpty != elec_2 )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[698,703]) ).
thf(746,plain,
( ( acks != pendack )
| ( setEmpty != elec_2 )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[745:[]]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(392,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(542,plain,
( ( ( sk2 @ host @ ( status @ index ) )
!= ( sk2 @ host @ ( pendack @ index ) ) )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[120,87]) ).
thf(548,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( status != pendack )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[542]) ).
thf(553,plain,
( ( status != pendack )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[548]) ).
thf(2036,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[553,408]) ).
thf(2037,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2036]) ).
thf(2050,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= nbr_proc )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2037]) ).
thf(2059,plain,
( ( ( elec_2 @ s )
!= nbr_proc )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2050]) ).
thf(3680,plain,
( ( ( elec_2 @ s )
!= ( elec_2 @ s ) )
| ( ( sk8 @ host )
!= nbr_proc )
| ( status != pendack )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[965,2059]) ).
thf(3681,plain,
( ( ( elec_2 @ s )
!= ( elec_2 @ s ) )
| ( ( sk8 @ host )
!= nbr_proc )
| ( status != pendack ) ),
inference(simp,[status(thm)],[3680]) ).
thf(3682,plain,
( ( ( sk8 @ host )
!= nbr_proc )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[3681:[]]) ).
thf(5923,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk6 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[398,4623]) ).
thf(5924,plain,
( ( q_nil @ ( sk6 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[5923:[bind(A,$thf( sk6 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(100,plain,
sk9 @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(801,plain,
sk5 @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[100,126]) ).
thf(943,plain,
sk8 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[801,942]) ).
thf(8263,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,239]) ).
thf(8264,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8263]) ).
thf(8265,plain,
sk8 @ host @ s @ ( nbr_proc @ s @ leq ),
inference(pattern_uni,[status(thm)],[8264:[bind(A,$thf( nbr_proc )),bind(B,$thf( sk8 @ host ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[196]) ).
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/sandbox2/benchmark/theBenchmark.p',axiom_53) ).
thf(324,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(6613,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ( q_nil != B )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[5736,2057]) ).
thf(6614,plain,
! [A: $i] :
( ( q_nil != A )
| ( A @ s @ ( A @ s @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[6613:[bind(A,$thf( C @ s )),bind(B,$thf( C ))]]) ).
thf(7627,plain,
q_nil @ s @ ( q_nil @ s @ last @ elem ),
inference(simp,[status(thm)],[6614]) ).
thf(7827,plain,
! [A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7627,424]) ).
thf(7828,plain,
! [A: $i] :
( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[7827]) ).
thf(7934,plain,
! [A: $i] :
( ( ( q_nil @ s )
!= q_nil )
| ( ( q_nil @ s @ last )
!= A ) ),
inference(simp,[status(thm)],[7828]) ).
thf(7977,plain,
( ( q_nil @ s )
!= q_nil ),
inference(simp,[status(thm)],[7934]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(252,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(2433,plain,
( ( sk9 != sk8 )
| ( ( sk7 @ host )
!= ( sk5 @ host ) ) ),
inference(simp,[status(thm)],[2426]) ).
thf(2032,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[943,408]) ).
thf(2033,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[2032]) ).
thf(2047,plain,
! [A: $i] :
( ( A
!= ( sk8 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2033]) ).
thf(2071,plain,
( ( sk8 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[2047]) ).
thf(2095,plain,
( ( ( sk9 @ host )
!= ( sk8 @ host ) )
| ( ( sk5 @ host @ s )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[126,2071]) ).
thf(2100,plain,
( ( sk9 != sk8 )
| ( ( sk5 @ host @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2095]) ).
thf(37,axiom,
elec_2 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_08) ).
thf(317,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(2650,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= ( nbr_proc @ s ) )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[2645]) ).
thf(2656,plain,
( ( sk7 @ host @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2650]) ).
thf(2685,plain,
( ( nbr_proc @ s )
!= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[2656,953]) ).
thf(185,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[184]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk12 ) )
= B ),
inference(cnf,[status(esa)],[185]) ).
thf(5345,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk12 ) )
= B ),
inference(lifteq,[status(thm)],[186]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
thf(388,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(354,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[353]) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[355]) ).
thf(8471,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8265,408]) ).
thf(8472,plain,
! [A: $i] :
( ( sk8 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8471]) ).
thf(8513,plain,
! [A: $i] :
( ( ( sk8 @ host @ s )
!= A )
| ( ( nbr_proc @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8472]) ).
thf(8530,plain,
( ( sk8 @ host @ s @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[8513]) ).
thf(3783,plain,
! [A: $i] :
( ( ( sk9 @ host )
!= ( A @ host ) )
| ~ ( sk5 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[126,1309]) ).
thf(3784,plain,
~ ( sk5 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[3783:[bind(A,$thf( sk9 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
thf(151,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)],[3]) ).
thf(152,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)],[151]) ).
thf(153,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)],[152]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[153]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).
thf(256,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(191,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)],[12]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) )
& ( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ) ),
inference(cnf,[status(esa)],[191]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(4259,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk5 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,3784]) ).
thf(4260,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk5 @ host @ queue @ ( sk9 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4259]) ).
thf(4341,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk5 @ host @ queue ) )
| ( A
!= ( sk9 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4260]) ).
thf(4389,plain,
! [A: $i] :
( ( A @ ( sk9 @ m_Ldr @ cons ) )
!= ( sk5 @ host @ queue ) ),
inference(simp,[status(thm)],[4341]) ).
thf(4515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,424]) ).
thf(4516,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[4515]) ).
thf(4600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[4516]) ).
thf(4648,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[4600]) ).
thf(2663,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( ( sk2 @ host )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[135,2657]) ).
thf(2666,plain,
( ( sk7 != sk6 )
| ( ( sk2 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2663]) ).
thf(2648,plain,
! [A: $i] :
( ( ( sk9 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk5 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[126,2061]) ).
thf(2649,plain,
( ( nbr_proc @ s )
!= ( sk5 @ host ) ),
inference(pattern_uni,[status(thm)],[2648:[bind(A,$thf( sk9 ))]]) ).
thf(5123,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( sk7 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5081,408]) ).
thf(5124,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( sk7 @ host @ leq ) ) ),
inference(simp,[status(thm)],[5123]) ).
thf(5159,plain,
! [A: $i] :
( ( A
!= ( sk8 @ host ) )
| ( ( A @ s )
!= ( sk7 @ host ) ) ),
inference(simp,[status(thm)],[5124]) ).
thf(5166,plain,
( ( sk8 @ host @ s )
!= ( sk7 @ host ) ),
inference(simp,[status(thm)],[5159]) ).
thf(2900,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[2063]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(554,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( sk5 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[120,82]) ).
thf(565,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != status )
| ( elec_2 @ ( sk5 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[554]) ).
thf(569,plain,
( ( acks != status )
| ( elec_2 @ ( sk5 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[565]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( pendack @ index ) @ ( A @ 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(133,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( pendack @ index ) @ ( A @ 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)],[103]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( pendack @ index ) @ ( A @ 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)],[133]) ).
thf(40,axiom,
elec_2 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_09) ).
thf(341,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(342,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[341]) ).
thf(343,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[342]) ).
thf(95,plain,
sk2 @ m_Ldr @ ( sk9 @ host @ queue @ snoc ) @ ( sk7 @ ( sk9 @ m_Ack ) @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(658,plain,
sk2 @ m_Ldr @ ( sk5 @ host @ queue @ snoc ) @ ( sk7 @ ( sk9 @ m_Ack ) @ elem ),
inference(rewrite,[status(thm)],[95,126]) ).
thf(671,plain,
! [A: $i] :
( ( ( sk2 @ m_Ldr @ ( sk5 @ host @ queue @ snoc ) @ ( sk7 @ ( sk9 @ m_Ack ) @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[658,424]) ).
thf(672,plain,
! [A: $i] :
( ( sk2 @ m_Ldr @ ( sk5 @ host @ queue @ snoc ) @ ( sk7 @ ( sk9 @ m_Ack ) @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(673,plain,
! [A: $i] :
( ( ( sk2 @ m_Ldr @ ( sk5 @ host @ queue @ snoc ) )
!= q_nil )
| ( ( sk7 @ ( sk9 @ m_Ack ) )
!= A ) ),
inference(simp,[status(thm)],[672]) ).
thf(674,plain,
( ( sk2 @ m_Ldr @ ( sk5 @ host @ queue @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[673]) ).
thf(2661,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( nbr_proc != elec_2 )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[615,2657]) ).
thf(2662,plain,
( ( nbr_proc != elec_2 )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[2661:[]]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(412,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ ordered )
<=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_54) ).
thf(425,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(75,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(3536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( C @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[74,140]) ).
thf(3537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( C @ host @ ( A @ host @ leq ) ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[3536]) ).
thf(3538,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk2 @ ( sk3 @ m_Ack ) @ elem ) ),
inference(pattern_uni,[status(thm)],[3537:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(3607,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk2 @ ( sk3 @ m_Ack ) @ elem ) ),
inference(simp,[status(thm)],[3538]) ).
thf(90,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(147,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(148,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[147]) ).
thf(4281,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,3780]) ).
thf(4282,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4281]) ).
thf(4317,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4282]) ).
thf(4365,plain,
! [A: $i] :
( ( A @ ( sk6 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[4317]) ).
thf(373,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[372]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[374]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).
thf(207,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(208,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[207]) ).
thf(209,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[208]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[209]) ).
thf(3288,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)],[398,210]) ).
thf(3289,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[3288:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(971,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[135,943]) ).
thf(975,plain,
( ( sk8 != sk6 )
| ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[971]) ).
thf(2014,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[74,408]) ).
thf(2015,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[2014]) ).
thf(2046,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[2015]) ).
thf(2070,plain,
( ( sk3 @ host @ s )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[2046]) ).
thf(2439,plain,
( ( ( sk7 @ host @ s )
!= ( sk3 @ host @ s ) )
| ( ( sk8 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[953,2070]) ).
thf(2449,plain,
( ( ( sk7 @ host )
!= ( sk3 @ host ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2439]) ).
thf(5933,plain,
( ( sk7 != sk3 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2449]) ).
thf(4444,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4258,3780]) ).
thf(4445,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4444]) ).
thf(4472,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk6 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4445]) ).
thf(4494,plain,
( ( sk3 @ m_Down )
!= ( sk6 @ m_Ldr ) ),
inference(simp,[status(thm)],[4472]) ).
thf(4261,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,3486]) ).
thf(4262,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4261]) ).
thf(4333,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4262]) ).
thf(4381,plain,
! [A: $i] :
( ( A @ ( sk6 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[4333]) ).
thf(202,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[201]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[202]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[203]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
thf(259,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(7,axiom,
elec_1 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_06) ).
thf(176,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(157,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[156]) ).
thf(158,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk10 )
= A ),
inference(cnf,[status(esa)],[157]) ).
thf(1833,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk10 )
= A ),
inference(lifteq,[status(thm)],[158]) ).
thf(4391,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4258,1024]) ).
thf(4392,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[4391]) ).
thf(4480,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Halt )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[4392]) ).
thf(4485,plain,
( ( sk3 @ m_Halt )
!= ( sk3 @ m_Down ) ),
inference(simp,[status(thm)],[4480]) ).
thf(5039,plain,
sk3 != sk2,
inference(simp,[status(thm)],[4982]) ).
thf(380,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[379]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[380]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[381]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[143]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).
thf(350,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(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(72,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[112]) ).
thf(218,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[217]) ).
thf(219,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[218]) ).
thf(2422,plain,
sk8 != sk7,
inference(simp,[status(thm)],[2421]) ).
thf(453,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)],[452]) ).
thf(454,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)],[453]) ).
thf(455,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[454]) ).
thf(457,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[455]) ).
thf(458,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[457]) ).
thf(459,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk20 )
= A ),
inference(cnf,[status(esa)],[458]) ).
thf(3182,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk20 )
= A ),
inference(lifteq,[status(thm)],[459]) ).
thf(804,plain,
( ( ( sk5 @ host @ ( status @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ( elec_2 @ s @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[533,801]) ).
thf(815,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( status != pendack )
| ( elec_2 @ s @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[804]) ).
thf(822,plain,
( ( status != pendack )
| ( elec_2 @ s @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[815]) ).
thf(2040,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ s @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[822,408]) ).
thf(2041,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ s @ ( nbr_proc @ leq ) ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2040]) ).
thf(2056,plain,
! [A: $i] :
( ( A
!= ( elec_2 @ s ) )
| ( ( A @ s )
!= nbr_proc )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2041]) ).
thf(2065,plain,
( ( ( elec_2 @ s @ s )
!= nbr_proc )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2056]) ).
thf(234,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk13 ) )
= A ),
inference(cnf,[status(esa)],[234]) ).
thf(5491,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk13 ) )
= A ),
inference(lifteq,[status(thm)],[235]) ).
thf(386,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[385]) ).
thf(387,plain,
wait != norm,
inference(lifteq,[status(thm)],[386]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_01) ).
thf(462,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(2910,plain,
! [A: $i] :
( ( ( sk9 @ host )
!= ( A @ host ) )
| ( ( sk5 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[126,2063]) ).
thf(2911,plain,
( ( sk5 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[2910:[bind(A,$thf( sk9 ))]]) ).
thf(588,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( setEmpty != elec_2 ) ),
inference(paramod_ordered,[status(thm)],[120,585]) ).
thf(592,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != status )
| ( setEmpty != elec_2 ) ),
inference(simp,[status(thm)],[588]) ).
thf(594,plain,
( ( acks != status )
| ( setEmpty != elec_2 ) ),
inference(simp,[status(thm)],[592]) ).
thf(97,plain,
sk2 @ m_Ldr @ ( sk9 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(769,plain,
sk2 @ m_Ldr @ ( sk5 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ),
inference(rewrite,[status(thm)],[97,126]) ).
thf(2646,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[135,2061]) ).
thf(2647,plain,
( ( nbr_proc @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[2646:[bind(A,$thf( sk6 ))]]) ).
thf(482,plain,
( ( sk5 @ host )
!= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[130,126]) ).
thf(518,plain,
( ( ( sk6 @ host )
!= ( sk5 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[135,482]) ).
thf(519,plain,
( ( sk6 @ host )
!= ( sk5 @ host ) ),
inference(simp,[status(thm)],[518]) ).
thf(521,plain,
sk6 != sk5,
inference(simp,[status(thm)],[519]) ).
thf(56,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_05) ).
thf(399,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(221,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[220]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[221]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[222]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[238]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(3521,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[137,197]) ).
thf(3522,plain,
( ( sk2 @ host @ queue @ head )
= ( sk3 @ m_Down ) ),
inference(pattern_uni,[status(thm)],[3521:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(2094,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( ( sk2 @ host @ s )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[135,2071]) ).
thf(2096,plain,
( ( sk8 != sk6 )
| ( ( sk2 @ host @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2094]) ).
thf(253,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[252]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[253]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[254]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
thf(294,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)],[33]) ).
thf(295,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)],[294]) ).
thf(296,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)],[295]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[296]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(300,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[299]) ).
thf(301,plain,
! [A: $i] :
( ( A @ m_Down @ sk17 )
= A ),
inference(cnf,[status(esa)],[300]) ).
thf(2684,plain,
! [A: $i] :
( ( A @ m_Down @ sk17 )
= A ),
inference(lifteq,[status(thm)],[301]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[192]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[274]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[277]) ).
thf(282,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[281]) ).
thf(413,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[412]) ).
thf(414,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[413]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_39) ).
thf(409,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(2012,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ~ $true
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[789,408]) ).
thf(2013,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2012]) ).
thf(2051,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2013]) ).
thf(2060,plain,
( ( ( nbr_proc @ s )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2051]) ).
thf(1097,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( elec_2 @ ( zero @ s @ leq ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[698,206]) ).
thf(1098,plain,
( ( elec_2 @ ( zero @ s @ leq ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[1097:[bind(A,$thf( sk3 ))]]) ).
thf(308,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[307]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[308]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[309]) ).
thf(5040,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[698,4982]) ).
thf(5041,plain,
( ( ( sk2 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[5040:[]]) ).
thf(5057,plain,
( ( ( sk7 @ host )
!= ( sk2 @ host ) )
| ( elec_2 != elec_2 )
| ( status != pendack )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[615,5041]) ).
thf(5058,plain,
( ( ( sk7 @ host )
!= ( sk2 @ host ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[5057]) ).
thf(5062,plain,
( ( sk7 != sk2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[5058]) ).
thf(6,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
thf(175,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(967,plain,
( ( ( sk9 @ host )
!= ( sk8 @ host ) )
| ( sk5 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[126,943]) ).
thf(976,plain,
( ( sk9 != sk8 )
| ( sk5 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[967]) ).
thf(517,plain,
sk5 != sk2,
inference(simp,[status(thm)],[482]) ).
thf(318,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[317]) ).
thf(319,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[318]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[256]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[257]) ).
thf(400,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[399]) ).
thf(401,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[400]) ).
thf(104,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 @ queue @ ( C @ m_Halt @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[138]) ).
thf(4440,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4258,497]) ).
thf(4441,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4440]) ).
thf(4474,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4441]) ).
thf(4495,plain,
( ( sk3 @ m_Down )
!= ( sk3 @ m_Ldr ) ),
inference(simp,[status(thm)],[4474]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(418,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(2431,plain,
( ( sk8 != sk6 )
| ( sk7 != sk2 ) ),
inference(simp,[status(thm)],[2425]) ).
thf(8022,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6079,3486]) ).
thf(8023,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[8022]) ).
thf(8145,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Halt ) ) ),
inference(simp,[status(thm)],[8023]) ).
thf(8172,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Halt ) ),
inference(simp,[status(thm)],[8145]) ).
thf(469,plain,
( ( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,180]) ).
thf(470,plain,
( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(475,plain,
( ( alive != alive )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[470]) ).
thf(478,plain,
sk2 != nil,
inference(simp,[status(thm)],[475]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_62) ).
thf(383,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(2901,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[698,2063]) ).
thf(2902,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[2901:[bind(A,$thf( sk3 ))]]) ).
thf(5698,plain,
( ( ( sk9 @ host )
!= ( sk7 @ host ) )
| ( sk9 != sk8 )
| ( ( sk5 @ host )
!= ( sk5 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[126,2433]) ).
thf(5699,plain,
( ( ( sk9 @ host )
!= ( sk7 @ host ) )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[5698]) ).
thf(5704,plain,
( ( sk9 != sk7 )
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[5699]) ).
thf(377,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[376]) ).
thf(378,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[377]) ).
thf(2373,plain,
( ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ~ ( elec_2 @ ( sk8 @ host @ leq ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[615,2023]) ).
thf(2374,plain,
( ~ ( elec_2 @ ( sk8 @ host @ leq ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[2373:[]]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( D @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[145]) ).
thf(188,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[187]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[188]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(3145,plain,
( ( sk5 @ host )
!= zero ),
inference(simp,[status(thm)],[2911]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m_Down @ elem ) )
& ( ( B @ host )
= ( C @ host ) )
& ( A @ ( B @ m_Halt @ cons ) @ ordered ) )
=> ( C @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_57) ).
thf(415,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(108,plain,
! [B: $i,A: $i] :
( ( B @ host @ ( pendack @ index ) @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( B @ host @ ( pendack @ index ) @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(393,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[392]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[393]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(5138,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk7 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[5081,76]) ).
thf(5139,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk7 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[5138]) ).
thf(5140,plain,
~ ( sk7 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[5139:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(489,plain,
( ( ( sk9 @ host )
!= ( sk6 @ host ) )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[135,126]) ).
thf(493,plain,
( ( sk9 != sk6 )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(992,plain,
sk9 != sk6,
inference(simplifyReflect,[status(thm)],[493,482]) ).
thf(177,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[176]) ).
thf(178,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[177]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ leq ) )
<=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_64) ).
thf(442,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(4237,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,1024]) ).
thf(4238,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4237]) ).
thf(4297,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4238]) ).
thf(4345,plain,
! [A: $i] :
( ( A @ ( sk3 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[4297]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).
thf(369,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(89,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(121,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(122,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[121]) ).
thf(3923,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[137,258]) ).
thf(3924,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[3923:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(705,plain,
( ( ( sk9 @ host )
!= ( sk3 @ host ) )
| ( acks != pendack )
| ( ( sk5 @ host )
!= setEmpty ) ),
inference(paramod_ordered,[status(thm)],[126,703]) ).
thf(708,plain,
( ( sk9 != sk3 )
| ( acks != pendack )
| ( ( sk5 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[705]) ).
thf(15131,plain,
$false,
inference(e,[status(thm)],[69,5437,1024,365,101,8154,2072,479,2921,468,481,2077,582,115,217,2062,8709,120,379,4623,5454,408,5967,385,533,1999,2434,698,3826,142,2918,174,4371,8165,320,2067,5269,3644,184,372,5150,357,3116,2667,110,3821,125,344,4353,4358,8468,4492,5493,8161,216,789,179,4258,376,2451,211,5914,348,353,480,2058,280,132,396,74,206,307,1074,117,942,270,5438,5070,2061,233,452,85,201,5487,220,5049,746,392,424,137,3682,5924,6079,8265,197,324,224,229,7977,252,5492,8270,2433,2100,317,2685,5345,388,356,5081,8530,3784,156,615,256,193,4389,4648,2666,2649,212,2023,5166,3486,2900,129,569,134,343,205,311,2057,398,674,718,2909,953,2662,412,3660,965,425,4613,3607,166,148,180,4365,375,161,3289,975,5933,732,4494,2657,291,4381,204,259,176,1833,191,402,4485,5039,382,144,236,181,350,187,406,113,219,2422,81,76,3182,2065,5491,230,387,367,213,943,198,462,2911,594,140,769,2647,521,399,223,306,135,226,241,658,3490,3522,675,2096,255,2449,2684,553,194,282,414,409,150,2060,1098,310,182,585,4982,5062,175,314,595,497,703,5736,465,7627,482,8260,976,368,2071,2907,517,319,304,258,401,139,4495,418,3780,171,2431,8172,207,1308,2066,478,272,383,2902,1309,5704,82,2421,119,378,151,2374,262,146,405,190,422,5041,3145,210,341,195,2070,2063,283,415,239,242,294,126,136,395,2430,5140,992,822,200,178,442,4345,369,111,227,122,3924,2059,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV466+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/10.42 % Computer : n007.cluster.edu
% 0.14/10.42 % Model : x86_64 x86_64
% 0.14/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.42 % Memory : 8046.5625MB
% 0.14/10.42 % OS : Linux 6.8.0-71-generic
% 0.14/10.42 % CPULimit : 300
% 0.14/10.42 % WCLimit : 300
% 0.14/10.42 % DateTime : Sat Sep 26 13:53:04 UTC 2026
% 0.14/10.43 % CPUTime :
% 0.14/10.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.31/11.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.11/11.66 % [INFO] Parsing done (393ms).
% 2.11/11.68 % [INFO] Running in sequential loop mode.
% 3.26/12.28 % [INFO] eprover registered as external prover.
% 3.26/12.29 % [INFO] Scanning for conjecture ...
% 3.86/12.57 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 4.43/12.71 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 4.43/12.76 % [INFO] Problem is first-order (TPTP FOF).
% 4.43/12.78 % [INFO] Type checking passed.
% 4.43/12.79 % [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 ...
% 104.02/31.61 % External prover 'e' found a proof!
% 104.02/31.61 % [INFO] Killing All external provers ...
% 104.02/31.61 % Time passed: 21003ms (effective reasoning time: 19922ms)
% 104.02/31.61 % 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)>
% 104.02/31.62 % 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
% 104.02/31.62 % No. of inferences in proof: 773
% 104.02/31.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21003 ms resp. 19922 ms w/o parsing
% 107.66/32.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 107.66/32.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------