%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV478+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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:59:33 AM UTC 2026
% Result : Theorem 83.42s 23.26s
% Output : Refutation 81.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 87
% Syntax : Number of formulae : 1023 ( 476 unt; 0 typ; 20 def)
% Number of atoms : 3710 (1894 equ; 0 cnn)
% Maximal formula atoms : 176 ( 3 avg)
% Number of connectives : 14456 (1890 ~;1141 |; 816 &;10291 @)
% ( 13 <=>; 305 =>; 0 <=; 0 <~>)
% Maximal formula depth : 89 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 27 con; 0-4 aty)
% Number of variables : 1917 ( 11 ^;1784 !; 102 ?;1917 :)
% ( 0 !>; 0 ?*; 0 @-; 20 @+)
% Comments :
%------------------------------------------------------------------------------
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Ldr_decl,type,
m_Ldr: $i > $i ).
thf(queue_decl,type,
queue: $i > $i ).
thf(host_decl,type,
host: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(setIn_decl,type,
setIn: $i > $i > $o ).
thf(alive_decl,type,
alive: $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(status_decl,type,
status: $i ).
thf(elec_1_decl,type,
elec_1: $i ).
thf(elec_2_decl,type,
elec_2: $i ).
thf(elid_decl,type,
elid: $i ).
thf(down_decl,type,
down: $i ).
thf(pendack_decl,type,
pendack: $i ).
thf(norm_decl,type,
norm: $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(wait_decl,type,
wait: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(nbr_proc_decl,type,
nbr_proc: $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(acks_decl,type,
acks: $i ).
thf(snoc_decl,type,
snoc: $i > $i > $i ).
thf(m_NotNorm_decl,type,
m_NotNorm: $i > $i ).
thf(m_Halt_decl,type,
m_Halt: $i > $i ).
thf(m_NormQ_decl,type,
m_NormQ: $i > $i ).
thf(pidMsg_decl,type,
pidMsg: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $o ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(nil_decl,type,
nil: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(last_decl,type,
last: $i > $i ).
thf(init_decl,type,
init: $i > $i ).
thf(setEmpty_decl,type,
setEmpty: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(pidElem_decl,type,
pidElem: $i > $o ).
thf(pids_decl,type,
pids: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host )
= ( F @ host @ s ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( F @ setIn ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( G @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( D @ host @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( elid @ index ) @ host )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= wait )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( E = D ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( C @ host @ ( B @ host @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( A @ host @ queue )
= ( sk1 @ ( B @ m_Down @ cons ) ) )
& ( ? [C: $i,D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( C @ host )
= ( E @ host @ s ) )
& ( E @ host @ queue @ ( C @ m_Down @ elem ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( E @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ? [C: $i] :
( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( F @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ ( C @ host @ leq ) )
& ( alive @ ( C @ setIn ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( C @ host @ queue @ ( D @ ( C @ m_Ack ) @ elem ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( elid @ index ) @ host )
= ( D @ host ) )
& ( ( E @ host @ ( status @ index ) )
= wait )
& ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ( ( E @ host )
!= ( D @ host ) ) )
=> ~ ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( alive @ ( D @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ( ( E @ host )
!= ( D @ host ) ) )
=> ~ ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( alive @ ( D @ setIn ) ) ) )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( ( E @ host )
!= ( C @ host ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( ( E @ host )
!= ( C @ host ) ) )
=> ~ ( ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i] :
( ? [D: $i,E: $i] :
( ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( D = C ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( C @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( C @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( C @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i] :
( ( ( alive @ ( C @ setIn ) )
& ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
| ( ( C @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( C @ host @ ( elid @ index ) )
= C ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ( ( D @ host )
!= ( C @ host ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Ldr @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ( ( B @ host @ ( A @ host @ leq ) )
=> ( ( ( ( B @ host )
= ( A @ host @ ( pendack @ index ) ) )
& ( ( A @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( A @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [C: $i] :
( ( A @ host @ ( acks @ index ) @ ( C @ host @ setIn ) )
=> ! [D: $i] :
( ( ( A @ host )
= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( A @ host )
!= ( G @ host ) )
=> ( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( G @ host @ s ) )
& ( A @ m_Ldr @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( A @ m_Ldr @ ( G @ host @ queue @ snoc ) @ ( E @ m_Down @ elem ) )
& ( G @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( ( A @ host )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( ( sk2 @ host @ queue )
= ( sk1 @ ( A @ m_Down @ cons ) ) )
& ( ? [B: $i,C: $i,D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_1 )
& ( ( B @ host )
= ( D @ host @ s ) )
& ( D @ host @ queue @ ( B @ m_Down @ elem ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( D @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( D @ host @ leq ) ) )
=> ( ( E
= ( C @ host ) )
| ( D @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ~ ? [B: $i] :
( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host )
= ( E @ host ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( E @ host @ ( B @ host @ leq ) )
& ( alive @ ( B @ setIn ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ( B @ host @ queue @ ( C @ ( B @ m_Ack ) @ elem ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( elid @ index ) @ host )
= ( C @ host ) )
& ( ( D @ host @ ( status @ index ) )
= wait )
& ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( B @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ( ( D @ host )
!= ( C @ host ) ) )
=> ~ ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( alive @ ( C @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( B @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ( ( D @ host )
!= ( C @ host ) ) )
=> ~ ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( alive @ ( C @ setIn ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ( ( D @ host )
!= ( B @ host ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ( ( D @ host )
!= ( B @ host ) ) )
=> ~ ( ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i] :
( ? [C: $i,D: $i] :
( ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( C = B ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( C @ host )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( B @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( B @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( ( B @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( B @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i] :
( ( ( alive @ ( B @ setIn ) )
& ( ( ( B @ host @ ( status @ index ) )
= elec_2 )
| ( ( B @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( B @ host @ ( elid @ index ) )
= B ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ( ( C @ host )
!= ( B @ host ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Ldr @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) ) )
=> ( ( alive @ ( sk2 @ setIn ) )
=> ( ( A @ host @ ( sk2 @ host @ leq ) )
=> ( ( ( ( A @ host )
= ( sk2 @ host @ ( pendack @ index ) ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [B: $i] :
( ( sk2 @ host @ ( acks @ index ) @ ( B @ host @ setIn ) )
=> ! [C: $i] :
( ( ( sk2 @ host )
= ( C @ host ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( B @ host )
= ( F @ host ) )
=> ( ( ( sk2 @ host )
!= ( F @ host ) )
=> ( ( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host )
= ( F @ host @ s ) )
& ( sk2 @ m_Ldr @ ( F @ host @ queue @ snoc ) @ ( E @ m_Down @ elem ) )
& ( sk2 @ m_Ldr @ ( F @ host @ queue @ snoc ) @ ( D @ m_Down @ elem ) )
& ( F @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( F @ setIn ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( A @ host @ leq ) ) )
=> ( ( E
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( A @ host @ leq ) ) )
=> ( ( D
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( sk2 @ host @ ( acks @ index ) @ ( A @ host @ setIn ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
= ( B @ host ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ host )
= ( E @ host ) )
=> ( ( ( sk2 @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( C @ host )
= ( E @ host @ s ) )
& ( sk2 @ m_Ldr @ ( E @ host @ queue @ snoc ) @ ( D @ m_Down @ elem ) )
& ( sk2 @ m_Ldr @ ( E @ host @ queue @ snoc ) @ ( C @ m_Down @ elem ) )
& ( E @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
= ( A @ host ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( sk6 @ host )
= ( D @ host ) )
=> ( ( ( sk2 @ host )
!= ( D @ host ) )
=> ( ( ( ( D @ host @ ( status @ index ) )
= elec_1 )
& ( ( B @ host )
= ( D @ host @ s ) )
& ( sk2 @ m_Ldr @ ( D @ host @ queue @ snoc ) @ ( C @ m_Down @ elem ) )
& ( sk2 @ m_Ldr @ ( D @ host @ queue @ snoc ) @ ( B @ m_Down @ elem ) )
& ( D @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( D @ host @ leq ) ) )
=> ( ( E
= ( C @ host ) )
| ( D @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( A @ host ) )
& ( alive @ ( A @ setIn ) ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk6 @ host )
= ( C @ host ) )
=> ( ( ( sk2 @ host )
!= ( C @ host ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ( ( A @ host )
= ( C @ host @ s ) )
& ( sk2 @ m_Ldr @ ( C @ host @ queue @ snoc ) @ ( B @ m_Down @ elem ) )
& ( sk2 @ m_Ldr @ ( C @ host @ queue @ snoc ) @ ( A @ m_Down @ elem ) )
& ( C @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( C @ setIn ) )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( C @ host @ leq ) ) )
=> ( ( D
= ( B @ host ) )
| ( C @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk6 @ host )
= ( B @ host ) )
=> ( ( ( sk2 @ host )
!= ( B @ host ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk8 @ host )
= ( B @ host @ s ) )
& ( sk2 @ m_Ldr @ ( B @ host @ queue @ snoc ) @ ( A @ m_Down @ elem ) )
& ( sk2 @ m_Ldr @ ( B @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
& ( B @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( B @ setIn ) )
& ! [C: $i] :
( ( ( C @ ( zero @ s @ leq ) )
& ~ ( C @ ( B @ host @ leq ) ) )
=> ( ( C
= ( A @ host ) )
| ( B @ host @ ( down @ index ) @ ( C @ setIn ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( ( sk6 @ host )
= ( A @ host ) )
=> ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk8 @ host )
= ( A @ host @ s ) )
& ( sk2 @ m_Ldr @ ( A @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ) )
& ( sk2 @ m_Ldr @ ( A @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
& ( A @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( A @ setIn ) )
& ! [B: $i] :
( ( ( B @ ( zero @ s @ leq ) )
& ~ ( B @ ( A @ host @ leq ) ) )
=> ( ( B
= ( sk9 @ host ) )
| ( A @ host @ ( down @ index ) @ ( B @ setIn ) ) ) ) )
=> ~ ( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( ( C @ pidMsg @ host )
= ( B @ pidMsg @ host ) )
& ( C @ pidElem )
& ( B @ pidElem )
& ( A @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( B @ pidMsg @ leq ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( H @ host @ queue @ ( F @ m_Down @ elem ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( H @ host ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( E @ host @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( elid @ index ) @ host )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= wait )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( G @ host @ ( F @ host @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( G @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( G @ host ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( I @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) )
& ! [J: $i] :
( ( ( J @ ( zero @ s @ leq ) )
& ~ ( J @ ( I @ host @ leq ) ) )
=> ( ( J
= ( H @ host ) )
| ( I @ host @ ( down @ index ) @ ( J @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( H @ host @ queue @ ( F @ m_Down @ elem ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( H @ host ) )
& ( H @ host @ queue @ ( G @ m_Down @ elem ) )
& ( H @ host @ ( E @ host @ leq ) )
& ( alive @ ( E @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( elid @ index ) @ host )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= wait )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( ( G @ host )
!= ( F @ host ) ) )
=> ~ ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ~ ( G @ host @ ( F @ host @ leq ) ) )
=> ~ ( ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( ldr @ index ) )
= ( G @ host ) )
& ( ( G @ host @ ( status @ index ) )
= norm )
& ( ( F @ host )
= ( G @ host ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Ldr @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( D @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( C @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( C @ host @ ( acks @ index ) @ ( E @ host @ setIn ) )
=> ! [F: $i] :
( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( E @ host )
= ( I @ host ) )
=> ( ( ( C @ host )
!= ( I @ host ) )
=> ( ( ( ( I @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= ( I @ host @ s ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( C @ m_Ldr @ ( I @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( I @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( I @ setIn ) )
& ! [J: $i] :
( ( ( J @ ( zero @ s @ leq ) )
& ~ ( J @ ( I @ host @ leq ) ) )
=> ( ( J
= ( H @ host ) )
| ( I @ host @ ( down @ index ) @ ( J @ setIn ) ) ) ) )
=> ~ ( ( ( C @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= ( G @ host @ s ) )
& ( G @ host @ queue @ ( E @ m_Down @ elem ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( G @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( D @ host @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( elid @ index ) @ host )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= wait )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( E = D ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( C @ host @ ( B @ host @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host )
= ( F @ host @ s ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( F @ setIn ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( G @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( D @ host @ leq ) )
& ( alive @ ( D @ setIn ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( elid @ index ) @ host )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= wait )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( ( F @ host )
!= ( E @ host ) ) )
=> ~ ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( E = D ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( ldr @ index ) )
= ( F @ host ) )
& ( ( F @ host @ ( status @ index ) )
= norm )
& ( ( E @ host )
= ( F @ host ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( ldr @ index ) )
= ( E @ host ) )
& ( ( E @ host @ ( status @ index ) )
= norm )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( C @ host @ ( B @ host @ leq ) )
=> ( ( ( ( C @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 ) )
=> ( ( B @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( B @ host @ ( acks @ index ) @ ( D @ host @ setIn ) )
=> ! [E: $i] :
( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( D @ host )
= ( H @ host ) )
=> ( ( ( B @ host )
!= ( H @ host ) )
=> ( ( ( ( H @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= ( H @ host @ s ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( B @ m_Ldr @ ( H @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( H @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( H @ setIn ) )
& ! [I: $i] :
( ( ( I @ ( zero @ s @ leq ) )
& ~ ( I @ ( H @ host @ leq ) ) )
=> ( ( I
= ( G @ host ) )
| ( H @ host @ ( down @ index ) @ ( I @ setIn ) ) ) ) )
=> ~ ( ( ( B @ host )
= ( E @ host ) )
& ( alive @ ( E @ setIn ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(71,plain,
! [ZS: $i,ZR: $i,ZQ: $i,ZP: $i,ZO: $i,ZN: $i,ZM: $i,ZL: $i,ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( alive @ ( sk7 @ setIn ) )
& ( ( sk10 @ host @ ( status @ index ) )
= elec_1 )
& ( ( sk8 @ host )
= ( sk10 @ host @ s ) )
& ( sk2 @ m_Ldr @ ( sk10 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ) )
& ( sk2 @ m_Ldr @ ( sk10 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
& ( sk10 @ host @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( sk10 @ setIn ) )
& ( ( ZS
= ( sk9 @ host ) )
| ( sk10 @ host @ ( down @ index ) @ ( ZS @ setIn ) )
| ~ ( ZS @ ( zero @ s @ leq ) )
| ( ZS @ ( sk10 @ host @ leq ) ) )
& ( ( sk2 @ host )
!= ( sk10 @ host ) )
& ( ( sk6 @ host )
= ( sk10 @ host ) )
& ( ( sk2 @ host )
= ( sk7 @ host ) )
& ( sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ) )
& ( sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ) )
& ( ( sk3 @ host )
= ( sk2 @ host @ ( pendack @ index ) ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_2 )
& ( sk3 @ host @ ( sk2 @ host @ leq ) )
& ( alive @ ( sk2 @ setIn ) )
& ( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ( ( ZO @ ( ZP @ ( ZQ @ sk5 ) ) )
!= ( ZP @ host ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ~ ( ZQ @ host @ ( down @ index ) @ ( ZO @ ( ZP @ ( ZQ @ sk5 ) ) @ setIn ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ( ZO @ ( ZP @ ( ZQ @ sk5 ) ) @ ( zero @ s @ leq ) ) )
& ( ( ( ZR @ host @ ( status @ index ) )
!= norm )
| ( ( ZR @ host @ ( ldr @ index ) )
!= ( ZR @ host ) )
| ~ ( alive @ ( ZR @ setIn ) )
| ( ( ZQ @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZO @ host )
!= ( ZQ @ host @ s ) )
| ~ ( ZQ @ host @ queue @ ( ZO @ m_Down @ elem ) )
| ~ ( ZQ @ host @ queue @ ( ZP @ m_Down @ elem ) )
| ~ ( ZQ @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( ZQ @ setIn ) )
| ~ ( ZO @ ( ZP @ ( ZQ @ sk5 ) ) @ ( ZQ @ host @ leq ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ( ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk4 ) ) ) )
!= ( ZM @ host ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ~ ( ZN @ host @ ( down @ index ) @ ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk4 ) ) ) @ setIn ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk4 ) ) ) @ ( zero @ s @ leq ) ) )
& ( ~ ( ZK @ host @ queue @ ( ZL @ ( ZK @ m_Ack ) @ elem ) )
| ( ( ZN @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZK @ host @ ( status @ index ) )
!= elec_2 )
| ( ( ZL @ host )
!= ( ZN @ host ) )
| ~ ( ZN @ host @ queue @ ( ZM @ m_Down @ elem ) )
| ~ ( ZN @ host @ ( ZK @ host @ leq ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ~ ( ZK @ ( ZL @ ( ZM @ ( ZN @ sk4 ) ) ) @ ( ZN @ host @ leq ) ) )
& ( ( ( ZI @ host @ ( ldr @ index ) )
!= ( ZI @ host ) )
| ( ( ZI @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( ZI @ setIn ) )
| ( ( ZJ @ host @ ( elid @ index ) @ host )
!= ( ZI @ host ) )
| ( ( ZJ @ host @ ( status @ index ) )
!= wait )
| ( ( ZI @ host )
!= ( ZH @ host ) )
| ~ ( ZJ @ host @ queue @ ( ZH @ m_Down @ elem ) )
| ~ ( alive @ ( ZJ @ setIn ) )
| ( ( ZJ @ host )
= ( ZI @ host ) ) )
& ( ( ( ZF @ host @ ( ldr @ index ) )
!= ( ZF @ host ) )
| ( ( ZF @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( ZF @ setIn ) )
| ( ( ZG @ host @ ( ldr @ index ) )
!= ( ZF @ host ) )
| ( ( ZG @ host @ ( status @ index ) )
!= norm )
| ( ( ZF @ host )
!= ( ZE @ host ) )
| ~ ( ZG @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZG @ setIn ) )
| ( ( ZG @ host )
= ( ZF @ host ) ) )
& ( ~ ( ZC @ host @ ( down @ index ) @ ( ZB @ host @ setIn ) )
| ~ ( ZA @ host @ queue @ ( ZD @ m_Down @ elem ) )
| ( ( ZD @ host )
!= ( ZC @ host ) )
| ( ( ZB @ host )
!= ( ZA @ host ) )
| ~ ( alive @ ( ZC @ setIn ) )
| ~ ( alive @ ( ZA @ setIn ) )
| ( ( ZC @ host )
= ( ZA @ host ) ) )
& ( ~ ( Y @ host @ queue @ ( X @ m_Down @ elem ) )
| ~ ( W @ host @ queue @ ( Z @ m_Down @ elem ) )
| ( ( Z @ host )
!= ( Y @ host ) )
| ( ( X @ host )
!= ( W @ host ) )
| ~ ( alive @ ( Y @ setIn ) )
| ~ ( alive @ ( W @ setIn ) )
| ( ( Y @ host )
= ( W @ host ) ) )
& ( ( ( T @ host @ ( status @ index ) )
!= norm )
| ( ( T @ host @ ( ldr @ index ) )
!= ( T @ host ) )
| ~ ( alive @ ( T @ setIn ) )
| ( ( U @ host )
!= ( T @ host ) )
| ~ ( V @ host @ queue @ ( U @ m_Down @ elem ) )
| ~ ( alive @ ( V @ setIn ) )
| ( V @ host @ ( U @ host @ leq ) ) )
& ( ( S = R )
| ( ( S @ host @ ( ldr @ index ) )
!= ( S @ host ) )
| ( ( S @ host @ ( status @ index ) )
!= norm )
| ( ( R @ host @ ( status @ index ) )
!= norm )
| ( ( R @ host @ ( ldr @ index ) )
!= ( R @ host ) )
| ~ ( alive @ ( S @ setIn ) )
| ~ ( alive @ ( R @ setIn ) ) )
& ( ~ ( O @ host @ queue @ ( P @ m_Down @ elem ) )
| ~ ( alive @ ( O @ setIn ) )
| ( ( Q @ host @ ( ldr @ index ) )
!= ( Q @ host ) )
| ( ( Q @ host @ ( status @ index ) )
!= norm )
| ( ( P @ host )
!= ( Q @ host ) )
| ~ ( alive @ ( Q @ setIn ) ) )
& ( ( L @ host @ ( N @ host @ ( pendack @ index ) @ leq ) )
| ( ( N @ host @ ( status @ index ) )
!= elec_2 )
| ( ( N @ host )
!= ( M @ host ) )
| ~ ( L @ host @ queue @ ( M @ m_Down @ elem ) )
| ~ ( alive @ ( N @ setIn ) )
| ~ ( alive @ ( L @ setIn ) ) )
& ( ~ ( J @ host @ ( down @ index ) @ ( K @ host @ setIn ) )
| ~ ( alive @ ( J @ setIn ) )
| ( ( K @ host @ ( ldr @ index ) )
!= ( K @ host ) )
| ( ( K @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( K @ setIn ) ) )
& ( ( H @ host @ ( I @ host @ ( pendack @ index ) @ leq ) )
| ( ( I @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( H @ host @ ( down @ index ) @ ( I @ host @ setIn ) )
| ~ ( alive @ ( I @ setIn ) )
| ~ ( alive @ ( H @ setIn ) ) )
& ( ( ( G @ host @ ( elid @ index ) )
= G )
| ~ ( alive @ ( G @ setIn ) )
| ( ( G @ host @ ( status @ index ) )
!= elec_2 ) )
& ( ( ( G @ host @ ( elid @ index ) )
= G )
| ~ ( alive @ ( G @ setIn ) )
| ( ( G @ host @ ( status @ index ) )
!= elec_1 ) )
& ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) )
| ( ( F @ host )
!= ( E @ host ) )
| ( F = E ) )
& ( ( ( D @ host )
!= ( C @ host ) )
| ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(96,plain,
( ( sk2 @ host )
= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(137,plain,
( ( sk7 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(84,plain,
( ( sk8 @ host )
= ( sk10 @ host @ s ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(124,plain,
( ( sk10 @ host @ s )
= ( sk8 @ host ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(88,plain,
( ( sk6 @ host )
= ( sk10 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(120,plain,
( ( sk10 @ host )
= ( sk6 @ host ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(531,plain,
( ( sk6 @ host @ s )
= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[124,120]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).
thf(421,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(422,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[421]) ).
thf(423,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[422]) ).
thf(1913,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk8 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[531,423]) ).
thf(1914,plain,
~ ( sk6 @ host @ ( sk8 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[1913:[bind(A,$thf( sk6 @ host ))]]) ).
thf(1987,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ~ ( sk6 @ host @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[137,1914]) ).
thf(2031,plain,
( ( sk8 != sk7 )
| ~ ( sk6 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[1987]) ).
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(468,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(18,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_02) ).
thf(234,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(481,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
thf(330,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(331,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[330]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[331]) ).
thf(333,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[332]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(249,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(235,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[234]) ).
thf(1925,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,423]) ).
thf(1926,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1925]) ).
thf(1941,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1926]) ).
thf(1956,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1941]) ).
thf(112,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(115,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[112]) ).
thf(97,plain,
( ( sk3 @ host )
= ( sk2 @ host @ ( pendack @ index ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(133,plain,
( ( sk2 @ host @ ( pendack @ index ) )
= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(580,plain,
( ( ( sk2 @ host @ ( pendack @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[115,133]) ).
thf(583,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( pendack != status )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[580]) ).
thf(588,plain,
( ( pendack != status )
| ( ( sk3 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[583]) ).
thf(20,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_04) ).
thf(240,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(241,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[240]) ).
thf(730,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,241]) ).
thf(731,plain,
( ( nbr_proc @ ( elec_2 @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[730:[bind(A,$thf( sk3 ))]]) ).
thf(1923,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[731,423]) ).
thf(1924,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1923]) ).
thf(1935,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1924]) ).
thf(1950,plain,
( ( ( nbr_proc @ s )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1935]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(168,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[167]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[168]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(12,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
thf(216,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(217,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[216]) ).
thf(2897,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[137,1956]) ).
thf(2898,plain,
( ( sk2 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[2897:[bind(A,$thf( sk7 ))]]) ).
thf(3230,plain,
( ( sk2 @ host )
!= zero ),
inference(simp,[status(thm)],[2898]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).
thf(302,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) ) )
& ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(303,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) ) )
& ! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[302]) ).
thf(304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ leq ) )
| ( C != D ) )
& ( ( D @ ( C @ leq ) )
| ( C != D ) )
& ( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[303]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[304]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(63,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_45) ).
thf(438,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(439,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[438]) ).
thf(440,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[439]) ).
thf(95,plain,
sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(636,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( sk6 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[115,95]) ).
thf(645,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != status )
| ( elec_2 @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[636]) ).
thf(651,plain,
( ( acks != status )
| ( elec_2 @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(1489,plain,
( ( ( elec_2 @ ( sk6 @ host @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true
| ( acks != status ) ),
inference(paramod_ordered,[status(thm)],[651,217]) ).
thf(1490,plain,
( ( ( elec_2 @ ( sk6 @ host @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ( acks != status ) ),
inference(simp,[status(thm)],[1489]) ).
thf(1533,plain,
( ( elec_2 != alive )
| ( ( sk6 @ host )
!= nil )
| ( acks != status ) ),
inference(simp,[status(thm)],[1490]) ).
thf(86,plain,
sk3 @ host @ ( sk2 @ host @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(612,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[86,92]) ).
thf(613,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[612]) ).
thf(614,plain,
~ ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[613:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).
thf(376,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( B @ ( C @ snoc ) @ ( A @ elem ) ) )
& ( ( B @ ( C @ snoc ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(377,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)],[376]) ).
thf(378,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)],[377]) ).
thf(380,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[378]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[380]) ).
thf(384,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[383]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(7214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ~ $true
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(paramod_ordered,[status(thm)],[384,139]) ).
thf(7215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[7214]) ).
thf(7262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( C @ host @ queue ) )
| ( A
!= ( D @ m_Down ) )
| ( D != C ) ),
inference(simp,[status(thm)],[7215]) ).
thf(7322,plain,
! [B: $i,A: $i] :
( ( B @ m_Down @ ( A @ snoc ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[7262]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_63) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( ( B @ s @ ( A @ s @ leq ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( B @ s @ ( A @ s @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(266,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)],[265]) ).
thf(267,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)],[266]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[267]) ).
thf(18543,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,268]) ).
thf(18544,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[18543]) ).
thf(18545,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[18544:[bind(A,$thf( E )),bind(B,$thf( zero @ s )),bind(C,$thf( E @ host ))]]) ).
thf(18615,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(simp,[status(thm)],[18545]) ).
thf(29676,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ host @ s ) )
| ( sk8 @ host @ ( zero @ s @ s @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[531,18615]) ).
thf(29677,plain,
sk8 @ host @ ( zero @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[29676:[bind(A,$thf( sk6 ))]]) ).
thf(77,plain,
( ( sk10 @ host @ ( status @ index ) )
= elec_1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(136,plain,
( ( sk10 @ host @ ( status @ index ) )
= elec_1 ),
inference(lifteq,[status(thm)],[77]) ).
thf(550,plain,
( ( sk6 @ host @ ( status @ index ) )
= elec_1 ),
inference(rewrite,[status(thm)],[136,120]) ).
thf(55,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(411,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(412,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[411]) ).
thf(413,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[412]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).
thf(388,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(7170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,440]) ).
thf(7171,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[7170]) ).
thf(7249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[7171]) ).
thf(7309,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[7249]) ).
thf(17504,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ cons ) @ snoc ) )
!= ( E @ ( D @ snoc ) ) )
| ( ( B @ ( C @ snoc ) @ ( A @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[390,7309]) ).
thf(17505,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ snoc ) @ ( B @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[17504:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ cons ) )),bind(E,$thf( B ))]]) ).
thf(17554,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ snoc ) @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[17505]) ).
thf(17580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( D @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) @ ( C @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[413,17554]) ).
thf(17581,plain,
! [B: $i,A: $i] :
( ( q_nil @ ( A @ cons ) @ ( B @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[17580:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( q_nil ))]]) ).
thf(17594,plain,
! [B: $i,A: $i] :
( ( q_nil @ ( A @ cons ) @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[17581]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).
thf(281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(282,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[281]) ).
thf(283,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ cons ) @ ( D @ elem ) )
| ~ ( F @ ( D @ elem ) ) )
& ( ( F @ ( E @ cons ) @ ( D @ elem ) )
| ( D != E ) )
& ( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ) ),
inference(cnf,[status(esa)],[282]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[283]) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[285]) ).
thf(289,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[288]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[304]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(310,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[309]) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[310,92]) ).
thf(947,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)],[946]) ).
thf(948,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[947:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(949,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(simp,[status(thm)],[948]) ).
thf(3746,plain,
! [A: $i] :
( ( ( sk10 @ host )
!= ( A @ host ) )
| ~ ( sk6 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[120,949]) ).
thf(3747,plain,
~ ( sk6 @ host @ queue @ ( sk10 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[3746:[bind(A,$thf( sk10 ))]]) ).
thf(6874,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,3747]) ).
thf(6875,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[6874]) ).
thf(6946,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk10 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[6875]) ).
thf(6996,plain,
! [A: $i] :
( ( A @ ( sk10 @ m_Ldr @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[6946]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( B @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(3274,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( B != A ) ),
inference(simp,[status(thm)],[139]) ).
thf(3319,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(simp,[status(thm)],[3274]) ).
thf(4077,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[137,3319]) ).
thf(4078,plain,
~ ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[4077:[bind(A,$thf( sk7 ))]]) ).
thf(7212,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,4078]) ).
thf(7213,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7212]) ).
thf(7228,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Down ) ) ),
inference(simp,[status(thm)],[7213]) ).
thf(7288,plain,
! [A: $i] :
( ( sk7 @ m_Down @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7228]) ).
thf(9773,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk7 @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,7288]) ).
thf(9774,plain,
( ( q_nil @ ( sk7 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[9773:[bind(A,$thf( sk7 @ m_Down )),bind(B,$thf( q_nil ))]]) ).
thf(18510,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,268]) ).
thf(18511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[18510]) ).
thf(18512,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[18511:[bind(A,$thf( D )),bind(B,$thf( D @ host )),bind(C,$thf( nbr_proc ))]]) ).
thf(18611,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(simp,[status(thm)],[18512]) ).
thf(27357,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18611,423]) ).
thf(27358,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[27357]) ).
thf(27423,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s )
!= B )
| ( ( A @ host @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[27358]) ).
thf(27440,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[27423]) ).
thf(28195,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s )
!= ( sk2 @ host @ s ) ) ),
inference(paramod_ordered,[status(thm)],[137,27440]) ).
thf(28196,plain,
( ( nbr_proc @ s @ s )
!= ( sk2 @ host @ s ) ),
inference(pattern_uni,[status(thm)],[28195:[bind(A,$thf( sk7 ))]]) ).
thf(90,plain,
sk2 @ host @ ( pendack @ index ) @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(575,plain,
sk3 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[90,133]) ).
thf(1931,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,423]) ).
thf(1932,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[1931]) ).
thf(1938,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1932]) ).
thf(1953,plain,
( ( sk3 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[1938]) ).
thf(1967,plain,
( ( ( sk6 @ host @ s )
!= ( sk3 @ host @ s ) )
| ( ( sk8 @ host )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[531,1953]) ).
thf(1972,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( ( sk8 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1967]) ).
thf(17375,plain,
( ( sk6 != sk3 )
| ( ( sk8 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1972]) ).
thf(673,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( elec_2 @ ( sk2 @ host @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,86]) ).
thf(674,plain,
( ( elec_2 @ ( sk2 @ host @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[673:[]]) ).
thf(1905,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( sk2 @ host @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[674,423]) ).
thf(1906,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( sk2 @ host @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1905]) ).
thf(1939,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= ( sk2 @ host ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1906]) ).
thf(1954,plain,
( ( ( elec_2 @ s )
!= ( sk2 @ host ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1939]) ).
thf(20569,plain,
( ( ( sk6 @ host @ ( sk2 @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ( sk8 != sk7 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,2031]) ).
thf(20570,plain,
( ( ( sk6 @ host @ ( sk2 @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[20569]) ).
thf(20622,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[20570]) ).
thf(20662,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[20622]) ).
thf(93,plain,
sk10 @ host @ s @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(522,plain,
sk6 @ host @ s @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[93,120]) ).
thf(532,plain,
sk8 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[522,531]) ).
thf(18552,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[532,268]) ).
thf(18553,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18552]) ).
thf(18554,plain,
sk8 @ host @ s @ ( nbr_proc @ s @ leq ),
inference(pattern_uni,[status(thm)],[18553:[bind(A,$thf( nbr_proc )),bind(B,$thf( sk8 @ host ))]]) ).
thf(18762,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18554,423]) ).
thf(18763,plain,
! [A: $i] :
( ( sk8 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18762]) ).
thf(18811,plain,
! [A: $i] :
( ( ( sk8 @ host @ s )
!= A )
| ( ( nbr_proc @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[18763]) ).
thf(18834,plain,
( ( sk8 @ host @ s @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[18811]) ).
thf(107,plain,
sk2 @ m_Ldr @ ( sk10 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(693,plain,
sk2 @ m_Ldr @ ( sk6 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ),
inference(rewrite,[status(thm)],[107,120]) ).
thf(697,plain,
! [A: $i] :
( ( ( sk2 @ m_Ldr @ ( sk6 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[693,440]) ).
thf(698,plain,
! [A: $i] :
( ( sk2 @ m_Ldr @ ( sk6 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[697]) ).
thf(703,plain,
! [A: $i] :
( ( ( sk2 @ m_Ldr @ ( sk6 @ host @ queue @ snoc ) )
!= q_nil )
| ( ( sk8 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[698]) ).
thf(709,plain,
( ( sk2 @ m_Ldr @ ( sk6 @ host @ queue @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[703]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
thf(417,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(7196,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,3747]) ).
thf(7197,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7196]) ).
thf(7266,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk10 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7197]) ).
thf(7326,plain,
! [A: $i] :
( ( sk10 @ m_Ldr @ ( A @ snoc ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[7266]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ pidElem )
<=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).
thf(291,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) )
=> ( A @ pidElem ) )
& ( ( A @ pidElem )
=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(292,plain,
( ! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ m_Down ) )
| ? [B: $i] :
( A
= ( B @ m_Halt ) ) )
=> ( A @ pidElem ) )
& ! [A: $i] :
( ( A @ pidElem )
=> ( ? [B: $i] :
( A
= ( B @ m_Down ) )
| ? [B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ),
inference(miniscope,[status(thm)],[291]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk17 @ m_Down ) )
| ( A
= ( A @ sk16 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[292]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(301,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[300]) ).
thf(94,plain,
( ( sk2 @ host )
!= ( sk10 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(162,plain,
( ( sk10 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(497,plain,
sk10 != sk2,
inference(simp,[status(thm)],[162]) ).
thf(33480,plain,
! [B: $i,A: $i] :
( ( A != sk10 )
| ( B != sk2 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[308,497]) ).
thf(33481,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk10 @ ( A @ leq ) )
| ~ ( A @ ( sk10 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[33480:[bind(A,$thf( sk10 ))]]) ).
thf(34975,plain,
( ~ ( sk10 @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( sk10 @ leq ) ) ),
inference(simp,[status(thm)],[33481]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).
thf(386,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[386]) ).
thf(13164,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ~ $true
| ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[387,423]) ).
thf(13165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[13164]) ).
thf(13166,plain,
! [A: $i] : ( A @ s @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[13165:[bind(A,$thf( A )),bind(B,$thf( A @ s )),bind(C,$thf( A ))]]) ).
thf(13400,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13166,423]) ).
thf(13401,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[13400]) ).
thf(13422,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[13401]) ).
thf(13447,plain,
! [A: $i] :
( ( A @ s @ s )
!= A ),
inference(simp,[status(thm)],[13422]) ).
thf(3750,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[137,949]) ).
thf(3751,plain,
~ ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[3750:[bind(A,$thf( sk7 ))]]) ).
thf(7194,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,3751]) ).
thf(7195,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7194]) ).
thf(7280,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7195]) ).
thf(7340,plain,
! [A: $i] :
( ( sk7 @ m_Ldr @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7280]) ).
thf(11150,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk7 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,7340]) ).
thf(11151,plain,
( ( q_nil @ ( sk7 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[11150:[bind(A,$thf( sk7 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(13,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_03) ).
thf(218,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18532,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,268]) ).
thf(18533,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18532]) ).
thf(18534,plain,
nbr_proc @ s @ ( zero @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[18533:[bind(A,$thf( zero @ s )),bind(B,$thf( nbr_proc ))]]) ).
thf(18655,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18534,423]) ).
thf(18656,plain,
! [A: $i] :
( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18655]) ).
thf(18681,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= A )
| ( ( zero @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[18656]) ).
thf(18717,plain,
( ( nbr_proc @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[18681]) ).
thf(10350,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk10 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,7326]) ).
thf(10351,plain,
( ( q_nil @ ( sk10 @ m_Ldr @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[10350:[bind(A,$thf( sk10 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(53,axiom,
norm != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(404,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(106,plain,
( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(123,plain,
( ( sk1 @ ( sk3 @ m_Down @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).
thf(224,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[224]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[225]) ).
thf(3349,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[123,226]) ).
thf(3350,plain,
( ( sk2 @ host @ queue @ head )
= ( sk3 @ m_Down ) ),
inference(pattern_uni,[status(thm)],[3349:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(29863,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29677,268]) ).
thf(29864,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[29863]) ).
thf(29865,plain,
sk8 @ host @ s @ ( zero @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[29864:[bind(A,$thf( zero @ s @ s )),bind(B,$thf( sk8 @ host ))]]) ).
thf(36739,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29865,268]) ).
thf(36740,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[36739]) ).
thf(36741,plain,
sk8 @ host @ s @ s @ ( zero @ s @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[36740:[bind(A,$thf( zero @ s @ s @ s )),bind(B,$thf( sk8 @ host @ s ))]]) ).
thf(39067,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36741,423]) ).
thf(39068,plain,
! [A: $i] :
( ( sk8 @ host @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[39067]) ).
thf(39172,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ s )
!= A )
| ( ( zero @ s @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[39068]) ).
thf(39192,plain,
( ( zero @ s @ s @ s @ s )
!= ( sk8 @ host @ s @ s @ s ) ),
inference(simp,[status(thm)],[39172]) ).
thf(91,plain,
! [A: $i] :
( ( A
= ( sk9 @ host ) )
| ( sk10 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk10 @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(150,plain,
! [A: $i] :
( ( sk10 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk10 @ host @ leq ) )
| ( A
= ( sk9 @ host ) ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(151,plain,
! [A: $i] :
( ( sk10 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk10 @ host @ leq ) )
| ( A
= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(7914,plain,
! [A: $i] :
( ( sk6 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk6 @ host @ leq ) )
| ( A
= ( sk9 @ host ) ) ),
inference(rewrite,[status(thm)],[151,120]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(372,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(110,plain,
alive @ ( sk10 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(6884,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[123,289]) ).
thf(6885,plain,
sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[6884:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(7084,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)],[6885,139]) ).
thf(7085,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[7084]) ).
thf(7086,plain,
( ( sk3 @ host )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[7085:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(7148,plain,
( ( ( sk7 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[137,7086]) ).
thf(7149,plain,
( ( sk7 @ host )
!= ( sk3 @ host ) ),
inference(simp,[status(thm)],[7148]) ).
thf(7159,plain,
sk7 != sk3,
inference(simp,[status(thm)],[7149]) ).
thf(33210,plain,
! [B: $i,A: $i] :
( ( A != sk7 )
| ( B != sk3 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[308,7159]) ).
thf(33211,plain,
! [A: $i] :
( ( A != sk3 )
| ~ ( sk7 @ ( A @ leq ) )
| ~ ( A @ ( sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[33210:[bind(A,$thf( sk7 ))]]) ).
thf(34854,plain,
( ~ ( sk7 @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( sk7 @ leq ) ) ),
inference(simp,[status(thm)],[33211]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( B @ setIn ) )
| ( ( C @ host @ ( elid @ index ) @ host )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= wait )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( elid @ index ) @ host )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= wait )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( C @ host @ ( elid @ index ) @ host )
!= ( B @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= wait )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( B @ host ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(35,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).
thf(323,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(324,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[323]) ).
thf(325,plain,
! [A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[324]) ).
thf(27367,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ host @ s ) )
| ( nbr_proc @ s @ ( sk8 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[531,18611]) ).
thf(27368,plain,
nbr_proc @ s @ ( sk8 @ host @ leq ),
inference(pattern_uni,[status(thm)],[27367:[bind(A,$thf( sk6 ))]]) ).
thf(27533,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( sk8 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27368,268]) ).
thf(27534,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( sk8 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[27533]) ).
thf(27535,plain,
nbr_proc @ s @ s @ ( sk8 @ host @ s @ leq ),
inference(pattern_uni,[status(thm)],[27534:[bind(A,$thf( sk8 @ host )),bind(B,$thf( nbr_proc @ s ))]]) ).
thf(28019,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk8 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27535,268]) ).
thf(28020,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk8 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[28019]) ).
thf(28021,plain,
nbr_proc @ s @ s @ s @ ( sk8 @ host @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[28020:[bind(A,$thf( sk8 @ host @ s )),bind(B,$thf( nbr_proc @ s @ s ))]]) ).
thf(28427,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( sk8 @ host @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28021,268]) ).
thf(28428,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( sk8 @ host @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[28427]) ).
thf(28429,plain,
nbr_proc @ s @ s @ s @ s @ ( sk8 @ host @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[28428:[bind(A,$thf( sk8 @ host @ s @ s )),bind(B,$thf( nbr_proc @ s @ s @ s ))]]) ).
thf(1919,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,423]) ).
thf(1920,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[1919]) ).
thf(1948,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[1920]) ).
thf(1963,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1948]) ).
thf(1909,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,423]) ).
thf(1910,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[1909]) ).
thf(1949,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[1910]) ).
thf(1964,plain,
( ( sk3 @ host @ s )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[1949]) ).
thf(2755,plain,
( ( ( sk6 @ host @ s )
!= ( sk3 @ host @ s ) )
| ( ( sk8 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[531,1964]) ).
thf(2760,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2755]) ).
thf(10682,plain,
( ( sk6 != sk3 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2760]) ).
thf(869,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,235]) ).
thf(870,plain,
( ( elec_2 @ ( zero @ s @ leq ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( sk3 ))]]) ).
thf(27499,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( sk8 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27368,423]) ).
thf(27500,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( sk8 @ host @ leq ) ) ),
inference(simp,[status(thm)],[27499]) ).
thf(27553,plain,
! [A: $i] :
( ( A
!= ( nbr_proc @ s ) )
| ( ( A @ s )
!= ( sk8 @ host ) ) ),
inference(simp,[status(thm)],[27500]) ).
thf(27583,plain,
( ( nbr_proc @ s @ s )
!= ( sk8 @ host ) ),
inference(simp,[status(thm)],[27553]) ).
thf(56,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_05) ).
thf(414,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(415,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[414]) ).
thf(416,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[415]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(6894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ~ $true
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(paramod_ordered,[status(thm)],[289,139]) ).
thf(6895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
| ( ( D @ host )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[6894]) ).
thf(6914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( C @ host @ queue ) )
| ( A
!= ( D @ m_Down ) )
| ( D != C ) ),
inference(simp,[status(thm)],[6895]) ).
thf(6964,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Down @ cons ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[6914]) ).
thf(1929,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[532,423]) ).
thf(1930,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[1929]) ).
thf(1945,plain,
! [A: $i] :
( ( A
!= ( sk8 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1930]) ).
thf(1960,plain,
( ( sk8 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[1945]) ).
thf(18496,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,268]) ).
thf(18497,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18496]) ).
thf(18498,plain,
sk3 @ host @ s @ ( sk2 @ host @ s @ leq ),
inference(pattern_uni,[status(thm)],[18497:[bind(A,$thf( sk2 @ host )),bind(B,$thf( sk3 @ host ))]]) ).
thf(19418,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ ( sk2 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18498,423]) ).
thf(19419,plain,
! [A: $i] :
( ( sk3 @ host @ s @ ( sk2 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19418]) ).
thf(19464,plain,
! [A: $i] :
( ( ( sk3 @ host @ s )
!= A )
| ( ( sk2 @ host @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[19419]) ).
thf(19485,plain,
( ( sk3 @ host @ s @ s )
!= ( sk2 @ host @ s ) ),
inference(simp,[status(thm)],[19464]) ).
thf(8789,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk6 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk6 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[310,7914]) ).
thf(8790,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk6 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk6 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[8789]) ).
thf(8791,plain,
( ( sk6 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk6 @ host @ leq ) )
| ( ( zero @ s )
= ( sk9 @ host ) ) ),
inference(pattern_uni,[status(thm)],[8790:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s ))]]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).
thf(253,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ ordered )
<=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_53) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ( A @ cons ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(344,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 ) )
& ! [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 ) ) ) ),
inference(miniscope,[status(thm)],[343]) ).
thf(345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ cons ) @ ordered )
| ~ ( D @ ( E @ sk19 ) @ pidMsg @ ( D @ pidMsg @ leq ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( ( D @ ( E @ sk19 ) @ pidMsg @ host )
= ( D @ pidMsg @ host ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ ( E @ sk19 ) @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( E @ ( D @ ( E @ sk19 ) @ elem ) )
| ~ ( E @ ordered ) )
& ( ( C @ pidMsg @ ( A @ pidMsg @ leq ) )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ordered )
| ~ ( B @ ( A @ cons ) @ ordered ) ) ),
inference(cnf,[status(esa)],[344]) ).
thf(348,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[345]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[348]) ).
thf(17528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( C @ ( A @ cons ) ) )
| ( ( B @ ( sk2 @ host @ queue @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ) ),
inference(paramod_ordered,[status(thm)],[123,390]) ).
thf(17529,plain,
! [A: $i] :
( ( A @ ( sk2 @ host @ queue @ snoc ) )
= ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) ) ),
inference(pattern_uni,[status(thm)],[17528:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(17564,plain,
! [A: $i] :
( ( A @ ( sk2 @ host @ queue @ snoc ) )
= ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[17529]) ).
thf(17657,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk7 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17564,7340]) ).
thf(17658,plain,
( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17657:[bind(A,$thf( sk7 @ m_Ldr )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(17852,plain,
( ( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[123,17658]) ).
thf(17853,plain,
( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[17852]) ).
thf(17858,plain,
( ( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[17853]) ).
thf(17862,plain,
( ( sk7 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17858]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B = A )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B = A )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_50) ).
thf(395,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(396,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[395]) ).
thf(397,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[396]) ).
thf(27394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18611,268]) ).
thf(27395,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[27394]) ).
thf(27396,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[27395:[bind(A,$thf( E )),bind(B,$thf( E @ host @ s )),bind(C,$thf( nbr_proc @ s ))]]) ).
thf(27430,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(simp,[status(thm)],[27396]) ).
thf(41318,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27430,423]) ).
thf(41319,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[41318]) ).
thf(41400,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s )
!= B )
| ( ( A @ host @ s @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[41319]) ).
thf(41456,plain,
! [A: $i] :
( ( A @ host @ s @ s )
!= ( nbr_proc @ s @ s @ s ) ),
inference(simp,[status(thm)],[41400]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
thf(278,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(279,plain,
! [A: $i] :
( ( A @ ordered )
=> ! [B: $i] : ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(miniscope,[status(thm)],[278]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ ( A @ ordered ) ),
inference(cnf,[status(esa)],[279]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(219,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[219]) ).
thf(221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[131]) ).
thf(13123,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk8 @ host @ leq ) ) )
| ~ $true
| ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[387,1914]) ).
thf(13124,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk8 @ host @ leq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[13123]) ).
thf(13125,plain,
sk8 @ host @ ( sk6 @ host @ leq ),
inference(pattern_uni,[status(thm)],[13124:[bind(A,$thf( sk8 @ host )),bind(B,$thf( sk6 @ host ))]]) ).
thf(13229,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[13125,92]) ).
thf(13230,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13229]) ).
thf(13231,plain,
~ ( sk6 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[13230:[bind(A,$thf( sk6 )),bind(B,$thf( sk8 ))]]) ).
thf(7172,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,614]) ).
thf(7173,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7172]) ).
thf(7271,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7173]) ).
thf(7331,plain,
! [A: $i] :
( ( sk3 @ m_Ldr @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7271]) ).
thf(17673,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk3 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17564,7331]) ).
thf(17674,plain,
( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17673:[bind(A,$thf( sk3 @ m_Ldr )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(6892,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,4078]) ).
thf(6893,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[6892]) ).
thf(6954,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Down ) ) ),
inference(simp,[status(thm)],[6893]) ).
thf(7004,plain,
! [A: $i] :
( ( A @ ( sk7 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[6954]) ).
thf(18490,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13125,268]) ).
thf(18491,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18490]) ).
thf(18492,plain,
sk8 @ host @ s @ ( sk6 @ host @ s @ leq ),
inference(pattern_uni,[status(thm)],[18491:[bind(A,$thf( sk6 @ host )),bind(B,$thf( sk8 @ host ))]]) ).
thf(19102,plain,
sk8 @ host @ s @ ( sk8 @ host @ leq ),
inference(rewrite,[status(thm)],[18492,531]) ).
thf(18781,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18554,268]) ).
thf(18782,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18781]) ).
thf(18783,plain,
sk8 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[18782:[bind(A,$thf( nbr_proc @ s )),bind(B,$thf( sk8 @ host @ s ))]]) ).
thf(19766,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18783,268]) ).
thf(19767,plain,
! [B: $i,A: $i] :
( ( ( sk8 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19766]) ).
thf(19768,plain,
sk8 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[19767:[bind(A,$thf( nbr_proc @ s @ s )),bind(B,$thf( sk8 @ host @ s @ s ))]]) ).
thf(38186,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19768,423]) ).
thf(38187,plain,
! [A: $i] :
( ( sk8 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[38186]) ).
thf(38288,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ s @ s )
!= A )
| ( ( nbr_proc @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[38187]) ).
thf(38337,plain,
( ( sk8 @ host @ s @ s @ s @ s )
!= ( nbr_proc @ s @ s @ s ) ),
inference(simp,[status(thm)],[38288]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(230,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(231,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[230]) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[231]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[232]) ).
thf(22,axiom,
elec_1 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_07) ).
thf(246,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(247,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[246]) ).
thf(248,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[247]) ).
thf(72,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(116,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(117,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[116]) ).
thf(498,plain,
( ( sk6 @ host )
!= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[162,120]) ).
thf(512,plain,
sk6 != sk2,
inference(simp,[status(thm)],[498]) ).
thf(670,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( pendack != status )
| ( ( sk6 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[120,588]) ).
thf(678,plain,
( ( sk10 != sk3 )
| ( pendack != status )
| ( ( sk6 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[670]) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[267]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(13332,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,13231]) ).
thf(13333,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13332]) ).
thf(13371,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13333]) ).
thf(13375,plain,
! [A: $i] :
( ( sk8 @ m_Ldr @ ( A @ snoc ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[13371]) ).
thf(15765,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,13375]) ).
thf(15766,plain,
( ( q_nil @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[15765:[bind(A,$thf( sk8 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(363,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(364,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[363]) ).
thf(365,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[364]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_39) ).
thf(424,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1911,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,423]) ).
thf(1912,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1911]) ).
thf(1946,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1912]) ).
thf(1961,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[1946]) ).
thf(2773,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( nbr_proc @ s ) )
| ( ( sk8 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[531,1961]) ).
thf(2776,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( nbr_proc @ s ) )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[2773]) ).
thf(2779,plain,
( ( sk6 @ host @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2776]) ).
thf(2890,plain,
( ( nbr_proc @ s )
!= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[2779,531]) ).
thf(19443,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ ( sk2 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18498,268]) ).
thf(19444,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ ( sk2 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19443]) ).
thf(19445,plain,
sk3 @ host @ s @ s @ ( sk2 @ host @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[19444:[bind(A,$thf( sk2 @ host @ s )),bind(B,$thf( sk3 @ host @ s ))]]) ).
thf(20745,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ s @ ( sk2 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19445,423]) ).
thf(20746,plain,
! [A: $i] :
( ( sk3 @ host @ s @ s @ ( sk2 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[20745]) ).
thf(20785,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ s )
!= A )
| ( ( sk2 @ host @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[20746]) ).
thf(20829,plain,
( ( sk3 @ host @ s @ s @ s )
!= ( sk2 @ host @ s @ s ) ),
inference(simp,[status(thm)],[20785]) ).
thf(294,plain,
! [A: $i] :
( ( A
= ( A @ sk17 @ m_Down ) )
| ( A
= ( A @ sk16 @ m_Halt ) )
| ~ ( A @ pidElem ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(297,plain,
! [A: $i] :
( ~ ( A @ pidElem )
| ( ( A @ sk17 @ m_Down )
= A )
| ( ( A @ sk16 @ m_Halt )
= A ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(4073,plain,
! [A: $i] :
( ( ( sk10 @ host )
!= ( A @ host ) )
| ~ ( sk6 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[120,3319]) ).
thf(4074,plain,
~ ( sk6 @ host @ queue @ ( sk10 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[4073:[bind(A,$thf( sk10 ))]]) ).
thf(7220,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,4074]) ).
thf(7221,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7220]) ).
thf(7235,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk10 @ m_Down ) ) ),
inference(simp,[status(thm)],[7221]) ).
thf(7295,plain,
! [A: $i] :
( ( sk10 @ m_Down @ ( A @ snoc ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[7235]) ).
thf(17682,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk10 @ m_Down @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17564,7295]) ).
thf(17683,plain,
( ( sk10 @ m_Down @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17682:[bind(A,$thf( sk10 @ m_Down )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
thf(407,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).
thf(275,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).
thf(236,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(237,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[236]) ).
thf(238,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[238]) ).
thf(3338,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)],[413,239]) ).
thf(3339,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[3338:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(500,plain,
( ( ( sk10 @ host )
!= ( sk7 @ host ) )
| ( ( sk6 @ host )
= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[137,120]) ).
thf(502,plain,
( ( sk10 != sk7 )
| ( ( sk6 @ host )
= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[500]) ).
thf(744,plain,
sk10 != sk7,
inference(simplifyReflect,[status(thm)],[502,498]) ).
thf(33346,plain,
! [B: $i,A: $i] :
( ( A != sk10 )
| ( B != sk7 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[308,744]) ).
thf(33347,plain,
! [A: $i] :
( ( A != sk7 )
| ~ ( sk10 @ ( A @ leq ) )
| ~ ( A @ ( sk10 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[33346:[bind(A,$thf( sk10 ))]]) ).
thf(34913,plain,
( ~ ( sk10 @ ( sk7 @ leq ) )
| ~ ( sk7 @ ( sk10 @ leq ) ) ),
inference(simp,[status(thm)],[33347]) ).
thf(506,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( sk6 @ host @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[120,86]) ).
thf(510,plain,
( ( sk10 != sk3 )
| ( sk6 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(17116,plain,
( ( ( sk6 @ host @ ( sk8 @ host @ leq ) )
!= ( sk6 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true
| ( sk10 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[510,1914]) ).
thf(17117,plain,
( ( ( sk6 @ host @ ( sk8 @ host @ leq ) )
!= ( sk6 @ host @ ( sk2 @ host @ leq ) ) )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[17116]) ).
thf(17195,plain,
( ( ( sk6 @ host )
!= ( sk6 @ host ) )
| ( ( sk8 @ host )
!= ( sk2 @ host ) )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[17117]) ).
thf(17217,plain,
( ( ( sk8 @ host )
!= ( sk2 @ host ) )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[17195]) ).
thf(17238,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk10 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[137,17217]) ).
thf(17239,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[17238]) ).
thf(17245,plain,
( ( sk8 != sk7 )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[17239]) ).
thf(250,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[249]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(326,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(327,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[326]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[327]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[328]) ).
thf(6900,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,4074]) ).
thf(6901,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk10 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[6900]) ).
thf(6922,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk10 @ m_Down ) ) ),
inference(simp,[status(thm)],[6901]) ).
thf(6972,plain,
! [A: $i] :
( ( A @ ( sk10 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[6922]) ).
thf(18555,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,268]) ).
thf(18556,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18555]) ).
thf(18557,plain,
sk3 @ host @ s @ ( nbr_proc @ s @ leq ),
inference(pattern_uni,[status(thm)],[18556:[bind(A,$thf( nbr_proc )),bind(B,$thf( sk3 @ host ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(227,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[228]) ).
thf(3798,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)],[413,229]) ).
thf(3799,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[3798:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(482,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[481]) ).
thf(483,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(7142,plain,
sk3 != sk2,
inference(simp,[status(thm)],[7086]) ).
thf(631,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( pendack @ index ) ) )
| ( sk3 @ host @ ( sk6 @ host @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[133,95]) ).
thf(644,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != pendack )
| ( sk3 @ host @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[631]) ).
thf(650,plain,
( ( acks != pendack )
| ( sk3 @ host @ ( sk6 @ host @ setIn ) ) ),
inference(simp,[status(thm)],[644]) ).
thf(591,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( sk6 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[120,575]) ).
thf(593,plain,
( ( sk10 != sk3 )
| ( sk6 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[591]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(418,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[417]) ).
thf(419,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[418]) ).
thf(420,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[419]) ).
thf(79,plain,
sk2 @ m_Ldr @ ( sk10 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(499,plain,
sk2 @ m_Ldr @ ( sk6 @ host @ queue @ snoc ) @ ( sk9 @ m_Down @ elem ),
inference(rewrite,[status(thm)],[79,120]) ).
thf(6852,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,614]) ).
thf(6853,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[6852]) ).
thf(6945,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[6853]) ).
thf(6995,plain,
! [A: $i] :
( ( A @ ( sk3 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[6945]) ).
thf(25,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).
thf(256,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(339,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(18670,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18534,268]) ).
thf(18671,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18670]) ).
thf(18672,plain,
nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[18671:[bind(A,$thf( zero @ s @ s )),bind(B,$thf( nbr_proc @ s ))]]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(210,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[210]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[211]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(191,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(192,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[191]) ).
thf(193,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[192]) ).
thf(257,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[256]) ).
thf(258,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[257]) ).
thf(634,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[95,258]) ).
thf(635,plain,
! [A: $i] :
( ( sk2 @ host @ ( acks @ index ) @ ( sk6 @ host @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[634]) ).
thf(648,plain,
! [A: $i] :
( ( ( sk2 @ host @ ( acks @ index ) )
!= setEmpty )
| ( ( sk6 @ host )
!= A ) ),
inference(simp,[status(thm)],[635]) ).
thf(652,plain,
( ( sk2 @ host @ ( acks @ index ) )
!= setEmpty ),
inference(simp,[status(thm)],[648]) ).
thf(711,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( pendack @ index ) ) )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(paramod_ordered,[status(thm)],[133,652]) ).
thf(719,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != pendack )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[711]) ).
thf(723,plain,
( ( acks != pendack )
| ( ( sk3 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[719]) ).
thf(737,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( acks != pendack )
| ( setEmpty != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,723]) ).
thf(738,plain,
( ( acks != pendack )
| ( setEmpty != elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[737:[]]) ).
thf(6854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,949]) ).
thf(6855,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[6854]) ).
thf(6904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( C @ host @ queue ) )
| ( A
!= ( C @ m_Ldr ) ) ),
inference(simp,[status(thm)],[6855]) ).
thf(7014,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Ldr @ cons ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[6904]) ).
thf(29824,plain,
! [A: $i] :
( ( ( sk8 @ host @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29677,423]) ).
thf(29825,plain,
! [A: $i] :
( ( sk8 @ host @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[29824]) ).
thf(29887,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= A )
| ( ( zero @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[29825]) ).
thf(29922,plain,
( ( zero @ s @ s )
!= ( sk8 @ host @ s ) ),
inference(simp,[status(thm)],[29887]) ).
thf(2765,plain,
! [A: $i] :
( ( ( sk10 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk6 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,1961]) ).
thf(2766,plain,
( ( nbr_proc @ s )
!= ( sk6 @ host ) ),
inference(pattern_uni,[status(thm)],[2765:[bind(A,$thf( sk10 ))]]) ).
thf(41,axiom,
elec_2 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_09) ).
thf(360,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1988,plain,
( ( ( sk6 @ host @ ( sk8 @ host @ leq ) )
!= ( sk6 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk10 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[593,1914]) ).
thf(1989,plain,
( ( ( sk6 @ host @ ( sk8 @ host @ leq ) )
!= ( sk6 @ host @ ( nbr_proc @ leq ) ) )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[1988]) ).
thf(2034,plain,
( ( ( sk6 @ host )
!= ( sk6 @ host ) )
| ( ( sk8 @ host )
!= nbr_proc )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[1989]) ).
thf(2043,plain,
( ( ( sk8 @ host )
!= nbr_proc )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[2034]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(398,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(18048,plain,
( ( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[123,17674]) ).
thf(18049,plain,
( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[18048]) ).
thf(18054,plain,
( ( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[18049]) ).
thf(18059,plain,
( ( sk3 @ m_Ldr @ ( sk1 @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[18054]) ).
thf(17222,plain,
( ( sk8 != sk2 )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[17217]) ).
thf(2903,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ host @ s ) )
| ( ( zero @ s )
!= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[531,1956]) ).
thf(2904,plain,
( ( zero @ s )
!= ( sk8 @ host ) ),
inference(pattern_uni,[status(thm)],[2903:[bind(A,$thf( sk6 ))]]) ).
thf(2907,plain,
( ( ( sk6 @ host @ s )
!= ( zero @ s ) )
| ( ( sk8 @ host )
!= ( sk8 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[531,2904]) ).
thf(2908,plain,
( ( sk6 @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2907]) ).
thf(2909,plain,
( ( sk6 @ host )
!= zero ),
inference(simp,[status(thm)],[2908]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(2778,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= nbr_proc )
| ( sk8 != A ) ),
inference(simp,[status(thm)],[2773]) ).
thf(2780,plain,
( ( sk6 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[2778]) ).
thf(2787,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,2780]) ).
thf(2788,plain,
( ( sk6 != sk3 )
| ( nbr_proc != elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[2787]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[253]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[254]) ).
thf(4130,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)],[413,255]) ).
thf(4131,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[4130:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(18898,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18557,268]) ).
thf(18899,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18898]) ).
thf(18900,plain,
sk3 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[18899:[bind(A,$thf( nbr_proc @ s )),bind(B,$thf( sk3 @ host @ s ))]]) ).
thf(19907,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18900,268]) ).
thf(19908,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19907]) ).
thf(19909,plain,
sk3 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[19908:[bind(A,$thf( nbr_proc @ s @ s )),bind(B,$thf( sk3 @ host @ s @ s ))]]) ).
thf(540,plain,
( ( ( sk2 @ host @ ( pendack @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[115,90]) ).
thf(543,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[540]) ).
thf(545,plain,
( ( pendack != status )
| ( elec_2 @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[543]) ).
thf(1907,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[545,423]) ).
thf(1908,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( elec_2 @ ( nbr_proc @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1907]) ).
thf(1944,plain,
! [A: $i] :
( ( A != elec_2 )
| ( ( A @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1908]) ).
thf(1959,plain,
( ( ( elec_2 @ s )
!= nbr_proc )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1944]) ).
thf(7054,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6885,3751]) ).
thf(7055,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7054]) ).
thf(7118,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7055]) ).
thf(7128,plain,
( ( sk3 @ m_Down )
!= ( sk7 @ m_Ldr ) ),
inference(simp,[status(thm)],[7118]) ).
thf(19885,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18900,423]) ).
thf(19886,plain,
! [A: $i] :
( ( sk3 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19885]) ).
thf(19934,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ s )
!= A )
| ( ( nbr_proc @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[19886]) ).
thf(19963,plain,
( ( sk3 @ host @ s @ s @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[19934]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk5 ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk5 ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( C @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ sk5 ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(7154,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,7086]) ).
thf(7155,plain,
( ( ( sk2 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[7154:[]]) ).
thf(9,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
thf(208,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20340,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,280]) ).
thf(20341,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(simp,[status(thm)],[20340]) ).
thf(20342,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(pattern_uni,[status(thm)],[20341:[bind(A,$thf( q_nil ))]]) ).
thf(20359,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(simp,[status(thm)],[20342]) ).
thf(20363,plain,
! [A: $i] : ( q_nil @ ( A @ m_Ldr @ cons ) @ ordered ),
inference(rewrite,[status(thm)],[20359,413]) ).
thf(2894,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[1956]) ).
thf(373,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[372]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[374]) ).
thf(19745,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18783,423]) ).
thf(19746,plain,
! [A: $i] :
( ( sk8 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19745]) ).
thf(19804,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ s )
!= A )
| ( ( nbr_proc @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[19746]) ).
thf(19822,plain,
( ( sk8 @ host @ s @ s @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[19804]) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(3271,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( zero != elec_2 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,2894]) ).
thf(3272,plain,
( ( zero != elec_2 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[3271:[bind(A,$thf( sk3 ))]]) ).
thf(7174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[384,949]) ).
thf(7175,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7174]) ).
thf(7227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( C @ host @ queue ) )
| ( A
!= ( C @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7175]) ).
thf(7287,plain,
! [B: $i,A: $i] :
( ( B @ m_Ldr @ ( A @ snoc ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[7227]) ).
thf(17025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( C @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( C @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,7287]) ).
thf(17026,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Ldr @ cons ) )
!= ( A @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17025:[bind(A,$thf( D @ m_Ldr )),bind(B,$thf( q_nil )),bind(C,$thf( D ))]]) ).
thf(17028,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Ldr @ cons ) )
!= ( A @ host @ queue ) ),
inference(simp,[status(thm)],[17026]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
thf(259,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
thf(171,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(172,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ) ),
inference(miniscope,[status(thm)],[171]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_NotNorm )
= ( D @ m_NotNorm ) ) )
& ( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[173]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_62) ).
thf(402,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(204,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(182,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ) ),
inference(miniscope,[status(thm)],[181]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_NormQ )
= ( D @ m_NormQ ) ) )
& ( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[183]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(187,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk12 )
= A ),
inference(cnf,[status(esa)],[187]) ).
thf(1488,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk12 )
= A ),
inference(lifteq,[status(thm)],[188]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(391,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(563,plain,
! [A: $i] :
( ( ( alive @ ( sk10 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,258]) ).
thf(564,plain,
! [A: $i] :
( ( alive @ ( sk10 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[563]) ).
thf(569,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk10 != A ) ),
inference(simp,[status(thm)],[564]) ).
thf(572,plain,
setEmpty != alive,
inference(simp,[status(thm)],[569]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
thf(313,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Down )
!= ( B @ m_Down ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(6872,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,3751]) ).
thf(6873,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[6872]) ).
thf(6911,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[6873]) ).
thf(7021,plain,
! [A: $i] :
( ( A @ ( sk7 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[6911]) ).
thf(13384,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( A @ s ) )
| ( sk9 @ host @ ( A @ leq ) )
| ( sk6 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk6 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[8791,13166]) ).
thf(13385,plain,
( ( sk9 @ host @ ( zero @ leq ) )
| ( sk6 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk6 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[13384:[bind(A,$thf( zero ))]]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ ( B @ ( C @ sk5 ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(405,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[404]) ).
thf(406,plain,
wait != norm,
inference(lifteq,[status(thm)],[405]) ).
thf(7081,plain,
( ( ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6885,4078]) ).
thf(7082,plain,
( ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7081]) ).
thf(7120,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk7 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[7082]) ).
thf(7130,plain,
( ( sk7 @ m_Down )
!= ( sk3 @ m_Down ) ),
inference(simp,[status(thm)],[7120]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(271,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(272,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[271]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[272]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(2905,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[588,1956]) ).
thf(2906,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[2905:[bind(A,$thf( sk3 ))]]) ).
thf(15673,plain,
! [A: $i] :
( ( ( A @ s @ s )
!= ( sk6 @ host @ s ) )
| ( ( sk8 @ host )
!= A ) ),
inference(paramod_ordered,[status(thm)],[531,13447]) ).
thf(15676,plain,
( ( sk8 @ host @ s @ s )
!= ( sk6 @ host @ s ) ),
inference(simp,[status(thm)],[15673]) ).
thf(15686,plain,
( ( sk8 @ host @ s @ s )
!= ( sk8 @ host ) ),
inference(rewrite,[status(thm)],[15676,531]) ).
thf(361,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[360]) ).
thf(362,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[361]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(243,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[242]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[243]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(314,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ) ),
inference(miniscope,[status(thm)],[313]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Down )
= ( D @ m_Down ) ) )
& ( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[314]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[315]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[316]) ).
thf(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(434,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[283]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(27717,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6885,290]) ).
thf(27718,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[27717]) ).
thf(27719,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[27718:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(27889,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[27719]) ).
thf(41498,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27889,440]) ).
thf(41499,plain,
! [B: $i,A: $i] :
( ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[41498]) ).
thf(41695,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ cons ) )
!= q_nil )
| ( ( sk3 @ m_Down )
!= B ) ),
inference(simp,[status(thm)],[41499]) ).
thf(41785,plain,
! [A: $i] :
( ( sk2 @ host @ queue @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[41695]) ).
thf(20772,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ s @ ( sk2 @ host @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19445,268]) ).
thf(20773,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ host @ s @ s @ ( sk2 @ host @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[20772]) ).
thf(20774,plain,
sk3 @ host @ s @ s @ s @ ( sk2 @ host @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[20773:[bind(A,$thf( sk2 @ host @ s @ s )),bind(B,$thf( sk3 @ host @ s @ s ))]]) ).
thf(17636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( C @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[17564,7309]) ).
thf(17637,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[17636:[bind(A,$thf( A )),bind(B,$thf( sk2 @ host @ queue )),bind(C,$thf( A ))]]) ).
thf(485,plain,
( ( ( alive @ ( sk10 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,217]) ).
thf(486,plain,
( ( alive @ ( sk10 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[485]) ).
thf(491,plain,
( ( alive != alive )
| ( sk10 != nil ) ),
inference(simp,[status(thm)],[486]) ).
thf(494,plain,
sk10 != nil,
inference(simp,[status(thm)],[491]) ).
thf(43,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).
thf(367,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
elec_1 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_06) ).
thf(213,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19632,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18672,268]) ).
thf(19633,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19632]) ).
thf(19634,plain,
nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[19633:[bind(A,$thf( zero @ s @ s @ s )),bind(B,$thf( nbr_proc @ s @ s ))]]) ).
thf(99,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(154,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(155,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[154]) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(392,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[391]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[392]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[393]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[295]) ).
thf(299,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[298]) ).
thf(17675,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk7 @ m_Down @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17564,7288]) ).
thf(17676,plain,
( ( sk7 @ m_Down @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17675:[bind(A,$thf( sk7 @ m_Down )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
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(431,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m_Down @ elem ) )
& ( ( B @ host )
= ( C @ host ) )
& ( A @ ( B @ m_Halt @ cons ) @ ordered ) )
=> ( C @ ( B @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(319,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[318]) ).
thf(320,plain,
! [A: $i] :
( ( A @ m_Down @ sk18 )
= A ),
inference(cnf,[status(esa)],[319]) ).
thf(2797,plain,
! [A: $i] :
( ( A @ m_Down @ sk18 )
= A ),
inference(lifteq,[status(thm)],[320]) ).
thf(712,plain,
( ( ( sk2 @ host @ ( acks @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( setEmpty != elec_2 ) ),
inference(paramod_ordered,[status(thm)],[115,652]) ).
thf(721,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( acks != status )
| ( setEmpty != elec_2 ) ),
inference(simp,[status(thm)],[712]) ).
thf(722,plain,
( ( acks != status )
| ( setEmpty != elec_2 ) ),
inference(simp,[status(thm)],[721]) ).
thf(10310,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk10 @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,7295]) ).
thf(10311,plain,
( ( q_nil @ ( sk10 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[10310:[bind(A,$thf( sk10 @ m_Down )),bind(B,$thf( q_nil ))]]) ).
thf(13242,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( sk6 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13125,423]) ).
thf(13243,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk8 @ host @ ( sk6 @ host @ leq ) ) ),
inference(simp,[status(thm)],[13242]) ).
thf(13282,plain,
! [A: $i] :
( ( A
!= ( sk8 @ host ) )
| ( ( A @ s )
!= ( sk6 @ host ) ) ),
inference(simp,[status(thm)],[13243]) ).
thf(13293,plain,
( ( sk8 @ host @ s )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[13282]) ).
thf(513,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[137,498]) ).
thf(514,plain,
( ( sk7 @ host )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[513]) ).
thf(516,plain,
sk7 != sk6,
inference(simp,[status(thm)],[514]) ).
thf(1917,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[310,423]) ).
thf(1918,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1917]) ).
thf(1943,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1918]) ).
thf(1958,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[1943]) ).
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(458,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) )
=> ( B @ s @ ( A @ leq ) ) )
& ( ( B @ s @ ( A @ leq ) )
=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20843,plain,
( ( sk6 != sk3 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[20662]) ).
thf(546,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[137,532]) ).
thf(548,plain,
( ( sk8 != sk7 )
| ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[546]) ).
thf(340,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[339]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[340]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(194,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( A @ host @ leq ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( B @ host )
!= ( D @ host ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(735,plain,
( ( ( sk10 @ host )
!= ( sk3 @ host ) )
| ( acks != pendack )
| ( ( sk6 @ host )
!= setEmpty ) ),
inference(paramod_ordered,[status(thm)],[120,723]) ).
thf(739,plain,
( ( sk10 != sk3 )
| ( acks != pendack )
| ( ( sk6 @ host )
!= setEmpty ) ),
inference(simp,[status(thm)],[735]) ).
thf(853,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[123,333]) ).
thf(854,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Down )
!= A )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[853]) ).
thf(855,plain,
( ( sk1 != q_nil )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[854]) ).
thf(195,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)],[194]) ).
thf(196,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)],[195]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[196]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(6850,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,440]) ).
thf(6851,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[6850]) ).
thf(6931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[6851]) ).
thf(6981,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[6931]) ).
thf(469,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ) ),
inference(miniscope,[status(thm)],[468]) ).
thf(470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Ldr )
= ( D @ m_Ldr ) ) )
& ( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[469]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[470]) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[471]) ).
thf(474,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[473]) ).
thf(475,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk21 )
= A ),
inference(cnf,[status(esa)],[474]) ).
thf(3273,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk21 )
= A ),
inference(lifteq,[status(thm)],[475]) ).
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(441,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( A @ ( B @ snoc ) @ ordered ) )
& ( ( A @ ( B @ snoc ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(17071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( C @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( C @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,7322]) ).
thf(17072,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Down @ cons ) )
!= ( A @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17071:[bind(A,$thf( D @ m_Down )),bind(B,$thf( q_nil )),bind(C,$thf( D ))]]) ).
thf(17073,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Down @ cons ) )
!= ( A @ host @ queue ) ),
inference(simp,[status(thm)],[17072]) ).
thf(38,axiom,
elec_2 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_08) ).
thf(336,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(337,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[336]) ).
thf(338,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[337]) ).
thf(200,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[199]) ).
thf(201,plain,
! [A: $i] :
( ( A @ m_Halt @ sk13 )
= A ),
inference(cnf,[status(esa)],[200]) ).
thf(2044,plain,
! [A: $i] :
( ( A @ m_Halt @ sk13 )
= A ),
inference(lifteq,[status(thm)],[201]) ).
thf(7025,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6885,614]) ).
thf(7026,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[7025]) ).
thf(7117,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[7026]) ).
thf(7127,plain,
( ( sk3 @ m_Down )
!= ( sk3 @ m_Ldr ) ),
inference(simp,[status(thm)],[7117]) ).
thf(1981,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[1963]) ).
thf(42613,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s @ s )
!= ( sk2 @ host @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[137,41456]) ).
thf(42614,plain,
( ( nbr_proc @ s @ s @ s )
!= ( sk2 @ host @ s @ s ) ),
inference(pattern_uni,[status(thm)],[42613:[bind(A,$thf( sk7 ))]]) ).
thf(1915,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk8 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[548,423]) ).
thf(1916,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1915]) ).
thf(1940,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host ) )
| ( ( A @ s )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1916]) ).
thf(1955,plain,
( ( ( sk2 @ host @ s )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1940]) ).
thf(13340,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,13231]) ).
thf(13341,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[13340]) ).
thf(13364,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[13341]) ).
thf(13374,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[13364]) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( C @ ( A @ m_Ack ) )
= ( D @ ( B @ m_Ack ) ) ) ),
inference(miniscope,[status(thm)],[259]) ).
thf(261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(263,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[262]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk15 ) )
= A ),
inference(cnf,[status(esa)],[263]) ).
thf(17320,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk15 ) )
= A ),
inference(lifteq,[status(thm)],[264]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(2000,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk8 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[310,1914]) ).
thf(2001,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk8 @ host @ leq ) ) ),
inference(simp,[status(thm)],[2000]) ).
thf(2027,plain,
! [A: $i] :
( ( A
!= ( sk6 @ host ) )
| ( A
!= ( sk8 @ host ) ) ),
inference(simp,[status(thm)],[2001]) ).
thf(2041,plain,
( ( sk8 @ host )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[2027]) ).
thf(2045,plain,
sk8 != sk6,
inference(simp,[status(thm)],[2041]) ).
thf(36690,plain,
! [A: $i] :
( ( ( sk8 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29865,423]) ).
thf(36691,plain,
! [A: $i] :
( ( sk8 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[36690]) ).
thf(36773,plain,
! [A: $i] :
( ( ( sk8 @ host @ s )
!= A )
| ( ( zero @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[36691]) ).
thf(36799,plain,
( ( zero @ s @ s @ s )
!= ( sk8 @ host @ s @ s ) ),
inference(simp,[status(thm)],[36773]) ).
thf(18878,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18557,423]) ).
thf(18879,plain,
! [A: $i] :
( ( sk3 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[18878]) ).
thf(18915,plain,
! [A: $i] :
( ( ( sk3 @ host @ s )
!= A )
| ( ( nbr_proc @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[18879]) ).
thf(18943,plain,
( ( sk3 @ host @ s @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[18915]) ).
thf(75,plain,
alive @ ( sk2 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(487,plain,
( ( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,217]) ).
thf(488,plain,
( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(492,plain,
( ( alive != alive )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[488]) ).
thf(495,plain,
sk2 != nil,
inference(simp,[status(thm)],[492]) ).
thf(29664,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18615,423]) ).
thf(29665,plain,
! [B: $i,A: $i] :
( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[29664]) ).
thf(29726,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s )
!= B )
| ( ( zero @ s @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[29665]) ).
thf(29754,plain,
! [A: $i] :
( ( A @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[29726]) ).
thf(37333,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19634,423]) ).
thf(37334,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[37333]) ).
thf(37406,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s )
!= A )
| ( ( zero @ s @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[37334]) ).
thf(37461,plain,
( ( nbr_proc @ s @ s @ s @ s )
!= ( zero @ s @ s @ s @ s ) ),
inference(simp,[status(thm)],[37406]) ).
thf(222,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[221]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk14 ) )
= B ),
inference(cnf,[status(esa)],[222]) ).
thf(17301,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk14 ) )
= B ),
inference(lifteq,[status(thm)],[223]) ).
thf(37392,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19634,268]) ).
thf(37393,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[37392]) ).
thf(37394,plain,
nbr_proc @ s @ s @ s @ s @ ( zero @ s @ s @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[37393:[bind(A,$thf( zero @ s @ s @ s @ s )),bind(B,$thf( nbr_proc @ s @ s @ s ))]]) ).
thf(1480,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[123,420]) ).
thf(1481,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[1480:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[113]) ).
thf(399,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[398]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[399]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[400]) ).
thf(19615,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18672,423]) ).
thf(19616,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[19615]) ).
thf(19671,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s )
!= A )
| ( ( zero @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[19616]) ).
thf(19686,plain,
( ( nbr_proc @ s @ s @ s )
!= ( zero @ s @ s @ s ) ),
inference(simp,[status(thm)],[19671]) ).
thf(17665,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk8 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17564,13375]) ).
thf(17666,plain,
( ( sk8 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17665:[bind(A,$thf( sk8 @ m_Ldr )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(17671,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ init )
= C ) ),
inference(paramod_ordered,[status(thm)],[17564,255]) ).
thf(17672,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ init )
= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17671:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(205,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[205]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[206]) ).
thf(177,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[176]) ).
thf(178,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk11 )
= A ),
inference(cnf,[status(esa)],[177]) ).
thf(1308,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk11 )
= A ),
inference(lifteq,[status(thm)],[178]) ).
thf(32978,plain,
! [B: $i,A: $i] :
( ( A != sk7 )
| ( B != sk6 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[308,516]) ).
thf(32979,plain,
! [A: $i] :
( ( A != sk6 )
| ~ ( sk7 @ ( A @ leq ) )
| ~ ( A @ ( sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[32978:[bind(A,$thf( sk7 ))]]) ).
thf(34768,plain,
( ~ ( sk7 @ ( sk6 @ leq ) )
| ~ ( sk6 @ ( sk7 @ leq ) ) ),
inference(simp,[status(thm)],[32979]) ).
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(478,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(38785,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19909,423]) ).
thf(38786,plain,
! [A: $i] :
( ( sk3 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[38785]) ).
thf(38878,plain,
! [A: $i] :
( ( ( sk3 @ host @ s @ s @ s )
!= A )
| ( ( nbr_proc @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[38786]) ).
thf(38942,plain,
( ( sk3 @ host @ s @ s @ s @ s )
!= ( nbr_proc @ s @ s @ s ) ),
inference(simp,[status(thm)],[38878]) ).
thf(284,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[283]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[284]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= ( B @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( A @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ s @ ( nbr_proc @ leq ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_1 )
| ( ( A @ host )
!= ( C @ host @ s ) )
| ( ( A @ ( B @ ( C @ sk5 ) ) )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( B @ ordered )
| ~ ( B @ ( A @ cons ) @ ordered ) ),
inference(cnfConj,[status(thm)],[345]) ).
thf(28373,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( sk8 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28021,423]) ).
thf(28374,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ ( sk8 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[28373]) ).
thf(28468,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s )
!= A )
| ( ( sk8 @ host @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[28374]) ).
thf(28495,plain,
( ( nbr_proc @ s @ s @ s @ s )
!= ( sk8 @ host @ s @ s ) ),
inference(simp,[status(thm)],[28468]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[275]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[276]) ).
thf(4705,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[123,277]) ).
thf(4706,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[4705:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(17625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ ( B @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[17564,384]) ).
thf(17626,plain,
! [A: $i] : ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) @ ( A @ elem ) ),
inference(pattern_uni,[status(thm)],[17625:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(37581,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s @ s )
!= ( zero @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[137,29754]) ).
thf(37582,plain,
( ( sk2 @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(pattern_uni,[status(thm)],[37581:[bind(A,$thf( sk7 ))]]) ).
thf(2046,plain,
( ( ( sk10 @ host )
!= ( sk8 @ host ) )
| ( ( sk6 @ host )
!= ( sk6 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,2041]) ).
thf(2047,plain,
( ( sk10 @ host )
!= ( sk8 @ host ) ),
inference(simp,[status(thm)],[2046]) ).
thf(2050,plain,
sk10 != sk8,
inference(simp,[status(thm)],[2047]) ).
thf(2767,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[137,1961]) ).
thf(2768,plain,
( ( nbr_proc @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[2767:[bind(A,$thf( sk7 ))]]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( C @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( C @ host ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( C @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( C @ host @ ( ldr @ index ) )
!= ( C @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= norm )
| ( ( B @ host )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(435,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Ldr ) ),
inference(miniscope,[status(thm)],[434]) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(cnf,[status(esa)],[435]) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(lifteq,[status(thm)],[436]) ).
thf(11113,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk3 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[413,7331]) ).
thf(11114,plain,
( ( q_nil @ ( sk3 @ m_Ldr @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[11113:[bind(A,$thf( sk3 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(427,plain,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(27975,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk8 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27535,423]) ).
thf(27976,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ ( sk8 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[27975]) ).
thf(28058,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s )
!= A )
| ( ( sk8 @ host @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[27976]) ).
thf(28072,plain,
( ( nbr_proc @ s @ s @ s )
!= ( sk8 @ host @ s ) ),
inference(simp,[status(thm)],[28058]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).
thf(369,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(17628,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= ( sk10 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( A @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[17564,7326]) ).
thf(17629,plain,
( ( sk10 @ m_Ldr @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[17628:[bind(A,$thf( sk10 @ m_Ldr )),bind(B,$thf( sk2 @ host @ queue ))]]) ).
thf(10481,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( zero @ s ) )
| ( A @ host @ ( sk9 @ host @ leq ) )
| ( sk6 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk6 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[8791,235]) ).
thf(10482,plain,
! [A: $i] :
( ( A @ host @ ( sk9 @ host @ leq ) )
| ( sk6 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk6 @ host @ leq ) ) ),
inference(pattern_uni,[status(thm)],[10481:[]]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( ldr @ index ) )
!= ( B @ host ) )
| ( ( B @ host @ ( status @ index ) )
!= norm ) ),
inference(simp,[status(thm)],[121]) ).
thf(214,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[213]) ).
thf(215,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[214]) ).
thf(83,plain,
alive @ ( sk7 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(489,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,217]) ).
thf(490,plain,
( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(493,plain,
( ( alive != alive )
| ( sk7 != nil ) ),
inference(simp,[status(thm)],[490]) ).
thf(496,plain,
sk7 != nil,
inference(simp,[status(thm)],[493]) ).
thf(13379,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk6 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk6 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[13166,7914]) ).
thf(13380,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk6 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk6 @ host @ leq ) )
| ( B
= ( sk9 @ host ) ) ),
inference(simp,[status(thm)],[13379]) ).
thf(13381,plain,
( ( sk6 @ host @ ( down @ index ) @ ( zero @ s @ s @ setIn ) )
| ( zero @ s @ s @ ( sk6 @ host @ leq ) )
| ( ( zero @ s @ s )
= ( sk9 @ host ) ) ),
inference(pattern_uni,[status(thm)],[13380:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s @ s ))]]) ).
thf(13060,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( A @ ( B @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( B @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[123,6964]) ).
thf(13061,plain,
( ( sk3 @ host @ queue )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[13060:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(28777,plain,
( ( ( sk6 @ host )
!= ( sk6 @ host ) )
| ( nbr_proc != elec_2 )
| ( sk10 != sk3 )
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[678,2780]) ).
thf(28778,plain,
( ( nbr_proc != elec_2 )
| ( sk10 != sk3 )
| ( pendack != status ) ),
inference(pattern_uni,[status(thm)],[28777:[]]) ).
thf(18119,plain,
( ( ( sk7 @ m_Down @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[123,17676]) ).
thf(18120,plain,
( ( sk7 @ m_Down @ ( sk1 @ snoc ) @ ( sk3 @ m_Down @ cons ) )
!= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(simp,[status(thm)],[18119]) ).
thf(18125,plain,
( ( ( sk7 @ m_Down @ ( sk1 @ snoc ) )
!= sk1 )
| ( ( sk3 @ m_Down )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[18120]) ).
thf(18130,plain,
( ( sk7 @ m_Down @ ( sk1 @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[18125]) ).
thf(349,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( B @ ( A @ ( B @ sk19 ) @ elem ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[345]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( B @ ( A @ ( B @ sk19 ) @ elem ) )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[349]) ).
thf(64299,plain,
$false,
inference(e,[status(thm)],[69,2031,468,234,481,333,249,1956,1950,170,115,217,3230,308,120,440,1533,614,7322,29677,550,17594,6996,153,9774,384,28196,17375,1954,1914,20662,18834,709,417,7326,301,34975,13447,11151,18717,651,10351,404,3350,39192,7914,372,110,34854,949,157,325,289,28429,1963,10682,7309,421,870,27583,416,216,164,13166,6964,1960,376,19485,8791,253,353,17862,147,397,41456,280,221,132,133,411,29865,265,13231,17674,7004,19102,38337,233,248,117,512,678,270,18498,15766,366,424,2890,20829,302,297,17683,407,693,275,137,3339,34913,92,17245,252,19768,329,6972,18557,3799,224,229,484,7142,650,593,141,420,499,1953,6995,388,27535,256,1964,339,18672,212,27440,193,7340,738,7014,7086,29922,2766,360,2043,398,674,18059,17222,2909,128,343,2788,4131,27368,19909,2904,1959,7128,19963,166,7155,20363,2894,375,19822,149,423,3319,3272,17028,259,413,176,7287,191,402,13125,291,281,204,545,1488,18783,391,3751,572,313,498,236,17554,181,7021,86,13385,159,406,219,7130,274,2906,15686,230,362,245,318,434,41785,20774,271,208,17637,3747,494,367,323,2780,213,19634,240,155,330,387,13375,130,278,394,299,17676,226,438,431,241,167,135,2797,722,36741,10311,531,13293,255,209,516,1958,458,20843,548,342,123,194,145,18554,17217,1961,6885,7159,739,310,17564,855,414,95,199,6981,3273,441,17073,338,2044,7127,18615,744,7331,1981,42614,1955,1972,386,13374,17320,336,143,497,2760,2045,363,36799,18943,18900,7288,495,218,4078,29754,18611,588,37461,17301,37394,1481,258,652,114,401,171,139,731,19686,17666,390,186,17672,27430,75,2041,510,207,1308,34768,478,38942,4074,287,290,119,235,246,346,28495,4706,262,17626,37582,2050,2768,326,126,19445,268,28021,437,27889,532,11114,239,242,395,575,427,2898,28072,723,277,369,227,17629,10482,122,215,18534,496,13381,13061,28778,18130,354,83,17658,7295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV478+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.07/2.68 % Computer : n012.cluster.edu
% 0.07/2.68 % Model : x86_64 x86_64
% 0.07/2.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/2.68 % Memory : 8046.5625MB
% 0.07/2.68 % OS : Linux 6.8.0-71-generic
% 0.07/2.68 % CPULimit : 300
% 0.07/2.68 % WCLimit : 300
% 0.07/2.68 % DateTime : Sat Sep 26 13:55:54 UTC 2026
% 0.07/2.69 % CPUTime :
% 0.07/2.69 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/3.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.82/3.13 % [INFO] Parsing done (135ms).
% 0.82/3.14 % [INFO] Running in sequential loop mode.
% 1.24/3.35 % [INFO] eprover registered as external prover.
% 1.24/3.36 % [INFO] Scanning for conjecture ...
% 1.45/3.48 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 1.69/3.56 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 1.69/3.59 % [INFO] Problem is first-order (TPTP FOF).
% 1.96/3.60 % [INFO] Type checking passed.
% 1.96/3.60 % [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 ...
% 83.42/23.26 % External prover 'e' found a proof!
% 83.42/23.26 % [INFO] Killing All external provers ...
% 83.42/23.26 % Time passed: 20494ms (effective reasoning time: 20113ms)
% 83.42/23.26 % 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)>
% 83.42/23.26 % 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
% 83.42/23.26 % No. of inferences in proof: 1003
% 83.42/23.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20494 ms resp. 20113 ms w/o parsing
% 81.45/23.52 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 81.45/23.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------