%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV462+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 : n005.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 08:59:31 AM UTC 2026
% Result : Theorem 85.61s 21.38s
% Output : Refutation 86.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 85
% Syntax : Number of formulae : 1037 ( 426 unt; 0 typ; 18 def)
% Number of atoms : 3341 (1732 equ; 0 cnn)
% Maximal formula atoms : 108 ( 3 avg)
% Number of connectives : 12081 (1765 ~;1051 |; 597 &;8410 @)
% ( 13 <=>; 245 =>; 0 <=; 0 <~>)
% Maximal formula depth : 72 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 56 usr; 25 con; 0-4 aty)
% Number of variables : 1737 ( 8 ^;1612 !; 99 ?;1737 :)
% ( 0 !>; 0 ?*; 0 @-; 18 @+)
% Comments :
%------------------------------------------------------------------------------
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Ldr_decl,type,
m_Ldr: $i > $i ).
thf(queue_decl,type,
queue: $i > $i ).
thf(host_decl,type,
host: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(m_Halt_decl,type,
m_Halt: $i > $i ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(setIn_decl,type,
setIn: $i > $i > $o ).
thf(alive_decl,type,
alive: $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(pendack_decl,type,
pendack: $i ).
thf(status_decl,type,
status: $i ).
thf(elec_1_decl,type,
elec_1: $i ).
thf(elec_2_decl,type,
elec_2: $i ).
thf(elid_decl,type,
elid: $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(norm_decl,type,
norm: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(down_decl,type,
down: $i ).
thf(nbr_proc_decl,type,
nbr_proc: $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(snoc_decl,type,
snoc: $i > $i > $i ).
thf(m_NotNorm_decl,type,
m_NotNorm: $i > $i ).
thf(m_NormQ_decl,type,
m_NormQ: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $o ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(wait_decl,type,
wait: $i ).
thf(nil_decl,type,
nil: $i ).
thf(pids_decl,type,
pids: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(last_decl,type,
last: $i > $i ).
thf(init_decl,type,
init: $i > $i ).
thf(setEmpty_decl,type,
setEmpty: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(pidElem_decl,type,
pidElem: $i > $o ).
thf(pidMsg_decl,type,
pidMsg: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Halt @ cons ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ( ( E @ host )
= ( F @ host @ ( pendack @ index ) @ s ) )
& ( ( D @ host )
= ( F @ host @ ( pendack @ index ) ) )
& ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( F @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= nbr_proc )
& ( ( G @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ! [D: $i] :
( ( ( B @ host )
!= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( A @ host @ queue )
= ( sk1 @ ( B @ m_Halt @ cons ) ) )
& ( ? [C: $i,D: $i,E: $i] :
( ( ( D @ host )
= ( E @ host @ ( pendack @ index ) @ s ) )
& ( ( C @ host )
= ( E @ host @ ( pendack @ index ) ) )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( E @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ? [C: $i] :
( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_1 )
& ( ( F @ host )
= nbr_proc )
& ( ( F @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ! [G: $i] :
( ( ( G @ ( zero @ s @ leq ) )
& ~ ( G @ ( F @ host @ leq ) ) )
=> ( ( G
= ( E @ host ) )
| ( F @ host @ ( down @ index ) @ ( G @ setIn ) ) ) ) )
=> ~ ( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i] :
( ? [D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
& ( alive @ ( E @ setIn ) )
& ~ ( C @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ~ ( D @ host @ ( pendack @ index ) @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i,D: $i] :
( ( ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) ) )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( C @ host @ queue @ ( D @ ( C @ m_Ack ) @ elem ) ) )
& ! [C: $i] :
( ? [D: $i,E: $i] :
( ( ( D @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i] :
( ( ( alive @ ( C @ setIn ) )
& ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
| ( ( C @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( C @ host @ ( elid @ index ) )
= C ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_1 )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( C @ ( D @ m_Ack ) @ elem ) ) )
& ! [C: $i,D: $i] :
( ( ( D @ host @ queue @ ( C @ ( D @ m_Ack ) @ elem ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( pendack @ index ) @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
=> ~ ( E @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ( ( D @ host )
!= ( C @ host ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Ldr @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ! [C: $i] :
( ( ( A @ host )
!= ( C @ host ) )
=> ! [D: $i,E: $i,F: $i] :
( ( ( B @ host )
= ( F @ host ) )
=> ( ( ( A @ host )
!= ( F @ host ) )
=> ( ( ( ( E @ host )
= ( F @ host @ ( pendack @ index ) @ s ) )
& ( ( D @ host )
= ( F @ host @ ( pendack @ index ) ) )
& ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( A @ ( B @ m_Ack ) @ ( F @ host @ queue @ snoc ) @ ( D @ ( F @ m_Ack ) @ elem ) )
& ( A @ ( B @ m_Ack ) @ ( F @ host @ queue @ snoc ) @ ( E @ m_Down @ elem ) )
& ( F @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) )
& ( alive @ ( C @ setIn ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( ( sk2 @ host @ queue )
= ( sk1 @ ( A @ m_Halt @ cons ) ) )
& ( ? [B: $i,C: $i,D: $i] :
( ( ( C @ host )
= ( D @ host @ ( pendack @ index ) @ s ) )
& ( ( B @ host )
= ( D @ host @ ( pendack @ index ) ) )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( D @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ? [B: $i] :
( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i,E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( ( E @ host )
= nbr_proc )
& ( ( E @ host )
= ( C @ host ) )
& ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ! [F: $i] :
( ( ( F @ ( zero @ s @ leq ) )
& ~ ( F @ ( E @ host @ leq ) ) )
=> ( ( F
= ( D @ host ) )
| ( E @ host @ ( down @ index ) @ ( F @ setIn ) ) ) ) )
=> ~ ( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i] :
( ? [C: $i,D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
& ( alive @ ( D @ setIn ) )
& ~ ( B @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( C @ host @ ( B @ host @ leq ) ) )
=> ~ ( C @ host @ ( pendack @ index ) @ ( B @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i,C: $i] :
( ( ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( D @ setIn ) ) )
& ( alive @ ( B @ setIn ) ) )
=> ~ ( B @ host @ queue @ ( C @ ( B @ m_Ack ) @ elem ) ) )
& ! [B: $i] :
( ? [C: $i,D: $i] :
( ( ( C @ host )
= ( B @ host ) )
& ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( C @ host @ ( B @ host @ leq ) ) )
=> ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i] :
( ( ( alive @ ( B @ setIn ) )
& ( ( ( B @ host @ ( status @ index ) )
= elec_2 )
| ( ( B @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( B @ host @ ( elid @ index ) )
= B ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( C @ host @ queue @ ( B @ ( C @ m_Ack ) @ elem ) ) )
& ! [B: $i,C: $i] :
( ( ( C @ host @ queue @ ( B @ ( C @ m_Ack ) @ elem ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( pendack @ index ) @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
=> ~ ( D @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ( ( C @ host )
!= ( B @ host ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Ldr @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) ) )
=> ( ( alive @ ( sk2 @ setIn ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
!= ( B @ host ) )
=> ! [C: $i,D: $i,E: $i] :
( ( ( A @ host )
= ( E @ host ) )
=> ( ( ( sk2 @ host )
!= ( E @ host ) )
=> ( ( ( ( D @ host )
= ( E @ host @ ( pendack @ index ) @ s ) )
& ( ( C @ host )
= ( E @ host @ ( pendack @ index ) ) )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ ( A @ m_Ack ) @ ( E @ host @ queue @ snoc ) @ ( C @ ( E @ m_Ack ) @ elem ) )
& ( sk2 @ ( A @ m_Ack ) @ ( E @ host @ queue @ snoc ) @ ( D @ m_Down @ elem ) )
& ( E @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) )
& ( alive @ ( B @ setIn ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( A @ host @ leq ) ) )
=> ( ( E
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ! [B: $i,C: $i,D: $i] :
( ( ( sk3 @ host )
= ( D @ host ) )
=> ( ( ( sk2 @ host )
!= ( D @ host ) )
=> ( ( ( ( C @ host )
= ( D @ host @ ( pendack @ index ) @ s ) )
& ( ( B @ host )
= ( D @ host @ ( pendack @ index ) ) )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( D @ host @ queue @ snoc ) @ ( B @ ( D @ m_Ack ) @ elem ) )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( D @ host @ queue @ snoc ) @ ( C @ m_Down @ elem ) )
& ( D @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( ( ( A @ host @ ( status @ index ) )
= norm )
& ( ( A @ host @ ( ldr @ index ) )
= ( A @ host ) )
& ( alive @ ( A @ setIn ) ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk3 @ host )
= ( C @ host ) )
=> ( ( ( sk2 @ host )
!= ( C @ host ) )
=> ( ( ( ( B @ host )
= ( C @ host @ ( pendack @ index ) @ s ) )
& ( ( A @ host )
= ( C @ host @ ( pendack @ index ) ) )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( C @ host @ queue @ snoc ) @ ( A @ ( C @ m_Ack ) @ elem ) )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( C @ host @ queue @ snoc ) @ ( B @ m_Down @ elem ) )
& ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( ( ( sk5 @ host @ ( status @ index ) )
= norm )
& ( ( sk5 @ host @ ( ldr @ index ) )
= ( sk5 @ host ) )
& ( alive @ ( sk5 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk3 @ host )
= ( B @ host ) )
=> ( ( ( sk2 @ host )
!= ( B @ host ) )
=> ( ( ( ( A @ host )
= ( B @ host @ ( pendack @ index ) @ s ) )
& ( ( sk6 @ host )
= ( B @ host @ ( pendack @ index ) ) )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( B @ host @ queue @ snoc ) @ ( sk6 @ ( B @ m_Ack ) @ elem ) )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( B @ host @ queue @ snoc ) @ ( A @ m_Down @ elem ) )
& ( B @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( B @ setIn ) ) )
=> ~ ( ( ( sk5 @ host @ ( status @ index ) )
= norm )
& ( ( sk5 @ host @ ( ldr @ index ) )
= ( sk5 @ host ) )
& ( alive @ ( sk5 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( ( sk3 @ host )
= ( A @ host ) )
=> ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ( ( ( ( sk7 @ host )
= ( A @ host @ ( pendack @ index ) @ s ) )
& ( ( sk6 @ host )
= ( A @ host @ ( pendack @ index ) ) )
& ( ( A @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( A @ host @ queue @ snoc ) @ ( sk6 @ ( A @ m_Ack ) @ elem ) )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( A @ host @ queue @ snoc ) @ ( sk7 @ m_Down @ elem ) )
& ( A @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( A @ setIn ) ) )
=> ~ ( ( ( sk5 @ host @ ( status @ index ) )
= norm )
& ( ( sk5 @ host @ ( ldr @ index ) )
= ( sk5 @ host ) )
& ( alive @ ( sk5 @ setIn ) ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [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(sk19_def,definition,
( sk19
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Halt @ cons ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= nbr_proc )
& ( ( G @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ! [D: $i] :
( ( ( B @ host )
!= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Halt @ cons ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= nbr_proc )
& ( ( G @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ! [D: $i] :
( ( ( B @ host )
!= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Halt @ cons ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( G @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= nbr_proc )
& ( ( G @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ! [D: $i] :
( ( ( B @ host )
!= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[364]) ).
thf(70,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Halt @ cons ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ( ( E @ host )
= ( F @ host @ ( pendack @ index ) @ s ) )
& ( ( D @ host )
= ( F @ host @ ( pendack @ index ) ) )
& ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( F @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( F @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ( ( G @ host @ ( status @ index ) )
= elec_1 )
& ( ( G @ host )
= nbr_proc )
& ( ( G @ host )
= ( E @ host ) )
& ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ! [H: $i] :
( ( ( H @ ( zero @ s @ leq ) )
& ~ ( H @ ( G @ host @ leq ) ) )
=> ( ( H
= ( F @ host ) )
| ( G @ host @ ( down @ index ) @ ( H @ setIn ) ) ) ) )
=> ~ ( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
& ( alive @ ( F @ setIn ) )
& ~ ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ( ( E @ host )
= ( D @ host ) )
& ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_1 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( E @ host @ queue @ ( D @ ( E @ m_Ack ) @ elem ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( pendack @ index ) @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Ldr @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ! [D: $i] :
( ( ( B @ host )
!= ( D @ host ) )
=> ! [E: $i,F: $i,G: $i] :
( ( ( C @ host )
= ( G @ host ) )
=> ( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( ( F @ host )
= ( G @ host @ ( pendack @ index ) @ s ) )
& ( ( E @ host )
= ( G @ host @ ( pendack @ index ) ) )
& ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( E @ ( G @ m_Ack ) @ elem ) )
& ( B @ ( C @ m_Ack ) @ ( G @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( G @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( G @ setIn ) ) )
=> ~ ( ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) )
& ( alive @ ( D @ setIn ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(71,plain,
! [ZK: $i,ZJ: $i,ZI: $i,ZH: $i,ZG: $i,ZF: $i,ZE: $i,ZD: $i,ZC: $i,ZB: $i,ZA: $i,Z: $i,Y: $i,X: $i,W: $i,V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ host @ ( status @ index ) )
= norm )
& ( ( sk5 @ host @ ( ldr @ index ) )
= ( sk5 @ host ) )
& ( alive @ ( sk5 @ setIn ) )
& ( ( sk7 @ host )
= ( sk8 @ host @ ( pendack @ index ) @ s ) )
& ( ( sk6 @ host )
= ( sk8 @ host @ ( pendack @ index ) ) )
& ( ( sk8 @ host @ ( status @ index ) )
= elec_2 )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( sk8 @ host @ queue @ snoc ) @ ( sk6 @ ( sk8 @ m_Ack ) @ elem ) )
& ( sk2 @ ( sk3 @ m_Ack ) @ ( sk8 @ host @ queue @ snoc ) @ ( sk7 @ m_Down @ elem ) )
& ( sk8 @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
& ( alive @ ( sk8 @ setIn ) )
& ( ( sk2 @ host )
!= ( sk8 @ host ) )
& ( ( sk3 @ host )
= ( sk8 @ host ) )
& ( ( sk2 @ host )
!= ( sk5 @ host ) )
& ( alive @ ( sk2 @ setIn ) )
& ( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Halt @ cons ) ) )
& ( ( ( ZK @ host @ ( status @ index ) )
!= norm )
| ( ( ZK @ host @ ( ldr @ index ) )
!= ( ZK @ host ) )
| ~ ( alive @ ( ZK @ setIn ) )
| ( ( ZI @ host )
!= ( ZJ @ host @ ( pendack @ index ) @ s ) )
| ( ( ZH @ host )
!= ( ZJ @ host @ ( pendack @ index ) ) )
| ( ( ZJ @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( ZJ @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( ZJ @ host @ queue @ ( ZI @ m_Down @ elem ) )
| ~ ( ZJ @ host @ queue @ ( ZH @ ( ZJ @ m_Ack ) @ elem ) )
| ~ ( alive @ ( ZJ @ setIn ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= nbr_proc )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ( ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) )
!= ( ZF @ host ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= nbr_proc )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ~ ( ZG @ host @ ( down @ index ) @ ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) @ setIn ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= nbr_proc )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) @ ( zero @ s @ leq ) ) )
& ( ~ ( ZD @ host @ queue @ ( ZE @ m_Down @ elem ) )
| ~ ( alive @ ( ZD @ setIn ) )
| ( ( ZG @ host @ ( status @ index ) )
!= elec_1 )
| ( ( ZG @ host )
!= nbr_proc )
| ( ( ZG @ host )
!= ( ZE @ host ) )
| ~ ( ZG @ host @ queue @ ( ZF @ m_Down @ elem ) )
| ~ ( ZD @ ( ZE @ ( ZF @ ( ZG @ sk4 ) ) ) @ ( ZG @ host @ leq ) ) )
& ( ( ( ZA @ host @ ( status @ index ) )
!= norm )
| ( ( ZA @ host @ ( ldr @ index ) )
!= ( ZA @ host ) )
| ~ ( alive @ ( ZA @ setIn ) )
| ( ( ZC @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( ZB @ host @ queue @ ( ZC @ m_Halt @ elem ) )
| ~ ( alive @ ( ZC @ setIn ) )
| ( ZA @ host @ ( ZC @ host @ ( pendack @ index ) @ leq ) ) )
& ( ~ ( Z @ host @ ( pendack @ index ) @ ( Y @ host @ ( pendack @ index ) @ leq ) )
| ( ( Z @ host @ ( status @ index ) )
!= elec_2 )
| ( ( Y @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( Z @ setIn ) )
| ~ ( alive @ ( Y @ setIn ) )
| ( Z @ host @ ( Y @ host @ leq ) ) )
& ( ~ ( V @ host @ queue @ ( W @ ( V @ m_Ack ) @ elem ) )
| ( ( X @ host @ ( status @ index ) )
!= elec_2 )
| ( ( V @ host @ ( status @ index ) )
!= elec_2 )
| ( ( X @ host )
!= ( W @ host ) )
| ~ ( alive @ ( X @ setIn ) )
| ~ ( alive @ ( V @ setIn ) ) )
& ( ( ( S @ host @ ( status @ index ) )
!= norm )
| ( ( S @ host @ ( ldr @ index ) )
!= ( S @ host ) )
| ~ ( alive @ ( S @ setIn ) )
| ( ( T @ host )
!= ( S @ host ) )
| ~ ( U @ host @ queue @ ( T @ m_Down @ elem ) )
| ~ ( alive @ ( U @ setIn ) ) )
& ( ( Q @ host @ ( R @ host @ ( pendack @ index ) @ leq ) )
| ( ( R @ host @ ( status @ index ) )
!= elec_2 )
| ( ( Q @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( R @ setIn ) )
| ~ ( alive @ ( Q @ setIn ) )
| ( R @ host @ ( Q @ host @ leq ) ) )
& ( ( ( P @ host @ ( elid @ index ) )
= P )
| ~ ( alive @ ( P @ setIn ) )
| ( ( P @ host @ ( status @ index ) )
!= elec_2 ) )
& ( ( ( P @ host @ ( elid @ index ) )
= P )
| ~ ( alive @ ( P @ setIn ) )
| ( ( P @ host @ ( status @ index ) )
!= elec_1 ) )
& ( ~ ( O @ host @ queue @ ( N @ ( O @ m_Ack ) @ elem ) )
| ( ( O @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( alive @ ( O @ setIn ) ) )
& ( ( M @ host @ ( pendack @ index ) @ ( L @ host @ leq ) )
| ~ ( M @ host @ queue @ ( L @ ( M @ m_Ack ) @ elem ) )
| ~ ( alive @ ( M @ setIn ) ) )
& ( ~ ( alive @ ( K @ setIn ) )
| ~ ( alive @ ( J @ setIn ) )
| ( ( K @ host )
!= ( J @ host ) )
| ( K = J ) )
& ( ~ ( I @ host @ ( G @ host @ leq ) )
| ~ ( H @ host @ queue @ ( G @ ( I @ m_Ack ) @ elem ) ) )
& ( ~ ( F @ host @ ( E @ host @ leq ) )
| ~ ( E @ host @ queue @ ( F @ m_Halt @ elem ) ) )
& ( ( ( D @ host )
!= ( C @ host ) )
| ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(77,plain,
( ( sk2 @ host )
!= ( sk8 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(127,plain,
( ( sk8 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(78,plain,
( ( sk3 @ host )
= ( sk8 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(117,plain,
( ( sk8 @ host )
= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(479,plain,
( ( sk3 @ host )
!= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[127,117]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).
thf(347,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(97,plain,
( ( sk8 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(126,plain,
( ( sk8 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[97]) ).
thf(494,plain,
( ( sk3 @ host @ ( status @ index ) )
= elec_2 ),
inference(rewrite,[status(thm)],[126,117]) ).
thf(98,plain,
( ( sk7 @ host )
= ( sk8 @ host @ ( pendack @ index ) @ s ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(135,plain,
( ( sk8 @ host @ ( pendack @ index ) @ s )
= ( sk7 @ host ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(767,plain,
( ( sk3 @ host @ ( pendack @ index ) @ s )
= ( sk7 @ host ) ),
inference(rewrite,[status(thm)],[135,117]) ).
thf(770,plain,
( ( ( sk3 @ host @ ( status @ index ) )
!= ( sk3 @ host @ ( pendack @ index ) ) )
| ( ( elec_2 @ s )
= ( sk7 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[494,767]) ).
thf(777,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( status != pendack )
| ( ( elec_2 @ s )
= ( sk7 @ host ) ) ),
inference(simp,[status(thm)],[770]) ).
thf(784,plain,
( ( status != pendack )
| ( ( elec_2 @ s )
= ( sk7 @ host ) ) ),
inference(simp,[status(thm)],[777]) ).
thf(84,plain,
( ( sk6 @ host )
= ( sk8 @ host @ ( pendack @ index ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(106,plain,
( ( sk8 @ host @ ( pendack @ index ) )
= ( sk6 @ host ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(505,plain,
( ( sk3 @ host @ ( pendack @ index ) )
= ( sk6 @ host ) ),
inference(rewrite,[status(thm)],[106,117]) ).
thf(771,plain,
( ( ( sk3 @ host @ ( pendack @ index ) )
!= ( sk3 @ host @ ( pendack @ index ) ) )
| ( ( sk6 @ host @ s )
= ( sk7 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[505,767]) ).
thf(772,plain,
( ( sk6 @ host @ s )
= ( sk7 @ host ) ),
inference(pattern_uni,[status(thm)],[771:[]]) ).
thf(16,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_02) ).
thf(202,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(203,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[202]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).
thf(403,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(404,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[403]) ).
thf(405,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[404]) ).
thf(1827,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,405]) ).
thf(1828,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1827]) ).
thf(1838,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1828]) ).
thf(1851,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1838]) ).
thf(2410,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ host @ s ) )
| ( ( zero @ s )
!= ( sk7 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[772,1851]) ).
thf(2411,plain,
( ( zero @ s )
!= ( sk7 @ host ) ),
inference(pattern_uni,[status(thm)],[2410:[bind(A,$thf( sk6 ))]]) ).
thf(2422,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( ( sk7 @ host )
!= ( sk7 @ host ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[784,2411]) ).
thf(2423,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2422]) ).
thf(2427,plain,
( ( zero != elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2423]) ).
thf(72,plain,
sk8 @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(480,plain,
sk3 @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[72,117]) ).
thf(928,plain,
sk7 @ host @ ( nbr_proc @ leq ),
inference(rewrite,[status(thm)],[480,767]) ).
thf(929,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[117,928]) ).
thf(941,plain,
( ( sk8 != sk7 )
| ( sk3 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[929]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_63) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( ( B @ s @ ( A @ s @ leq ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( B @ s @ ( A @ s @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(234,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)],[233]) ).
thf(235,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)],[234]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[235]) ).
thf(8085,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)],[203,236]) ).
thf(8086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[8085]) ).
thf(8087,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[8086:[bind(A,$thf( E )),bind(B,$thf( zero @ s )),bind(C,$thf( E @ host ))]]) ).
thf(8129,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(simp,[status(thm)],[8087]) ).
thf(16734,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8129,236]) ).
thf(16735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[16734]) ).
thf(16736,plain,
! [A: $i] : ( A @ host @ s @ s @ ( zero @ s @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[16735:[bind(A,$thf( G )),bind(B,$thf( zero @ s @ s )),bind(C,$thf( G @ host @ s ))]]) ).
thf(16797,plain,
! [A: $i] : ( A @ host @ s @ s @ ( zero @ s @ s @ s @ leq ) ),
inference(simp,[status(thm)],[16736]) ).
thf(1817,plain,
! [A: $i] :
( ( ( elec_2 @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk7 @ host @ leq ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[784,405]) ).
thf(1818,plain,
( ~ ( elec_2 @ ( sk7 @ host @ leq ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[1817:[bind(A,$thf( elec_2 ))]]) ).
thf(96,plain,
( ( sk2 @ host )
!= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(128,plain,
( ( sk5 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(481,plain,
sk5 != sk2,
inference(simp,[status(thm)],[128]) ).
thf(4073,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ~ $true
| ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[365,405]) ).
thf(4074,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[4073]) ).
thf(4075,plain,
! [A: $i] : ( A @ s @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[4074:[bind(A,$thf( A )),bind(B,$thf( A @ s )),bind(C,$thf( A ))]]) ).
thf(4456,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4075,405]) ).
thf(4457,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[4456]) ).
thf(4465,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[4457]) ).
thf(4477,plain,
! [A: $i] :
( ( A @ s @ s )
!= A ),
inference(simp,[status(thm)],[4465]) ).
thf(4508,plain,
! [A: $i] :
( ( ( A @ s @ s )
!= ( sk6 @ host @ s ) )
| ( ( sk7 @ host )
!= A ) ),
inference(paramod_ordered,[status(thm)],[772,4477]) ).
thf(4521,plain,
( ( sk7 @ host @ s @ s )
!= ( sk6 @ host @ s ) ),
inference(simp,[status(thm)],[4508]) ).
thf(4571,plain,
( ( sk7 @ host @ s @ s )
!= ( sk7 @ host ) ),
inference(rewrite,[status(thm)],[4521,772]) ).
thf(29402,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16797,405]) ).
thf(29403,plain,
! [B: $i,A: $i] :
( ( A @ host @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[29402]) ).
thf(29422,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s @ s )
!= B )
| ( ( zero @ s @ s @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[29403]) ).
thf(29477,plain,
! [A: $i] :
( ( A @ host @ s @ s @ s )
!= ( zero @ s @ s @ s ) ),
inference(simp,[status(thm)],[29422]) ).
thf(29504,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host @ s @ s @ s )
!= ( zero @ s @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[117,29477]) ).
thf(29505,plain,
( ( sk3 @ host @ s @ s @ s )
!= ( zero @ s @ s @ s ) ),
inference(pattern_uni,[status(thm)],[29504:[bind(A,$thf( sk8 ))]]) ).
thf(18,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_04) ).
thf(208,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(209,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[208]) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[209,405]) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1823]) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1824]) ).
thf(1852,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[1839]) ).
thf(2108,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[117,1852]) ).
thf(2109,plain,
( ( nbr_proc @ s )
!= ( sk3 @ host ) ),
inference(pattern_uni,[status(thm)],[2108:[bind(A,$thf( sk8 ))]]) ).
thf(2110,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( nbr_proc @ s ) )
| ( ( sk7 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[772,1852]) ).
thf(2125,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= nbr_proc )
| ( sk7 != A ) ),
inference(simp,[status(thm)],[2110]) ).
thf(2131,plain,
( ( sk6 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[2125]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ ordered )
<=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_53) ).
thf(321,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ( A @ cons ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(322,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)],[321]) ).
thf(323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ cons ) @ ordered )
| ~ ( D @ ( E @ sk17 ) @ pidMsg @ ( D @ pidMsg @ leq ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( ( D @ ( E @ sk17 ) @ pidMsg @ host )
= ( D @ pidMsg @ host ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ ( E @ sk17 ) @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( E @ ( D @ ( E @ sk17 ) @ 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)],[322]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[328]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(249,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(83,plain,
sk2 @ ( sk3 @ m_Ack ) @ ( sk8 @ host @ queue @ snoc ) @ ( sk6 @ ( sk8 @ m_Ack ) @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(518,plain,
sk2 @ ( sk3 @ m_Ack ) @ ( sk3 @ host @ queue @ snoc ) @ ( sk6 @ ( sk8 @ m_Ack ) @ elem ),
inference(rewrite,[status(thm)],[83,117]) ).
thf(1807,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk8 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[941,405]) ).
thf(1808,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1807]) ).
thf(1837,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( ( A @ s )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1808]) ).
thf(1850,plain,
( ( ( sk3 @ host @ s )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[1837]) ).
thf(509,plain,
( ( ( sk3 @ host @ ( status @ index ) )
!= ( sk3 @ host @ ( pendack @ index ) ) )
| ( ( sk6 @ host )
= elec_2 ) ),
inference(paramod_ordered,[status(thm)],[505,494]) ).
thf(513,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( status != pendack )
| ( ( sk6 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[509]) ).
thf(516,plain,
( ( status != pendack )
| ( ( sk6 @ host )
= elec_2 ) ),
inference(simp,[status(thm)],[513]) ).
thf(955,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( elec_2 @ ( zero @ s @ leq ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,203]) ).
thf(956,plain,
( ( elec_2 @ ( zero @ s @ leq ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[955:[bind(A,$thf( sk6 ))]]) ).
thf(1813,plain,
! [A: $i] :
( ( ( elec_2 @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[956,405]) ).
thf(1814,plain,
! [A: $i] :
( ( ( elec_2 @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1813]) ).
thf(1842,plain,
! [A: $i] :
( ( elec_2 != A )
| ( ( zero @ s )
!= ( A @ s ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1814]) ).
thf(1855,plain,
( ( ( zero @ s )
!= ( elec_2 @ s ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1842]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).
thf(280,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) ) )
& ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(281,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)],[280]) ).
thf(282,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)],[281]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[282]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[284]) ).
thf(288,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[287]) ).
thf(1815,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk7 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[772,405]) ).
thf(1816,plain,
~ ( sk6 @ host @ ( sk7 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[1815:[bind(A,$thf( sk6 @ host ))]]) ).
thf(1892,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ~ ( sk3 @ host @ ( sk7 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[117,1816]) ).
thf(1916,plain,
( ( sk8 != sk6 )
| ~ ( sk3 @ host @ ( sk7 @ host @ leq ) ) ),
inference(simp,[status(thm)],[1892]) ).
thf(17604,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk7 @ host @ leq ) ) )
| ( sk8 != sk6 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,1916]) ).
thf(17605,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk7 @ host @ leq ) ) )
| ( sk8 != sk6 ) ),
inference(simp,[status(thm)],[17604]) ).
thf(17701,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( A
!= ( sk7 @ host ) )
| ( sk8 != sk6 ) ),
inference(simp,[status(thm)],[17605]) ).
thf(17739,plain,
( ( ( sk7 @ host )
!= ( sk3 @ host ) )
| ( sk8 != sk6 ) ),
inference(simp,[status(thm)],[17701]) ).
thf(24087,plain,
( ( sk7 != sk3 )
| ( sk8 != sk6 ) ),
inference(simp,[status(thm)],[17739]) ).
thf(34,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).
thf(301,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(302,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[301]) ).
thf(303,plain,
! [A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[302]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).
thf(354,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( B @ ( C @ snoc ) @ ( A @ elem ) ) )
& ( ( B @ ( C @ snoc ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(355,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)],[354]) ).
thf(356,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)],[355]) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[356]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(362,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[361]) ).
thf(4670,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( A @ ( B @ elem ) )
| ( A = q_nil ) ),
inference(paramod_ordered,[status(thm)],[303,362]) ).
thf(4671,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(pattern_uni,[status(thm)],[4670:[bind(A,$thf( E )),bind(B,$thf( E @ last )),bind(C,$thf( E @ init ))]]) ).
thf(4703,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(simp,[status(thm)],[4671]) ).
thf(93,plain,
alive @ ( sk8 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(8,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
thf(176,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(177,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[176]) ).
thf(466,plain,
( ( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,177]) ).
thf(467,plain,
( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[466]) ).
thf(472,plain,
( ( alive != alive )
| ( sk8 != nil ) ),
inference(simp,[status(thm)],[467]) ).
thf(475,plain,
sk8 != nil,
inference(simp,[status(thm)],[472]) ).
thf(5140,plain,
! [A: $i] :
( ( A != sk8 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,475]) ).
thf(5141,plain,
( ( nil != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5140:[bind(A,$thf( sk8 ))]]) ).
thf(76,plain,
( ( sk5 @ host @ ( status @ index ) )
= norm ),
inference(cnfConj,[status(thm)],[71]) ).
thf(134,plain,
( ( sk5 @ host @ ( status @ index ) )
= norm ),
inference(lifteq,[status(thm)],[76]) ).
thf(498,plain,
( ( ( sk5 @ host @ ( status @ index ) )
!= ( sk3 @ host @ ( status @ index ) ) )
| ( norm = elec_2 ) ),
inference(paramod_ordered,[status(thm)],[134,494]) ).
thf(501,plain,
( ( ( sk5 @ host )
!= ( sk3 @ host ) )
| ( status != status )
| ( norm = elec_2 ) ),
inference(simp,[status(thm)],[498]) ).
thf(503,plain,
( ( ( sk5 @ host )
!= ( sk3 @ host ) )
| ( norm = elec_2 ) ),
inference(simp,[status(thm)],[501]) ).
thf(40,axiom,
elec_2 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_09) ).
thf(338,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(339,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[338]) ).
thf(340,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[339]) ).
thf(986,plain,
( ( sk5 @ host )
!= ( sk3 @ host ) ),
inference(simplifyReflect,[status(thm)],[503,340]) ).
thf(988,plain,
( ( ( sk8 @ host )
!= ( sk5 @ host ) )
| ( ( sk3 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[117,986]) ).
thf(989,plain,
( ( sk8 @ host )
!= ( sk5 @ host ) ),
inference(simp,[status(thm)],[988]) ).
thf(993,plain,
sk8 != sk5,
inference(simp,[status(thm)],[989]) ).
thf(5915,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk5 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,993]) ).
thf(5916,plain,
( ( sk5 != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5915:[bind(A,$thf( sk8 ))]]) ).
thf(63,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_45) ).
thf(419,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(420,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[419]) ).
thf(421,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[420]) ).
thf(16162,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk5 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[5916,421]) ).
thf(16163,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[16162]) ).
thf(16274,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( sk8 @ last )
!= A )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[16163]) ).
thf(16308,plain,
( ( sk8 != q_nil )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[16274]) ).
thf(992,plain,
( ( ( sk6 @ host )
!= ( sk5 @ host ) )
| ( ( sk3 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,986]) ).
thf(994,plain,
( ( sk6 != sk5 )
| ( ( sk3 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[992]) ).
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(449,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(50,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(376,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(377,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[376]) ).
thf(378,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[377]) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[378]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ pidElem )
<=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).
thf(269,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) )
=> ( A @ pidElem ) )
& ( ( A @ pidElem )
=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(217,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
thf(308,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1882,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk7 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,1816]) ).
thf(1883,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk7 @ host @ leq ) ) ),
inference(simp,[status(thm)],[1882]) ).
thf(1917,plain,
! [A: $i] :
( ( A
!= ( sk6 @ host ) )
| ( A
!= ( sk7 @ host ) ) ),
inference(simp,[status(thm)],[1883]) ).
thf(1932,plain,
( ( sk7 @ host )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[1917]) ).
thf(1934,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( ( sk6 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[117,1932]) ).
thf(1939,plain,
( ( sk8 != sk7 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[1934]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
thf(385,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(52,axiom,
norm != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(382,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(383,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[382]) ).
thf(384,plain,
wait != norm,
inference(lifteq,[status(thm)],[383]) ).
thf(6,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
thf(172,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
thf(256,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(257,plain,
! [A: $i] :
( ( A @ ordered )
=> ! [B: $i] : ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(miniscope,[status(thm)],[256]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ ( A @ ordered ) ),
inference(cnf,[status(esa)],[257]) ).
thf(9616,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,258]) ).
thf(9617,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(simp,[status(thm)],[9616]) ).
thf(9618,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(pattern_uni,[status(thm)],[9617:[bind(A,$thf( q_nil ))]]) ).
thf(9630,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(simp,[status(thm)],[9618]) ).
thf(55,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(393,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(394,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[393]) ).
thf(395,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(15282,plain,
! [A: $i] : ( q_nil @ ( A @ m_Ldr @ cons ) @ ordered ),
inference(rewrite,[status(thm)],[9630,395]) ).
thf(1933,plain,
sk7 != sk6,
inference(simp,[status(thm)],[1932]) ).
thf(5644,plain,
! [A: $i] :
( ( A != sk7 )
| ( sk6 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,1933]) ).
thf(5645,plain,
( ( sk6 != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5644:[bind(A,$thf( sk7 ))]]) ).
thf(9507,plain,
! [A: $i] :
( ( A != sk6 )
| ( q_nil != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,5645]) ).
thf(9508,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[9507]) ).
thf(9509,plain,
( ( sk7 @ ( sk7 @ last @ elem ) )
| ( sk6 @ ( sk6 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[9508:[bind(A,$thf( sk6 ))]]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(90,plain,
( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Halt @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(145,plain,
( ( sk1 @ ( sk3 @ m_Halt @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).
thf(259,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(260,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)],[259]) ).
thf(261,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)],[260]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[261]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[263]) ).
thf(267,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[266]) ).
thf(3379,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Halt @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[145,267]) ).
thf(3380,plain,
sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ),
inference(pattern_uni,[status(thm)],[3379:[bind(A,$thf( sk3 @ m_Halt )),bind(B,$thf( sk1 ))]]) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[261]) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(16436,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3380,268]) ).
thf(16437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[16436]) ).
thf(16438,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[16437:[bind(A,$thf( sk3 @ m_Halt )),bind(B,$thf( B )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(16572,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Halt @ elem ) ),
inference(simp,[status(thm)],[16438]) ).
thf(4076,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk7 @ host @ leq ) ) )
| ~ $true
| ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[365,1816]) ).
thf(4077,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk6 @ host @ ( sk7 @ host @ leq ) ) )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[4076]) ).
thf(4078,plain,
sk7 @ host @ ( sk6 @ host @ leq ),
inference(pattern_uni,[status(thm)],[4077:[bind(A,$thf( sk7 @ host )),bind(B,$thf( sk6 @ host ))]]) ).
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(4106,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4078,92]) ).
thf(4107,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4106]) ).
thf(4108,plain,
~ ( sk6 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[4107:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(4420,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,4108]) ).
thf(4421,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4420]) ).
thf(4428,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4421]) ).
thf(4435,plain,
! [A: $i] :
( ( A @ ( sk7 @ m_Ldr @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[4428]) ).
thf(8105,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[928,236]) ).
thf(8106,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( nbr_proc @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8105]) ).
thf(8107,plain,
sk7 @ host @ s @ ( nbr_proc @ s @ leq ),
inference(pattern_uni,[status(thm)],[8106:[bind(A,$thf( nbr_proc )),bind(B,$thf( sk7 @ host ))]]) ).
thf(8177,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8107,405]) ).
thf(8178,plain,
! [A: $i] :
( ( sk7 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8177]) ).
thf(8197,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= A )
| ( ( nbr_proc @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8178]) ).
thf(8204,plain,
( ( sk7 @ host @ s @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[8197]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[282]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(7,axiom,
elec_1 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_06) ).
thf(173,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(174,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[173]) ).
thf(175,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[174]) ).
thf(21155,plain,
! [B: $i,A: $i] :
( ( A != wait )
| ( B != elec_1 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[286,175]) ).
thf(21156,plain,
! [A: $i] :
( ( A != elec_1 )
| ~ ( wait @ ( A @ leq ) )
| ~ ( A @ ( wait @ leq ) ) ),
inference(pattern_uni,[status(thm)],[21155:[bind(A,$thf( wait ))]]) ).
thf(22300,plain,
( ~ ( wait @ ( elec_1 @ leq ) )
| ~ ( elec_1 @ ( wait @ leq ) ) ),
inference(simp,[status(thm)],[21156]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(149,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)],[148]) ).
thf(150,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)],[149]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[150]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(4940,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,481]) ).
thf(4941,plain,
( ( sk2 != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4940:[bind(A,$thf( sk5 ))]]) ).
thf(5665,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ( q_nil != B )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,4477]) ).
thf(5666,plain,
! [A: $i] :
( ( q_nil != A )
| ( A @ s @ s @ ( A @ s @ s @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5665:[bind(A,$thf( D @ s @ s )),bind(B,$thf( D ))]]) ).
thf(6466,plain,
q_nil @ s @ s @ ( q_nil @ s @ s @ last @ elem ),
inference(simp,[status(thm)],[5666]) ).
thf(967,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)],[288,92]) ).
thf(968,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)],[967]) ).
thf(969,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[968:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(975,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Ldr @ elem ) ),
inference(simp,[status(thm)],[969]) ).
thf(2603,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk3 @ host @ queue @ ( A @ m_Ldr @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[117,975]) ).
thf(2604,plain,
~ ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ),
inference(pattern_uni,[status(thm)],[2603:[bind(A,$thf( sk8 ))]]) ).
thf(3637,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,2604]) ).
thf(3638,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[3637]) ).
thf(3671,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[3638]) ).
thf(3707,plain,
! [A: $i] :
( ( sk8 @ m_Ldr @ ( A @ snoc ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[3671]) ).
thf(3993,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[395,3707]) ).
thf(3994,plain,
( ( q_nil @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[3993:[bind(A,$thf( sk8 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(1641,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( sk6 != sk5 )
| ( elec_2 != elec_2 )
| ( status != pendack )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,994]) ).
thf(1642,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( sk6 != sk5 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1641]) ).
thf(1645,plain,
( ( sk6 != sk3 )
| ( sk6 != sk5 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1642]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(317,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(318,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[317]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[318]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[319]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(2365,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( B != A ) ),
inference(simp,[status(thm)],[130]) ).
thf(2405,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(simp,[status(thm)],[2365]) ).
thf(1938,plain,
( ( sk8 != sk7 )
| ( ( sk6 @ host )
!= ( sk3 @ host ) ) ),
inference(simp,[status(thm)],[1934]) ).
thf(3592,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( sk8 != sk7 )
| ( ( sk3 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[117,1938]) ).
thf(3593,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[3592]) ).
thf(3597,plain,
( ( sk8 != sk6 )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[3593]) ).
thf(103,plain,
alive @ ( sk5 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(23,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).
thf(224,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(225,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[224]) ).
thf(226,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[225]) ).
thf(523,plain,
! [A: $i] :
( ( ( alive @ ( sk5 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,226]) ).
thf(524,plain,
! [A: $i] :
( ( alive @ ( sk5 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[523]) ).
thf(528,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk5 != A ) ),
inference(simp,[status(thm)],[524]) ).
thf(530,plain,
setEmpty != alive,
inference(simp,[status(thm)],[528]) ).
thf(5497,plain,
! [A: $i] :
( ( A != setEmpty )
| ( q_nil != alive )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,530]) ).
thf(5498,plain,
( ( q_nil != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5497:[bind(A,$thf( setEmpty ))]]) ).
thf(9038,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( q_nil != alive ) ),
inference(paramod_ordered,[status(thm)],[5498,421]) ).
thf(9039,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[9038]) ).
thf(9104,plain,
! [A: $i] :
( ( setEmpty != q_nil )
| ( ( setEmpty @ last )
!= A )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[9039]) ).
thf(9159,plain,
( ( setEmpty != q_nil )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[9104]) ).
thf(2132,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( ( sk3 @ host )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[117,2131]) ).
thf(2136,plain,
( ( sk8 != sk6 )
| ( ( sk3 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2132]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
thf(227,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(228,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( C @ ( A @ m_Ack ) )
= ( D @ ( B @ m_Ack ) ) ) ),
inference(miniscope,[status(thm)],[227]) ).
thf(229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[228]) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[229]) ).
thf(231,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[230]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk12 ) )
= A ),
inference(cnf,[status(esa)],[231]) ).
thf(4610,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk12 ) )
= A ),
inference(lifteq,[status(thm)],[232]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[179]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[180]) ).
thf(182,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[181]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk11 ) )
= B ),
inference(cnf,[status(esa)],[182]) ).
thf(4524,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk11 ) )
= B ),
inference(lifteq,[status(thm)],[183]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(184,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(369,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(370,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[369]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[370]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[371]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[109]) ).
thf(607,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( elec_2 @ leq ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,209]) ).
thf(608,plain,
( ( nbr_proc @ ( elec_2 @ leq ) )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[607:[bind(A,$thf( sk6 ))]]) ).
thf(1821,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ~ $true
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[608,405]) ).
thf(1822,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( elec_2 @ leq ) ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1821]) ).
thf(1847,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1822]) ).
thf(1860,plain,
( ( ( nbr_proc @ s )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1847]) ).
thf(5129,plain,
! [A: $i] :
( ( A != sk8 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,93]) ).
thf(5130,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5129:[bind(A,$thf( sk8 ))]]) ).
thf(8077,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)],[209,236]) ).
thf(8078,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[8077]) ).
thf(8079,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[8078:[bind(A,$thf( D )),bind(B,$thf( D @ host )),bind(C,$thf( nbr_proc ))]]) ).
thf(8128,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(simp,[status(thm)],[8079]) ).
thf(9303,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ host @ s ) )
| ( nbr_proc @ s @ ( sk7 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[772,8128]) ).
thf(9304,plain,
nbr_proc @ s @ ( sk7 @ host @ leq ),
inference(pattern_uni,[status(thm)],[9303:[bind(A,$thf( sk6 ))]]) ).
thf(9375,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( sk7 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9304,236]) ).
thf(9376,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( sk7 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[9375]) ).
thf(9377,plain,
nbr_proc @ s @ s @ ( sk7 @ host @ s @ leq ),
inference(pattern_uni,[status(thm)],[9376:[bind(A,$thf( sk7 @ host )),bind(B,$thf( nbr_proc @ s ))]]) ).
thf(9656,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk7 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9377,236]) ).
thf(9657,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk7 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[9656]) ).
thf(9658,plain,
nbr_proc @ s @ s @ s @ ( sk7 @ host @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[9657:[bind(A,$thf( sk7 @ host @ s )),bind(B,$thf( nbr_proc @ s @ s ))]]) ).
thf(15485,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( sk7 @ host @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9658,236]) ).
thf(15486,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( sk7 @ host @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[15485]) ).
thf(15487,plain,
nbr_proc @ s @ s @ s @ s @ ( sk7 @ host @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[15486:[bind(A,$thf( sk7 @ host @ s @ s )),bind(B,$thf( nbr_proc @ s @ s @ s ))]]) ).
thf(28604,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ s @ ( sk7 @ host @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15487,405]) ).
thf(28605,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ s @ ( sk7 @ host @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[28604]) ).
thf(28627,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ s )
!= A )
| ( ( sk7 @ host @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[28605]) ).
thf(28691,plain,
( ( nbr_proc @ s @ s @ s @ s @ s )
!= ( sk7 @ host @ s @ s @ s ) ),
inference(simp,[status(thm)],[28627]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(389,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( zero @ s @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(341,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(342,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[341]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[342]) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[343]) ).
thf(21075,plain,
! [B: $i,A: $i] :
( ( A != sk8 )
| ( B != sk5 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[286,993]) ).
thf(21076,plain,
! [A: $i] :
( ( A != sk5 )
| ~ ( sk8 @ ( A @ leq ) )
| ~ ( A @ ( sk8 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[21075:[bind(A,$thf( sk8 ))]]) ).
thf(22268,plain,
( ~ ( sk8 @ ( sk5 @ leq ) )
| ~ ( sk5 @ ( sk8 @ leq ) ) ),
inference(simp,[status(thm)],[21076]) ).
thf(2627,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk3 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[117,2405]) ).
thf(2628,plain,
~ ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[2627:[bind(A,$thf( sk8 ))]]) ).
thf(3361,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,2628]) ).
thf(3362,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3361]) ).
thf(3430,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[3362]) ).
thf(3470,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[3430]) ).
thf(37,axiom,
elec_2 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_08) ).
thf(314,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(315,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[314]) ).
thf(316,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[315]) ).
thf(478,plain,
sk8 != sk2,
inference(simp,[status(thm)],[127]) ).
thf(6125,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,478]) ).
thf(6126,plain,
( ( sk2 != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[6125:[bind(A,$thf( sk8 ))]]) ).
thf(16954,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk2 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[6126,421]) ).
thf(16955,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[16954]) ).
thf(17060,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( sk8 @ last )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[16955]) ).
thf(17107,plain,
( ( sk8 != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[17060]) ).
thf(9681,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk7 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9377,405]) ).
thf(9682,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ ( sk7 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[9681]) ).
thf(9690,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s )
!= A )
| ( ( sk7 @ host @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[9682]) ).
thf(9712,plain,
( ( nbr_proc @ s @ s @ s )
!= ( sk7 @ host @ s ) ),
inference(simp,[status(thm)],[9690]) ).
thf(91,plain,
alive @ ( sk2 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(470,plain,
( ( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[91,177]) ).
thf(471,plain,
( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[470]) ).
thf(474,plain,
( ( alive != alive )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[471]) ).
thf(477,plain,
sk2 != nil,
inference(simp,[status(thm)],[474]) ).
thf(5692,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,477]) ).
thf(5693,plain,
( ( nil != q_nil )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5692:[bind(A,$thf( sk2 ))]]) ).
thf(9913,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( nil != q_nil ) ),
inference(paramod_ordered,[status(thm)],[5693,421]) ).
thf(9914,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[9913]) ).
thf(10009,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( sk2 @ last )
!= A )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[9914]) ).
thf(10046,plain,
( ( sk2 != q_nil )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[10009]) ).
thf(1805,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,405]) ).
thf(1806,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1805]) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1806]) ).
thf(1856,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[1843]) ).
thf(5401,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ( q_nil != B )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,1856]) ).
thf(5402,plain,
! [A: $i] :
( ( q_nil != A )
| ( A @ s @ ( A @ s @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5401:[bind(A,$thf( C @ s )),bind(B,$thf( C ))]]) ).
thf(6413,plain,
q_nil @ s @ ( q_nil @ s @ last @ elem ),
inference(simp,[status(thm)],[5402]) ).
thf(16393,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6413,268]) ).
thf(16394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[16393]) ).
thf(16395,plain,
! [A: $i] : ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[16394:[bind(A,$thf( q_nil @ s @ last )),bind(B,$thf( B )),bind(C,$thf( q_nil @ s ))]]) ).
thf(16550,plain,
! [A: $i] : ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) ),
inference(simp,[status(thm)],[16395]) ).
thf(25863,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16550,421]) ).
thf(25864,plain,
! [B: $i,A: $i] :
( ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[25863]) ).
thf(26026,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ s @ ( A @ cons ) )
!= q_nil )
| ( ( q_nil @ s @ last )
!= B ) ),
inference(simp,[status(thm)],[25864]) ).
thf(26100,plain,
! [A: $i] :
( ( q_nil @ s @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[26026]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).
thf(253,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[235]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(309,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[308]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[310]) ).
thf(804,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Halt @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[145,311]) ).
thf(805,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Halt )
!= A )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[804]) ).
thf(806,plain,
( ( sk1 != q_nil )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[805]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(350,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(351,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[350]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[351]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[352]) ).
thf(20,axiom,
elec_1 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_07) ).
thf(214,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(215,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[214]) ).
thf(216,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[215]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(4094,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4078,144]) ).
thf(4095,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ host @ ( A @ host @ leq ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4094]) ).
thf(4096,plain,
~ ( sk6 @ host @ queue @ ( sk7 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[4095:[bind(A,$thf( sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(4395,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,4096]) ).
thf(4396,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4395]) ).
thf(4406,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4396]) ).
thf(4411,plain,
! [A: $i] :
( ( sk7 @ m_Halt @ ( A @ snoc ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[4406]) ).
thf(6970,plain,
! [A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6413,421]) ).
thf(6971,plain,
! [A: $i] :
( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[6970]) ).
thf(7046,plain,
! [A: $i] :
( ( ( q_nil @ s )
!= q_nil )
| ( ( q_nil @ s @ last )
!= A ) ),
inference(simp,[status(thm)],[6971]) ).
thf(7107,plain,
( ( q_nil @ s )
!= q_nil ),
inference(simp,[status(thm)],[7046]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
thf(399,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(400,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[399]) ).
thf(401,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[400]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[401]) ).
thf(1631,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Halt @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[145,402]) ).
thf(1632,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[1631:[bind(A,$thf( sk3 @ m_Halt )),bind(B,$thf( sk1 ))]]) ).
thf(7532,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( nil != q_nil ) ),
inference(paramod_ordered,[status(thm)],[5141,421]) ).
thf(7533,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[7532]) ).
thf(7616,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( sk8 @ last )
!= A )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[7533]) ).
thf(7656,plain,
( ( sk8 != q_nil )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[7616]) ).
thf(7675,plain,
! [A: $i] :
( ( A != nil )
| ( sk8 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,7656]) ).
thf(7676,plain,
! [A: $i] :
( ( A != nil )
| ( sk8 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[7675]) ).
thf(7677,plain,
( ( sk8 != q_nil )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[7676:[bind(A,$thf( nil ))]]) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) )
| ( ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) )
!= ( C @ host ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(409,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(410,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[409]) ).
thf(411,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[410]) ).
thf(88,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(115,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(116,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[115]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[261]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[262]) ).
thf(9,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_03) ).
thf(178,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8111,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,236]) ).
thf(8112,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8111]) ).
thf(8113,plain,
nbr_proc @ s @ ( zero @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[8112:[bind(A,$thf( zero @ s )),bind(B,$thf( nbr_proc ))]]) ).
thf(8220,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)],[8113,236]) ).
thf(8221,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8220]) ).
thf(8222,plain,
nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[8221:[bind(A,$thf( zero @ s @ s )),bind(B,$thf( nbr_proc @ s ))]]) ).
thf(8886,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8222,405]) ).
thf(8887,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8886]) ).
thf(8910,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s )
!= A )
| ( ( zero @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8887]) ).
thf(8924,plain,
( ( nbr_proc @ s @ s @ s )
!= ( zero @ s @ s @ s ) ),
inference(simp,[status(thm)],[8910]) ).
thf(56,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_05) ).
thf(396,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(79,plain,
( ( sk5 @ host @ ( ldr @ index ) )
= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(143,plain,
( ( sk5 @ host @ ( ldr @ index ) )
= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(535,plain,
( ( ( sk5 @ host @ ( ldr @ index ) )
!= ( sk5 @ host @ ( status @ index ) ) )
| ( ( sk5 @ host )
= norm ) ),
inference(paramod_ordered,[status(thm)],[143,134]) ).
thf(545,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( ldr != status )
| ( ( sk5 @ host )
= norm ) ),
inference(simp,[status(thm)],[535]) ).
thf(548,plain,
( ( ldr != status )
| ( ( sk5 @ host )
= norm ) ),
inference(simp,[status(thm)],[545]) ).
thf(2133,plain,
( ( ( sk6 @ host )
!= ( sk5 @ host ) )
| ( nbr_proc != norm )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,2131]) ).
thf(2137,plain,
( ( sk6 != sk5 )
| ( nbr_proc != norm )
| ( ldr != status ) ),
inference(simp,[status(thm)],[2133]) ).
thf(8088,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4078,236]) ).
thf(8089,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8088]) ).
thf(8090,plain,
sk7 @ host @ s @ ( sk6 @ host @ s @ leq ),
inference(pattern_uni,[status(thm)],[8089:[bind(A,$thf( sk6 @ host )),bind(B,$thf( sk7 @ host ))]]) ).
thf(8686,plain,
sk7 @ host @ s @ ( sk7 @ host @ leq ),
inference(rewrite,[status(thm)],[8090,772]) ).
thf(556,plain,
( ( ( sk6 @ host )
!= ( sk5 @ host ) )
| ( ( sk2 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,128]) ).
thf(569,plain,
( ( sk6 != sk5 )
| ( ( sk2 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[556]) ).
thf(1347,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( sk6 != sk5 )
| ( elec_2 != elec_2 )
| ( status != pendack )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,569]) ).
thf(1348,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( sk6 != sk5 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1351,plain,
( ( sk6 != sk2 )
| ( sk6 != sk5 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1348]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[132]) ).
thf(1835,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[178,405]) ).
thf(1836,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[1835]) ).
thf(1840,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1853,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1840]) ).
thf(1863,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[1853]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(304,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(305,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[304]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[306]) ).
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(439,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(4436,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( elec_2 @ ( sk7 @ host @ leq ) ) )
| ~ $true
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[4075,1818]) ).
thf(4437,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( elec_2 @ ( sk7 @ host @ leq ) ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[4436]) ).
thf(4468,plain,
! [A: $i] :
( ( ( A @ s )
!= elec_2 )
| ( A
!= ( sk7 @ host ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[4437]) ).
thf(4480,plain,
( ( ( sk7 @ host @ s )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[4468]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(198,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(199,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[198]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[199]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[200]) ).
thf(489,plain,
sk3 != sk2,
inference(simp,[status(thm)],[479]) ).
thf(5433,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,489]) ).
thf(5434,plain,
( ( sk2 != q_nil )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5433:[bind(A,$thf( sk3 ))]]) ).
thf(8479,plain,
! [A: $i] :
( ( A != sk2 )
| ( q_nil != q_nil )
| ( sk3 @ ( sk3 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,5434]) ).
thf(8480,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 @ ( sk3 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[8479]) ).
thf(8481,plain,
( ( sk3 @ ( sk3 @ last @ elem ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[8480:[bind(A,$thf( sk2 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[196]) ).
thf(2904,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)],[395,197]) ).
thf(2905,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[2904:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_62) ).
thf(380,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(218,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[217]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[218]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).
thf(366,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ pidMsg @ ( A @ pidMsg @ leq ) )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( B @ ( A @ cons ) @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ pidMsg @ ( A @ pidMsg @ leq ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( B @ ( A @ cons ) @ ordered )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) ) ),
inference(lifteq,[status(thm)],[330]) ).
thf(2408,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[117,1851]) ).
thf(2409,plain,
( ( sk3 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[2408:[bind(A,$thf( sk8 ))]]) ).
thf(8155,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8107,236]) ).
thf(8156,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ s @ ( nbr_proc @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8155]) ).
thf(8157,plain,
sk7 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[8156:[bind(A,$thf( nbr_proc @ s )),bind(B,$thf( sk7 @ host @ s ))]]) ).
thf(8776,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8157,236]) ).
thf(8777,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8776]) ).
thf(8778,plain,
sk7 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[8777:[bind(A,$thf( nbr_proc @ s @ s )),bind(B,$thf( sk7 @ host @ s @ s ))]]) ).
thf(4418,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,4108]) ).
thf(4419,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[4418]) ).
thf(4433,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[4419]) ).
thf(4434,plain,
! [A: $i] :
( ( sk7 @ m_Ldr @ ( A @ snoc ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[4433]) ).
thf(5265,plain,
! [A: $i] :
( ( A != sk8 )
| ( ( sk3 @ host )
= ( q_nil @ host ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,117]) ).
thf(5266,plain,
( ( ( sk3 @ host )
= ( q_nil @ host ) )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5265:[bind(A,$thf( sk8 ))]]) ).
thf(390,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[389]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[390]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[391]) ).
thf(3870,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) )
| ~ ( B @ host @ ( A @ host @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3380,144]) ).
thf(3871,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) )
| ~ ( B @ host @ ( A @ host @ leq ) ) ),
inference(simp,[status(thm)],[3870]) ).
thf(3872,plain,
~ ( sk3 @ host @ ( sk2 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[3871:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(3931,plain,
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( sk8 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[941,3872]) ).
thf(3932,plain,
( ( ( sk3 @ host @ ( sk2 @ host @ leq ) )
!= ( sk3 @ host @ ( nbr_proc @ leq ) ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[3931]) ).
thf(3970,plain,
( ( ( sk3 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[3932]) ).
thf(3989,plain,
( ( ( sk2 @ host )
!= nbr_proc )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[3970]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).
thf(192,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(270,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)],[269]) ).
thf(271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk15 @ m_Down ) )
| ( A
= ( A @ sk14 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[270]) ).
thf(272,plain,
! [A: $i] :
( ( A
= ( A @ sk15 @ m_Down ) )
| ( A
= ( A @ sk14 @ m_Halt ) )
| ~ ( A @ pidElem ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(275,plain,
! [A: $i] :
( ~ ( A @ pidElem )
| ( ( A @ sk15 @ m_Down )
= A )
| ( ( A @ sk14 @ m_Halt )
= A ) ),
inference(lifteq,[status(thm)],[272]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( pendack @ index ) @ ( A @ host @ ( pendack @ index ) @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( pendack @ index ) @ ( A @ host @ ( pendack @ index ) @ leq ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( pendack @ index ) @ ( A @ host @ ( pendack @ index ) @ leq ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( B @ host @ ( A @ host @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[136]) ).
thf(250,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[249]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(21631,plain,
! [B: $i,A: $i] :
( ( A != sk8 )
| ( B != sk2 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[286,478]) ).
thf(21632,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( sk8 @ ( A @ leq ) )
| ~ ( A @ ( sk8 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[21631:[bind(A,$thf( sk8 ))]]) ).
thf(22505,plain,
( ~ ( sk8 @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( sk8 @ leq ) ) ),
inference(simp,[status(thm)],[21632]) ).
thf(2123,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( nbr_proc @ s ) )
| ( sk7 != A ) ),
inference(simp,[status(thm)],[2110]) ).
thf(2130,plain,
( ( sk6 @ host @ s )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2123]) ).
thf(2345,plain,
( ( nbr_proc @ s )
!= ( sk7 @ host ) ),
inference(rewrite,[status(thm)],[2130,772]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).
thf(204,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(205,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[205]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[206]) ).
thf(2546,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)],[395,207]) ).
thf(2547,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2546:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(8439,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk2 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[5434,421]) ).
thf(8440,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[8439]) ).
thf(8547,plain,
! [A: $i] :
( ( sk3 != q_nil )
| ( ( sk3 @ last )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[8440]) ).
thf(8577,plain,
( ( sk3 != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[8547]) ).
thf(624,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( ( norm @ ( status @ index ) )
= norm )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,134]) ).
thf(625,plain,
( ( ( norm @ ( status @ index ) )
= norm )
| ( ldr != status ) ),
inference(pattern_uni,[status(thm)],[624:[]]) ).
thf(8240,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8113,405]) ).
thf(8241,plain,
! [A: $i] :
( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8240]) ).
thf(8253,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= A )
| ( ( zero @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8241]) ).
thf(8270,plain,
( ( nbr_proc @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[8253]) ).
thf(5713,plain,
! [A: $i] :
( ( A != sk2 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,91]) ).
thf(5714,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5713:[bind(A,$thf( sk2 ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(188,plain,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9308,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)],[8128,236]) ).
thf(9309,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)],[9308]) ).
thf(9310,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[9309:[bind(A,$thf( E )),bind(B,$thf( E @ host @ s )),bind(C,$thf( nbr_proc @ s ))]]) ).
thf(9357,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(simp,[status(thm)],[9310]) ).
thf(25784,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9357,405]) ).
thf(25785,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[25784]) ).
thf(25808,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s )
!= B )
| ( ( A @ host @ s @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[25785]) ).
thf(25836,plain,
! [A: $i] :
( ( A @ host @ s @ s )
!= ( nbr_proc @ s @ s @ s ) ),
inference(simp,[status(thm)],[25808]) ).
thf(26947,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s @ s )
!= ( sk3 @ host @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[117,25836]) ).
thf(26948,plain,
( ( nbr_proc @ s @ s @ s )
!= ( sk3 @ host @ s @ s ) ),
inference(pattern_uni,[status(thm)],[26947:[bind(A,$thf( sk8 ))]]) ).
thf(7697,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk7 @ m_Ldr @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[395,4434]) ).
thf(7698,plain,
( ( q_nil @ ( sk7 @ m_Ldr @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[7697:[bind(A,$thf( sk7 @ m_Ldr )),bind(B,$thf( q_nil ))]]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_1 )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[140]) ).
thf(450,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)],[449]) ).
thf(451,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)],[450]) ).
thf(452,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[451]) ).
thf(454,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[452]) ).
thf(455,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[454]) ).
thf(456,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk19 )
= A ),
inference(cnf,[status(esa)],[455]) ).
thf(2460,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk19 )
= A ),
inference(lifteq,[status(thm)],[456]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(239,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(240,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)],[239]) ).
thf(241,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)],[240]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(245,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[244]) ).
thf(246,plain,
! [A: $i] :
( ( A @ m_Halt @ sk13 )
= A ),
inference(cnf,[status(esa)],[245]) ).
thf(1942,plain,
! [A: $i] :
( ( A @ m_Halt @ sk13 )
= A ),
inference(lifteq,[status(thm)],[246]) ).
thf(3846,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[288,144]) ).
thf(3847,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[3846]) ).
thf(3848,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[3847:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(3921,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(simp,[status(thm)],[3848]) ).
thf(4003,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk3 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[117,3921]) ).
thf(4004,plain,
~ ( sk3 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[4003:[bind(A,$thf( sk8 ))]]) ).
thf(4372,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,4004]) ).
thf(4373,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4372]) ).
thf(4385,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4373]) ).
thf(4389,plain,
! [A: $i] :
( ( sk8 @ m_Halt @ ( A @ snoc ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[4385]) ).
thf(3605,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,421]) ).
thf(3606,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[3605]) ).
thf(3646,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[3606]) ).
thf(3723,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[3646]) ).
thf(16759,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8129,405]) ).
thf(16760,plain,
! [B: $i,A: $i] :
( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[16759]) ).
thf(16770,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s )
!= B )
| ( ( zero @ s @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[16760]) ).
thf(16787,plain,
! [A: $i] :
( ( A @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[16770]) ).
thf(17517,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host @ s @ s )
!= ( zero @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[117,16787]) ).
thf(17518,plain,
( ( sk3 @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(pattern_uni,[status(thm)],[17517:[bind(A,$thf( sk8 ))]]) ).
thf(9394,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( sk7 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9304,405]) ).
thf(9395,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( sk7 @ host @ leq ) ) ),
inference(simp,[status(thm)],[9394]) ).
thf(9414,plain,
! [A: $i] :
( ( A
!= ( nbr_proc @ s ) )
| ( ( A @ s )
!= ( sk7 @ host ) ) ),
inference(simp,[status(thm)],[9395]) ).
thf(9419,plain,
( ( nbr_proc @ s @ s )
!= ( sk7 @ host ) ),
inference(simp,[status(thm)],[9414]) ).
thf(468,plain,
( ( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[103,177]) ).
thf(469,plain,
( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[468]) ).
thf(473,plain,
( ( alive != alive )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[469]) ).
thf(476,plain,
sk5 != nil,
inference(simp,[status(thm)],[473]) ).
thf(553,plain,
( ( ( sk6 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,479]) ).
thf(567,plain,
( ( sk6 != sk3 )
| ( ( sk2 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[553]) ).
thf(981,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( sk6 != sk3 )
| ( elec_2 != elec_2 )
| ( status != pendack )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,567]) ).
thf(982,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( sk6 != sk3 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[981]) ).
thf(985,plain,
( ( sk6 != sk2 )
| ( sk6 != sk3 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[982]) ).
thf(16730,plain,
! [A: $i] :
( ( ( sk6 @ host @ s )
!= ( A @ host @ s ) )
| ( sk7 @ host @ ( zero @ s @ s @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[772,8129]) ).
thf(16731,plain,
sk7 @ host @ ( zero @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[16730:[bind(A,$thf( sk6 ))]]) ).
thf(16841,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16731,236]) ).
thf(16842,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[16841]) ).
thf(16843,plain,
sk7 @ host @ s @ ( zero @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[16842:[bind(A,$thf( zero @ s @ s )),bind(B,$thf( sk7 @ host ))]]) ).
thf(17391,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16843,405]) ).
thf(17392,plain,
! [A: $i] :
( ( sk7 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[17391]) ).
thf(17422,plain,
! [A: $i] :
( ( ( sk7 @ host @ s )
!= A )
| ( ( zero @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[17392]) ).
thf(17429,plain,
( ( zero @ s @ s @ s )
!= ( sk7 @ host @ s @ s ) ),
inference(simp,[status(thm)],[17422]) ).
thf(630,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( norm @ leq ) )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,209]) ).
thf(631,plain,
( ( nbr_proc @ ( norm @ leq ) )
| ( ldr != status ) ),
inference(pattern_uni,[status(thm)],[630:[bind(A,$thf( sk5 ))]]) ).
thf(1819,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( norm @ leq ) ) )
| ~ $true
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[631,405]) ).
thf(1820,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( norm @ leq ) ) )
| ( ldr != status ) ),
inference(simp,[status(thm)],[1819]) ).
thf(1844,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= norm )
| ( ldr != status ) ),
inference(simp,[status(thm)],[1820]) ).
thf(1857,plain,
( ( ( nbr_proc @ s )
!= norm )
| ( ldr != status ) ),
inference(simp,[status(thm)],[1844]) ).
thf(1937,plain,
( ( ( sk8 @ host )
!= ( sk7 @ host ) )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[1934]) ).
thf(3278,plain,
( ( ( sk7 @ host )
!= ( sk3 @ host ) )
| ( sk6 != sk3 ) ),
inference(rewrite,[status(thm)],[1937,117]) ).
thf(3279,plain,
( ( sk7 != sk3 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[3278]) ).
thf(397,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[396]) ).
thf(398,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[397]) ).
thf(6633,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk2 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4941,421]) ).
thf(6634,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[6633]) ).
thf(6711,plain,
! [A: $i] :
( ( sk5 != q_nil )
| ( ( sk5 @ last )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[6634]) ).
thf(6756,plain,
( ( sk5 != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[6711]) ).
thf(3613,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,2628]) ).
thf(3614,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3613]) ).
thf(3660,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[3614]) ).
thf(3696,plain,
! [A: $i] :
( ( sk8 @ m_Down @ ( A @ snoc ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[3660]) ).
thf(3833,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Down @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[395,3696]) ).
thf(3834,plain,
( ( q_nil @ ( sk8 @ m_Down @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[3833:[bind(A,$thf( sk8 @ m_Down )),bind(B,$thf( q_nil ))]]) ).
thf(8804,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8157,405]) ).
thf(8805,plain,
! [A: $i] :
( ( sk7 @ host @ s @ s @ ( nbr_proc @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8804]) ).
thf(8836,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ s )
!= A )
| ( ( nbr_proc @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8805]) ).
thf(8839,plain,
( ( sk7 @ host @ s @ s @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[8836]) ).
thf(4643,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk8 @ m_Halt @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[395,4389]) ).
thf(4644,plain,
( ( q_nil @ ( sk8 @ m_Halt @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[4643:[bind(A,$thf( sk8 @ m_Halt )),bind(B,$thf( q_nil ))]]) ).
thf(4034,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( elec_2 @ ( sk7 @ host @ leq ) ) )
| ~ $true
| ( status != pendack )
| ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[365,1818]) ).
thf(4035,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( elec_2 @ ( sk7 @ host @ leq ) ) )
| ( status != pendack )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[4034]) ).
thf(4036,plain,
( ( status != pendack )
| ( sk7 @ host @ ( elec_2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[4035:[bind(A,$thf( sk7 @ host )),bind(B,$thf( elec_2 ))]]) ).
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(412,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(4397,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,4096]) ).
thf(4398,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk6 @ host @ queue @ ( sk7 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4397]) ).
thf(4410,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4398]) ).
thf(4412,plain,
! [A: $i] :
( ( A @ ( sk7 @ m_Halt @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(simp,[status(thm)],[4410]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[274]) ).
thf(279,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[278]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
thf(291,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Down )
!= ( B @ m_Down ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(292,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)],[291]) ).
thf(293,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)],[292]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[293]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_50) ).
thf(373,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(374,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[374]) ).
thf(82,plain,
sk2 @ ( sk3 @ m_Ack ) @ ( sk8 @ host @ queue @ snoc ) @ ( sk7 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[71]) ).
thf(486,plain,
sk2 @ ( sk3 @ m_Ack ) @ ( sk3 @ host @ queue @ snoc ) @ ( sk7 @ m_Down @ elem ),
inference(rewrite,[status(thm)],[82,117]) ).
thf(595,plain,
! [A: $i] :
( ( ( sk2 @ ( sk3 @ m_Ack ) @ ( sk3 @ host @ queue @ snoc ) @ ( sk7 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[486,421]) ).
thf(596,plain,
! [A: $i] :
( ( sk2 @ ( sk3 @ m_Ack ) @ ( sk3 @ host @ queue @ snoc ) @ ( sk7 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[595]) ).
thf(599,plain,
! [A: $i] :
( ( ( sk2 @ ( sk3 @ m_Ack ) @ ( sk3 @ host @ queue @ snoc ) )
!= q_nil )
| ( ( sk7 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[596]) ).
thf(601,plain,
( ( sk2 @ ( sk3 @ m_Ack ) @ ( sk3 @ host @ queue @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[599]) ).
thf(4452,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4075,3872]) ).
thf(4453,plain,
! [A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[4452]) ).
thf(4466,plain,
! [A: $i] :
( ( ( A @ s )
!= ( sk3 @ host ) )
| ( A
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[4453]) ).
thf(4478,plain,
( ( sk2 @ host @ s )
!= ( sk3 @ host ) ),
inference(simp,[status(thm)],[4466]) ).
thf(4487,plain,
( ( ( sk6 @ host @ s )
!= ( sk2 @ host @ s ) )
| ( ( sk7 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[772,4478]) ).
thf(4494,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( sk7 != sk3 ) ),
inference(simp,[status(thm)],[4487]) ).
thf(7495,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk5 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,6756]) ).
thf(7496,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk5 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[7495]) ).
thf(7497,plain,
( ( sk5 != q_nil )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[7496:[bind(A,$thf( sk2 ))]]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) )
& ( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[189]) ).
thf(4645,plain,
( ( sk6 != sk2 )
| ( sk7 != sk3 ) ),
inference(simp,[status(thm)],[4494]) ).
thf(6671,plain,
! [A: $i] :
( ( A != sk2 )
| ( q_nil != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,4941]) ).
thf(6672,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk5 @ ( sk5 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[6671]) ).
thf(6673,plain,
( ( sk5 @ ( sk5 @ last @ elem ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[6672:[bind(A,$thf( sk2 ))]]) ).
thf(5431,plain,
! [A: $i] :
( ( A != sk5 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,476]) ).
thf(5432,plain,
( ( nil != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5431:[bind(A,$thf( sk5 ))]]) ).
thf(7865,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( nil != q_nil ) ),
inference(paramod_ordered,[status(thm)],[5432,421]) ).
thf(7866,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[7865]) ).
thf(7945,plain,
! [A: $i] :
( ( sk5 != q_nil )
| ( ( sk5 @ last )
!= A )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[7866]) ).
thf(7991,plain,
( ( sk5 != q_nil )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[7945]) ).
thf(8008,plain,
! [A: $i] :
( ( A != nil )
| ( sk5 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,7991]) ).
thf(8009,plain,
! [A: $i] :
( ( A != nil )
| ( sk5 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[8008]) ).
thf(8010,plain,
( ( sk5 != q_nil )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[8009:[bind(A,$thf( nil ))]]) ).
thf(8860,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)],[8222,236]) ).
thf(8861,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8860]) ).
thf(8862,plain,
nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[8861:[bind(A,$thf( zero @ s @ s @ s )),bind(B,$thf( nbr_proc @ s @ s ))]]) ).
thf(1635,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( ( elec_2 @ queue )
!= q_nil )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[516,1632]) ).
thf(1638,plain,
( ( sk6 != sk2 )
| ( ( elec_2 @ queue )
!= q_nil )
| ( status != pendack ) ),
inference(simp,[status(thm)],[1635]) ).
thf(16863,plain,
! [A: $i] :
( ( ( sk7 @ host @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16731,405]) ).
thf(16864,plain,
! [A: $i] :
( ( sk7 @ host @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[16863]) ).
thf(16887,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= A )
| ( ( zero @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[16864]) ).
thf(16900,plain,
( ( zero @ s @ s )
!= ( sk7 @ host @ s ) ),
inference(simp,[status(thm)],[16887]) ).
thf(185,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[184]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_39) ).
thf(406,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(297,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[296]) ).
thf(298,plain,
! [A: $i] :
( ( A @ m_Down @ sk16 )
= A ),
inference(cnf,[status(esa)],[297]) ).
thf(2151,plain,
! [A: $i] :
( ( A @ m_Down @ sk16 )
= A ),
inference(lifteq,[status(thm)],[298]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[221]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[222]) ).
thf(3269,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)],[395,223]) ).
thf(3270,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[3269:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(4120,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk7 @ host @ ( sk6 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4078,405]) ).
thf(4121,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk7 @ host @ ( sk6 @ host @ leq ) ) ),
inference(simp,[status(thm)],[4120]) ).
thf(4134,plain,
! [A: $i] :
( ( A
!= ( sk7 @ host ) )
| ( ( A @ s )
!= ( sk6 @ host ) ) ),
inference(simp,[status(thm)],[4121]) ).
thf(4139,plain,
( ( sk7 @ host @ s )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[4134]) ).
thf(987,plain,
sk5 != sk3,
inference(simp,[status(thm)],[986]) ).
thf(6195,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk3 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,987]) ).
thf(6196,plain,
( ( sk3 != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[6195:[bind(A,$thf( sk5 ))]]) ).
thf(4374,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,4004]) ).
thf(4375,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[4374]) ).
thf(4384,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Halt ) ) ),
inference(simp,[status(thm)],[4375]) ).
thf(4388,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Halt @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[4384]) ).
thf(2537,plain,
! [A: $i] :
( ( ( elec_2 @ s )
!= ( A @ s ) )
| ( ( sk7 @ host )
!= A )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[784,1856]) ).
thf(2538,plain,
( ( ( sk7 @ host )
!= elec_2 )
| ( status != pendack ) ),
inference(pattern_uni,[status(thm)],[2537:[bind(A,$thf( elec_2 ))]]) ).
thf(7905,plain,
! [A: $i] :
( ( A != nil )
| ( q_nil != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,5432]) ).
thf(7906,plain,
! [A: $i] :
( ( A != nil )
| ( sk5 @ ( sk5 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[7905]) ).
thf(7907,plain,
( ( sk5 @ ( sk5 @ last @ elem ) )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[7906:[bind(A,$thf( nil ))]]) ).
thf(3387,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,2604]) ).
thf(3388,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk3 @ host @ queue @ ( sk8 @ m_Ldr @ elem ) ) ),
inference(simp,[status(thm)],[3387]) ).
thf(3428,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk3 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Ldr ) ) ),
inference(simp,[status(thm)],[3388]) ).
thf(3468,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Ldr @ cons ) )
!= ( sk3 @ host @ queue ) ),
inference(simp,[status(thm)],[3428]) ).
thf(42,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).
thf(345,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(2111,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= ( elec_2 @ s ) )
| ( ( sk7 @ host )
!= ( A @ host ) )
| ( status != pendack ) ),
inference(paramod_ordered,[status(thm)],[784,1852]) ).
thf(2122,plain,
! [A: $i] :
( ( nbr_proc != elec_2 )
| ( sk7 != A )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2111]) ).
thf(2129,plain,
( ( nbr_proc != elec_2 )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2122]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(211,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[210]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(953,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= ( A @ host ) )
| ( norm @ ( zero @ s @ leq ) )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,203]) ).
thf(954,plain,
( ( norm @ ( zero @ s @ leq ) )
| ( ldr != status ) ),
inference(pattern_uni,[status(thm)],[953:[bind(A,$thf( sk5 ))]]) ).
thf(1825,plain,
! [A: $i] :
( ( ( norm @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[954,405]) ).
thf(1826,plain,
! [A: $i] :
( ( ( norm @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ( ldr != status ) ),
inference(simp,[status(thm)],[1825]) ).
thf(1849,plain,
! [A: $i] :
( ( norm != A )
| ( ( zero @ s )
!= ( A @ s ) )
| ( ldr != status ) ),
inference(simp,[status(thm)],[1826]) ).
thf(1862,plain,
( ( ( zero @ s )
!= ( norm @ s ) )
| ( ldr != status ) ),
inference(simp,[status(thm)],[1849]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ ( D @ host @ leq ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(462,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(7130,plain,
( ( ( sk6 @ host @ s )
!= ( q_nil @ s ) )
| ( ( sk7 @ host )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[772,7107]) ).
thf(7141,plain,
( ( ( sk6 @ host )
!= q_nil )
| ( ( sk7 @ host )
!= q_nil ) ),
inference(simp,[status(thm)],[7130]) ).
thf(26606,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Halt @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16572,421]) ).
thf(26607,plain,
! [B: $i,A: $i] :
( ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk3 @ m_Halt @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[26606]) ).
thf(26783,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ cons ) )
!= q_nil )
| ( ( sk3 @ m_Halt )
!= B ) ),
inference(simp,[status(thm)],[26607]) ).
thf(26812,plain,
! [A: $i] :
( ( sk2 @ host @ queue @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[26783]) ).
thf(9330,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8128,405]) ).
thf(9331,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[9330]) ).
thf(9348,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s )
!= B )
| ( ( A @ host @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[9331]) ).
thf(9353,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[9348]) ).
thf(15339,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s )
!= ( sk3 @ host @ s ) ) ),
inference(paramod_ordered,[status(thm)],[117,9353]) ).
thf(15340,plain,
( ( nbr_proc @ s @ s )
!= ( sk3 @ host @ s ) ),
inference(pattern_uni,[status(thm)],[15339:[bind(A,$thf( sk8 ))]]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[253]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[254]) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( A @ setIn ) )
| ~ ( D @ host @ queue @ ( C @ m_Down @ elem ) )
| ~ ( D @ host @ ( down @ index ) @ ( A @ ( B @ ( C @ ( D @ sk4 ) ) ) @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= elec_1 )
| ( ( D @ host )
!= nbr_proc )
| ( ( D @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[193]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( B @ ordered )
| ~ ( B @ ( A @ cons ) @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(2407,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[1851]) ).
thf(9080,plain,
! [A: $i] :
( ( q_nil != q_nil )
| ( A != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,5498]) ).
thf(9081,plain,
! [A: $i] :
( ( A != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[9080:[]]) ).
thf(9182,plain,
( ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( alive @ ( alive @ last @ elem ) ) ),
inference(simp,[status(thm)],[9081]) ).
thf(2120,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= ( elec_2 @ s ) )
| ( sk7 != A )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2111]) ).
thf(2128,plain,
( ( ( nbr_proc @ s )
!= ( elec_2 @ s ) )
| ( status != pendack ) ),
inference(simp,[status(thm)],[2120]) ).
thf(15516,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( sk7 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9658,405]) ).
thf(15517,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ ( sk7 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[15516]) ).
thf(15547,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s )
!= A )
| ( ( sk7 @ host @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[15517]) ).
thf(15557,plain,
( ( nbr_proc @ s @ s @ s @ s )
!= ( sk7 @ host @ s @ s ) ),
inference(simp,[status(thm)],[15547]) ).
thf(2420,plain,
( ( ( sk6 @ host @ s )
!= ( zero @ s ) )
| ( ( sk7 @ host )
!= ( sk7 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[772,2411]) ).
thf(2421,plain,
( ( sk6 @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2420]) ).
thf(2426,plain,
( ( sk6 @ host )
!= zero ),
inference(simp,[status(thm)],[2421]) ).
thf(17842,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[6196,421]) ).
thf(17843,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[17842]) ).
thf(17946,plain,
! [A: $i] :
( ( sk5 != q_nil )
| ( ( sk5 @ last )
!= A )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[17843]) ).
thf(17992,plain,
( ( sk5 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[17946]) ).
thf(9613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ ( A @ cons ) @ ordered )
!= ( B @ ordered ) )
| ( C @ m_Ldr @ ( B @ snoc ) @ ordered )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[311,258]) ).
thf(9614,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ ( A @ cons ) @ ordered )
!= ( B @ ordered ) )
| ( C @ m_Ldr @ ( B @ snoc ) @ ordered ) ),
inference(simp,[status(thm)],[9613]) ).
thf(9615,plain,
! [B: $i,A: $i] : ( A @ m_Ldr @ ( q_nil @ ( B @ cons ) @ snoc ) @ ordered ),
inference(pattern_uni,[status(thm)],[9614:[bind(A,$thf( D )),bind(B,$thf( q_nil @ ( D @ cons ) )),bind(C,$thf( C ))]]) ).
thf(9637,plain,
! [B: $i,A: $i] : ( A @ m_Ldr @ ( q_nil @ ( B @ cons ) @ snoc ) @ ordered ),
inference(simp,[status(thm)],[9615]) ).
thf(9467,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk6 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[5645,421]) ).
thf(9468,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[9467]) ).
thf(9566,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( sk7 @ last )
!= A )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[9468]) ).
thf(9601,plain,
( ( sk7 != q_nil )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[9566]) ).
thf(3287,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Halt @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[145,255]) ).
thf(3288,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[3287:[bind(A,$thf( sk3 @ m_Halt )),bind(B,$thf( sk1 ))]]) ).
thf(990,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( ( sk3 @ host )
!= norm )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,986]) ).
thf(991,plain,
( ( ( sk3 @ host )
!= norm )
| ( ldr != status ) ),
inference(pattern_uni,[status(thm)],[990:[]]) ).
thf(6187,plain,
! [A: $i] :
( ( A != sk7 )
| ( q_nil @ host @ ( nbr_proc @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,928]) ).
thf(6188,plain,
( ( q_nil @ host @ ( nbr_proc @ leq ) )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[6187:[bind(A,$thf( sk7 ))]]) ).
thf(2435,plain,
( ( sk3 @ host )
!= zero ),
inference(simp,[status(thm)],[2409]) ).
thf(626,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( ( sk2 @ host )
!= norm )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,128]) ).
thf(627,plain,
( ( ( sk2 @ host )
!= norm )
| ( ldr != status ) ),
inference(pattern_uni,[status(thm)],[626:[]]) ).
thf(24012,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8862,405]) ).
thf(24013,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[24012]) ).
thf(24028,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s )
!= A )
| ( ( zero @ s @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[24013]) ).
thf(24073,plain,
( ( nbr_proc @ s @ s @ s @ s )
!= ( zero @ s @ s @ s @ s ) ),
inference(simp,[status(thm)],[24028]) ).
thf(2642,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Halt @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[145,194]) ).
thf(2643,plain,
( ( sk2 @ host @ queue @ head )
= ( sk3 @ m_Halt ) ),
inference(pattern_uni,[status(thm)],[2642:[bind(A,$thf( sk3 @ m_Halt )),bind(B,$thf( sk1 ))]]) ).
thf(463,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[462]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[463]) ).
thf(465,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[464]) ).
thf(4099,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( C @ host @ ( A @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4078,142]) ).
thf(4100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk7 @ host @ ( sk6 @ host @ leq ) )
!= ( C @ host @ ( A @ host @ leq ) ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[4099]) ).
thf(4101,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk6 @ ( sk7 @ m_Ack ) @ elem ) ),
inference(pattern_uni,[status(thm)],[4100:[bind(A,$thf( sk6 )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).
thf(4138,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk6 @ ( sk7 @ m_Ack ) @ elem ) ),
inference(simp,[status(thm)],[4101]) ).
thf(3353,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[267,421]) ).
thf(3354,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[3353]) ).
thf(3417,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[3354]) ).
thf(3457,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[3417]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(159,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)],[158]) ).
thf(160,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)],[159]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(164,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[163]) ).
thf(165,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk10 )
= A ),
inference(cnf,[status(esa)],[164]) ).
thf(1646,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk10 )
= A ),
inference(lifteq,[status(thm)],[165]) ).
thf(2531,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= ( A @ host ) )
| ( zero != norm )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,2407]) ).
thf(2532,plain,
( ( zero != norm )
| ( ldr != status ) ),
inference(pattern_uni,[status(thm)],[2531:[bind(A,$thf( sk5 ))]]) ).
thf(154,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[153]) ).
thf(155,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk9 )
= A ),
inference(cnf,[status(esa)],[154]) ).
thf(1481,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk9 )
= A ),
inference(lifteq,[status(thm)],[155]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= norm )
| ( ( A @ host @ ( ldr @ index ) )
!= ( A @ host ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[113]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(168,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(169,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[168]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ~ ( alive @ ( D @ setIn ) )
| ( ( B @ host )
!= ( C @ host @ ( pendack @ index ) @ s ) )
| ( ( A @ host )
!= ( C @ host @ ( pendack @ index ) ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( B @ host )
!= ( C @ host @ ( pendack @ index ) @ s ) )
| ( ( A @ host )
!= ( C @ host @ ( pendack @ index ) ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ ( pendack @ index ) @ s @ ( nbr_proc @ leq ) )
| ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( C @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ( ( D @ host @ ( status @ index ) )
!= norm )
| ( ( D @ host @ ( ldr @ index ) )
!= ( D @ host ) )
| ( ( B @ host )
!= ( C @ host @ ( pendack @ index ) @ s ) )
| ( ( A @ host )
!= ( C @ host @ ( pendack @ index ) ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[138]) ).
thf(17363,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16843,236]) ).
thf(17364,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[17363]) ).
thf(17365,plain,
sk7 @ host @ s @ s @ ( zero @ s @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[17364:[bind(A,$thf( zero @ s @ s @ s )),bind(B,$thf( sk7 @ host @ s ))]]) ).
thf(24737,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17365,405]) ).
thf(24738,plain,
! [A: $i] :
( ( sk7 @ host @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[24737]) ).
thf(24770,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ s )
!= A )
| ( ( zero @ s @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[24738]) ).
thf(24801,plain,
( ( zero @ s @ s @ s @ s )
!= ( sk7 @ host @ s @ s @ s ) ),
inference(simp,[status(thm)],[24770]) ).
thf(8582,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,8577]) ).
thf(8583,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[8582]) ).
thf(8584,plain,
( ( sk3 != q_nil )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[8583:[bind(A,$thf( sk2 ))]]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(118,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(119,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[118]) ).
thf(9396,plain,
( ( ( nbr_proc @ s @ ( sk7 @ host @ leq ) )
!= ( sk6 @ host @ ( sk7 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9304,1816]) ).
thf(9397,plain,
( ( nbr_proc @ s @ ( sk7 @ host @ leq ) )
!= ( sk6 @ host @ ( sk7 @ host @ leq ) ) ),
inference(simp,[status(thm)],[9396]) ).
thf(9403,plain,
( ( ( nbr_proc @ s )
!= ( sk6 @ host ) )
| ( ( sk7 @ host )
!= ( sk7 @ host ) ) ),
inference(simp,[status(thm)],[9397]) ).
thf(9421,plain,
( ( nbr_proc @ s )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[9403]) ).
thf(5142,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,1632]) ).
thf(5143,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5142]) ).
thf(5144,plain,
sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ),
inference(pattern_uni,[status(thm)],[5143:[bind(A,$thf( sk2 @ host @ queue ))]]) ).
thf(23805,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8778,405]) ).
thf(23806,plain,
! [A: $i] :
( ( sk7 @ host @ s @ s @ s @ ( nbr_proc @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[23805]) ).
thf(23848,plain,
! [A: $i] :
( ( ( sk7 @ host @ s @ s @ s )
!= A )
| ( ( nbr_proc @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[23806]) ).
thf(23869,plain,
( ( sk7 @ host @ s @ s @ s @ s )
!= ( nbr_proc @ s @ s @ s ) ),
inference(simp,[status(thm)],[23848]) ).
thf(7572,plain,
! [A: $i] :
( ( A != nil )
| ( q_nil != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,5141]) ).
thf(7573,plain,
! [A: $i] :
( ( A != nil )
| ( sk8 @ ( sk8 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[7572]) ).
thf(7574,plain,
( ( sk8 @ ( sk8 @ last @ elem ) )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[7573:[bind(A,$thf( nil ))]]) ).
thf(5185,plain,
! [A: $i] :
( ( A != sk1 )
| ( q_nil != q_nil )
| ( sk2 @ host @ queue @ ordered )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,806]) ).
thf(5186,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 @ host @ queue @ ordered )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5185]) ).
thf(5187,plain,
( ( sk2 @ host @ queue @ ordered )
| ( sk1 @ ( sk1 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5186:[bind(A,$thf( sk1 ))]]) ).
thf(4879,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk7 @ m_Halt @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk6 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[395,4411]) ).
thf(4880,plain,
( ( q_nil @ ( sk7 @ m_Halt @ cons ) )
!= ( sk6 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[4879:[bind(A,$thf( sk7 @ m_Halt )),bind(B,$thf( q_nil ))]]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[189]) ).
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(422,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(7319,plain,
! [A: $i] :
( ( ( q_nil @ s @ s @ ( q_nil @ s @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6466,421]) ).
thf(7320,plain,
! [A: $i] :
( ( q_nil @ s @ s @ ( q_nil @ s @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[7319]) ).
thf(7413,plain,
! [A: $i] :
( ( ( q_nil @ s @ s )
!= q_nil )
| ( ( q_nil @ s @ s @ last )
!= A ) ),
inference(simp,[status(thm)],[7320]) ).
thf(7489,plain,
( ( q_nil @ s @ s )
!= q_nil ),
inference(simp,[status(thm)],[7413]) ).
thf(1833,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk7 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[928,405]) ).
thf(1834,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk7 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[1833]) ).
thf(1846,plain,
! [A: $i] :
( ( A
!= ( sk7 @ host ) )
| ( ( A @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1834]) ).
thf(1859,plain,
( ( sk7 @ host @ s )
!= nbr_proc ),
inference(simp,[status(thm)],[1846]) ).
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(415,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( ( A @ ( B @ sk17 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ~ ( B @ ordered )
| ( ( A @ ( B @ sk17 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ~ ( B @ ordered )
| ( ( A @ ( B @ sk17 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) ) ),
inference(simp,[status(thm)],[331]) ).
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(459,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( B @ host @ ( pendack @ index ) @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( B @ host @ ( pendack @ index ) @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( B @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(1873,plain,
( ( ( sk7 @ host )
!= ( sk5 @ host ) )
| ( ( norm @ s )
!= nbr_proc )
| ( ldr != status ) ),
inference(paramod_ordered,[status(thm)],[548,1859]) ).
thf(1880,plain,
( ( sk7 != sk5 )
| ( ( norm @ s )
!= nbr_proc )
| ( ldr != status ) ),
inference(simp,[status(thm)],[1873]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(277,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[276]) ).
thf(5706,plain,
! [A: $i] :
( ( A != sk5 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[4703,103]) ).
thf(5707,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5706:[bind(A,$thf( sk5 ))]]) ).
thf(47116,plain,
$false,
inference(e,[status(thm)],[69,365,479,347,2427,941,16797,1818,481,4571,29505,2109,2131,333,249,518,1850,1855,24087,8129,5141,16308,994,449,379,269,202,4075,217,308,1939,385,384,15282,9509,340,142,16572,4435,8204,22300,153,4941,6466,3994,1645,320,2405,3597,9159,288,301,17739,2136,4610,4524,184,372,110,1860,5130,28691,389,125,344,22268,421,93,3470,316,17107,9712,10046,26100,179,376,253,238,806,353,29477,216,4411,475,9304,7107,1632,321,7677,121,147,280,221,956,411,116,265,8924,396,2137,8686,1351,133,1863,307,233,439,4480,201,8481,2905,380,117,220,366,8113,334,2409,8778,4434,5266,392,3989,192,275,137,92,1938,252,197,2628,9658,22505,2345,2547,8577,224,625,8270,6413,5714,4108,1856,403,188,26948,7698,141,1851,317,256,2460,1942,4389,489,3723,17518,9419,476,393,985,17429,173,1852,569,5498,1932,134,1857,244,3279,311,5434,398,6756,530,4004,128,3834,8839,4644,7656,4036,412,3707,148,4412,279,296,3696,375,601,975,176,4494,7497,772,286,8222,291,204,259,191,1916,402,8107,382,4096,4645,6673,236,181,8010,350,8862,144,1638,5432,16900,187,406,172,2151,419,3270,1933,4139,303,208,6196,4477,4388,2538,1853,784,9377,7907,230,3468,362,567,477,494,631,345,2129,103,213,91,1862,108,462,15487,7141,26812,198,16731,130,399,986,4703,226,267,3380,223,608,505,5693,15340,548,255,209,112,516,3921,123,5916,3278,16787,194,145,16843,327,954,8128,2407,3872,409,993,177,9182,2128,338,15557,2426,17992,9353,175,9637,314,143,9601,3288,991,6188,2411,2435,627,203,24073,4078,2643,16550,465,4138,3457,1646,304,2532,1481,158,114,171,139,24801,8584,258,119,207,4478,478,9421,5144,23869,7574,214,5187,4880,7991,168,405,190,422,373,7489,2604,239,268,195,767,25836,1859,210,341,1816,928,415,395,332,459,131,163,1880,178,277,369,987,9357,5645,6126,227,486,364,354,5707,8157,17365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV462+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n005.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 13:55:17 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.24 % [INFO] Parsing done (241ms).
% 1.44/1.25 % [INFO] Running in sequential loop mode.
% 2.20/1.65 % [INFO] eprover registered as external prover.
% 2.20/1.66 % [INFO] Scanning for conjecture ...
% 2.66/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.87/2.02 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 3.17/2.07 % [INFO] Problem is first-order (TPTP FOF).
% 3.17/2.08 % [INFO] Type checking passed.
% 3.17/2.09 % [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 ...
% 85.61/21.38 % External prover 'e' found a proof!
% 85.61/21.38 % [INFO] Killing All external provers ...
% 85.61/21.38 % Time passed: 20814ms (effective reasoning time: 20122ms)
% 85.61/21.38 % 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)>
% 85.61/21.38 % 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
% 85.61/21.38 % No. of inferences in proof: 1019
% 85.61/21.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20814 ms resp. 20122 ms w/o parsing
% 86.83/21.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 86.83/21.73 % [INFO] Killing All external provers ...
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