%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV460+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 : n016.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 08:59:30 AM UTC 2026
% Result : Theorem 79.27s 20.30s
% Output : Refutation 80.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 81
% Syntax : Number of formulae : 825 ( 365 unt; 0 typ; 14 def)
% Number of atoms : 2493 (1322 equ; 0 cnn)
% Maximal formula atoms : 74 ( 3 avg)
% Number of connectives : 8690 (1307 ~; 739 |; 427 &;5973 @)
% ( 13 <=>; 231 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 23 con; 0-2 aty)
% Number of variables : 1429 ( 2 ^;1347 !; 66 ?;1429 :)
% ( 0 !>; 0 ?*; 0 @-; 14 @+)
% Comments :
%------------------------------------------------------------------------------
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Halt_decl,type,
m_Halt: $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(index_decl,type,
index: $i > $i > $i ).
thf(status_decl,type,
status: $i ).
thf(elec_2_decl,type,
elec_2: $i ).
thf(pendack_decl,type,
pendack: $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(elec_1_decl,type,
elec_1: $i ).
thf(elid_decl,type,
elid: $i ).
thf(down_decl,type,
down: $i ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(norm_decl,type,
norm: $i ).
thf(wait_decl,type,
wait: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(nbr_proc_decl,type,
nbr_proc: $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(snoc_decl,type,
snoc: $i > $i > $i ).
thf(m_Ldr_decl,type,
m_Ldr: $i > $i ).
thf(last_decl,type,
last: $i > $i ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(init_decl,type,
init: $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(pids_decl,type,
pids: $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(head_decl,type,
head: $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 ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ! [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 )
& ( ( F @ host )
= ( E @ host ) )
& ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( F @ host @ leq ) ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
=> ~ ( D @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ~ ( C @ host @ ( B @ host @ leq ) )
=> ( ~ ( ( ( ( C @ host )
= ( B @ host @ ( elid @ index ) @ host ) )
& ( ( B @ host @ ( status @ index ) )
= wait ) )
| ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( C @ host ) ) ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( B @ host @ leq ) ) )
=> ( ( D
= ( C @ host ) )
| ( B @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ( ~ ( B @ host @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ! [E: $i] :
( ( ( B @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( B @ host @ s @ leq ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( A @ host @ queue )
= ( sk1 @ ( B @ m_Down @ cons ) ) )
& ! [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 )
& ( ( E @ host )
= ( D @ host ) )
& ( C @ host @ queue @ ( D @ m_Down @ elem ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i,D: $i] :
( ( ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) ) )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( C @ host @ queue @ ( D @ ( C @ m_Ack ) @ elem ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i,D: $i] :
( ? [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( C @ host @ ( E @ host @ leq ) ) )
=> ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( C @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) ) )
=> ( C @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i] :
( ( ( alive @ ( C @ setIn ) )
& ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
| ( ( C @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( C @ host @ ( elid @ index ) )
= C ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( C @ host @ queue @ ( D @ ( C @ m_Ack ) @ elem ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
=> ~ ( E @ host @ ( C @ host @ leq ) ) )
& ! [C: $i] :
( ( ( C @ host @ ( status @ index ) )
= elec_2 )
=> ~ ( C @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ( ~ ( B @ host @ ( A @ host @ leq ) )
=> ( ~ ( ( ( ( B @ host )
= ( A @ host @ ( elid @ index ) @ host ) )
& ( ( A @ host @ ( status @ index ) )
= wait ) )
| ( ( ( A @ host @ ( status @ index ) )
= norm )
& ( ( A @ host @ ( ldr @ index ) )
= ( B @ host ) ) ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_1 )
& ! [C: $i] :
( ( ( C @ ( zero @ s @ leq ) )
& ~ ( C @ ( A @ host @ leq ) ) )
=> ( ( C
= ( B @ host ) )
| ( A @ host @ ( down @ index ) @ ( C @ setIn ) ) ) ) )
=> ( ~ ( A @ host @ ( nbr_proc @ leq ) )
=> ! [C: $i] :
( ( ( A @ host )
= ( C @ host ) )
=> ! [D: $i] :
( ( ( A @ host )
!= ( D @ host ) )
=> ( ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ~ ( D @ host @ ( C @ host @ leq ) ) )
=> ~ ( D @ host @ ( pendack @ index ) @ ( A @ host @ s @ leq ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( ( sk2 @ host @ queue )
= ( sk1 @ ( A @ m_Down @ cons ) ) )
& ! [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 )
& ( ( D @ host )
= ( C @ host ) )
& ( B @ host @ queue @ ( C @ m_Down @ elem ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( B @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i,C: $i] :
( ( ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( D @ setIn ) ) )
& ( alive @ ( B @ setIn ) ) )
=> ~ ( B @ host @ queue @ ( C @ ( B @ m_Ack ) @ elem ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( C @ host @ ( B @ host @ leq ) ) )
=> ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i,C: $i] :
( ? [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( B @ host @ ( D @ host @ leq ) ) )
=> ~ ( B @ host @ queue @ ( C @ m_Down @ elem ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( B @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) ) )
=> ( B @ host @ ( C @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i] :
( ( ( alive @ ( B @ setIn ) )
& ( ( ( B @ host @ ( status @ index ) )
= elec_2 )
| ( ( B @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( B @ host @ ( elid @ index ) )
= B ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) ) )
=> ~ ( B @ host @ queue @ ( C @ ( B @ m_Ack ) @ elem ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
=> ~ ( D @ host @ ( B @ host @ leq ) ) )
& ! [B: $i] :
( ( ( B @ host @ ( status @ index ) )
= elec_2 )
=> ~ ( B @ host @ ( B @ host @ ( pendack @ index ) @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) ) )
=> ( ( alive @ ( sk2 @ setIn ) )
=> ( ~ ( A @ host @ ( sk2 @ host @ leq ) )
=> ( ~ ( ( ( ( A @ host )
= ( sk2 @ host @ ( elid @ index ) @ host ) )
& ( ( sk2 @ host @ ( status @ index ) )
= wait ) )
| ( ( ( sk2 @ host @ ( status @ index ) )
= norm )
& ( ( sk2 @ host @ ( ldr @ index ) )
= ( A @ host ) ) ) )
=> ( ( ( ( sk2 @ host @ ( status @ index ) )
= elec_1 )
& ! [B: $i] :
( ( ( B @ ( zero @ s @ leq ) )
& ~ ( B @ ( sk2 @ host @ leq ) ) )
=> ( ( B
= ( A @ host ) )
| ( sk2 @ host @ ( down @ index ) @ ( B @ setIn ) ) ) ) )
=> ( ~ ( sk2 @ host @ ( nbr_proc @ leq ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
= ( B @ host ) )
=> ! [C: $i] :
( ( ( sk2 @ host )
!= ( C @ host ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( C @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ~ ( C @ host @ ( B @ host @ leq ) ) )
=> ~ ( C @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
= ( A @ host ) )
=> ! [B: $i] :
( ( ( sk2 @ host )
!= ( B @ host ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( B @ setIn ) )
& ( alive @ ( A @ setIn ) )
& ~ ( B @ host @ ( A @ host @ leq ) ) )
=> ~ ( B @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ( ( ( ( A @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( A @ setIn ) )
& ( alive @ ( sk4 @ setIn ) )
& ~ ( A @ host @ ( sk4 @ host @ leq ) ) )
=> ~ ( A @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( F @ host @ ( pendack @ index ) @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( E @ host @ ( G @ host @ leq ) ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
=> ~ ( E @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ~ ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( C @ host @ leq ) ) )
=> ( ( E
= ( D @ host ) )
| ( C @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ( ~ ( C @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i] :
( ( ( C @ host )
!= ( F @ host ) )
=> ( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( F @ host @ ( pendack @ index ) @ ( C @ host @ s @ leq ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( F @ host @ ( pendack @ index ) @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( E @ host @ queue @ ( F @ m_Down @ elem ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( G @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( G @ host @ ( status @ index ) )
= elec_2 )
& ( ( G @ host )
= ( F @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( E @ host @ ( G @ host @ leq ) ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( E @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) ) )
=> ( E @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i] :
( ( ( alive @ ( E @ setIn ) )
& ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
| ( ( E @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( E @ host @ ( elid @ index ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) ) )
=> ~ ( E @ host @ queue @ ( F @ ( E @ m_Ack ) @ elem ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i] :
( ( ( E @ host @ ( status @ index ) )
= elec_2 )
=> ~ ( E @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ~ ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host @ ( status @ index ) )
= elec_1 )
& ! [E: $i] :
( ( ( E @ ( zero @ s @ leq ) )
& ~ ( E @ ( C @ host @ leq ) ) )
=> ( ( E
= ( D @ host ) )
| ( C @ host @ ( down @ index ) @ ( E @ setIn ) ) ) ) )
=> ( ~ ( C @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i] :
( ( ( C @ host )
!= ( F @ host ) )
=> ( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ~ ( F @ host @ ( E @ host @ leq ) ) )
=> ~ ( F @ host @ ( pendack @ index ) @ ( C @ host @ s @ leq ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ! [D: $i,E: $i] :
( ( ( ( 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 )
& ( ( F @ host )
= ( E @ host ) )
& ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( F @ host @ leq ) ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
=> ~ ( D @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ~ ( C @ host @ ( B @ host @ leq ) )
=> ( ~ ( ( ( ( C @ host )
= ( B @ host @ ( elid @ index ) @ host ) )
& ( ( B @ host @ ( status @ index ) )
= wait ) )
| ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( C @ host ) ) ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( B @ host @ leq ) ) )
=> ( ( D
= ( C @ host ) )
| ( B @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ( ~ ( B @ host @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ! [E: $i] :
( ( ( B @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( B @ host @ s @ leq ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).
thf(169,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(170,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).
thf(349,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( B @ ( C @ snoc ) @ ( A @ elem ) ) )
& ( ( B @ ( C @ snoc ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(350,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)],[349]) ).
thf(351,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)],[350]) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[351]) ).
thf(356,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[353]) ).
thf(357,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[356]) ).
thf(3783,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)],[171,357]) ).
thf(3784,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(pattern_uni,[status(thm)],[3783:[bind(A,$thf( E )),bind(B,$thf( E @ last )),bind(C,$thf( E @ init ))]]) ).
thf(3828,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(simp,[status(thm)],[3784]) ).
thf(70,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( A @ ( C @ m_Down @ cons ) ) )
& ! [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 )
& ( ( F @ host )
= ( E @ host ) )
& ( D @ host @ queue @ ( E @ m_Down @ elem ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( F @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) ) )
& ( alive @ ( D @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( ( D @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( F @ host @ ( status @ index ) )
= elec_2 )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( D @ host @ ( F @ host @ leq ) ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( D @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) ) )
=> ( D @ host @ ( E @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i] :
( ( ( alive @ ( D @ setIn ) )
& ( ( ( D @ host @ ( status @ index ) )
= elec_2 )
| ( ( D @ host @ ( status @ index ) )
= elec_1 ) ) )
=> ( ( D @ host @ ( elid @ index ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) ) )
=> ~ ( D @ host @ queue @ ( E @ ( D @ m_Ack ) @ elem ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i] :
( ( ( D @ host @ ( status @ index ) )
= elec_2 )
=> ~ ( D @ host @ ( D @ host @ ( pendack @ index ) @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ~ ( C @ host @ ( B @ host @ leq ) )
=> ( ~ ( ( ( ( C @ host )
= ( B @ host @ ( elid @ index ) @ host ) )
& ( ( B @ host @ ( status @ index ) )
= wait ) )
| ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( C @ host ) ) ) )
=> ( ( ( ( B @ host @ ( status @ index ) )
= elec_1 )
& ! [D: $i] :
( ( ( D @ ( zero @ s @ leq ) )
& ~ ( D @ ( B @ host @ leq ) ) )
=> ( ( D
= ( C @ host ) )
| ( B @ host @ ( down @ index ) @ ( D @ setIn ) ) ) ) )
=> ( ~ ( B @ host @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ! [E: $i] :
( ( ( B @ host )
!= ( E @ host ) )
=> ( ( ( ( E @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ~ ( E @ host @ ( D @ host @ leq ) ) )
=> ~ ( E @ host @ ( pendack @ index ) @ ( B @ host @ s @ leq ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(71,plain,
! [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 @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) )
& ( ( sk5 @ host @ ( status @ index ) )
= elec_2 )
& ( alive @ ( sk5 @ setIn ) )
& ( alive @ ( sk4 @ setIn ) )
& ~ ( sk5 @ host @ ( sk4 @ host @ leq ) )
& ( ( sk2 @ host )
!= ( sk5 @ host ) )
& ( ( sk2 @ host )
= ( sk4 @ host ) )
& ~ ( sk2 @ host @ ( nbr_proc @ leq ) )
& ( ( sk2 @ host @ ( status @ index ) )
= elec_1 )
& ( ( ZA
= ( sk3 @ host ) )
| ( sk2 @ host @ ( down @ index ) @ ( ZA @ setIn ) )
| ~ ( ZA @ ( zero @ s @ leq ) )
| ( ZA @ ( sk2 @ host @ leq ) ) )
& ( ( ( sk3 @ host )
!= ( sk2 @ host @ ( elid @ index ) @ host ) )
| ( ( sk2 @ host @ ( status @ index ) )
!= wait ) )
& ( ( ( sk2 @ host @ ( status @ index ) )
!= norm )
| ( ( sk2 @ host @ ( ldr @ index ) )
!= ( sk3 @ host ) ) )
& ~ ( sk3 @ host @ ( sk2 @ host @ leq ) )
& ( alive @ ( sk2 @ setIn ) )
& ( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) )
& ( ~ ( 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 @ ( X @ host @ ( pendack @ index ) @ leq ) )
| ( ( X @ host @ ( status @ index ) )
!= elec_2 )
| ( ( X @ host )
!= ( W @ host ) )
| ~ ( V @ host @ queue @ ( W @ m_Down @ elem ) )
| ~ ( alive @ ( X @ setIn ) )
| ~ ( alive @ ( V @ setIn ) ) )
& ( ~ ( S @ host @ queue @ ( T @ ( S @ m_Ack ) @ elem ) )
| ( ( U @ host @ ( status @ index ) )
!= elec_2 )
| ( ( S @ host @ ( status @ index ) )
!= elec_2 )
| ( ( U @ host )
!= ( T @ host ) )
| ~ ( alive @ ( U @ setIn ) )
| ~ ( alive @ ( S @ 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 ) ) )
& ( ~ ( N @ host @ queue @ ( O @ m_Down @ elem ) )
| ( ( P @ host @ ( status @ index ) )
!= elec_2 )
| ( ( P @ host )
!= ( O @ host ) )
| ~ ( alive @ ( P @ setIn ) )
| ~ ( alive @ ( N @ setIn ) )
| ( N @ host @ ( P @ host @ leq ) ) )
& ( ( L @ host @ ( M @ host @ ( pendack @ index ) @ leq ) )
| ( ( M @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( L @ host @ ( down @ index ) @ ( M @ host @ setIn ) )
| ~ ( alive @ ( M @ setIn ) )
| ~ ( alive @ ( L @ setIn ) ) )
& ( ( ( K @ host @ ( elid @ index ) )
= K )
| ~ ( alive @ ( K @ setIn ) )
| ( ( K @ host @ ( status @ index ) )
!= elec_2 ) )
& ( ( ( K @ host @ ( elid @ index ) )
= K )
| ~ ( alive @ ( K @ setIn ) )
| ( ( K @ host @ ( status @ index ) )
!= elec_1 ) )
& ( ~ ( I @ host @ queue @ ( J @ ( I @ m_Ack ) @ elem ) )
| ( ( J @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( J @ setIn ) ) )
& ( ~ ( alive @ ( H @ setIn ) )
| ~ ( alive @ ( G @ setIn ) )
| ( ( H @ host )
!= ( G @ host ) )
| ( H = G ) )
& ( ~ ( F @ host @ ( D @ host @ leq ) )
| ~ ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) ) )
& ( ~ ( C @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 ) )
& ( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(73,plain,
alive @ ( sk4 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(27,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).
thf(229,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(230,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[229]) ).
thf(231,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[230]) ).
thf(533,plain,
! [A: $i] :
( ( ( alive @ ( sk4 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[73,231]) ).
thf(534,plain,
! [A: $i] :
( ( alive @ ( sk4 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[533]) ).
thf(539,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[534]) ).
thf(542,plain,
setEmpty != alive,
inference(simp,[status(thm)],[539]) ).
thf(4036,plain,
! [A: $i] :
( ( A != setEmpty )
| ( q_nil != alive )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,542]) ).
thf(4037,plain,
( ( q_nil != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4036:[bind(A,$thf( setEmpty ))]]) ).
thf(64,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_45) ).
thf(413,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(414,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[413]) ).
thf(415,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[414]) ).
thf(5481,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( q_nil != alive ) ),
inference(paramod_ordered,[status(thm)],[4037,415]) ).
thf(5482,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[5481]) ).
thf(5496,plain,
! [A: $i] :
( ( setEmpty != q_nil )
| ( ( setEmpty @ last )
!= A )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[5482]) ).
thf(5509,plain,
( ( setEmpty != q_nil )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[5496]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(244,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)],[30]) ).
thf(245,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)],[244]) ).
thf(246,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)],[245]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[246]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(33,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(261,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)],[33]) ).
thf(262,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)],[261]) ).
thf(263,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)],[262]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[263]) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(269,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[268]) ).
thf(1808,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,415]) ).
thf(1809,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[1808]) ).
thf(1822,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[1809]) ).
thf(1840,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[1822]) ).
thf(99,plain,
( ( sk2 @ host )
!= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(124,plain,
( ( sk5 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(468,plain,
sk5 != sk2,
inference(simp,[status(thm)],[124]) ).
thf(88,plain,
~ ( sk2 @ host @ ( nbr_proc @ leq ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).
thf(282,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)],[35]) ).
thf(283,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)],[282]) ).
thf(284,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)],[283]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[284]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[286]) ).
thf(290,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[289]) ).
thf(81,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(120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(1524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( D @ host @ ( B @ host @ leq ) ) )
| ~ $true
| ~ ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[290,120]) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( D @ host @ ( B @ host @ leq ) ) )
| ~ ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[1524]) ).
thf(1526,plain,
! [B: $i,A: $i] :
~ ( A @ host @ queue @ ( B @ ( B @ m_Ack ) @ elem ) ),
inference(pattern_uni,[status(thm)],[1525:[bind(A,$thf( E @ host )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(1549,plain,
! [B: $i,A: $i] :
~ ( A @ host @ queue @ ( B @ ( B @ m_Ack ) @ elem ) ),
inference(simp,[status(thm)],[1526]) ).
thf(22,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_02) ).
thf(214,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(215,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[214]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).
thf(394,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(395,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[394]) ).
thf(396,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[395]) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[215,396]) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1197]) ).
thf(1211,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1204]) ).
thf(17,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_03) ).
thf(196,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_63) ).
thf(238,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)],[29]) ).
thf(239,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)],[238]) ).
thf(240,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)],[239]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[240]) ).
thf(7124,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[196,241]) ).
thf(7125,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7124]) ).
thf(7126,plain,
nbr_proc @ s @ ( zero @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[7125:[bind(A,$thf( zero @ s )),bind(B,$thf( nbr_proc ))]]) ).
thf(7250,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)],[7126,241]) ).
thf(7251,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7250]) ).
thf(7252,plain,
nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[7251:[bind(A,$thf( zero @ s @ s )),bind(B,$thf( nbr_proc @ s ))]]) ).
thf(7342,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)],[7252,241]) ).
thf(7343,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7342]) ).
thf(7344,plain,
nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[7343:[bind(A,$thf( zero @ s @ s @ s )),bind(B,$thf( nbr_proc @ s @ s ))]]) ).
thf(13115,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7344,396]) ).
thf(13116,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[13115]) ).
thf(13217,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s )
!= A )
| ( ( zero @ s @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[13116]) ).
thf(13244,plain,
( ( nbr_proc @ s @ s @ s @ s )
!= ( zero @ s @ s @ s @ s ) ),
inference(simp,[status(thm)],[13217]) ).
thf(23,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_04) ).
thf(216,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(217,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[216]) ).
thf(83,plain,
( ( sk2 @ host @ queue )
= ( sk1 @ ( sk3 @ m_Down @ cons ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(131,plain,
( ( sk1 @ ( sk3 @ m_Down @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
thf(390,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(391,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[390]) ).
thf(392,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[391]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[392]) ).
thf(1180,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[131,393]) ).
thf(1181,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[1180:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(4513,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,1181]) ).
thf(4514,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4513]) ).
thf(4515,plain,
sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ),
inference(pattern_uni,[status(thm)],[4514:[bind(A,$thf( sk2 @ host @ queue ))]]) ).
thf(96,plain,
( ( sk5 @ host @ ( status @ index ) )
= elec_2 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(119,plain,
( ( sk5 @ host @ ( status @ index ) )
= elec_2 ),
inference(lifteq,[status(thm)],[96]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(111,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(112,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[111]) ).
thf(1082,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( status @ index ) )
!= ( A @ host @ ( status @ index ) ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( elec_2 != elec_2 ) ),
inference(paramod_ordered,[status(thm)],[119,112]) ).
thf(1083,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( status @ index ) )
!= ( A @ host @ ( status @ index ) ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A ) ),
inference(simp,[status(thm)],[1082]) ).
thf(1084,plain,
( ~ ( alive @ ( sk5 @ setIn ) )
| ( ( sk5 @ host @ ( elid @ index ) )
= sk5 ) ),
inference(pattern_uni,[status(thm)],[1083:[bind(A,$thf( sk5 ))]]) ).
thf(97,plain,
alive @ ( sk5 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(3105,plain,
( ~ $true
| ( ( sk5 @ host @ ( elid @ index ) )
= sk5 ) ),
inference(rewrite,[status(thm)],[1084,97]) ).
thf(3106,plain,
( ( sk5 @ host @ ( elid @ index ) )
= sk5 ),
inference(simp,[status(thm)],[3105]) ).
thf(3149,plain,
( ( ( sk5 @ host @ ( elid @ index ) )
!= ( sk5 @ host @ ( status @ index ) ) )
| ( sk5 = elec_2 ) ),
inference(paramod_ordered,[status(thm)],[3106,119]) ).
thf(3167,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( elid != status )
| ( sk5 = elec_2 ) ),
inference(simp,[status(thm)],[3149]) ).
thf(3200,plain,
( ( elid != status )
| ( sk5 = elec_2 ) ),
inference(simp,[status(thm)],[3167]) ).
thf(3229,plain,
( ( sk5 != sk5 )
| ( ( sk2 @ host )
!= ( elec_2 @ host ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,124]) ).
thf(3230,plain,
( ( ( sk2 @ host )
!= ( elec_2 @ host ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3229:[]]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(446,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(447,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[446]) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[447]) ).
thf(449,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[448]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(202,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(55,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(384,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(385,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[384]) ).
thf(386,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[385]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[167]) ).
thf(1590,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)],[386,168]) ).
thf(1591,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[1590:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(85,plain,
! [A: $i] :
( ~ ( A @ host @ ( A @ host @ ( pendack @ index ) @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(101,plain,
! [A: $i] :
( ~ ( A @ host @ ( A @ host @ ( pendack @ index ) @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(102,plain,
! [A: $i] :
( ~ ( A @ host @ ( A @ host @ ( pendack @ index ) @ leq ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[101]) ).
thf(565,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( status @ index ) )
!= ( A @ host @ ( status @ index ) ) )
| ~ ( A @ host @ ( A @ host @ ( pendack @ index ) @ leq ) )
| ( elec_2 != elec_2 ) ),
inference(paramod_ordered,[status(thm)],[119,102]) ).
thf(566,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( status @ index ) )
!= ( A @ host @ ( status @ index ) ) )
| ~ ( A @ host @ ( A @ host @ ( pendack @ index ) @ leq ) ) ),
inference(simp,[status(thm)],[565]) ).
thf(567,plain,
~ ( sk5 @ host @ ( sk5 @ host @ ( pendack @ index ) @ leq ) ),
inference(pattern_uni,[status(thm)],[566:[bind(A,$thf( sk5 ))]]) ).
thf(3132,plain,
( ( ( sk5 @ host @ ( elid @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ~ ( sk5 @ host @ ( sk5 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[3106,567]) ).
thf(3168,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( elid != pendack )
| ~ ( sk5 @ host @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[3132]) ).
thf(3201,plain,
( ( elid != pendack )
| ~ ( sk5 @ host @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[3168]) ).
thf(3744,plain,
( ( sk5 != sk5 )
| ( elid != pendack )
| ~ ( sk5 @ host @ ( elec_2 @ leq ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,3201]) ).
thf(3745,plain,
( ( elid != pendack )
| ~ ( sk5 @ host @ ( elec_2 @ leq ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3744:[]]) ).
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(142,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(84,plain,
( ( sk2 @ host )
= ( sk4 @ host ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(100,plain,
( ( sk4 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,396]) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1184]) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1185]) ).
thf(1213,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[1206]) ).
thf(1326,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[100,1213]) ).
thf(1327,plain,
( ( nbr_proc @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[1326:[bind(A,$thf( sk4 ))]]) ).
thf(769,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk5 @ host @ ( sk5 @ host @ ( pendack @ index ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,567]) ).
thf(770,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk5 @ host @ ( sk5 @ host @ ( pendack @ index ) @ leq ) ) ),
inference(simp,[status(thm)],[769]) ).
thf(782,plain,
! [A: $i] :
( ( A
!= ( sk5 @ host ) )
| ( A
!= ( sk5 @ host @ ( pendack @ index ) ) ) ),
inference(simp,[status(thm)],[770]) ).
thf(793,plain,
( ( sk5 @ host @ ( pendack @ index ) )
!= ( sk5 @ host ) ),
inference(simp,[status(thm)],[782]) ).
thf(3115,plain,
( ( ( sk5 @ host @ ( elid @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ( ( sk5 @ host )
!= sk5 ) ),
inference(paramod_ordered,[status(thm)],[3106,793]) ).
thf(3183,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( elid != pendack )
| ( ( sk5 @ host )
!= sk5 ) ),
inference(simp,[status(thm)],[3115]) ).
thf(3209,plain,
( ( elid != pendack )
| ( ( sk5 @ host )
!= sk5 ) ),
inference(simp,[status(thm)],[3183]) ).
thf(3561,plain,
( ( sk5 != sk5 )
| ( elid != pendack )
| ( ( elec_2 @ host )
!= sk5 )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,3209]) ).
thf(3562,plain,
( ( elid != pendack )
| ( ( elec_2 @ host )
!= sk5 )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3561:[]]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(340,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(3277,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( B @ ( B @ m_Ack ) @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[100,1549]) ).
thf(3278,plain,
! [A: $i] :
~ ( sk2 @ host @ queue @ ( A @ ( A @ m_Ack ) @ elem ) ),
inference(pattern_uni,[status(thm)],[3277:[bind(A,$thf( sk4 ))]]) ).
thf(3288,plain,
! [A: $i] :
~ ( sk2 @ host @ queue @ ( A @ ( A @ m_Ack ) @ elem ) ),
inference(simp,[status(thm)],[3278]) ).
thf(3291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( C @ ( C @ m_Ack ) @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[357,3288]) ).
thf(3292,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( C @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[3291]) ).
thf(3304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( C @ ( C @ m_Ack ) ) ) ),
inference(simp,[status(thm)],[3292]) ).
thf(3309,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ m_Ack ) @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3304]) ).
thf(3366,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( C @ ( C @ m_Ack ) @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[386,3309]) ).
thf(3367,plain,
! [A: $i] :
( ( q_nil @ ( A @ ( A @ m_Ack ) @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[3366:[bind(A,$thf( E @ ( E @ m_Ack ) )),bind(B,$thf( q_nil )),bind(C,$thf( E ))]]) ).
thf(3370,plain,
! [A: $i] :
( ( q_nil @ ( A @ ( A @ m_Ack ) @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3367]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
thf(180,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)],[13]) ).
thf(181,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)],[180]) ).
thf(182,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)],[181]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[182]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(41,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(320,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)],[41]) ).
thf(72,plain,
~ ( sk3 @ host @ ( sk2 @ host @ leq ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(463,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ~ ( sk2 @ host @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[100,72]) ).
thf(466,plain,
( ( sk4 != sk3 )
| ~ ( sk2 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[463]) ).
thf(765,plain,
( ( sk4 != sk3 )
| ~ $true ),
inference(rewrite,[status(thm)],[466,290]) ).
thf(766,plain,
sk4 != sk3,
inference(simp,[status(thm)],[765]) ).
thf(4113,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk3 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,766]) ).
thf(4114,plain,
( ( sk3 != q_nil )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4113:[bind(A,$thf( sk4 ))]]) ).
thf(6265,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4114,415]) ).
thf(6266,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[6265]) ).
thf(6286,plain,
! [A: $i] :
( ( sk4 != q_nil )
| ( ( sk4 @ last )
!= A )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[6266]) ).
thf(6291,plain,
( ( sk4 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[6286]) ).
thf(1810,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[131,269]) ).
thf(1811,plain,
sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[1810:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(3293,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ ( A @ m_Ack ) @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1811,3288]) ).
thf(3294,plain,
! [A: $i] :
( ( sk2 @ host @ queue @ ( A @ ( A @ m_Ack ) @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3293]) ).
thf(3303,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( A @ ( A @ m_Ack ) )
!= ( sk3 @ m_Down ) ) ),
inference(simp,[status(thm)],[3294]) ).
thf(3308,plain,
! [A: $i] :
( ( A @ ( A @ m_Ack ) )
!= ( sk3 @ m_Down ) ),
inference(simp,[status(thm)],[3303]) ).
thf(16,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
thf(194,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(195,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[194]) ).
thf(450,plain,
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[73,195]) ).
thf(451,plain,
( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(456,plain,
( ( alive != alive )
| ( sk4 != nil ) ),
inference(simp,[status(thm)],[451]) ).
thf(459,plain,
sk4 != nil,
inference(simp,[status(thm)],[456]) ).
thf(4802,plain,
! [A: $i] :
( ( A != sk4 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,459]) ).
thf(4803,plain,
( ( nil != q_nil )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4802:[bind(A,$thf( sk4 ))]]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(254,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(255,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[254]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(454,plain,
( ( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,195]) ).
thf(455,plain,
( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(458,plain,
( ( alive != alive )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[455]) ).
thf(461,plain,
sk5 != nil,
inference(simp,[status(thm)],[458]) ).
thf(4237,plain,
! [A: $i] :
( ( A != sk5 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,461]) ).
thf(4238,plain,
( ( nil != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4237:[bind(A,$thf( sk5 ))]]) ).
thf(6676,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( nil != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4238,415]) ).
thf(6677,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[6676]) ).
thf(6697,plain,
! [A: $i] :
( ( sk5 != q_nil )
| ( ( sk5 @ last )
!= A )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[6677]) ).
thf(6707,plain,
( ( sk5 != q_nil )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[6697]) ).
thf(56,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_05) ).
thf(387,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(388,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[387]) ).
thf(389,plain,
elec_1 != elec_2,
inference(lifteq,[status(thm)],[388]) ).
thf(1192,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,396]) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[1192]) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[1193]) ).
thf(1210,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[1203]) ).
thf(4239,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ( q_nil != B )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,1210]) ).
thf(4240,plain,
! [A: $i] :
( ( q_nil != A )
| ( A @ s @ ( A @ s @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4239:[bind(A,$thf( C @ s )),bind(B,$thf( C ))]]) ).
thf(4885,plain,
q_nil @ s @ ( q_nil @ s @ last @ elem ),
inference(simp,[status(thm)],[4240]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[263]) ).
thf(270,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(13695,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)],[4885,270]) ).
thf(13696,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)],[13695]) ).
thf(13697,plain,
! [A: $i] : ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[13696:[bind(A,$thf( q_nil @ s @ last )),bind(B,$thf( B )),bind(C,$thf( q_nil @ s ))]]) ).
thf(13732,plain,
! [A: $i] : ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) ),
inference(simp,[status(thm)],[13697]) ).
thf(709,plain,
( ( ( sk5 @ host @ ( pendack @ index ) )
!= ( sk5 @ host @ ( status @ index ) ) )
| ~ ( sk5 @ host @ ( elec_2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[119,567]) ).
thf(712,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( pendack != status )
| ~ ( sk5 @ host @ ( elec_2 @ leq ) ) ),
inference(simp,[status(thm)],[709]) ).
thf(719,plain,
( ( pendack != status )
| ~ ( sk5 @ host @ ( elec_2 @ leq ) ) ),
inference(simp,[status(thm)],[712]) ).
thf(51,axiom,
norm != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(370,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(371,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[370]) ).
thf(372,plain,
wait != norm,
inference(lifteq,[status(thm)],[371]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( B @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
| ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[109]) ).
thf(1329,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[100,1211]) ).
thf(1330,plain,
( ( sk2 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[1329:[bind(A,$thf( sk4 ))]]) ).
thf(80,plain,
~ ( sk5 @ host @ ( sk4 @ host @ leq ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(489,plain,
~ ( sk5 @ host @ ( sk2 @ host @ leq ) ),
inference(rewrite,[status(thm)],[80,100]) ).
thf(587,plain,
! [A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( sk5 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,489]) ).
thf(588,plain,
! [A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( sk5 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[587]) ).
thf(598,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= nbr_proc )
| ( ( A @ host )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[588]) ).
thf(1559,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk5 @ host )
!= nbr_proc )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[100,598]) ).
thf(1560,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk5 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1561,plain,
( ( sk5 @ host )
!= nbr_proc ),
inference(pattern_uni,[status(thm)],[1560:[bind(A,$thf( sk4 ))]]) ).
thf(3247,plain,
( ( sk5 != sk5 )
| ( ( elec_2 @ host )
!= nbr_proc )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,1561]) ).
thf(3248,plain,
( ( ( elec_2 @ host )
!= nbr_proc )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3247:[]]) ).
thf(87,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_1 ),
inference(cnfConj,[status(thm)],[71]) ).
thf(125,plain,
( ( sk2 @ host @ ( status @ index ) )
= elec_1 ),
inference(lifteq,[status(thm)],[87]) ).
thf(44,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).
thf(344,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(75,plain,
alive @ ( sk2 @ setIn ),
inference(cnfConj,[status(thm)],[71]) ).
thf(452,plain,
( ( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,195]) ).
thf(453,plain,
( ( alive @ ( sk2 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(457,plain,
( ( alive != alive )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[453]) ).
thf(460,plain,
sk2 != nil,
inference(simp,[status(thm)],[457]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).
thf(162,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(163,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[162]) ).
thf(164,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[164]) ).
thf(1554,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)],[386,165]) ).
thf(1555,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[1554:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(4219,plain,
! [B: $i,A: $i] :
( ( A
!= ( q_nil @ ( B @ cons ) ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,1555]) ).
thf(4220,plain,
! [B: $i,A: $i] :
( ( A
!= ( q_nil @ ( B @ cons ) ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4219]) ).
thf(4221,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ( q_nil @ ( A @ cons ) @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[4220:[bind(A,$thf( q_nil @ ( C @ cons ) )),bind(B,$thf( C ))]]) ).
thf(4880,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ( q_nil @ ( A @ cons ) @ last @ elem ) ),
inference(simp,[status(thm)],[4221]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[159]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[160]) ).
thf(1556,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)],[386,161]) ).
thf(1557,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[1556:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(5542,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ( A @ elem ) ),
inference(rewrite,[status(thm)],[4880,1557]) ).
thf(5543,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ ( A @ cons ) @ ( A @ elem ) )
!= ( B @ host @ queue @ ( C @ ( C @ m_Ack ) @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5542,1549]) ).
thf(5544,plain,
! [C: $i,B: $i,A: $i] :
( ( q_nil @ ( A @ cons ) @ ( A @ elem ) )
!= ( B @ host @ queue @ ( C @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[5543]) ).
thf(5585,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ ( A @ cons ) )
!= ( B @ host @ queue ) )
| ( A
!= ( C @ ( C @ m_Ack ) ) ) ),
inference(simp,[status(thm)],[5544]) ).
thf(5604,plain,
! [B: $i,A: $i] :
( ( q_nil @ ( B @ ( B @ m_Ack ) @ cons ) )
!= ( A @ host @ queue ) ),
inference(simp,[status(thm)],[5585]) ).
thf(93,plain,
sk5 @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ),
inference(cnfConj,[status(thm)],[71]) ).
thf(3215,plain,
( ( sk5 != sk5 )
| ( pendack != status )
| ~ ( elec_2 @ host @ ( elec_2 @ leq ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,719]) ).
thf(3216,plain,
( ( pendack != status )
| ~ ( elec_2 @ host @ ( elec_2 @ leq ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3215:[]]) ).
thf(65,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(416,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)],[65]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(225,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(226,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[225]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[226]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[227]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(316,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(469,plain,
( ( ( sk5 @ host )
!= ( sk4 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[100,124]) ).
thf(470,plain,
( ( sk5 @ host )
!= ( sk4 @ host ) ),
inference(simp,[status(thm)],[469]) ).
thf(471,plain,
sk5 != sk4,
inference(simp,[status(thm)],[470]) ).
thf(4252,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk4 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,471]) ).
thf(4253,plain,
( ( sk4 != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4252:[bind(A,$thf( sk5 ))]]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(779,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)],[290,79]) ).
thf(780,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)],[779]) ).
thf(781,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[780:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(792,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(simp,[status(thm)],[781]) ).
thf(1588,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[100,792]) ).
thf(1589,plain,
~ ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[1588:[bind(A,$thf( sk4 ))]]) ).
thf(1892,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[357,1589]) ).
thf(1893,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1892]) ).
thf(1916,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk4 @ m_Halt ) ) ),
inference(simp,[status(thm)],[1893]) ).
thf(1931,plain,
! [A: $i] :
( ( sk4 @ m_Halt @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[1916]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
thf(152,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(443,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1628,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ init )
= q_nil ) ),
inference(paramod_ordered,[status(thm)],[131,1591]) ).
thf(1631,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Down )
!= A )
| ( ( sk2 @ host @ queue @ init )
= q_nil ) ),
inference(simp,[status(thm)],[1628]) ).
thf(1632,plain,
( ( sk1 != q_nil )
| ( ( sk2 @ host @ queue @ init )
= q_nil ) ),
inference(simp,[status(thm)],[1631]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
thf(376,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(91,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(105,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)],[91]) ).
thf(106,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)],[105]) ).
thf(4038,plain,
! [A: $i] :
( ( A != sk2 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,460]) ).
thf(4039,plain,
( ( nil != q_nil )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4038:[bind(A,$thf( sk2 ))]]) ).
thf(5740,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( nil != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4039,415]) ).
thf(5741,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[5740]) ).
thf(5760,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( sk2 @ last )
!= A )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[5741]) ).
thf(5761,plain,
( ( sk2 != q_nil )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[5760]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(177,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[176]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[177]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(143,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)],[142]) ).
thf(144,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)],[143]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_39) ).
thf(397,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(218,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(219,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[218]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[219]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
thf(293,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)],[36]) ).
thf(5770,plain,
! [A: $i] :
( ( A != nil )
| ( sk2 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,5761]) ).
thf(5771,plain,
! [A: $i] :
( ( A != nil )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5770]) ).
thf(5772,plain,
( ( sk2 != q_nil )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5771:[bind(A,$thf( nil ))]]) ).
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(132,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(3225,plain,
( ( sk5 != sk5 )
| ( nil != elec_2 )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,461]) ).
thf(3226,plain,
( ( nil != elec_2 )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3225:[]]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ host @ ( C @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ host @ ( C @ host @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( A @ host @ ( C @ host @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[240]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(20,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(206,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)],[20]) ).
thf(771,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,72]) ).
thf(772,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[771]) ).
thf(784,plain,
! [A: $i] :
( ( A
!= ( sk3 @ host ) )
| ( A
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[772]) ).
thf(788,plain,
( ( sk3 @ host )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[784]) ).
thf(851,plain,
sk3 != sk2,
inference(simp,[status(thm)],[788]) ).
thf(4474,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,851]) ).
thf(4475,plain,
( ( sk2 != q_nil )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4474:[bind(A,$thf( sk3 ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
thf(307,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(380,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(18,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(197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[197]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(200,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[199]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk9 ) )
= B ),
inference(cnf,[status(esa)],[200]) ).
thf(3852,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk9 ) )
= B ),
inference(lifteq,[status(thm)],[201]) ).
thf(133,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)],[132]) ).
thf(134,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)],[133]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[134]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(138,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[137]) ).
thf(139,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk6 )
= A ),
inference(cnf,[status(esa)],[138]) ).
thf(1153,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk6 )
= A ),
inference(lifteq,[status(thm)],[139]) ).
thf(3923,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,468]) ).
thf(3924,plain,
( ( sk2 != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3923:[bind(A,$thf( sk5 ))]]) ).
thf(5115,plain,
! [A: $i] :
( ( A != sk2 )
| ( q_nil != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,3924]) ).
thf(5116,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk5 @ ( sk5 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5115]) ).
thf(5117,plain,
( ( sk5 @ ( sk5 @ last @ elem ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5116:[bind(A,$thf( sk2 ))]]) ).
thf(1186,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,396]) ).
thf(1187,plain,
! [A: $i] :
( ( sk5 @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[1186]) ).
thf(1205,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( pendack @ index ) )
!= A )
| ( ( sk2 @ host @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[1187]) ).
thf(1212,plain,
( ( sk5 @ host @ ( pendack @ index ) @ s )
!= ( sk2 @ host @ s ) ),
inference(simp,[status(thm)],[1205]) ).
thf(1470,plain,
( ( sk5 @ host @ ( pendack @ index ) )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[1212]) ).
thf(308,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[307]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[308]) ).
thf(310,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[309]) ).
thf(153,plain,
! [A: $i] :
( ( A @ ordered )
=> ! [B: $i] : ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(miniscope,[status(thm)],[152]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ ( A @ ordered ) ),
inference(cnf,[status(esa)],[153]) ).
thf(3643,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)],[310,154]) ).
thf(3644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ ( A @ cons ) @ ordered )
!= ( B @ ordered ) )
| ( C @ m_Ldr @ ( B @ snoc ) @ ordered ) ),
inference(simp,[status(thm)],[3643]) ).
thf(3645,plain,
! [B: $i,A: $i] : ( A @ m_Ldr @ ( q_nil @ ( B @ cons ) @ snoc ) @ ordered ),
inference(pattern_uni,[status(thm)],[3644:[bind(A,$thf( D )),bind(B,$thf( q_nil @ ( D @ cons ) )),bind(C,$thf( C ))]]) ).
thf(3663,plain,
! [B: $i,A: $i] : ( A @ m_Ldr @ ( q_nil @ ( B @ cons ) @ snoc ) @ ordered ),
inference(simp,[status(thm)],[3645]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).
thf(361,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[362]) ).
thf(6806,plain,
! [B: $i,A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ( B @ cons ) @ ordered ),
inference(rewrite,[status(thm)],[3663,363]) ).
thf(6865,plain,
! [B: $i,A: $i] : ( q_nil @ ( A @ m_Ldr @ cons ) @ ( B @ cons ) @ ordered ),
inference(rewrite,[status(thm)],[6806,386]) ).
thf(7127,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[93,241]) ).
thf(7128,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ host @ ( pendack @ index ) @ ( sk2 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7127]) ).
thf(7129,plain,
sk5 @ host @ ( pendack @ index ) @ s @ ( sk2 @ host @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[7128:[bind(A,$thf( sk2 @ host @ s )),bind(B,$thf( sk5 @ host @ ( pendack @ index ) ))]]) ).
thf(4193,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ snoc ) ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,165]) ).
thf(4194,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ ( C @ snoc ) ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4193]) ).
thf(4195,plain,
! [B: $i,A: $i] : ( B @ ( A @ snoc ) @ ( B @ ( A @ snoc ) @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[4194:[bind(A,$thf( E @ ( D @ snoc ) )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(4874,plain,
! [B: $i,A: $i] : ( B @ ( A @ snoc ) @ ( B @ ( A @ snoc ) @ last @ elem ) ),
inference(simp,[status(thm)],[4195]) ).
thf(6064,plain,
! [B: $i,A: $i] : ( B @ ( A @ snoc ) @ ( B @ elem ) ),
inference(rewrite,[status(thm)],[4874,161]) ).
thf(5126,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk2 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3924,415]) ).
thf(5127,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[5126]) ).
thf(5142,plain,
! [A: $i] :
( ( sk5 != q_nil )
| ( ( sk5 @ last )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[5127]) ).
thf(5153,plain,
( ( sk5 != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[5142]) ).
thf(5166,plain,
( ( sk5 != sk5 )
| ( q_nil != elec_2 )
| ( sk2 != q_nil )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,5153]) ).
thf(5167,plain,
( ( q_nil != elec_2 )
| ( sk2 != q_nil )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[5166:[]]) ).
thf(5517,plain,
! [A: $i] :
( ( q_nil != q_nil )
| ( setEmpty != q_nil )
| ( A != alive )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,5509]) ).
thf(5518,plain,
! [A: $i] :
( ( setEmpty != q_nil )
| ( A != alive )
| ( A @ ( A @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5517:[]]) ).
thf(5519,plain,
( ( setEmpty != q_nil )
| ( alive @ ( alive @ last @ elem ) ) ),
inference(simp,[status(thm)],[5518]) ).
thf(5308,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ ( A @ m_Ack ) @ elem ) )
!= ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4515,3288]) ).
thf(5309,plain,
! [A: $i] :
( ( sk2 @ host @ queue @ ( A @ ( A @ m_Ack ) @ elem ) )
!= ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) ) ),
inference(simp,[status(thm)],[5308]) ).
thf(5338,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( A @ ( A @ m_Ack ) )
!= ( sk2 @ host @ queue @ last ) ) ),
inference(simp,[status(thm)],[5309]) ).
thf(5349,plain,
! [A: $i] :
( ( A @ ( A @ m_Ack ) )
!= ( sk2 @ host @ queue @ last ) ),
inference(simp,[status(thm)],[5338]) ).
thf(148,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[147]) ).
thf(149,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk7 )
= A ),
inference(cnf,[status(esa)],[148]) ).
thf(1217,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk7 )
= A ),
inference(lifteq,[status(thm)],[149]) ).
thf(14,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
thf(190,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3651,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,154]) ).
thf(3652,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(simp,[status(thm)],[3651]) ).
thf(3653,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(pattern_uni,[status(thm)],[3652:[bind(A,$thf( q_nil ))]]) ).
thf(3659,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(simp,[status(thm)],[3653]) ).
thf(3664,plain,
! [A: $i] : ( q_nil @ ( A @ m_Ldr @ cons ) @ ordered ),
inference(rewrite,[status(thm)],[3659,386]) ).
thf(3148,plain,
( ( ( sk5 @ host @ ( elid @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ( ( sk2 @ host @ s )
!= ( sk5 @ s ) ) ),
inference(paramod_ordered,[status(thm)],[3106,1212]) ).
thf(3178,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( elid != pendack )
| ( ( sk2 @ host @ s )
!= ( sk5 @ s ) ) ),
inference(simp,[status(thm)],[3148]) ).
thf(3207,plain,
( ( elid != pendack )
| ( ( sk2 @ host @ s )
!= ( sk5 @ s ) ) ),
inference(simp,[status(thm)],[3178]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_36) ).
thf(258,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[258]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[259]) ).
thf(3263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ ( D @ m_Ack ) @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,1549]) ).
thf(3264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ ( D @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[3263]) ).
thf(3280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( C @ host @ queue ) )
| ( A
!= ( D @ ( D @ m_Ack ) ) ) ),
inference(simp,[status(thm)],[3264]) ).
thf(3282,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ m_Ack ) @ cons ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[3280]) ).
thf(7117,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)],[217,241]) ).
thf(7118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[7117]) ).
thf(7119,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[7118:[bind(A,$thf( D )),bind(B,$thf( D @ host )),bind(C,$thf( nbr_proc ))]]) ).
thf(7205,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(simp,[status(thm)],[7119]) ).
thf(7924,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7205,396]) ).
thf(7925,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[7924]) ).
thf(7979,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s )
!= B )
| ( ( A @ host @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[7925]) ).
thf(7996,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[7979]) ).
thf(8025,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s )
!= ( sk2 @ host @ s ) ) ),
inference(paramod_ordered,[status(thm)],[100,7996]) ).
thf(8026,plain,
( ( nbr_proc @ s @ s )
!= ( sk2 @ host @ s ) ),
inference(pattern_uni,[status(thm)],[8025:[bind(A,$thf( sk4 ))]]) ).
thf(1890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[357,792]) ).
thf(1891,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1890]) ).
thf(1917,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( C @ host @ queue ) )
| ( A
!= ( C @ m_Halt ) ) ),
inference(simp,[status(thm)],[1891]) ).
thf(1932,plain,
! [B: $i,A: $i] :
( ( B @ m_Halt @ ( A @ snoc ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[1917]) ).
thf(3346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( C @ m_Halt @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( C @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[386,1932]) ).
thf(3347,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Halt @ cons ) )
!= ( A @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[3346:[bind(A,$thf( D @ m_Halt )),bind(B,$thf( q_nil )),bind(C,$thf( D ))]]) ).
thf(3349,plain,
! [A: $i] :
( ( q_nil @ ( A @ m_Halt @ cons ) )
!= ( A @ host @ queue ) ),
inference(simp,[status(thm)],[3347]) ).
thf(25,axiom,
elec_1 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_07) ).
thf(222,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(223,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[222]) ).
thf(224,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[223]) ).
thf(7813,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk2 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4475,415]) ).
thf(7814,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[7813]) ).
thf(7831,plain,
! [A: $i] :
( ( sk3 != q_nil )
| ( ( sk3 @ last )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[7814]) ).
thf(7842,plain,
( ( sk3 != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[7831]) ).
thf(1328,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[1211]) ).
thf(5471,plain,
! [A: $i] :
( ( q_nil != q_nil )
| ( A != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,4037]) ).
thf(5472,plain,
! [A: $i] :
( ( A != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5471:[]]) ).
thf(5502,plain,
( ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( alive @ ( alive @ last @ elem ) ) ),
inference(simp,[status(thm)],[5472]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).
thf(403,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(404,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[403]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[404]) ).
thf(3086,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[131,405]) ).
thf(3087,plain,
( ( sk2 @ host @ queue @ head )
= ( sk3 @ m_Down ) ),
inference(pattern_uni,[status(thm)],[3086:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(42,axiom,
elec_2 != norm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_09) ).
thf(337,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(338,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[337]) ).
thf(339,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[338]) ).
thf(15,axiom,
elec_1 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_06) ).
thf(191,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(192,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[191]) ).
thf(193,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[192]) ).
thf(601,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( q_nil @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ordered ) ),
inference(paramod_ordered,[status(thm)],[131,310]) ).
thf(602,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk3 @ m_Down )
!= A )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[601]) ).
thf(603,plain,
( ( sk1 != q_nil )
| ( sk2 @ host @ queue @ ordered ) ),
inference(simp,[status(thm)],[602]) ).
thf(4748,plain,
! [A: $i] :
( ( A != sk1 )
| ( q_nil != q_nil )
| ( sk2 @ host @ queue @ ordered )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,603]) ).
thf(4749,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 @ host @ queue @ ordered )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4748]) ).
thf(4750,plain,
( ( sk2 @ host @ queue @ ordered )
| ( sk1 @ ( sk1 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4749:[bind(A,$thf( sk1 ))]]) ).
thf(7187,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)],[215,241]) ).
thf(7188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[7187]) ).
thf(7189,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[7188:[bind(A,$thf( E )),bind(B,$thf( zero @ s )),bind(C,$thf( E @ host ))]]) ).
thf(7206,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(simp,[status(thm)],[7189]) ).
thf(8336,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7206,396]) ).
thf(8337,plain,
! [B: $i,A: $i] :
( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[8336]) ).
thf(8394,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s )
!= B )
| ( ( zero @ s @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[8337]) ).
thf(8407,plain,
! [A: $i] :
( ( A @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[8394]) ).
thf(6254,plain,
! [A: $i] :
( ( A != sk3 )
| ( q_nil != q_nil )
| ( sk4 @ ( sk4 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,4114]) ).
thf(6255,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk4 @ ( sk4 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[6254]) ).
thf(6256,plain,
( ( sk4 @ ( sk4 @ last @ elem ) )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[6255:[bind(A,$thf( sk3 ))]]) ).
thf(3221,plain,
( ( sk5 != sk5 )
| ( ( elec_2 @ host @ ( pendack @ index ) )
!= ( sk2 @ host ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,1470]) ).
thf(3222,plain,
( ( ( elec_2 @ host @ ( pendack @ index ) )
!= ( sk2 @ host ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3221:[]]) ).
thf(94,plain,
! [A: $i] :
( ( A
= ( sk3 @ host ) )
| ( sk2 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk2 @ host @ leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(128,plain,
! [A: $i] :
( ( sk2 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk2 @ host @ leq ) )
| ( A
= ( sk3 @ host ) ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(129,plain,
! [A: $i] :
( ( sk2 @ host @ ( down @ index ) @ ( A @ setIn ) )
| ~ ( A @ ( zero @ s @ leq ) )
| ( A @ ( sk2 @ host @ leq ) )
| ( A
= ( sk3 @ host ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(341,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[340]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[341]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(203,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[202]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[203]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(409,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(410,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Ldr ) ),
inference(miniscope,[status(thm)],[409]) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(cnf,[status(esa)],[410]) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(lifteq,[status(thm)],[411]) ).
thf(521,plain,
( ( ( sk5 @ host @ ( pendack @ index ) )
!= ( sk5 @ host @ ( status @ index ) ) )
| ( elec_2 @ ( sk2 @ host @ s @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[119,93]) ).
thf(530,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( pendack != status )
| ( elec_2 @ ( sk2 @ host @ s @ leq ) ) ),
inference(simp,[status(thm)],[521]) ).
thf(532,plain,
( ( pendack != status )
| ( elec_2 @ ( sk2 @ host @ s @ leq ) ) ),
inference(simp,[status(thm)],[530]) ).
thf(1194,plain,
! [A: $i] :
( ( ( elec_2 @ ( sk2 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true
| ( pendack != status ) ),
inference(paramod_ordered,[status(thm)],[532,396]) ).
thf(1195,plain,
! [A: $i] :
( ( ( elec_2 @ ( sk2 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1201,plain,
! [A: $i] :
( ( elec_2 != A )
| ( ( sk2 @ host @ s )
!= ( A @ s ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1195]) ).
thf(1208,plain,
( ( ( sk2 @ host @ s )
!= ( elec_2 @ s ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1201]) ).
thf(1219,plain,
( ( ( sk2 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[1208]) ).
thf(34,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(271,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)],[34]) ).
thf(272,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)],[271]) ).
thf(273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk13 @ m_Down ) )
| ( A
= ( A @ sk12 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(279,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[278]) ).
thf(52,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)],[52]) ).
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(7310,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7252,396]) ).
thf(7311,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7310]) ).
thf(7369,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s )
!= A )
| ( ( zero @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[7311]) ).
thf(7382,plain,
( ( nbr_proc @ s @ s @ s )
!= ( zero @ s @ s @ s ) ),
inference(simp,[status(thm)],[7369]) ).
thf(3265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ ( D @ m_Ack ) @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[357,1549]) ).
thf(3266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( D @ ( D @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[3265]) ).
thf(3281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( C @ host @ queue ) )
| ( A
!= ( D @ ( D @ m_Ack ) ) ) ),
inference(simp,[status(thm)],[3266]) ).
thf(3283,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ m_Ack ) @ ( A @ snoc ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[3281]) ).
thf(77,plain,
! [A: $i] :
( ( ( A @ host @ ( elid @ index ) )
= A )
| ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(117,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(118,plain,
! [A: $i] :
( ~ ( alive @ ( A @ setIn ) )
| ( ( A @ host @ ( elid @ index ) )
= A )
| ( ( A @ host @ ( status @ index ) )
!= elec_1 ) ),
inference(simp,[status(thm)],[117]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(280,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[276]) ).
thf(281,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[280]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(400,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(401,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[400]) ).
thf(402,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[401]) ).
thf(8121,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk5 @ host @ ( elec_2 @ leq ) ) )
| ( elid != pendack )
| ~ $true
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[290,3745]) ).
thf(8122,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk5 @ host @ ( elec_2 @ leq ) ) )
| ( elid != pendack )
| ( elid != status ) ),
inference(simp,[status(thm)],[8121]) ).
thf(8155,plain,
! [A: $i] :
( ( A
!= ( sk5 @ host ) )
| ( A != elec_2 )
| ( elid != pendack )
| ( elid != status ) ),
inference(simp,[status(thm)],[8122]) ).
thf(8160,plain,
( ( ( sk5 @ host )
!= elec_2 )
| ( elid != pendack )
| ( elid != status ) ),
inference(simp,[status(thm)],[8155]) ).
thf(8495,plain,
( ( sk5 != sk5 )
| ( ( elec_2 @ host )
!= elec_2 )
| ( elid != pendack )
| ( elid != status )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,8160]) ).
thf(8496,plain,
( ( sk5 != sk5 )
| ( ( elec_2 @ host )
!= elec_2 )
| ( elid != pendack )
| ( elid != status ) ),
inference(simp,[status(thm)],[8495]) ).
thf(8497,plain,
( ( ( elec_2 @ host )
!= elec_2 )
| ( elid != pendack )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[8496:[]]) ).
thf(4268,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ cons ) ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,393]) ).
thf(4269,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ cons ) ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4268]) ).
thf(4270,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( B @ ( A @ cons ) @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[4269:[bind(A,$thf( E @ ( D @ cons ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(4887,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( B @ ( A @ cons ) @ last @ elem ) ),
inference(simp,[status(thm)],[4270]) ).
thf(8274,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( nil != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4803,415]) ).
thf(8275,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[8274]) ).
thf(8289,plain,
! [A: $i] :
( ( sk4 != q_nil )
| ( ( sk4 @ last )
!= A )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[8275]) ).
thf(8301,plain,
( ( sk4 != q_nil )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[8289]) ).
thf(39,axiom,
elec_2 != wait,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_08) ).
thf(313,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(728,plain,
! [A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[215,88]) ).
thf(729,plain,
! [A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[728]) ).
thf(736,plain,
! [A: $i] :
( ( ( A @ host )
!= ( sk2 @ host ) )
| ( ( zero @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[729]) ).
thf(3049,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( ( zero @ s )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[100,736]) ).
thf(3050,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( zero @ s )
!= nbr_proc ) ),
inference(simp,[status(thm)],[3049]) ).
thf(3051,plain,
( ( zero @ s )
!= nbr_proc ),
inference(pattern_uni,[status(thm)],[3050:[bind(A,$thf( sk4 ))]]) ).
thf(1188,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[196,396]) ).
thf(1189,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[1188]) ).
thf(1202,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[1189]) ).
thf(1209,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[1202]) ).
thf(62,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(406,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)],[62]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12946,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( pendack @ index ) @ s @ ( sk2 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7129,396]) ).
thf(12947,plain,
! [A: $i] :
( ( sk5 @ host @ ( pendack @ index ) @ s @ ( sk2 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[12946]) ).
thf(13073,plain,
! [A: $i] :
( ( ( sk5 @ host @ ( pendack @ index ) @ s )
!= A )
| ( ( sk2 @ host @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[12947]) ).
thf(13086,plain,
( ( sk5 @ host @ ( pendack @ index ) @ s @ s )
!= ( sk2 @ host @ s @ s ) ),
inference(simp,[status(thm)],[13073]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(303,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4299,plain,
! [A: $i] :
( ( A != sk4 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,73]) ).
thf(4300,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4299:[bind(A,$thf( sk4 ))]]) ).
thf(207,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)],[206]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[207]) ).
thf(3746,plain,
( ( sk5 != sk5 )
| ( elid != pendack )
| ~ ( elec_2 @ host @ ( sk5 @ leq ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,3201]) ).
thf(3747,plain,
( ( elid != pendack )
| ~ ( elec_2 @ host @ ( sk5 @ leq ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3746:[]]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(210,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(211,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[210]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(95,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(107,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)],[95]) ).
thf(108,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)],[107]) ).
thf(4683,plain,
! [A: $i] :
( ( A != sk2 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,75]) ).
thf(4684,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4683:[bind(A,$thf( sk2 ))]]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(365,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[364]) ).
thf(366,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[365]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[366]) ).
thf(7071,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk4 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4253,415]) ).
thf(7072,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[7071]) ).
thf(7077,plain,
! [A: $i] :
( ( sk5 != q_nil )
| ( ( sk5 @ last )
!= A )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[7072]) ).
thf(7098,plain,
( ( sk5 != q_nil )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[7077]) ).
thf(1800,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,1589]) ).
thf(1801,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1800]) ).
thf(1820,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk4 @ m_Halt ) ) ),
inference(simp,[status(thm)],[1801]) ).
thf(1838,plain,
! [A: $i] :
( ( A @ ( sk4 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[1820]) ).
thf(8439,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s @ s )
!= ( zero @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[100,8407]) ).
thf(8440,plain,
( ( sk2 @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(pattern_uni,[status(thm)],[8439:[bind(A,$thf( sk4 ))]]) ).
thf(2590,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk2 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ~ $true
| ( B @ ( sk2 @ host @ leq ) )
| ( B
= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[290,129]) ).
thf(2591,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( zero @ s @ leq ) ) )
| ( sk2 @ host @ ( down @ index ) @ ( B @ setIn ) )
| ( B @ ( sk2 @ host @ leq ) )
| ( B
= ( sk3 @ host ) ) ),
inference(simp,[status(thm)],[2590]) ).
thf(2592,plain,
( ( sk2 @ host @ ( down @ index ) @ ( zero @ s @ setIn ) )
| ( zero @ s @ ( sk2 @ host @ leq ) )
| ( ( zero @ s )
= ( sk3 @ host ) ) ),
inference(pattern_uni,[status(thm)],[2591:[bind(A,$thf( zero @ s )),bind(B,$thf( zero @ s ))]]) ).
thf(3289,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( C @ ( C @ m_Ack ) @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,3288]) ).
thf(3290,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( C @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[3289]) ).
thf(3305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( C @ ( C @ m_Ack ) ) ) ),
inference(simp,[status(thm)],[3290]) ).
thf(3310,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ m_Ack ) @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3305]) ).
thf(4826,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,100]) ).
thf(4827,plain,
( ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4826:[bind(A,$thf( sk4 ))]]) ).
thf(304,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[303]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[263]) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[264]) ).
thf(1851,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1811,1589]) ).
thf(1852,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1851]) ).
thf(1865,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Down )
!= ( sk4 @ m_Halt ) ) ),
inference(simp,[status(thm)],[1852]) ).
thf(1873,plain,
( ( sk3 @ m_Down )
!= ( sk4 @ m_Halt ) ),
inference(simp,[status(thm)],[1865]) ).
thf(3116,plain,
( ( ( sk5 @ host @ ( elid @ index ) )
!= ( sk5 @ host @ ( pendack @ index ) ) )
| ( ( sk2 @ host )
!= sk5 ) ),
inference(paramod_ordered,[status(thm)],[3106,1470]) ).
thf(3176,plain,
( ( ( sk5 @ host )
!= ( sk5 @ host ) )
| ( elid != pendack )
| ( ( sk2 @ host )
!= sk5 ) ),
inference(simp,[status(thm)],[3116]) ).
thf(3206,plain,
( ( elid != pendack )
| ( ( sk2 @ host )
!= sk5 ) ),
inference(simp,[status(thm)],[3176]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[207]) ).
thf(186,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[185]) ).
thf(187,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk8 )
= A ),
inference(cnf,[status(esa)],[186]) ).
thf(1340,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk8 )
= A ),
inference(lifteq,[status(thm)],[187]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[122]) ).
thf(6718,plain,
( ( sk5 != sk5 )
| ( q_nil != elec_2 )
| ( nil != q_nil )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,6707]) ).
thf(6719,plain,
( ( q_nil != elec_2 )
| ( nil != q_nil )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[6718:[]]) ).
thf(294,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)],[293]) ).
thf(295,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)],[294]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[295]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(299,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[298]) ).
thf(300,plain,
! [A: $i] :
( ( A @ m_Down @ sk14 )
= A ),
inference(cnf,[status(esa)],[299]) ).
thf(1551,plain,
! [A: $i] :
( ( A @ m_Down @ sk14 )
= A ),
inference(lifteq,[status(thm)],[300]) ).
thf(7224,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7126,396]) ).
thf(7225,plain,
! [A: $i] :
( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7224]) ).
thf(7276,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= A )
| ( ( zero @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[7225]) ).
thf(7283,plain,
( ( nbr_proc @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[7276]) ).
thf(3213,plain,
( ( sk5 != sk5 )
| ( sk2 != elec_2 )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,468]) ).
thf(3214,plain,
( ( sk2 != elec_2 )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3213:[]]) ).
thf(3227,plain,
( ( sk5 != sk5 )
| ( sk4 != elec_2 )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,471]) ).
thf(3228,plain,
( ( sk4 != elec_2 )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3227:[]]) ).
thf(775,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk5 @ host @ ( elec_2 @ leq ) ) )
| ( pendack != status )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,719]) ).
thf(776,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk5 @ host @ ( elec_2 @ leq ) ) )
| ( pendack != status ) ),
inference(simp,[status(thm)],[775]) ).
thf(786,plain,
! [A: $i] :
( ( A
!= ( sk5 @ host ) )
| ( A != elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[776]) ).
thf(790,plain,
( ( ( sk5 @ host )
!= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[786]) ).
thf(3245,plain,
( ( sk5 != sk5 )
| ( ( elec_2 @ host )
!= elec_2 )
| ( pendack != status )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,790]) ).
thf(3246,plain,
( ( ( elec_2 @ host )
!= elec_2 )
| ( pendack != status )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3245:[]]) ).
thf(5729,plain,
! [A: $i] :
( ( A != nil )
| ( q_nil != q_nil )
| ( sk2 @ ( sk2 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,4039]) ).
thf(5730,plain,
! [A: $i] :
( ( A != nil )
| ( sk2 @ ( sk2 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5729]) ).
thf(5731,plain,
( ( sk2 @ ( sk2 @ last @ elem ) )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5730:[bind(A,$thf( nil ))]]) ).
thf(1636,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[131,260]) ).
thf(1637,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[1636:[bind(A,$thf( sk3 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(773,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,88]) ).
thf(774,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[773]) ).
thf(787,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host ) )
| ( A != nbr_proc ) ),
inference(simp,[status(thm)],[774]) ).
thf(791,plain,
( ( sk2 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[787]) ).
thf(82,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(126,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)],[82]) ).
thf(127,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)],[126]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).
thf(359,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(583,plain,
! [A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[217,72]) ).
thf(584,plain,
! [A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( sk3 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[583]) ).
thf(596,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= nbr_proc )
| ( ( A @ host )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[584]) ).
thf(1036,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host )
!= nbr_proc )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[100,596]) ).
thf(1037,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( ( sk3 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[1036]) ).
thf(1038,plain,
( ( sk3 @ host )
!= nbr_proc ),
inference(pattern_uni,[status(thm)],[1037:[bind(A,$thf( sk4 ))]]) ).
thf(5291,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4515,1589]) ).
thf(5292,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[5291]) ).
thf(5333,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk4 @ m_Halt ) ) ),
inference(simp,[status(thm)],[5292]) ).
thf(5347,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk4 @ m_Halt ) ),
inference(simp,[status(thm)],[5333]) ).
thf(3223,plain,
( ( sk5 != sk5 )
| ( alive @ ( elec_2 @ setIn ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,97]) ).
thf(3224,plain,
( ( alive @ ( elec_2 @ setIn ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3223:[]]) ).
thf(4234,plain,
! [A: $i] :
( ( A != sk5 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,97]) ).
thf(4235,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4234:[bind(A,$thf( sk5 ))]]) ).
thf(173,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[173]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(1798,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[269,792]) ).
thf(1799,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( C @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1798]) ).
thf(1816,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( C @ host @ queue ) )
| ( A
!= ( C @ m_Halt ) ) ),
inference(simp,[status(thm)],[1799]) ).
thf(1834,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ m_Halt @ cons ) )
!= ( B @ host @ queue ) ),
inference(simp,[status(thm)],[1816]) ).
thf(1216,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[1209]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ host @ ( C @ host @ ( pendack @ index ) @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host @ ( status @ index ) )
!= elec_2 )
| ( ( C @ host )
!= ( B @ host ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(50,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(368,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(317,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[316]) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[317]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[318]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
| ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host @ ( status @ index ) )
!= elec_2 ) ),
inference(simp,[status(thm)],[113]) ).
thf(28,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(232,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)],[28]) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( C @ ( A @ m_Ack ) )
= ( D @ ( B @ m_Ack ) ) ) ),
inference(miniscope,[status(thm)],[232]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(236,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[235]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk10 ) )
= A ),
inference(cnf,[status(esa)],[236]) ).
thf(3859,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk10 ) )
= A ),
inference(lifteq,[status(thm)],[237]) ).
thf(7113,plain,
( ( sk5 != sk5 )
| ( q_nil != elec_2 )
| ( sk4 != q_nil )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,7098]) ).
thf(7114,plain,
( ( q_nil != elec_2 )
| ( sk4 != q_nil )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[7113:[]]) ).
thf(156,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[155]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[156]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(3219,plain,
( ( sk5 != sk5 )
| ( ( elec_2 @ host @ ( pendack @ index ) )
!= ( sk5 @ host ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,793]) ).
thf(3220,plain,
( ( ( elec_2 @ host @ ( pendack @ index ) )
!= ( sk5 @ host ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3219:[]]) ).
thf(66,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(433,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)],[66]) ).
thf(381,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[380]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[381]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[382]) ).
thf(45,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(346,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(5160,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk5 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3828,5153]) ).
thf(5161,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk5 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5160]) ).
thf(5162,plain,
( ( sk5 != q_nil )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5161:[bind(A,$thf( sk2 ))]]) ).
thf(250,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[249]) ).
thf(251,plain,
! [A: $i] :
( ( A @ m_Halt @ sk11 )
= A ),
inference(cnf,[status(esa)],[250]) ).
thf(1512,plain,
! [A: $i] :
( ( A @ m_Halt @ sk11 )
= A ),
inference(lifteq,[status(thm)],[251]) ).
thf(3231,plain,
( ( sk5 != sk5 )
| ~ ( elec_2 @ host @ ( sk2 @ host @ leq ) )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[3200,489]) ).
thf(3232,plain,
( ~ ( elec_2 @ host @ ( sk2 @ host @ leq ) )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[3231:[]]) ).
thf(314,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[313]) ).
thf(315,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[314]) ).
thf(7952,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)],[7205,241]) ).
thf(7953,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)],[7952]) ).
thf(7954,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[7953:[bind(A,$thf( E )),bind(B,$thf( E @ host @ s )),bind(C,$thf( nbr_proc @ s ))]]) ).
thf(7991,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(simp,[status(thm)],[7954]) ).
thf(5228,plain,
! [A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4885,415]) ).
thf(5229,plain,
! [A: $i] :
( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[5228]) ).
thf(5233,plain,
! [A: $i] :
( ( ( q_nil @ s )
!= q_nil )
| ( ( q_nil @ s @ last )
!= A ) ),
inference(simp,[status(thm)],[5229]) ).
thf(5251,plain,
( ( q_nil @ s )
!= q_nil ),
inference(simp,[status(thm)],[5233]) ).
thf(1902,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[357,415]) ).
thf(1903,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[1902]) ).
thf(1915,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[1903]) ).
thf(1930,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[1915]) ).
thf(3024,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk4 @ m_Halt @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[386,1931]) ).
thf(3025,plain,
( ( q_nil @ ( sk4 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[3024:[bind(A,$thf( sk4 @ m_Halt )),bind(B,$thf( q_nil ))]]) ).
thf(1331,plain,
( ( sk2 @ host )
!= zero ),
inference(simp,[status(thm)],[1330]) ).
thf(20192,plain,
$false,
inference(e,[status(thm)],[69,5509,249,1840,468,88,1549,1211,4037,13244,217,4515,3230,449,269,202,120,1591,384,3745,142,1327,3562,340,3370,185,320,6291,3308,4803,257,6707,389,13732,719,372,110,1330,196,3248,4238,125,344,542,460,5604,93,3216,416,228,316,261,4253,1931,152,216,443,1632,376,106,238,5761,1811,179,766,147,397,221,293,5772,132,396,3226,116,243,206,4475,307,380,270,793,3852,1153,5117,1470,6865,7129,6064,5167,5519,102,5349,1217,165,3664,3207,260,349,788,137,3282,229,197,8026,1555,3349,97,461,1210,224,361,7842,7205,1328,5502,403,169,3087,471,339,193,4750,8407,489,6256,124,225,393,1932,3222,129,3201,73,343,792,205,244,5153,412,1219,166,161,279,375,7382,180,176,3283,118,281,413,191,402,8497,4887,8301,159,313,3051,1209,406,172,1589,3106,567,7206,13086,303,4300,271,208,387,3747,213,155,108,4684,367,1557,7098,1838,8440,1213,2592,3310,241,4827,394,306,267,851,1873,1208,162,3206,8160,209,112,1340,123,1181,194,6719,1551,7283,282,3214,3228,3209,409,310,3246,199,5731,1637,791,127,3828,359,1038,370,5347,154,3224,72,446,3288,4235,175,386,231,363,1834,1216,218,104,368,319,7344,258,114,171,3859,7114,158,7996,3220,390,75,235,433,1212,383,346,214,290,119,5162,4039,1512,3232,168,405,190,790,4885,315,7991,7126,4114,373,603,3309,210,79,195,1561,400,5251,532,415,1930,3025,459,131,7252,337,5542,3924,215,3200,222,364,232,100,1331,254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV460+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.17/0.45 % Computer : n016.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sat Sep 26 14:00:17 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.22/1.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.64 % [INFO] Parsing done (353ms).
% 1.98/1.66 % [INFO] Running in sequential loop mode.
% 3.09/2.26 % [INFO] eprover registered as external prover.
% 3.09/2.27 % [INFO] Scanning for conjecture ...
% 3.67/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 4.07/2.71 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 4.07/2.79 % [INFO] Problem is first-order (TPTP FOF).
% 4.30/2.81 % [INFO] Type checking passed.
% 4.30/2.81 % [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 ...
% 93.63/20.29 % External prover 'e' found a proof!
% 93.63/20.29 % [INFO] Killing All external provers ...
% 79.27/20.30 % Time passed: 19632ms (effective reasoning time: 18624ms)
% 79.27/20.30 % 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)>
% 79.27/20.30 % 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
% 79.27/20.30 % No. of inferences in proof: 811
% 79.27/20.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19632 ms resp. 18624 ms w/o parsing
% 80.29/20.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 80.29/20.59 % [INFO] Killing All external provers ...
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