%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV451+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 08:59:29 AM UTC 2026
% Result : Theorem 92.95s 19.33s
% Output : Refutation 95.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 85
% Syntax : Number of formulae : 828 ( 398 unt; 0 typ; 18 def)
% Number of atoms : 2330 (1288 equ; 0 cnn)
% Maximal formula atoms : 53 ( 2 avg)
% Number of connectives : 7213 (1235 ~; 595 |; 341 &;4802 @)
% ( 13 <=>; 227 =>; 0 <=; 0 <~>)
% Maximal formula depth : 56 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 54 usr; 24 con; 0-2 aty)
% Number of variables : 1203 ( 4 ^;1129 !; 52 ?;1203 :)
% ( 0 !>; 0 ?*; 0 @-; 18 @+)
% Comments :
%------------------------------------------------------------------------------
thf(setIn_decl,type,
setIn: $i > $i > $o ).
thf(alive_decl,type,
alive: $i ).
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(queue_decl,type,
queue: $i > $i ).
thf(host_decl,type,
host: $i > $i ).
thf(m_Halt_decl,type,
m_Halt: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(m_NotNorm_decl,type,
m_NotNorm: $i > $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(status_decl,type,
status: $i ).
thf(norm_decl,type,
norm: $i ).
thf(elid_decl,type,
elid: $i ).
thf(pids_decl,type,
pids: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(nbr_proc_decl,type,
nbr_proc: $i ).
thf(snoc_decl,type,
snoc: $i > $i > $i ).
thf(elec_1_decl,type,
elec_1: $i ).
thf(wait_decl,type,
wait: $i ).
thf(m_NormQ_decl,type,
m_NormQ: $i > $i ).
thf(elec_2_decl,type,
elec_2: $i ).
thf(m_Ldr_decl,type,
m_Ldr: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $o ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(last_decl,type,
last: $i > $i ).
thf(init_decl,type,
init: $i > $i ).
thf(setEmpty_decl,type,
setEmpty: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(pidElem_decl,type,
pidElem: $i > $o ).
thf(pidMsg_decl,type,
pidMsg: $i > $i ).
thf(nil_decl,type,
nil: $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 ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( ( D @ host @ queue )
= ( A @ ( C @ m_NotNorm @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( D @ setIn ) )
=> ( ( ( ( D @ host @ ( elid @ index ) )
= C )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) ) )
=> ( ( ( ( D @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( D @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
= ( zero @ s ) )
=> ( ~ ( B @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( B @ host @ s )
= ( E @ host ) )
=> ( ( ( D @ host )
!= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host @ s )
!= ( G @ host ) )
=> ( ( ( D @ host )
= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != D ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != D ) ) ) )
=> ~ ( ( B @ m_Halt @ ( E @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( A @ ( F @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( ( C @ host @ queue )
= ( sk1 @ ( B @ m_NotNorm @ cons ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( D @ ( E @ leq ) )
& ~ ( alive @ ( D @ setIn ) ) )
=> ~ ( alive @ ( E @ setIn ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ~ ( alive @ ( E @ setIn ) ) )
& ! [D: $i,E: $i] :
( ( alive @ ( E @ setIn ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ( ( ( C @ host @ ( elid @ index ) )
= B )
& ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( C @ host ) ) )
=> ( ( ( ( C @ host )
= ( A @ host ) )
& ~ ( pids @ ( A @ setIn ) )
& ! [D: $i] :
( ( ( C @ host )
= ( D @ host ) )
=> ( A @ ( D @ leq ) ) ) )
=> ( ( ( A @ host )
= ( zero @ s ) )
=> ( ~ ( A @ host @ ( nbr_proc @ leq ) )
=> ! [D: $i] :
( ( ( A @ host @ s )
= ( D @ host ) )
=> ( ( ( C @ host )
!= ( D @ host ) )
=> ! [E: $i,F: $i] :
( ( ( A @ host @ s )
!= ( F @ host ) )
=> ( ( ( C @ host )
= ( F @ host ) )
=> ! [G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( ( F @ host )
!= ( D @ host ) )
& ( ( F = A )
| ( ( alive @ ( F @ setIn ) )
& ( F != C ) ) )
& ( ( D = A )
| ( ( alive @ ( D @ setIn ) )
& ( D != C ) ) ) )
=> ~ ( ( A @ m_Halt @ ( D @ host @ queue @ snoc ) @ ( G @ m_Down @ elem ) )
& ( sk1 @ ( E @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( B @ host @ queue )
= ( sk1 @ ( A @ m_NotNorm @ cons ) ) )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( ( E @ host )
!= ( C @ host ) ) )
=> ~ ( ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( C @ ( D @ leq ) )
& ~ ( alive @ ( C @ setIn ) ) )
=> ~ ( alive @ ( D @ setIn ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
=> ~ ( E @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ( ( D @ host )
!= ( C @ host ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ~ ( alive @ ( D @ setIn ) ) )
& ! [C: $i,D: $i] :
( ( alive @ ( D @ setIn ) )
=> ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ( ( ( B @ host @ ( elid @ index ) )
= A )
& ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( B @ host ) ) )
=> ( ( ( ( B @ host )
= ( sk2 @ host ) )
& ~ ( pids @ ( sk2 @ setIn ) )
& ! [C: $i] :
( ( ( B @ host )
= ( C @ host ) )
=> ( sk2 @ ( C @ leq ) ) ) )
=> ( ( ( sk2 @ host )
= ( zero @ s ) )
=> ( ~ ( sk2 @ host @ ( nbr_proc @ leq ) )
=> ! [C: $i] :
( ( ( sk2 @ host @ s )
= ( C @ host ) )
=> ( ( ( B @ host )
!= ( C @ host ) )
=> ! [D: $i,E: $i] :
( ( ( sk2 @ host @ s )
!= ( E @ host ) )
=> ( ( ( B @ host )
= ( E @ host ) )
=> ! [F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( ( E @ host )
!= ( C @ host ) )
& ( ( E = sk2 )
| ( ( alive @ ( E @ setIn ) )
& ( E != B ) ) )
& ( ( C = sk2 )
| ( ( alive @ ( C @ setIn ) )
& ( C != B ) ) ) )
=> ~ ( ( sk2 @ m_Halt @ ( C @ host @ queue @ snoc ) @ ( F @ m_Down @ elem ) )
& ( sk1 @ ( D @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( ( A @ host @ queue )
= ( sk1 @ ( sk3 @ m_NotNorm @ cons ) ) )
& ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ( ( D @ host )
!= ( B @ host ) ) )
=> ~ ( ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( B @ ( C @ leq ) )
& ~ ( alive @ ( B @ setIn ) ) )
=> ~ ( alive @ ( C @ setIn ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
=> ~ ( D @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ( ( C @ host )
!= ( B @ host ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ~ ( alive @ ( C @ setIn ) ) )
& ! [B: $i,C: $i] :
( ( alive @ ( C @ setIn ) )
=> ~ ( B @ host @ queue @ ( C @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ( ( ( ( A @ host @ ( elid @ index ) )
= sk3 )
& ( ( A @ host @ ( status @ index ) )
= norm )
& ( ( A @ host @ ( ldr @ index ) )
= ( A @ host ) ) )
=> ( ( ( ( A @ host )
= ( sk2 @ host ) )
& ~ ( pids @ ( sk2 @ setIn ) )
& ! [B: $i] :
( ( ( A @ host )
= ( B @ host ) )
=> ( sk2 @ ( B @ leq ) ) ) )
=> ( ( ( sk2 @ host )
= ( zero @ s ) )
=> ( ~ ( sk2 @ host @ ( nbr_proc @ leq ) )
=> ! [B: $i] :
( ( ( sk2 @ host @ s )
= ( B @ host ) )
=> ( ( ( A @ host )
!= ( B @ host ) )
=> ! [C: $i,D: $i] :
( ( ( sk2 @ host @ s )
!= ( D @ host ) )
=> ( ( ( A @ host )
= ( D @ host ) )
=> ! [E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( ( D @ host )
!= ( B @ host ) )
& ( ( D = sk2 )
| ( ( alive @ ( D @ setIn ) )
& ( D != A ) ) )
& ( ( B = sk2 )
| ( ( alive @ ( B @ setIn ) )
& ( B != A ) ) ) )
=> ~ ( ( sk2 @ m_Halt @ ( B @ host @ queue @ snoc ) @ ( E @ m_Down @ elem ) )
& ( sk1 @ ( C @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk2 @ host @ s )
= ( A @ host ) )
=> ( ( ( sk4 @ host )
!= ( A @ host ) )
=> ! [B: $i,C: $i] :
( ( ( sk2 @ host @ s )
!= ( C @ host ) )
=> ( ( ( sk4 @ host )
= ( C @ host ) )
=> ! [D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( ( B @ host )
= ( A @ host ) )
& ( ( C @ host )
!= ( A @ host ) )
& ( ( C = sk2 )
| ( ( alive @ ( C @ setIn ) )
& ( C != sk4 ) ) )
& ( ( A = sk2 )
| ( ( alive @ ( A @ setIn ) )
& ( A != sk4 ) ) ) )
=> ~ ( ( sk2 @ m_Halt @ ( A @ host @ queue @ snoc ) @ ( D @ m_Down @ elem ) )
& ( sk1 @ ( B @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk2 @ host @ s )
!= ( B @ host ) )
=> ( ( ( sk4 @ host )
= ( B @ host ) )
=> ! [C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( ( A @ host )
= ( sk5 @ host ) )
& ( ( B @ host )
!= ( sk5 @ host ) )
& ( ( B = sk2 )
| ( ( alive @ ( B @ setIn ) )
& ( B != sk4 ) ) )
& ( ( sk5 = sk2 )
| ( ( alive @ ( sk5 @ setIn ) )
& ( sk5 != sk4 ) ) ) )
=> ~ ( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( C @ m_Down @ elem ) )
& ( sk1 @ ( A @ m_Down @ elem ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( sk2 @ host @ s )
!= ( A @ host ) )
=> ( ( ( sk4 @ host )
= ( A @ host ) )
=> ! [B: $i] :
( ( ( ( B @ host )
= ( A @ host ) )
& ( ( sk6 @ host )
= ( sk5 @ host ) )
& ( ( A @ host )
!= ( sk5 @ host ) )
& ( ( A = sk2 )
| ( ( alive @ ( A @ setIn ) )
& ( A != sk4 ) ) )
& ( ( sk5 = sk2 )
| ( ( alive @ ( sk5 @ setIn ) )
& ( sk5 != sk4 ) ) ) )
=> ~ ( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( B @ m_Down @ elem ) )
& ( sk1 @ ( sk6 @ m_Down @ elem ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( ( ( A @ host )
= ( sk7 @ host ) )
& ( ( sk6 @ host )
= ( sk5 @ host ) )
& ( ( sk7 @ host )
!= ( sk5 @ host ) )
& ( ( sk7 = sk2 )
| ( ( alive @ ( sk7 @ setIn ) )
& ( sk7 != sk4 ) ) )
& ( ( sk5 = sk2 )
| ( ( alive @ ( sk5 @ setIn ) )
& ( sk5 != sk4 ) ) ) )
=> ~ ( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( A @ m_Down @ elem ) )
& ( sk1 @ ( sk6 @ m_Down @ elem ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( ( C @ pidMsg @ host )
= ( B @ pidMsg @ host ) )
& ( C @ pidElem )
& ( B @ pidElem )
& ( A @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( B @ pidMsg @ leq ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ host @ queue )
= ( A @ ( C @ m_NotNorm @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( D @ setIn ) )
=> ( ( ( ( D @ host @ ( elid @ index ) )
= C )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) ) )
=> ( ( ( ( D @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( D @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
= ( zero @ s ) )
=> ( ~ ( B @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( B @ host @ s )
= ( E @ host ) )
=> ( ( ( D @ host )
!= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host @ s )
!= ( G @ host ) )
=> ( ( ( D @ host )
= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != D ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != D ) ) ) )
=> ~ ( ( B @ m_Halt @ ( E @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( A @ ( F @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ host @ queue )
= ( A @ ( C @ m_NotNorm @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( D @ setIn ) )
=> ( ( ( ( D @ host @ ( elid @ index ) )
= C )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) ) )
=> ( ( ( ( D @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( D @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
= ( zero @ s ) )
=> ( ~ ( B @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( B @ host @ s )
= ( E @ host ) )
=> ( ( ( D @ host )
!= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host @ s )
!= ( G @ host ) )
=> ( ( ( D @ host )
= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != D ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != D ) ) ) )
=> ~ ( ( B @ m_Halt @ ( E @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( A @ ( F @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ host @ queue )
= ( A @ ( C @ m_NotNorm @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( D @ setIn ) )
=> ( ( ( ( D @ host @ ( elid @ index ) )
= C )
& ( ( D @ host @ ( status @ index ) )
= norm )
& ( ( D @ host @ ( ldr @ index ) )
= ( D @ host ) ) )
=> ( ( ( ( D @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( D @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
= ( zero @ s ) )
=> ( ~ ( B @ host @ ( nbr_proc @ leq ) )
=> ! [E: $i] :
( ( ( B @ host @ s )
= ( E @ host ) )
=> ( ( ( D @ host )
!= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host @ s )
!= ( G @ host ) )
=> ( ( ( D @ host )
= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != D ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != D ) ) ) )
=> ~ ( ( B @ m_Halt @ ( E @ host @ queue @ snoc ) @ ( H @ m_Down @ elem ) )
& ( A @ ( F @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
& ( sk1 @ ( sk6 @ m_Down @ elem ) )
& ( ( sk8 @ host )
= ( sk7 @ host ) )
& ( ( sk6 @ host )
= ( sk5 @ host ) )
& ( ( sk7 @ host )
!= ( sk5 @ host ) )
& ( ( sk7 = sk2 )
| ( alive @ ( sk7 @ setIn ) ) )
& ( ( sk7 = sk2 )
| ( sk7 != sk4 ) )
& ( ( sk5 = sk2 )
| ( alive @ ( sk5 @ setIn ) ) )
& ( ( sk5 = sk2 )
| ( sk5 != sk4 ) )
& ( ( sk4 @ host )
= ( sk7 @ host ) )
& ( ( sk2 @ host @ s )
!= ( sk7 @ host ) )
& ( ( sk4 @ host )
!= ( sk5 @ host ) )
& ( ( sk2 @ host @ s )
= ( sk5 @ host ) )
& ~ ( sk2 @ host @ ( nbr_proc @ leq ) )
& ( ( sk2 @ host )
= ( zero @ s ) )
& ( ( sk4 @ host )
= ( sk2 @ host ) )
& ~ ( pids @ ( sk2 @ setIn ) )
& ( ( sk2 @ ( T @ leq ) )
| ( ( sk4 @ host )
!= ( T @ host ) ) )
& ( ( sk4 @ host @ ( elid @ index ) )
= sk3 )
& ( ( sk4 @ host @ ( status @ index ) )
= norm )
& ( ( sk4 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) )
& ( alive @ ( sk4 @ setIn ) )
& ( ( sk4 @ host @ queue )
= ( sk1 @ ( sk3 @ m_NotNorm @ cons ) ) )
& ( ~ ( R @ host @ queue @ ( Q @ m_Down @ elem ) )
| ~ ( P @ host @ queue @ ( S @ m_Down @ elem ) )
| ( ( S @ host )
!= ( R @ host ) )
| ( ( Q @ host )
!= ( P @ host ) )
| ~ ( alive @ ( R @ setIn ) )
| ~ ( alive @ ( P @ setIn ) )
| ( ( R @ host )
= ( P @ host ) ) )
& ( ~ ( alive @ ( O @ setIn ) )
| ~ ( alive @ ( N @ setIn ) )
| ( ( O @ host )
!= ( N @ host ) )
| ( O = N ) )
& ( ~ ( alive @ ( M @ setIn ) )
| ( ( M @ host )
!= ( L @ host ) )
| ~ ( L @ ( M @ leq ) )
| ( alive @ ( L @ setIn ) ) )
& ( ~ ( K @ host @ ( I @ host @ leq ) )
| ~ ( J @ host @ queue @ ( I @ ( K @ m_Ack ) @ elem ) ) )
& ( ~ ( H @ host @ ( G @ host @ leq ) )
| ~ ( G @ host @ queue @ ( H @ m_Halt @ elem ) ) )
& ( ( ( F @ host )
!= ( E @ host ) )
| ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) )
& ( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(87,plain,
( ( sk2 @ host @ s )
= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(125,plain,
( ( sk2 @ host @ s )
= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(20,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(206,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(207,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[206]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(231,plain,
! [A: $i,B: $i] :
( ( ( B @ s @ ( A @ s @ leq ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( B @ s @ ( A @ s @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(232,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)],[231]) ).
thf(233,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)],[232]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(3148,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)],[207,234]) ).
thf(3149,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[3148]) ).
thf(3150,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[3149:[bind(A,$thf( D )),bind(B,$thf( D @ host )),bind(C,$thf( nbr_proc ))]]) ).
thf(3170,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(simp,[status(thm)],[3150]) ).
thf(3872,plain,
! [A: $i] :
( ( ( sk2 @ host @ s )
!= ( A @ host @ s ) )
| ( nbr_proc @ s @ ( sk5 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[125,3170]) ).
thf(3873,plain,
nbr_proc @ s @ ( sk5 @ host @ leq ),
inference(pattern_uni,[status(thm)],[3872:[bind(A,$thf( sk2 ))]]) ).
thf(92,plain,
( ( sk4 @ host @ queue )
= ( sk1 @ ( sk3 @ m_NotNorm @ cons ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(116,plain,
( ( sk1 @ ( sk3 @ m_NotNorm @ cons ) )
= ( sk4 @ host @ queue ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(73,plain,
( ( sk4 @ host )
= ( sk2 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(104,plain,
( ( sk4 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(864,plain,
( ( sk1 @ ( sk3 @ m_NotNorm @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(rewrite,[status(thm)],[116,104]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(391,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(392,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[391]) ).
thf(393,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[392]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[393]) ).
thf(2093,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_NotNorm @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[864,394]) ).
thf(2094,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2093:[bind(A,$thf( sk3 @ m_NotNorm )),bind(B,$thf( sk1 ))]]) ).
thf(86,plain,
sk1 @ ( sk6 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[70]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(257,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)],[32]) ).
thf(258,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)],[257]) ).
thf(259,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)],[258]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[259]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(7213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk6 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,266]) ).
thf(7214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk6 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[7213]) ).
thf(7215,plain,
! [A: $i] : ( sk1 @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[7214:[bind(A,$thf( sk6 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(7315,plain,
! [A: $i] : ( sk1 @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[7215]) ).
thf(7797,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ m_NotNorm @ cons ) )
!= ( sk1 @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[864,7315]) ).
thf(7798,plain,
sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[7797:[bind(A,$thf( sk3 @ m_NotNorm ))]]) ).
thf(88,plain,
sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[70]) ).
thf(77,plain,
( ( sk2 @ host )
= ( zero @ s ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(118,plain,
( ( zero @ s )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(97,plain,
( ( sk4 @ host )
= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(117,plain,
( ( sk7 @ host )
= ( sk4 @ host ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(480,plain,
( ( sk7 @ host )
= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[117,104]) ).
thf(101,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk4 @ host )
!= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(111,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk4 @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(112,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk4 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(802,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(rewrite,[status(thm)],[112,104]) ).
thf(806,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[480,802]) ).
thf(807,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[806]) ).
thf(808,plain,
sk2 @ ( sk7 @ leq ),
inference(pattern_uni,[status(thm)],[807:[bind(A,$thf( sk7 ))]]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(395,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(396,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[395]) ).
thf(397,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[396]) ).
thf(2132,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk7 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[808,397]) ).
thf(2133,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk7 @ leq ) ) ),
inference(simp,[status(thm)],[2132]) ).
thf(2140,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk7 ) ),
inference(simp,[status(thm)],[2133]) ).
thf(2152,plain,
( ( sk2 @ s )
!= sk7 ),
inference(simp,[status(thm)],[2140]) ).
thf(2161,plain,
( ( ( sk2 @ s )
!= ( zero @ s ) )
| ( ( sk2 @ host )
!= sk7 ) ),
inference(paramod_ordered,[status(thm)],[118,2152]) ).
thf(2163,plain,
( ( sk2 != zero )
| ( ( sk2 @ host )
!= sk7 ) ),
inference(simp,[status(thm)],[2161]) ).
thf(2116,plain,
! [A: $i] :
( ( ( sk2 @ host @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk5 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[125,397]) ).
thf(2117,plain,
~ ( sk2 @ host @ ( sk5 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[2116:[bind(A,$thf( sk2 @ host ))]]) ).
thf(8,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(162,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(254,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(255,plain,
! [A: $i] :
( ( A @ ordered )
=> ! [B: $i] : ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(miniscope,[status(thm)],[254]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ ( A @ ordered ) ),
inference(cnf,[status(esa)],[255]) ).
thf(3807,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[162,256]) ).
thf(3808,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ ordered )
!= ( A @ ordered ) )
| ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(simp,[status(thm)],[3807]) ).
thf(3809,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(pattern_uni,[status(thm)],[3808:[bind(A,$thf( q_nil ))]]) ).
thf(3812,plain,
! [A: $i] : ( A @ m_Ldr @ ( q_nil @ snoc ) @ ordered ),
inference(simp,[status(thm)],[3809]) ).
thf(56,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(388,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(389,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(3858,plain,
! [A: $i] : ( q_nil @ ( A @ m_Ldr @ cons ) @ ordered ),
inference(rewrite,[status(thm)],[3812,390]) ).
thf(53,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(377,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(378,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[377]) ).
thf(379,plain,
wait != norm,
inference(lifteq,[status(thm)],[378]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(202,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(71,plain,
( ( sk6 @ host )
= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(120,plain,
( ( sk6 @ host )
= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(18,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(200,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(201,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[200]) ).
thf(1112,plain,
! [A: $i] : ( A @ host @ ( sk2 @ host @ leq ) ),
inference(rewrite,[status(thm)],[201,118]) ).
thf(2126,plain,
! [A: $i] :
( ( ( zero @ s )
!= ( A @ s ) )
| ~ ( A @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[118,397]) ).
thf(2127,plain,
~ ( zero @ ( sk2 @ host @ leq ) ),
inference(pattern_uni,[status(thm)],[2126:[bind(A,$thf( zero ))]]) ).
thf(2183,plain,
! [A: $i] :
( ( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( zero @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1112,2127]) ).
thf(2184,plain,
! [A: $i] :
( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( zero @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2201,plain,
! [A: $i] :
( ( ( A @ host )
!= zero )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[2184]) ).
thf(2223,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[2201]) ).
thf(2362,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk5 @ host )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[120,2223]) ).
thf(2363,plain,
( ( sk5 @ host )
!= zero ),
inference(pattern_uni,[status(thm)],[2362:[bind(A,$thf( sk6 ))]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(152,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)],[7]) ).
thf(153,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)],[152]) ).
thf(154,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)],[153]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[154]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(158,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[157]) ).
thf(159,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk10 )
= A ),
inference(cnf,[status(esa)],[158]) ).
thf(2077,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk10 )
= A ),
inference(lifteq,[status(thm)],[159]) ).
thf(64,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox/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(867,plain,
! [A: $i] :
( ( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,415]) ).
thf(868,plain,
! [A: $i] :
( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[867]) ).
thf(871,plain,
! [A: $i] :
( ( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) )
!= q_nil )
| ( ( sk8 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[868]) ).
thf(873,plain,
( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[871]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox/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(29,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(247,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(384,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(95,plain,
( ( sk8 @ host )
= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(108,plain,
( ( sk8 @ host )
= ( sk7 @ host ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(482,plain,
( ( sk8 @ host )
= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[108,480]) ).
thf(813,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[482,802]) ).
thf(814,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[813]) ).
thf(815,plain,
sk2 @ ( sk8 @ leq ),
inference(pattern_uni,[status(thm)],[814:[bind(A,$thf( sk8 ))]]) ).
thf(3113,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk8 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[815,234]) ).
thf(3114,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk8 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3113]) ).
thf(3115,plain,
sk2 @ s @ ( sk8 @ s @ leq ),
inference(pattern_uni,[status(thm)],[3114:[bind(A,$thf( sk8 )),bind(B,$thf( sk2 ))]]) ).
thf(3177,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk8 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3115,234]) ).
thf(3178,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk8 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3177]) ).
thf(3179,plain,
sk2 @ s @ s @ ( sk8 @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[3178:[bind(A,$thf( sk8 @ s )),bind(B,$thf( sk2 @ s ))]]) ).
thf(3599,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ ( sk8 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3179,397]) ).
thf(3600,plain,
! [A: $i] :
( ( sk2 @ s @ s @ ( sk8 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3599]) ).
thf(3642,plain,
! [A: $i] :
( ( ( sk2 @ s @ s )
!= A )
| ( ( sk8 @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[3600]) ).
thf(3648,plain,
( ( sk2 @ s @ s @ s )
!= ( sk8 @ s @ s ) ),
inference(simp,[status(thm)],[3642]) ).
thf(3137,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk7 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[808,234]) ).
thf(3138,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk7 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3137]) ).
thf(3139,plain,
sk2 @ s @ ( sk7 @ s @ leq ),
inference(pattern_uni,[status(thm)],[3138:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).
thf(3274,plain,
! [A: $i] :
( ( ( sk2 @ s @ ( sk7 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3139,397]) ).
thf(3275,plain,
! [A: $i] :
( ( sk2 @ s @ ( sk7 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3274]) ).
thf(3300,plain,
! [A: $i] :
( ( ( sk2 @ s )
!= A )
| ( ( sk7 @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[3275]) ).
thf(3313,plain,
( ( sk2 @ s @ s )
!= ( sk7 @ s ) ),
inference(simp,[status(thm)],[3300]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox/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(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(194,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[194]) ).
thf(2626,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)],[390,195]) ).
thf(2627,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[2626:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(2118,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk8 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[815,397]) ).
thf(2119,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk8 @ leq ) ) ),
inference(simp,[status(thm)],[2118]) ).
thf(2143,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk8 ) ),
inference(simp,[status(thm)],[2119]) ).
thf(2155,plain,
( ( sk2 @ s )
!= sk8 ),
inference(simp,[status(thm)],[2143]) ).
thf(2166,plain,
( ( ( sk2 @ s )
!= ( zero @ s ) )
| ( ( sk2 @ host )
!= sk8 ) ),
inference(paramod_ordered,[status(thm)],[118,2155]) ).
thf(2168,plain,
( ( sk2 != zero )
| ( ( sk2 @ host )
!= sk8 ) ),
inference(simp,[status(thm)],[2166]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[259]) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(265,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[264]) ).
thf(3014,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_NotNorm @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[864,265]) ).
thf(3015,plain,
sk2 @ host @ queue @ ( sk3 @ m_NotNorm @ elem ),
inference(pattern_uni,[status(thm)],[3014:[bind(A,$thf( sk3 @ m_NotNorm )),bind(B,$thf( sk1 ))]]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(711,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( B != A ) ),
inference(simp,[status(thm)],[110]) ).
thf(750,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(simp,[status(thm)],[711]) ).
thf(2759,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[480,750]) ).
thf(2760,plain,
~ ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[2759:[bind(A,$thf( sk7 ))]]) ).
thf(3354,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_NotNorm @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3015,2760]) ).
thf(3355,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_NotNorm @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3354]) ).
thf(3396,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_NotNorm )
!= ( sk7 @ m_Down ) ) ),
inference(simp,[status(thm)],[3355]) ).
thf(3414,plain,
( ( sk3 @ m_NotNorm )
!= ( sk7 @ m_Down ) ),
inference(simp,[status(thm)],[3396]) ).
thf(817,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[104,802]) ).
thf(818,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[817]) ).
thf(819,plain,
sk2 @ ( sk4 @ leq ),
inference(pattern_uni,[status(thm)],[818:[bind(A,$thf( sk4 ))]]) ).
thf(3119,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[819,234]) ).
thf(3120,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3119]) ).
thf(3121,plain,
sk2 @ s @ ( sk4 @ s @ leq ),
inference(pattern_uni,[status(thm)],[3120:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(180,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)],[14]) ).
thf(181,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)],[180]) ).
thf(182,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)],[181]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[182]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(91,plain,
( ( sk4 @ host @ ( elid @ index ) )
= sk3 ),
inference(cnfConj,[status(thm)],[70]) ).
thf(105,plain,
( ( sk4 @ host @ ( elid @ index ) )
= sk3 ),
inference(lifteq,[status(thm)],[91]) ).
thf(575,plain,
( ( sk2 @ host @ ( elid @ index ) )
= sk3 ),
inference(rewrite,[status(thm)],[105,104]) ).
thf(90,plain,
( ( sk4 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(128,plain,
( ( sk4 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(781,plain,
( ( sk2 @ host @ ( ldr @ index ) )
= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[128,104]) ).
thf(789,plain,
( ( ( sk2 @ host @ ( elid @ index ) )
!= ( sk2 @ host @ ( ldr @ index ) ) )
| ( ( sk2 @ host )
= sk3 ) ),
inference(paramod_ordered,[status(thm)],[575,781]) ).
thf(792,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( elid != ldr )
| ( ( sk2 @ host )
= sk3 ) ),
inference(simp,[status(thm)],[789]) ).
thf(798,plain,
( ( elid != ldr )
| ( ( sk2 @ host )
= sk3 ) ),
inference(simp,[status(thm)],[792]) ).
thf(10,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(166,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(503,plain,
nbr_proc @ ( sk2 @ host @ leq ),
inference(rewrite,[status(thm)],[166,118]) ).
thf(79,plain,
~ ( sk2 @ host @ ( nbr_proc @ leq ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(506,plain,
( ( ( nbr_proc @ ( sk2 @ host @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[503,79]) ).
thf(507,plain,
( ( nbr_proc @ ( sk2 @ host @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(511,plain,
( ( ( sk2 @ host )
!= nbr_proc )
| ( ( sk2 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[507]) ).
thf(513,plain,
( ( sk2 @ host )
!= nbr_proc ),
inference(simp,[status(thm)],[511]) ).
thf(1000,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk3 != nbr_proc )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,513]) ).
thf(1001,plain,
( ( sk3 != nbr_proc )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[1000:[]]) ).
thf(3937,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( sk5 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3873,234]) ).
thf(3938,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( sk5 @ host @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3937]) ).
thf(3939,plain,
nbr_proc @ s @ s @ ( sk5 @ host @ s @ leq ),
inference(pattern_uni,[status(thm)],[3938:[bind(A,$thf( sk5 @ host )),bind(B,$thf( nbr_proc @ s ))]]) ).
thf(7077,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk5 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3939,234]) ).
thf(7078,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk5 @ host @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7077]) ).
thf(7079,plain,
nbr_proc @ s @ s @ s @ ( sk5 @ host @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[7078:[bind(A,$thf( sk5 @ host @ s )),bind(B,$thf( nbr_proc @ s @ s ))]]) ).
thf(82,plain,
( ( sk4 @ host @ ( status @ index ) )
= norm ),
inference(cnfConj,[status(thm)],[70]) ).
thf(126,plain,
( ( sk4 @ host @ ( status @ index ) )
= norm ),
inference(lifteq,[status(thm)],[82]) ).
thf(676,plain,
( ( sk2 @ host @ ( status @ index ) )
= norm ),
inference(rewrite,[status(thm)],[126,104]) ).
thf(783,plain,
( ( ( sk2 @ host @ ( status @ index ) )
!= ( sk2 @ host @ ( ldr @ index ) ) )
| ( ( sk2 @ host )
= norm ) ),
inference(paramod_ordered,[status(thm)],[781,676]) ).
thf(794,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( status != ldr )
| ( ( sk2 @ host )
= norm ) ),
inference(simp,[status(thm)],[783]) ).
thf(800,plain,
( ( status != ldr )
| ( ( sk2 @ host )
= norm ) ),
inference(simp,[status(thm)],[794]) ).
thf(854,plain,
( ( ( sk2 @ ( sk7 @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[808,79]) ).
thf(855,plain,
( ( sk2 @ ( sk7 @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[854]) ).
thf(856,plain,
( ( ( sk2 @ host )
!= sk2 )
| ( sk7 != nbr_proc ) ),
inference(simp,[status(thm)],[855]) ).
thf(1358,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk2 != norm )
| ( sk7 != nbr_proc )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,856]) ).
thf(1359,plain,
( ( sk2 != norm )
| ( sk7 != nbr_proc )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[1358:[]]) ).
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/sandbox/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(74,plain,
( ( sk2 @ host @ s )
!= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(115,plain,
( ( sk2 @ host @ s )
!= ( sk7 @ host ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(643,plain,
( ( sk2 @ host @ s )
!= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[115,480]) ).
thf(646,plain,
( ( ( sk2 @ host @ s )
!= ( zero @ s ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[118,643]) ).
thf(647,plain,
( ( sk2 @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[646]) ).
thf(651,plain,
( ( sk2 @ host )
!= zero ),
inference(simp,[status(thm)],[647]) ).
thf(3184,plain,
! [A: $i] :
( ( ( sk2 @ s @ ( sk8 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3115,397]) ).
thf(3185,plain,
! [A: $i] :
( ( sk2 @ s @ ( sk8 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3184]) ).
thf(3207,plain,
! [A: $i] :
( ( ( sk2 @ s )
!= A )
| ( ( sk8 @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[3185]) ).
thf(3221,plain,
( ( sk2 @ s @ s )
!= ( sk8 @ s ) ),
inference(simp,[status(thm)],[3207]) ).
thf(2134,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,397]) ).
thf(2135,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2134]) ).
thf(2145,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2135]) ).
thf(2148,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2145]) ).
thf(2465,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk5 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,2148]) ).
thf(2466,plain,
( ( nbr_proc @ s )
!= ( sk5 @ host ) ),
inference(pattern_uni,[status(thm)],[2465:[bind(A,$thf( sk6 ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(196,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3222,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk4 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,234]) ).
thf(3223,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk4 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3222]) ).
thf(3224,plain,
sk2 @ s @ s @ ( sk4 @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[3223:[bind(A,$thf( sk4 @ s )),bind(B,$thf( sk2 @ s ))]]) ).
thf(3664,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ ( sk4 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3224,397]) ).
thf(3665,plain,
! [A: $i] :
( ( sk2 @ s @ s @ ( sk4 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3664]) ).
thf(3707,plain,
! [A: $i] :
( ( ( sk2 @ s @ s )
!= A )
| ( ( sk4 @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[3665]) ).
thf(3713,plain,
( ( sk2 @ s @ s @ s )
!= ( sk4 @ s @ s ) ),
inference(simp,[status(thm)],[3707]) ).
thf(44,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(344,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
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/sandbox/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(2757,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ~ ( sk5 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[120,750]) ).
thf(2758,plain,
~ ( sk5 @ host @ queue @ ( sk6 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[2757:[bind(A,$thf( sk6 ))]]) ).
thf(7761,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) )
!= ( sk5 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7315,2758]) ).
thf(7762,plain,
! [A: $i] :
( ( sk1 @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) )
!= ( sk5 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7761]) ).
thf(7836,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ cons ) )
!= ( sk5 @ host @ queue ) )
| ( ( sk6 @ m_Down )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[7762]) ).
thf(7857,plain,
! [A: $i] :
( ( sk1 @ ( A @ cons ) )
!= ( sk5 @ host @ queue ) ),
inference(simp,[status(thm)],[7836]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(225,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( C @ ( A @ m_Ack ) )
= ( D @ ( B @ m_Ack ) ) ) ),
inference(miniscope,[status(thm)],[225]) ).
thf(227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[226]) ).
thf(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[227]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(289,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox/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(7087,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ ( sk5 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3939,397]) ).
thf(7088,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ ( sk5 @ host @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7087]) ).
thf(7155,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s )
!= A )
| ( ( sk5 @ host @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[7088]) ).
thf(7183,plain,
( ( nbr_proc @ s @ s @ s )
!= ( sk5 @ host @ s ) ),
inference(simp,[status(thm)],[7155]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(278,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)],[34]) ).
thf(279,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)],[278]) ).
thf(280,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)],[279]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[280]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[281]) ).
thf(98,plain,
alive @ ( sk4 @ setIn ),
inference(cnfConj,[status(thm)],[70]) ).
thf(25,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(222,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(223,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[222]) ).
thf(224,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[223]) ).
thf(763,plain,
! [A: $i] :
( ( ( alive @ ( sk4 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,224]) ).
thf(764,plain,
! [A: $i] :
( ( alive @ ( sk4 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[763]) ).
thf(768,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[764]) ).
thf(770,plain,
setEmpty != alive,
inference(simp,[status(thm)],[768]) ).
thf(3655,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk4 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3224,234]) ).
thf(3656,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk4 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3655]) ).
thf(3657,plain,
sk2 @ s @ s @ s @ ( sk4 @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[3656:[bind(A,$thf( sk4 @ s @ s )),bind(B,$thf( sk2 @ s @ s ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(176,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)],[13]) ).
thf(177,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)],[176]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[177]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_01) ).
thf(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(2468,plain,
! [A: $i] :
( ( ( sk7 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[480,2148]) ).
thf(2469,plain,
( ( nbr_proc @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[2468:[bind(A,$thf( sk7 ))]]) ).
thf(2113,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[802,397]) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[2113]) ).
thf(2115,plain,
( ( sk2 @ s @ host )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[2114:[bind(A,$thf( sk2 @ s )),bind(B,$thf( sk2 ))]]) ).
thf(2254,plain,
( ( sk2 @ s )
!= sk2 ),
inference(simp,[status(thm)],[2115]) ).
thf(1182,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( nbr_proc != norm )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,513]) ).
thf(1183,plain,
( ( nbr_proc != norm )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[1182:[]]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(209,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[208]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[251]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[252]) ).
thf(78,plain,
( ( sk7 = sk2 )
| ( alive @ ( sk7 @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(113,plain,
( ( alive @ ( sk7 @ setIn ) )
| ( sk7 = sk2 ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(60,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(401,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(402,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[401]) ).
thf(590,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true
| ( sk7 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[113,402]) ).
thf(591,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ( sk7 = sk2 ) ),
inference(simp,[status(thm)],[590]) ).
thf(600,plain,
( ( alive != alive )
| ( sk7 != nil )
| ( sk7 = sk2 ) ),
inference(simp,[status(thm)],[591]) ).
thf(602,plain,
( ( sk7 != nil )
| ( sk7 = sk2 ) ),
inference(simp,[status(thm)],[600]) ).
thf(5,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(145,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(146,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[145]) ).
thf(147,plain,
elec_2 != wait,
inference(lifteq,[status(thm)],[146]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[219]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[220]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox/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(3,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(132,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(809,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk5 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,802]) ).
thf(824,plain,
! [A: $i] :
( ( sk6 != sk2 )
| ( sk5 != A )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[809]) ).
thf(842,plain,
( ( sk6 != sk2 )
| ( sk2 @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[824]) ).
thf(2120,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk5 @ leq ) ) )
| ~ $true
| ( sk6 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[842,397]) ).
thf(2121,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk5 @ leq ) ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[2120]) ).
thf(2142,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk5 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[2121]) ).
thf(2154,plain,
( ( ( sk2 @ s )
!= sk5 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[2142]) ).
thf(290,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[289]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[290]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[291]) ).
thf(75,plain,
~ ( pids @ ( sk2 @ setIn ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(450,plain,
( ( ( alive @ ( sk4 @ setIn ) )
!= ( pids @ ( sk2 @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,75]) ).
thf(451,plain,
( ( alive @ ( sk4 @ setIn ) )
!= ( pids @ ( sk2 @ setIn ) ) ),
inference(simp,[status(thm)],[450]) ).
thf(452,plain,
( ( pids != alive )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[451]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(380,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(237,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)],[28]) ).
thf(238,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)],[237]) ).
thf(239,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)],[238]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[239]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[240]) ).
thf(243,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[242]) ).
thf(244,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(cnf,[status(esa)],[243]) ).
thf(2164,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(lifteq,[status(thm)],[244]) ).
thf(12040,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( sk5 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7079,397]) ).
thf(12041,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ ( sk5 @ host @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[12040]) ).
thf(12121,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s )
!= A )
| ( ( sk5 @ host @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[12041]) ).
thf(12159,plain,
( ( nbr_proc @ s @ s @ s @ s )
!= ( sk5 @ host @ s @ s ) ),
inference(simp,[status(thm)],[12121]) ).
thf(1020,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ~ ( sk3 @ ( nbr_proc @ leq ) )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,79]) ).
thf(1021,plain,
( ~ ( sk3 @ ( nbr_proc @ leq ) )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[1020:[]]) ).
thf(2128,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1112,397]) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2128]) ).
thf(2144,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( B @ s )
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[2129]) ).
thf(2147,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[2144]) ).
thf(84,plain,
( ( sk4 @ host )
!= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(102,plain,
( ( sk5 @ host )
!= ( sk4 @ host ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(459,plain,
( ( sk5 @ host )
!= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[102,104]) ).
thf(561,plain,
sk5 != sk2,
inference(simp,[status(thm)],[459]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(190,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[191]) ).
thf(860,plain,
( ( ( sk2 @ ( sk4 @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[819,79]) ).
thf(861,plain,
( ( sk2 @ ( sk4 @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[860]) ).
thf(862,plain,
( ( ( sk2 @ host )
!= sk2 )
| ( sk4 != nbr_proc ) ),
inference(simp,[status(thm)],[861]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(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(33,axiom,
! [A: $i] :
( ( A @ pidElem )
<=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(267,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)],[33]) ).
thf(268,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)],[267]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk16 @ m_Down ) )
| ( A
= ( A @ sk15 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[268]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[269]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(275,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[274]) ).
thf(1014,plain,
! [A: $i] :
( ( ( sk2 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( sk3 @ leq ) )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,207]) ).
thf(1015,plain,
( ( nbr_proc @ ( sk3 @ leq ) )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[1014:[bind(A,$thf( sk2 ))]]) ).
thf(2130,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( sk3 @ leq ) ) )
| ~ $true
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[1015,397]) ).
thf(2131,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( sk3 @ leq ) ) )
| ( elid != ldr ) ),
inference(simp,[status(thm)],[2130]) ).
thf(2138,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= sk3 )
| ( elid != ldr ) ),
inference(simp,[status(thm)],[2131]) ).
thf(2150,plain,
( ( ( nbr_proc @ s )
!= sk3 )
| ( elid != ldr ) ),
inference(simp,[status(thm)],[2138]) ).
thf(9,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(163,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(164,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[163]) ).
thf(165,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[164]) ).
thf(3267,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk7 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3139,234]) ).
thf(3268,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk7 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3267]) ).
thf(3269,plain,
sk2 @ s @ s @ ( sk7 @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[3268:[bind(A,$thf( sk7 @ s )),bind(B,$thf( sk2 @ s ))]]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(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(3016,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[265,2760]) ).
thf(3017,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3016]) ).
thf(3033,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk7 @ m_Down ) ) ),
inference(simp,[status(thm)],[3017]) ).
thf(3065,plain,
! [A: $i] :
( ( A @ ( sk7 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3033]) ).
thf(3129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1112,234]) ).
thf(3130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[3129]) ).
thf(3131,plain,
! [A: $i] : ( A @ host @ s @ ( sk2 @ host @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[3130:[bind(A,$thf( E )),bind(B,$thf( sk2 @ host )),bind(C,$thf( E @ host ))]]) ).
thf(3176,plain,
! [A: $i] : ( A @ host @ s @ ( sk2 @ host @ s @ leq ) ),
inference(simp,[status(thm)],[3131]) ).
thf(12802,plain,
! [A: $i] : ( A @ host @ s @ ( sk5 @ host @ leq ) ),
inference(rewrite,[status(thm)],[3176,125]) ).
thf(12838,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s @ ( sk5 @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12802,397]) ).
thf(12839,plain,
! [B: $i,A: $i] :
( ( A @ host @ s @ ( sk5 @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[12838]) ).
thf(12920,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s )
!= B )
| ( ( B @ s )
!= ( sk5 @ host ) ) ),
inference(simp,[status(thm)],[12839]) ).
thf(12947,plain,
! [A: $i] :
( ( A @ host @ s @ s )
!= ( sk5 @ host ) ),
inference(simp,[status(thm)],[12920]) ).
thf(13410,plain,
! [A: $i] :
( ( ( sk2 @ host @ s )
!= ( A @ host @ s ) )
| ( ( sk5 @ host @ s )
!= ( sk5 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[125,12947]) ).
thf(13411,plain,
( ( sk5 @ host @ s )
!= ( sk5 @ host ) ),
inference(pattern_uni,[status(thm)],[13410:[bind(A,$thf( sk2 ))]]) ).
thf(494,plain,
( ( ( sk6 @ host )
!= ( sk4 @ host ) )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,104]) ).
thf(499,plain,
( ( sk6 != sk4 )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[494]) ).
thf(3799,plain,
sk6 != sk4,
inference(simplifyReflect,[status(thm)],[499,459]) ).
thf(453,plain,
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,402]) ).
thf(454,plain,
( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[453]) ).
thf(455,plain,
( ( alive != alive )
| ( sk4 != nil ) ),
inference(simp,[status(thm)],[454]) ).
thf(456,plain,
sk4 != nil,
inference(simp,[status(thm)],[455]) ).
thf(516,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ( ( sk5 @ host )
!= nbr_proc ) ),
inference(paramod_ordered,[status(thm)],[120,513]) ).
thf(519,plain,
( ( sk6 != sk2 )
| ( ( sk5 @ host )
!= nbr_proc ) ),
inference(simp,[status(thm)],[516]) ).
thf(9283,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[819,284]) ).
thf(9284,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[9283]) ).
thf(9285,plain,
( ~ ( sk4 @ ( sk2 @ leq ) )
| ( sk4 = sk2 ) ),
inference(pattern_uni,[status(thm)],[9284:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(12986,plain,
( ( sk4 != sk4 )
| ( sk2 != nil )
| ~ ( sk4 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[9285,456]) ).
thf(12987,plain,
( ( sk2 != nil )
| ~ ( sk4 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12986:[]]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[1112,119]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( sk2 @ host @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1131,plain,
! [A: $i] :
~ ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[1130:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(3339,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue @ ( sk3 @ m_NotNorm @ elem ) )
!= ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3015,1131]) ).
thf(3340,plain,
! [A: $i] :
( ( sk2 @ host @ queue @ ( sk3 @ m_NotNorm @ elem ) )
!= ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[3339]) ).
thf(3395,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_NotNorm )
!= ( A @ m_Halt ) ) ),
inference(simp,[status(thm)],[3340]) ).
thf(3413,plain,
! [A: $i] :
( ( sk3 @ m_NotNorm )
!= ( A @ m_Halt ) ),
inference(simp,[status(thm)],[3395]) ).
thf(2782,plain,
( ( ( sk5 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk1 @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,2758]) ).
thf(2783,plain,
( ( sk5 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk1 @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2782]) ).
thf(2794,plain,
( ( ( sk5 @ host @ queue )
!= sk1 )
| ( ( sk6 @ m_Down )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[2783]) ).
thf(2801,plain,
( ( sk5 @ host @ queue )
!= sk1 ),
inference(simp,[status(thm)],[2794]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(403,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(167,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)],[11]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(869,plain,
! [A: $i] :
( ( ( sk1 @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,415]) ).
thf(870,plain,
! [A: $i] :
( ( sk1 @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[869]) ).
thf(872,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk6 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[870]) ).
thf(874,plain,
sk1 != q_nil,
inference(simp,[status(thm)],[872]) ).
thf(3877,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3170,397]) ).
thf(3878,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[3877]) ).
thf(3925,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s )
!= B )
| ( ( A @ host @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[3878]) ).
thf(3932,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[3925]) ).
thf(7364,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s )
!= ( sk5 @ host @ s ) ) ),
inference(paramod_ordered,[status(thm)],[120,3932]) ).
thf(7365,plain,
( ( nbr_proc @ s @ s )
!= ( sk5 @ host @ s ) ),
inference(pattern_uni,[status(thm)],[7364:[bind(A,$thf( sk6 ))]]) ).
thf(42,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/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,
elec_2 != norm,
inference(lifteq,[status(thm)],[338]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(135,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(136,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)],[135]) ).
thf(137,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)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[137]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(141,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[140]) ).
thf(142,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk9 )
= A ),
inference(cnf,[status(esa)],[141]) ).
thf(2053,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk9 )
= A ),
inference(lifteq,[status(thm)],[142]) ).
thf(7926,plain,
( ( ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7798,2760]) ).
thf(7927,plain,
( ( sk2 @ host @ queue @ ( sk7 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7926]) ).
thf(7955,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk7 @ m_Down )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[7927]) ).
thf(7976,plain,
( ( sk7 @ m_Down )
!= ( sk6 @ m_Down ) ),
inference(simp,[status(thm)],[7955]) ).
thf(22,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(212,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7888,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7798,1131]) ).
thf(7889,plain,
! [A: $i] :
( ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7888]) ).
thf(7968,plain,
! [A: $i] :
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( A @ m_Halt )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[7889]) ).
thf(7981,plain,
! [A: $i] :
( ( A @ m_Halt )
!= ( sk6 @ m_Down ) ),
inference(simp,[status(thm)],[7968]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[280]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(286,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[285]) ).
thf(2124,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[286,397]) ).
thf(2125,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2124]) ).
thf(2141,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2125]) ).
thf(2153,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[2141]) ).
thf(457,plain,
sk5 != sk4,
inference(simp,[status(thm)],[102]) ).
thf(565,plain,
( ( ( sk8 @ host )
!= ( sk5 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[482,459]) ).
thf(566,plain,
( ( sk8 @ host )
!= ( sk5 @ host ) ),
inference(simp,[status(thm)],[565]) ).
thf(569,plain,
sk8 != sk5,
inference(simp,[status(thm)],[566]) ).
thf(2765,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[482,750]) ).
thf(2766,plain,
~ ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[2765:[bind(A,$thf( sk8 ))]]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(371,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(133,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[132]) ).
thf(134,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[133]) ).
thf(203,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[202]) ).
thf(204,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[203]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[204]) ).
thf(3590,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk8 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3179,234]) ).
thf(3591,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk8 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3590]) ).
thf(3592,plain,
sk2 @ s @ s @ s @ ( sk8 @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[3591:[bind(A,$thf( sk8 @ s @ s )),bind(B,$thf( sk2 @ s @ s ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(398,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(492,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,480]) ).
thf(497,plain,
( ( sk7 != sk6 )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[492]) ).
thf(2089,plain,
sk7 != sk6,
inference(simplifyReflect,[status(thm)],[497,459]) ).
thf(820,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[802,79]) ).
thf(821,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[820]) ).
thf(827,plain,
! [A: $i] :
( ( ( sk2 @ host )
!= sk2 )
| ( A != nbr_proc )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[821]) ).
thf(845,plain,
( ( ( sk2 @ host )
!= sk2 )
| ( sk2 != nbr_proc ) ),
inference(simp,[status(thm)],[827]) ).
thf(1184,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk2 != norm )
| ( sk2 != nbr_proc )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,845]) ).
thf(1185,plain,
( ( sk2 != norm )
| ( sk2 != nbr_proc )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[1184:[]]) ).
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(2122,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk4 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[819,397]) ).
thf(2123,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk4 @ leq ) ) ),
inference(simp,[status(thm)],[2122]) ).
thf(2146,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk4 ) ),
inference(simp,[status(thm)],[2123]) ).
thf(2149,plain,
( ( sk2 @ s )
!= sk4 ),
inference(simp,[status(thm)],[2146]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(375,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(682,plain,
( ( ( sk2 @ host @ ( elid @ index ) )
!= ( sk2 @ host @ ( status @ index ) ) )
| ( sk3 = norm ) ),
inference(paramod_ordered,[status(thm)],[575,676]) ).
thf(685,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( elid != status )
| ( sk3 = norm ) ),
inference(simp,[status(thm)],[682]) ).
thf(689,plain,
( ( elid != status )
| ( sk3 = norm ) ),
inference(simp,[status(thm)],[685]) ).
thf(1145,plain,
( ( sk3 != sk3 )
| ( nbr_proc != norm )
| ( elid != ldr )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[689,1001]) ).
thf(1146,plain,
( ( nbr_proc != norm )
| ( elid != ldr )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[1145:[]]) ).
thf(974,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk3 != zero )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,651]) ).
thf(975,plain,
( ( sk3 != zero )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[974:[]]) ).
thf(89,plain,
( ( sk5 = sk2 )
| ( alive @ ( sk5 @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(114,plain,
( ( alive @ ( sk5 @ setIn ) )
| ( sk5 = sk2 ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(691,plain,
alive @ ( sk5 @ setIn ),
inference(simplifyReflect,[status(thm)],[114,561]) ).
thf(692,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[691,93]) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[692]) ).
thf(694,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk5 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[693:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
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 @ sk17 )
= A ),
inference(cnf,[status(esa)],[299]) ).
thf(2398,plain,
! [A: $i] :
( ( A @ m_Down @ sk17 )
= A ),
inference(lifteq,[status(thm)],[300]) ).
thf(8038,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s @ ( sk4 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3657,397]) ).
thf(8039,plain,
! [A: $i] :
( ( sk2 @ s @ s @ s @ ( sk4 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[8038]) ).
thf(8123,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s )
!= A )
| ( ( sk4 @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[8039]) ).
thf(8139,plain,
( ( sk2 @ s @ s @ s @ s )
!= ( sk4 @ s @ s @ s ) ),
inference(simp,[status(thm)],[8123]) ).
thf(3229,plain,
! [A: $i] :
( ( ( sk2 @ s @ ( sk4 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3121,397]) ).
thf(3230,plain,
! [A: $i] :
( ( sk2 @ s @ ( sk4 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3229]) ).
thf(3252,plain,
! [A: $i] :
( ( ( sk2 @ s )
!= A )
| ( ( sk4 @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[3230]) ).
thf(3266,plain,
( ( sk2 @ s @ s )
!= ( sk4 @ s ) ),
inference(simp,[status(thm)],[3252]) ).
thf(2513,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk5 @ host @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[120,2147]) ).
thf(2514,plain,
( ( sk5 @ host @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[2513:[bind(A,$thf( sk6 ))]]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(310,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(311,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[310]) ).
thf(312,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[311]) ).
thf(313,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[312]) ).
thf(857,plain,
( ( ( sk2 @ ( sk8 @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[815,79]) ).
thf(858,plain,
( ( sk2 @ ( sk8 @ leq ) )
!= ( sk2 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[857]) ).
thf(859,plain,
( ( ( sk2 @ host )
!= sk2 )
| ( sk8 != nbr_proc ) ),
inference(simp,[status(thm)],[858]) ).
thf(1370,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk2 != norm )
| ( sk8 != nbr_proc )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,859]) ).
thf(1371,plain,
( ( sk2 != norm )
| ( sk8 != nbr_proc )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[1370:[]]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(8863,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk8 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[815,284]) ).
thf(8864,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk8 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[8863]) ).
thf(8865,plain,
( ~ ( sk8 @ ( sk2 @ leq ) )
| ( sk8 = sk2 ) ),
inference(pattern_uni,[status(thm)],[8864:[bind(A,$thf( sk8 )),bind(B,$thf( sk2 ))]]) ).
thf(527,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[482,120]) ).
thf(534,plain,
( ( sk8 != sk6 )
| ( ( sk5 @ host )
= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[527]) ).
thf(7615,plain,
sk8 != sk6,
inference(simplifyReflect,[status(thm)],[534,459]) ).
thf(11840,plain,
( ( sk8 != sk8 )
| ( sk6 != sk2 )
| ~ ( sk8 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[8865,7615]) ).
thf(11841,plain,
( ( sk6 != sk2 )
| ~ ( sk8 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[11840:[]]) ).
thf(12977,plain,
( ( sk4 != sk4 )
| ( pids != alive )
| ( sk2 != sk2 )
| ~ ( sk4 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[9285,452]) ).
thf(12978,plain,
( ( sk4 != sk4 )
| ( pids != alive )
| ~ ( sk4 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[12977]) ).
thf(12979,plain,
( ( pids != alive )
| ~ ( sk4 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12978:[]]) ).
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/sandbox/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(12,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1196,plain,
! [A: $i] :
( ( ( sk2 @ host )
!= ( A @ host ) )
| ( nbr_proc @ ( norm @ leq ) )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,207]) ).
thf(1197,plain,
( ( nbr_proc @ ( norm @ leq ) )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[1196:[bind(A,$thf( sk2 ))]]) ).
thf(2136,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( norm @ leq ) ) )
| ~ $true
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[1197,397]) ).
thf(2137,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( norm @ leq ) ) )
| ( status != ldr ) ),
inference(simp,[status(thm)],[2136]) ).
thf(2139,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= norm )
| ( status != ldr ) ),
inference(simp,[status(thm)],[2137]) ).
thf(2151,plain,
( ( ( nbr_proc @ s )
!= norm )
| ( status != ldr ) ),
inference(simp,[status(thm)],[2139]) ).
thf(37,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(303,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(385,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[384]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[385]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[386]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(365,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[364]) ).
thf(366,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[365]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[366]) ).
thf(321,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( B @ ( A @ cons ) @ ordered ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(miniscope,[status(thm)],[320]) ).
thf(322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ cons ) @ ordered )
| ~ ( D @ ( E @ sk18 ) @ pidMsg @ ( D @ pidMsg @ leq ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( ( D @ ( E @ sk18 ) @ pidMsg @ host )
= ( D @ pidMsg @ host ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ ( E @ sk18 ) @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( E @ ( D @ ( E @ sk18 ) @ elem ) )
| ~ ( E @ ordered ) )
& ( ( C @ pidMsg @ ( A @ pidMsg @ leq ) )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ordered )
| ~ ( B @ ( A @ cons ) @ ordered ) ) ),
inference(cnf,[status(esa)],[321]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( B @ ordered )
| ~ ( B @ ( A @ cons ) @ ordered ) ),
inference(cnfConj,[status(thm)],[322]) ).
thf(2922,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_NotNorm @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[864,253]) ).
thf(2923,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[2922:[bind(A,$thf( sk3 @ m_NotNorm )),bind(B,$thf( sk1 ))]]) ).
thf(2577,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ m_NotNorm @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[864,192]) ).
thf(2578,plain,
( ( sk2 @ host @ queue @ head )
= ( sk3 @ m_NotNorm ) ),
inference(pattern_uni,[status(thm)],[2577:[bind(A,$thf( sk3 @ m_NotNorm )),bind(B,$thf( sk1 ))]]) ).
thf(1043,plain,
( ( sk3 != sk3 )
| ( zero != norm )
| ( elid != ldr )
| ( elid != status ) ),
inference(paramod_ordered,[status(thm)],[689,975]) ).
thf(1044,plain,
( ( zero != norm )
| ( elid != ldr )
| ( elid != status ) ),
inference(pattern_uni,[status(thm)],[1043:[]]) ).
thf(3714,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk7 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3269,234]) ).
thf(3715,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk7 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3714]) ).
thf(3716,plain,
sk2 @ s @ s @ s @ ( sk7 @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[3715:[bind(A,$thf( sk7 @ s @ s )),bind(B,$thf( sk2 @ s @ s ))]]) ).
thf(11668,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s @ ( sk7 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3716,397]) ).
thf(11669,plain,
! [A: $i] :
( ( sk2 @ s @ s @ s @ ( sk7 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[11668]) ).
thf(11750,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s )
!= A )
| ( ( sk7 @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[11669]) ).
thf(11775,plain,
( ( sk2 @ s @ s @ s @ s )
!= ( sk7 @ s @ s @ s ) ),
inference(simp,[status(thm)],[11750]) ).
thf(13270,plain,
( ( ( sk2 @ ( sk4 @ leq ) )
!= ( sk4 @ ( sk2 @ leq ) ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[819,12987]) ).
thf(13271,plain,
( ( ( sk2 @ ( sk4 @ leq ) )
!= ( sk4 @ ( sk2 @ leq ) ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[13270]) ).
thf(13315,plain,
( ( sk4 != sk2 )
| ( sk4 != sk2 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[13271]) ).
thf(13339,plain,
( ( sk4 != sk2 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[13315]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(306,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1202,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ~ ( norm @ ( nbr_proc @ leq ) )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,79]) ).
thf(1203,plain,
( ~ ( norm @ ( nbr_proc @ leq ) )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[1202:[]]) ).
thf(546,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,93]) ).
thf(547,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[546]) ).
thf(548,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk4 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[547:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(372,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[371]) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[372]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[373]) ).
thf(76,plain,
( ( sk7 = sk2 )
| ( sk7 != sk4 ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(123,plain,
( ( sk7 = sk2 )
| ( sk7 != sk4 ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(2563,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)],[390,205]) ).
thf(2564,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2563:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(85,plain,
( ( sk7 @ host )
!= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(103,plain,
( ( sk7 @ host )
!= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(458,plain,
sk7 != sk5,
inference(simp,[status(thm)],[103]) ).
thf(7886,plain,
( ( ( sk5 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7798,2758]) ).
thf(7887,plain,
( ( sk5 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7886]) ).
thf(7969,plain,
( ( ( sk5 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk6 @ m_Down )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[7887]) ).
thf(7982,plain,
( ( sk5 @ host @ queue )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[7969]) ).
thf(1002,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk3 != sk2 )
| ( sk2 != nbr_proc )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,845]) ).
thf(1003,plain,
( ( sk3 != sk2 )
| ( sk2 != nbr_proc )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[1002:[]]) ).
thf(695,plain,
( ( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[691,402]) ).
thf(696,plain,
( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[695]) ).
thf(706,plain,
( ( alive != alive )
| ( sk5 != nil ) ),
inference(simp,[status(thm)],[696]) ).
thf(707,plain,
sk5 != nil,
inference(simp,[status(thm)],[706]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
file('/export/starexec/sandbox/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(260,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[259]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(12261,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk8 @ ( sk2 @ leq ) ) )
| ( sk6 != sk2 )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[802,11841]) ).
thf(12262,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk8 @ ( sk2 @ leq ) ) )
| ( sk6 != sk2 )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[12261]) ).
thf(12336,plain,
! [A: $i] :
( ( sk8 != sk2 )
| ( A != sk2 )
| ( sk6 != sk2 )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[12262]) ).
thf(12364,plain,
( ( sk8 != sk2 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[12336]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(368,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(369,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[368]) ).
thf(370,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[369]) ).
thf(496,plain,
( ( ( sk6 @ host )
!= ( sk2 @ host ) )
| ~ ( sk5 @ host @ ( nbr_proc @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[120,79]) ).
thf(502,plain,
( ( sk6 != sk2 )
| ~ ( sk5 @ host @ ( nbr_proc @ leq ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(3723,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ ( sk7 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3269,397]) ).
thf(3724,plain,
! [A: $i] :
( ( sk2 @ s @ s @ ( sk7 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[3723]) ).
thf(3758,plain,
! [A: $i] :
( ( ( sk2 @ s @ s )
!= A )
| ( ( sk7 @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[3724]) ).
thf(3774,plain,
( ( sk2 @ s @ s @ s )
!= ( sk7 @ s @ s ) ),
inference(simp,[status(thm)],[3758]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/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(197,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[196]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[197]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(170,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[169]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk11 ) )
= B ),
inference(cnf,[status(esa)],[170]) ).
thf(2092,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk11 ) )
= B ),
inference(lifteq,[status(thm)],[171]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(2170,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( zero @ ( sk2 @ host @ leq ) ) )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[802,2127]) ).
thf(2171,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( zero @ ( sk2 @ host @ leq ) ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[2170]) ).
thf(2210,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A
!= ( sk2 @ host ) )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[2171]) ).
thf(2219,plain,
( ( sk2 != zero )
| ( ( sk2 @ host )
!= sk2 ) ),
inference(simp,[status(thm)],[2210]) ).
thf(1352,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk3 != sk2 )
| ( sk7 != nbr_proc )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,856]) ).
thf(1353,plain,
( ( sk3 != sk2 )
| ( sk7 != nbr_proc )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[1352:[]]) ).
thf(173,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[173]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(2868,plain,
( ( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,2766]) ).
thf(2869,plain,
( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2868]) ).
thf(2885,plain,
( ( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( ( sk8 @ m_Down )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[2869]) ).
thf(2892,plain,
( ( sk2 @ m_Halt @ ( sk5 @ host @ queue @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2885]) ).
thf(3024,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[265,415]) ).
thf(3025,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[3024]) ).
thf(3060,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[3025]) ).
thf(3092,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[3060]) ).
thf(2193,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ~ ( zero @ ( norm @ leq ) )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,2127]) ).
thf(2194,plain,
( ~ ( zero @ ( norm @ leq ) )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[2193:[]]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(215,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(216,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[215]) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[216]) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(229,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[228]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk13 ) )
= A ),
inference(cnf,[status(esa)],[229]) ).
thf(2924,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk13 ) )
= A ),
inference(lifteq,[status(thm)],[230]) ).
thf(248,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[247]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[248]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[249]) ).
thf(2472,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= ( zero @ s ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[118,2148]) ).
thf(2485,plain,
! [A: $i] :
( ( nbr_proc != zero )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[2472]) ).
thf(2490,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[2485]) ).
thf(2097,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( ( sk3 @ queue )
!= q_nil )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,2094]) ).
thf(2098,plain,
( ( ( sk3 @ queue )
!= q_nil )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[2097:[]]) ).
thf(1235,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)],[286,119]) ).
thf(1236,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)],[1235]) ).
thf(1237,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[1236:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(1244,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(simp,[status(thm)],[1237]) ).
thf(2173,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ~ ( zero @ ( sk3 @ leq ) )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,2127]) ).
thf(2174,plain,
( ~ ( zero @ ( sk3 @ leq ) )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[2173:[]]) ).
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(7808,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7315,415]) ).
thf(7809,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[7808]) ).
thf(7823,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ cons ) )
!= q_nil )
| ( ( sk6 @ m_Down )
!= B ) ),
inference(simp,[status(thm)],[7809]) ).
thf(7855,plain,
! [A: $i] :
( ( sk1 @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[7823]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ leq ) )
<=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(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(7890,plain,
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7798,2766]) ).
thf(7891,plain,
( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[7890]) ).
thf(7963,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk8 @ m_Down )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[7891]) ).
thf(7979,plain,
( ( sk8 @ m_Down )
!= ( sk6 @ m_Down ) ),
inference(simp,[status(thm)],[7963]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(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(213,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[212]) ).
thf(214,plain,
elec_1 != norm,
inference(lifteq,[status(thm)],[213]) ).
thf(1160,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( zero != norm )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,651]) ).
thf(1161,plain,
( ( zero != norm )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[1160:[]]) ).
thf(149,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[149]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(2101,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( ( norm @ queue )
!= q_nil )
| ( status != ldr ) ),
inference(paramod_ordered,[status(thm)],[800,2094]) ).
thf(2102,plain,
( ( ( norm @ queue )
!= q_nil )
| ( status != ldr ) ),
inference(pattern_uni,[status(thm)],[2101:[]]) ).
thf(270,plain,
! [A: $i] :
( ( A
= ( A @ sk16 @ m_Down ) )
| ( A
= ( A @ sk15 @ m_Halt ) )
| ~ ( A @ pidElem ) ),
inference(cnfConj,[status(thm)],[269]) ).
thf(273,plain,
! [A: $i] :
( ~ ( A @ pidElem )
| ( ( A @ sk16 @ m_Down )
= A )
| ( ( A @ sk15 @ m_Halt )
= A ) ),
inference(lifteq,[status(thm)],[270]) ).
thf(2950,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ~ ( sk5 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[120,1244]) ).
thf(2951,plain,
~ ( sk5 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[2950:[bind(A,$thf( sk6 ))]]) ).
thf(404,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[403]) ).
thf(405,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[404]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[106]) ).
thf(2090,plain,
( ( sk7 != sk7 )
| ( sk6 != sk2 )
| ( alive @ ( sk7 @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[113,2089]) ).
thf(2091,plain,
( ( sk6 != sk2 )
| ( alive @ ( sk7 @ setIn ) ) ),
inference(pattern_uni,[status(thm)],[2090:[]]) ).
thf(304,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[303]) ).
thf(305,plain,
! [A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[304]) ).
thf(7878,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ~ ( alive @ ( B @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[7798,93]) ).
thf(7879,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(simp,[status(thm)],[7878]) ).
thf(7880,plain,
~ ( alive @ ( sk6 @ setIn ) ),
inference(pattern_uni,[status(thm)],[7879:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 ))]]) ).
thf(8007,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( sk5 @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[691,7880]) ).
thf(8008,plain,
( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( sk5 @ setIn ) ) ),
inference(simp,[status(thm)],[8007]) ).
thf(8012,plain,
( ( alive != alive )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[8008]) ).
thf(8019,plain,
sk6 != sk5,
inference(simp,[status(thm)],[8012]) ).
thf(2157,plain,
( ( ( sk2 @ s )
!= ( zero @ s ) )
| ( ( sk2 @ host )
!= sk4 ) ),
inference(paramod_ordered,[status(thm)],[118,2149]) ).
thf(2159,plain,
( ( sk2 != zero )
| ( ( sk2 @ host )
!= sk4 ) ),
inference(simp,[status(thm)],[2157]) ).
thf(2846,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)],[390,221]) ).
thf(2847,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[2846:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[177]) ).
thf(2404,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true
| ( sk6 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[2091,402]) ).
thf(2405,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[2404]) ).
thf(2425,plain,
( ( alive != alive )
| ( sk7 != nil )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[2405]) ).
thf(2430,plain,
( ( sk7 != nil )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[2425]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[269]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[272]) ).
thf(277,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[276]) ).
thf(1366,plain,
( ( ( sk2 @ host )
!= ( sk2 @ host ) )
| ( sk3 != sk2 )
| ( sk8 != nbr_proc )
| ( elid != ldr ) ),
inference(paramod_ordered,[status(thm)],[798,859]) ).
thf(1367,plain,
( ( sk3 != sk2 )
| ( sk8 != nbr_proc )
| ( elid != ldr ) ),
inference(pattern_uni,[status(thm)],[1366:[]]) ).
thf(307,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[306]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[307]) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(3341,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_NotNorm @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3015,2766]) ).
thf(3342,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_NotNorm @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3341]) ).
thf(3391,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_NotNorm )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[3342]) ).
thf(3432,plain,
( ( sk3 @ m_NotNorm )
!= ( sk8 @ m_Down ) ),
inference(simp,[status(thm)],[3391]) ).
thf(3945,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( sk5 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3873,397]) ).
thf(3946,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( sk5 @ host @ leq ) ) ),
inference(simp,[status(thm)],[3945]) ).
thf(3988,plain,
! [A: $i] :
( ( A
!= ( nbr_proc @ s ) )
| ( ( A @ s )
!= ( sk5 @ host ) ) ),
inference(simp,[status(thm)],[3946]) ).
thf(4002,plain,
( ( nbr_proc @ s @ s )
!= ( sk5 @ host ) ),
inference(simp,[status(thm)],[3988]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ ( B @ leq ) )
| ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( A @ ( B @ leq ) )
| ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( A @ ( B @ leq ) )
| ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(7510,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s @ ( sk8 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3592,397]) ).
thf(7511,plain,
! [A: $i] :
( ( sk2 @ s @ s @ s @ ( sk8 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[7510]) ).
thf(7593,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s )
!= A )
| ( ( sk8 @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[7511]) ).
thf(7602,plain,
( ( sk2 @ s @ s @ s @ s )
!= ( sk8 @ s @ s @ s ) ),
inference(simp,[status(thm)],[7593]) ).
thf(186,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[185]) ).
thf(187,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk12 )
= A ),
inference(cnf,[status(esa)],[186]) ).
thf(2087,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk12 )
= A ),
inference(lifteq,[status(thm)],[187]) ).
thf(18707,plain,
$false,
inference(e,[status(thm)],[3873,2094,7798,234,88,2163,69,2117,3858,379,202,2363,2077,873,449,120,247,384,3648,3313,340,2627,2168,3414,3121,185,1001,7079,1359,320,651,257,3221,110,2466,196,3713,157,802,125,344,93,416,7857,228,289,316,7183,284,770,3657,152,179,443,2469,2254,1183,480,211,253,602,147,397,221,293,132,265,2154,206,292,452,380,2164,798,12159,1021,2147,561,192,862,349,275,2150,165,815,2758,3269,361,3065,13411,3799,224,456,842,519,12987,3413,2801,403,388,169,874,2115,256,7365,225,3179,339,2053,7976,212,7981,193,2153,1131,457,3115,569,2766,371,134,237,266,205,3592,398,2089,1185,298,750,2149,166,148,856,375,513,1146,180,689,819,975,176,694,402,118,2398,413,286,8139,3266,2514,391,9285,313,1371,236,11841,2148,3170,86,7315,12979,406,172,113,219,2151,377,208,98,303,387,367,323,140,3932,251,2923,1112,2578,12802,1044,278,11775,13339,1015,135,267,167,394,306,1203,162,548,374,123,2564,458,7982,145,7615,1003,12947,707,409,263,310,12364,370,502,3774,808,359,199,2092,127,2219,1353,864,3224,175,446,2892,859,3139,3092,482,2194,218,368,845,2760,2924,250,231,2490,104,2098,390,401,1244,781,2152,2174,319,8865,75,7855,119,433,207,7979,346,214,1161,800,151,2102,2155,190,273,2951,405,107,242,195,3716,1197,2091,2223,415,3015,305,79,8019,395,2127,2159,7880,2847,459,131,3939,178,2430,575,163,200,277,691,254,1367,309,3432,676,364,4002,337,122,7602,215,222,2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV451+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.20/0.47 % Computer : n015.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sat Sep 26 13:57:46 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.98/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.17 % [INFO] Parsing done (212ms).
% 1.63/1.18 % [INFO] Running in sequential loop mode.
% 2.67/1.60 % [INFO] eprover registered as external prover.
% 2.67/1.61 % [INFO] Scanning for conjecture ...
% 3.12/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 3.37/1.96 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 3.37/2.01 % [INFO] Problem is first-order (TPTP FOF).
% 3.37/2.02 % [INFO] Type checking passed.
% 3.37/2.03 % [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 ...
% 92.95/19.32 % External prover 'e' found a proof!
% 92.95/19.32 % [INFO] Killing All external provers ...
% 92.95/19.32 % Time passed: 18712ms (effective reasoning time: 18135ms)
% 92.95/19.32 % 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)>
% 92.95/19.33 % 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
% 92.95/19.33 % No. of inferences in proof: 810
% 92.95/19.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18712 ms resp. 18135 ms w/o parsing
% 95.00/19.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 95.00/19.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------