TSTP Solution File: SWV478+1 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWV478+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 17:24:22 EDT 2024
% Result : Theorem 77.23s 19.71s
% Output : Refutation 77.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 74
% Syntax : Number of formulae : 791 ( 384 unt; 0 typ; 0 def)
% Number of atoms : 2339 (1337 equ; 0 cnn)
% Maximal formula atoms : 126 ( 2 avg)
% Number of connectives : 8764 (1302 ~; 760 |; 427 &;6074 @)
% ( 13 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 56 usr; 26 con; 0-4 aty)
% Number of variables : 1298 ( 0 ^1236 !; 62 ?;1298 :)
% Comments :
%------------------------------------------------------------------------------
thf(elem_type,type,
elem: $i > $i > $o ).
thf(m_Ldr_type,type,
m_Ldr: $i > $i ).
thf(queue_type,type,
queue: $i > $i ).
thf(host_type,type,
host: $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(m_Down_type,type,
m_Down: $i > $i ).
thf(setIn_type,type,
setIn: $i > $i > $o ).
thf(alive_type,type,
alive: $i ).
thf(index_type,type,
index: $i > $i > $i ).
thf(status_type,type,
status: $i ).
thf(elec_1_type,type,
elec_1: $i ).
thf(elec_2_type,type,
elec_2: $i ).
thf(elid_type,type,
elid: $i ).
thf(down_type,type,
down: $i ).
thf(pendack_type,type,
pendack: $i ).
thf(norm_type,type,
norm: $i ).
thf(ldr_type,type,
ldr: $i ).
thf(wait_type,type,
wait: $i ).
thf(s_type,type,
s: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(m_Ack_type,type,
m_Ack: $i > $i > $i ).
thf(nbr_proc_type,type,
nbr_proc: $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(acks_type,type,
acks: $i ).
thf(snoc_type,type,
snoc: $i > $i > $i ).
thf(m_NotNorm_type,type,
m_NotNorm: $i > $i ).
thf(m_Halt_type,type,
m_Halt: $i > $i ).
thf(m_NormQ_type,type,
m_NormQ: $i > $i ).
thf(pidMsg_type,type,
pidMsg: $i > $i ).
thf(ordered_type,type,
ordered: $i > $o ).
thf(q_nil_type,type,
q_nil: $i ).
thf(nil_type,type,
nil: $i ).
thf(head_type,type,
head: $i > $i ).
thf(last_type,type,
last: $i > $i ).
thf(init_type,type,
init: $i > $i ).
thf(setEmpty_type,type,
setEmpty: $i ).
thf(tail_type,type,
tail: $i > $i ).
thf(pidElem_type,type,
pidElem: $i > $o ).
thf(pids_type,type,
pids: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i > $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i > $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i > $i ).
thf(sk15_type,type,
sk15: $i > $i > $i ).
thf(sk18_type,type,
sk18: $i > $i ).
thf(sk21_type,type,
sk21: $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( elem @ ( m_Ldr @ F ) @ ( queue @ ( host @ E ) ) )
=> ~ ( leq @ ( host @ E ) @ ( host @ F ) ) )
& ! [E: $i,F: $i] :
( ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) )
=> ( ( host @ F )
!= ( host @ E ) ) )
& ! [E: $i,F: $i] :
( ( ( F != E )
& ( ( host @ F )
= ( host @ E ) ) )
=> ( ~ ( setIn @ E @ alive )
| ~ ( setIn @ F @ alive ) ) )
& ! [E: $i] :
( ( ( ( ( index @ status @ ( host @ E ) )
= elec_1 )
| ( ( index @ status @ ( host @ E ) )
= elec_2 ) )
& ( setIn @ E @ alive ) )
=> ( ( index @ elid @ ( host @ E ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( setIn @ E @ alive )
& ( setIn @ F @ alive )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ E ) ) )
& ( ( index @ status @ ( host @ F ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ F ) ) @ ( host @ E ) ) )
& ! [E: $i,F: $i] :
( ( ( setIn @ F @ alive )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ E ) ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) )
& ( ( host @ G )
= ( host @ F ) )
& ( ( index @ status @ ( host @ G ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ G ) ) @ ( host @ E ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ G ) )
& ( ( index @ status @ ( host @ G ) )
= norm )
& ( ( index @ ldr @ ( host @ G ) )
= ( host @ G ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) )
& ! [E: $i,F: $i] :
( ( ( setIn @ E @ alive )
& ( setIn @ F @ alive )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ~ ( leq @ ( host @ F ) @ ( host @ G ) )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ F )
= ( host @ E ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) )
& ( ( index @ status @ ( host @ E ) )
= norm ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ F )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= norm )
& ( ( index @ ldr @ ( host @ G ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ F @ alive )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ F )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= wait )
& ( ( host @ ( index @ elid @ ( host @ G ) ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ F @ alive )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( setIn @ E @ alive )
& ( leq @ ( host @ E ) @ ( host @ H ) )
& ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ H ) ) )
& ( ( host @ F )
= ( host @ H ) )
& ( ( index @ status @ ( host @ E ) )
= elec_2 )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( elem @ ( m_Ack @ E @ F ) @ ( queue @ ( host @ E ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( setIn @ H @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ H ) ) )
& ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ H ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ H ) ) )
& ( ( host @ F )
= ( s @ ( host @ H ) ) )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) )
& ( ( index @ status @ ( host @ E ) )
= norm ) ) )
& ( ( queue @ ( host @ C ) )
= ( cons @ ( m_Down @ D ) @ A ) ) )
=> ( ( setIn @ C @ alive )
=> ( ( leq @ ( host @ C ) @ ( host @ D ) )
=> ( ( ( ( index @ status @ ( host @ C ) )
= elec_2 )
& ( ( host @ D )
= ( index @ pendack @ ( host @ C ) ) ) )
=> ( ( leq @ nbr_proc @ ( index @ pendack @ ( host @ C ) ) )
=> ! [E: $i] :
( ( setIn @ ( host @ E ) @ ( index @ acks @ ( host @ C ) ) )
=> ! [F: $i] :
( ( ( host @ C )
= ( host @ F ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( host @ E )
= ( host @ I ) )
=> ( ( ( host @ C )
!= ( host @ I ) )
=> ( ( ! [J: $i] :
( ( ~ ( leq @ ( host @ I ) @ J )
& ( leq @ ( s @ zero ) @ J ) )
=> ( ( setIn @ J @ ( index @ down @ ( host @ I ) ) )
| ( J
= ( host @ H ) ) ) )
& ( setIn @ I @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ I ) ) )
& ( elem @ ( m_Down @ G ) @ ( snoc @ ( queue @ ( host @ I ) ) @ ( m_Ldr @ C ) ) )
& ( elem @ ( m_Down @ H ) @ ( snoc @ ( queue @ ( host @ I ) ) @ ( m_Ldr @ C ) ) )
& ( ( host @ G )
= ( s @ ( host @ I ) ) )
& ( ( index @ status @ ( host @ I ) )
= elec_1 ) )
=> ~ ( ( setIn @ F @ alive )
& ( ( host @ C )
= ( host @ F ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( elem @ ( m_Ldr @ F ) @ ( queue @ ( host @ E ) ) )
=> ~ ( leq @ ( host @ E ) @ ( host @ F ) ) )
& ! [E: $i,F: $i] :
( ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) )
=> ( ( host @ F )
!= ( host @ E ) ) )
& ! [E: $i,F: $i] :
( ( ( F != E )
& ( ( host @ F )
= ( host @ E ) ) )
=> ( ~ ( setIn @ E @ alive )
| ~ ( setIn @ F @ alive ) ) )
& ! [E: $i] :
( ( ( ( ( index @ status @ ( host @ E ) )
= elec_1 )
| ( ( index @ status @ ( host @ E ) )
= elec_2 ) )
& ( setIn @ E @ alive ) )
=> ( ( index @ elid @ ( host @ E ) )
= E ) )
& ! [E: $i,F: $i] :
( ( ( setIn @ E @ alive )
& ( setIn @ F @ alive )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ E ) ) )
& ( ( index @ status @ ( host @ F ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ F ) ) @ ( host @ E ) ) )
& ! [E: $i,F: $i] :
( ( ( setIn @ F @ alive )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ E ) ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) )
& ( ( host @ G )
= ( host @ F ) )
& ( ( index @ status @ ( host @ G ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ G ) ) @ ( host @ E ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ G ) )
& ( ( index @ status @ ( host @ G ) )
= norm )
& ( ( index @ ldr @ ( host @ G ) )
= ( host @ G ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) )
& ! [E: $i,F: $i] :
( ( ( setIn @ E @ alive )
& ( setIn @ F @ alive )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) )
=> ( F = E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ~ ( leq @ ( host @ F ) @ ( host @ G ) )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ F )
= ( host @ E ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) )
& ( ( index @ status @ ( host @ E ) )
= norm ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ F )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= norm )
& ( ( index @ ldr @ ( host @ G ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ F @ alive )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ F )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= wait )
& ( ( host @ ( index @ elid @ ( host @ G ) ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ F @ alive )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( setIn @ E @ alive )
& ( leq @ ( host @ E ) @ ( host @ H ) )
& ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ H ) ) )
& ( ( host @ F )
= ( host @ H ) )
& ( ( index @ status @ ( host @ E ) )
= elec_2 )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( elem @ ( m_Ack @ E @ F ) @ ( queue @ ( host @ E ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( setIn @ H @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ H ) ) )
& ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ H ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ H ) ) )
& ( ( host @ F )
= ( s @ ( host @ H ) ) )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) )
& ( ( index @ status @ ( host @ E ) )
= norm ) ) )
& ( ( queue @ ( host @ C ) )
= ( cons @ ( m_Down @ D ) @ A ) ) )
=> ( ( setIn @ C @ alive )
=> ( ( leq @ ( host @ C ) @ ( host @ D ) )
=> ( ( ( ( index @ status @ ( host @ C ) )
= elec_2 )
& ( ( host @ D )
= ( index @ pendack @ ( host @ C ) ) ) )
=> ( ( leq @ nbr_proc @ ( index @ pendack @ ( host @ C ) ) )
=> ! [E: $i] :
( ( setIn @ ( host @ E ) @ ( index @ acks @ ( host @ C ) ) )
=> ! [F: $i] :
( ( ( host @ C )
= ( host @ F ) )
=> ! [G: $i,H: $i,I: $i] :
( ( ( host @ E )
= ( host @ I ) )
=> ( ( ( host @ C )
!= ( host @ I ) )
=> ( ( ! [J: $i] :
( ( ~ ( leq @ ( host @ I ) @ J )
& ( leq @ ( s @ zero ) @ J ) )
=> ( ( setIn @ J @ ( index @ down @ ( host @ I ) ) )
| ( J
= ( host @ H ) ) ) )
& ( setIn @ I @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ I ) ) )
& ( elem @ ( m_Down @ G ) @ ( snoc @ ( queue @ ( host @ I ) ) @ ( m_Ldr @ C ) ) )
& ( elem @ ( m_Down @ H ) @ ( snoc @ ( queue @ ( host @ I ) ) @ ( m_Ldr @ C ) ) )
& ( ( host @ G )
= ( s @ ( host @ I ) ) )
& ( ( index @ status @ ( host @ I ) )
= elec_1 ) )
=> ~ ( ( setIn @ F @ alive )
& ( ( host @ C )
= ( host @ F ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( elem @ ( m_Ldr @ E ) @ ( queue @ ( host @ D ) ) )
=> ~ ( leq @ ( host @ D ) @ ( host @ E ) ) )
& ! [D: $i,E: $i] :
( ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ D ) ) )
=> ( ( host @ E )
!= ( host @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( E != D )
& ( ( host @ E )
= ( host @ D ) ) )
=> ( ~ ( setIn @ D @ alive )
| ~ ( setIn @ E @ alive ) ) )
& ! [D: $i] :
( ( ( ( ( index @ status @ ( host @ D ) )
= elec_1 )
| ( ( index @ status @ ( host @ D ) )
= elec_2 ) )
& ( setIn @ D @ alive ) )
=> ( ( index @ elid @ ( host @ D ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( setIn @ D @ alive )
& ( setIn @ E @ alive )
& ( setIn @ ( host @ E ) @ ( index @ down @ ( host @ D ) ) )
& ( ( index @ status @ ( host @ E ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ E ) ) @ ( host @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( setIn @ E @ alive )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) )
=> ~ ( ( setIn @ D @ alive )
& ( setIn @ ( host @ E ) @ ( index @ down @ ( host @ D ) ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( setIn @ D @ alive )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ D ) ) )
& ( ( host @ F )
= ( host @ E ) )
& ( ( index @ status @ ( host @ F ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ F ) ) @ ( host @ D ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( setIn @ F @ alive )
& ( ( host @ E )
= ( host @ F ) )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ D @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ D ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( setIn @ D @ alive )
& ( setIn @ E @ alive )
& ( ( index @ ldr @ ( host @ D ) )
= ( host @ D ) )
& ( ( index @ status @ ( host @ D ) )
= norm )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) )
=> ( E = D ) )
& ! [D: $i,E: $i,F: $i] :
( ( ~ ( leq @ ( host @ E ) @ ( host @ F ) )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) )
& ( ( host @ E )
= ( host @ D ) ) )
=> ~ ( ( setIn @ D @ alive )
& ( ( index @ ldr @ ( host @ D ) )
= ( host @ D ) )
& ( ( index @ status @ ( host @ D ) )
= norm ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( host @ F )
!= ( host @ D ) )
& ( setIn @ D @ alive )
& ( setIn @ F @ alive )
& ( ( host @ E )
= ( host @ D ) )
& ( ( host @ G )
= ( host @ F ) ) )
=> ~ ( ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ D ) ) )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( host @ F )
!= ( host @ D ) )
& ( setIn @ D @ alive )
& ( setIn @ F @ alive )
& ( ( host @ E )
= ( host @ D ) )
& ( ( host @ G )
= ( host @ F ) ) )
=> ~ ( ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ D ) ) )
& ( setIn @ ( host @ E ) @ ( index @ down @ ( host @ F ) ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( host @ F )
!= ( host @ E ) )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ F ) ) )
& ( ( host @ E )
= ( host @ D ) )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ E ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( ( host @ F )
!= ( host @ E ) )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ F ) ) )
& ( ( host @ E )
= ( host @ D ) )
& ( ( index @ status @ ( host @ F ) )
= wait )
& ( ( host @ ( index @ elid @ ( host @ F ) ) )
= ( host @ E ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( ~ ( leq @ ( host @ G ) @ H )
& ( leq @ ( s @ zero ) @ H ) )
=> ( ( setIn @ H @ ( index @ down @ ( host @ G ) ) )
| ( H
= ( host @ F ) ) ) )
& ( setIn @ D @ alive )
& ( leq @ ( host @ D ) @ ( host @ G ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ E )
= ( host @ G ) )
& ( ( index @ status @ ( host @ D ) )
= elec_2 )
& ( ( index @ status @ ( host @ G ) )
= elec_1 ) )
=> ~ ( elem @ ( m_Ack @ D @ E ) @ ( queue @ ( host @ D ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( ~ ( leq @ ( host @ G ) @ H )
& ( leq @ ( s @ zero ) @ H ) )
=> ( ( setIn @ H @ ( index @ down @ ( host @ G ) ) )
| ( H
= ( host @ F ) ) ) )
& ( setIn @ G @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ G ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ E )
= ( s @ ( host @ G ) ) )
& ( ( index @ status @ ( host @ G ) )
= elec_1 ) )
=> ~ ( ( setIn @ D @ alive )
& ( ( index @ ldr @ ( host @ D ) )
= ( host @ D ) )
& ( ( index @ status @ ( host @ D ) )
= norm ) ) )
& ( ( queue @ ( host @ B ) )
= ( cons @ ( m_Down @ C ) @ A ) ) )
=> ( ( setIn @ B @ alive )
=> ( ( leq @ ( host @ B ) @ ( host @ C ) )
=> ( ( ( ( index @ status @ ( host @ B ) )
= elec_2 )
& ( ( host @ C )
= ( index @ pendack @ ( host @ B ) ) ) )
=> ( ( leq @ nbr_proc @ ( index @ pendack @ ( host @ B ) ) )
=> ! [D: $i] :
( ( setIn @ ( host @ D ) @ ( index @ acks @ ( host @ B ) ) )
=> ! [E: $i] :
( ( ( host @ B )
= ( host @ E ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( host @ D )
= ( host @ H ) )
=> ( ( ( host @ B )
!= ( host @ H ) )
=> ( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( setIn @ H @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ H ) ) )
& ( elem @ ( m_Down @ F ) @ ( snoc @ ( queue @ ( host @ H ) ) @ ( m_Ldr @ B ) ) )
& ( elem @ ( m_Down @ G ) @ ( snoc @ ( queue @ ( host @ H ) ) @ ( m_Ldr @ B ) ) )
& ( ( host @ F )
= ( s @ ( host @ H ) ) )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( host @ B )
= ( host @ E ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( elem @ ( m_Ldr @ E ) @ ( queue @ ( host @ D ) ) )
=> ~ ( leq @ ( host @ D ) @ ( host @ E ) ) )
& ! [D: $i,E: $i] :
( ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ D ) ) )
=> ( ( host @ E )
!= ( host @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( E != D )
& ( ( host @ E )
= ( host @ D ) ) )
=> ( ~ ( setIn @ D @ alive )
| ~ ( setIn @ E @ alive ) ) )
& ! [D: $i] :
( ( ( ( ( index @ status @ ( host @ D ) )
= elec_1 )
| ( ( index @ status @ ( host @ D ) )
= elec_2 ) )
& ( setIn @ D @ alive ) )
=> ( ( index @ elid @ ( host @ D ) )
= D ) )
& ! [D: $i,E: $i] :
( ( ( setIn @ D @ alive )
& ( setIn @ E @ alive )
& ( setIn @ ( host @ E ) @ ( index @ down @ ( host @ D ) ) )
& ( ( index @ status @ ( host @ E ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ E ) ) @ ( host @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( setIn @ E @ alive )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) )
=> ~ ( ( setIn @ D @ alive )
& ( setIn @ ( host @ E ) @ ( index @ down @ ( host @ D ) ) ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( ( setIn @ D @ alive )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ D ) ) )
& ( ( host @ F )
= ( host @ E ) )
& ( ( index @ status @ ( host @ F ) )
= elec_2 ) )
=> ( leq @ ( index @ pendack @ ( host @ F ) ) @ ( host @ D ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( setIn @ F @ alive )
& ( ( host @ E )
= ( host @ F ) )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ F ) ) )
=> ~ ( ( setIn @ D @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ D ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( setIn @ D @ alive )
& ( setIn @ E @ alive )
& ( ( index @ ldr @ ( host @ D ) )
= ( host @ D ) )
& ( ( index @ status @ ( host @ D ) )
= norm )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) )
=> ( E = D ) )
& ! [D: $i] :
( ? [E: $i,F: $i] :
( ~ ( leq @ ( host @ E ) @ ( host @ F ) )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) )
& ( ( host @ E )
= ( host @ D ) ) )
=> ~ ( ( setIn @ D @ alive )
& ( ( index @ ldr @ ( host @ D ) )
= ( host @ D ) )
& ( ( index @ status @ ( host @ D ) )
= norm ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( host @ F )
!= ( host @ D ) )
& ( setIn @ D @ alive )
& ( setIn @ F @ alive )
& ( ( host @ E )
= ( host @ D ) )
& ( ( host @ G )
= ( host @ F ) ) )
=> ~ ( ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ D ) ) )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( host @ F )
!= ( host @ D ) )
& ( setIn @ D @ alive )
& ( setIn @ F @ alive )
& ( ( host @ E )
= ( host @ D ) )
& ( ( host @ G )
= ( host @ F ) ) )
=> ~ ( ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ D ) ) )
& ( setIn @ ( host @ E ) @ ( index @ down @ ( host @ F ) ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( host @ F )
!= ( host @ E ) )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ F ) ) )
& ( ( host @ E )
= ( host @ D ) )
& ( ( index @ status @ ( host @ F ) )
= norm )
& ( ( index @ ldr @ ( host @ F ) )
= ( host @ E ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( ( host @ F )
!= ( host @ E ) )
& ( setIn @ F @ alive )
& ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ F ) ) )
& ( ( host @ E )
= ( host @ D ) )
& ( ( index @ status @ ( host @ F ) )
= wait )
& ( ( host @ ( index @ elid @ ( host @ F ) ) )
= ( host @ E ) ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( index @ status @ ( host @ E ) )
= norm )
& ( ( index @ ldr @ ( host @ E ) )
= ( host @ E ) ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i,G: $i] :
( ! [H: $i] :
( ( ~ ( leq @ ( host @ G ) @ H )
& ( leq @ ( s @ zero ) @ H ) )
=> ( ( setIn @ H @ ( index @ down @ ( host @ G ) ) )
| ( H
= ( host @ F ) ) ) )
& ( setIn @ D @ alive )
& ( leq @ ( host @ D ) @ ( host @ G ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) )
& ( ( host @ E )
= ( host @ G ) )
& ( ( index @ status @ ( host @ D ) )
= elec_2 )
& ( ( index @ status @ ( host @ G ) )
= elec_1 ) )
=> ~ ( elem @ ( m_Ack @ D @ E ) @ ( queue @ ( host @ D ) ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( ~ ( leq @ ( host @ F ) @ G )
& ( leq @ ( s @ zero ) @ G ) )
=> ( ( setIn @ G @ ( index @ down @ ( host @ F ) ) )
| ( G
= ( host @ E ) ) ) )
& ( setIn @ F @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ F ) ) )
& ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) )
& ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ F ) ) )
& ( ( host @ D )
= ( s @ ( host @ F ) ) )
& ( ( index @ status @ ( host @ F ) )
= elec_1 ) )
=> ~ ? [D: $i] :
( ( setIn @ D @ alive )
& ( ( index @ ldr @ ( host @ D ) )
= ( host @ D ) )
& ( ( index @ status @ ( host @ D ) )
= norm ) ) )
& ( ( queue @ ( host @ B ) )
= ( cons @ ( m_Down @ C ) @ A ) ) )
=> ( ( setIn @ B @ alive )
=> ( ( leq @ ( host @ B ) @ ( host @ C ) )
=> ( ( ( ( index @ status @ ( host @ B ) )
= elec_2 )
& ( ( host @ C )
= ( index @ pendack @ ( host @ B ) ) ) )
=> ( ( leq @ nbr_proc @ ( index @ pendack @ ( host @ B ) ) )
=> ! [D: $i] :
( ( setIn @ ( host @ D ) @ ( index @ acks @ ( host @ B ) ) )
=> ! [E: $i] :
( ( ( host @ B )
= ( host @ E ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( host @ D )
= ( host @ H ) )
=> ( ( ( host @ B )
!= ( host @ H ) )
=> ( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( setIn @ H @ alive )
& ( leq @ nbr_proc @ ( s @ ( host @ H ) ) )
& ( elem @ ( m_Down @ F ) @ ( snoc @ ( queue @ ( host @ H ) ) @ ( m_Ldr @ B ) ) )
& ( elem @ ( m_Down @ G ) @ ( snoc @ ( queue @ ( host @ H ) ) @ ( m_Ldr @ B ) ) )
& ( ( host @ F )
= ( s @ ( host @ H ) ) )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( ( host @ B )
= ( host @ E ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[69]) ).
thf(111,plain,
( ( index @ status @ ( host @ sk2 ) )
= elec_2 ),
inference(cnf,[status(esa)],[70]) ).
thf(165,plain,
( ( index @ status @ ( host @ sk2 ) )
= elec_2 ),
inference(lifteq,[status(thm)],[111]) ).
thf(96,plain,
( ( host @ sk3 )
= ( index @ pendack @ ( host @ sk2 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(132,plain,
( ( index @ pendack @ ( host @ sk2 ) )
= ( host @ sk3 ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(549,plain,
( ( ( host @ sk3 )
= elec_2 )
| ( ( index @ pendack @ ( host @ sk2 ) )
!= ( index @ status @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,132]) ).
thf(557,plain,
( ( ( host @ sk3 )
= elec_2 )
| ( pendack != status )
| ( ( host @ sk2 )
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[549]) ).
thf(560,plain,
( ( ( host @ sk3 )
= elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[557]) ).
thf(85,plain,
leq @ ( host @ sk2 ) @ ( host @ sk3 ),
inference(cnf,[status(esa)],[70]) ).
thf(628,plain,
( ( pendack != status )
| ( leq @ ( host @ sk2 ) @ elec_2 )
| ( ( host @ sk3 )
!= ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[560,85]) ).
thf(629,plain,
( ( pendack != status )
| ( leq @ ( host @ sk2 ) @ elec_2 ) ),
inference(pattern_uni,[status(thm)],[628:[]]) ).
thf(105,plain,
( ( queue @ ( host @ sk2 ) )
= ( cons @ ( m_Down @ sk3 ) @ sk1 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(135,plain,
( ( cons @ ( m_Down @ sk3 ) @ sk1 )
= ( queue @ ( host @ sk2 ) ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( cons @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(399,plain,
! [A: $i,B: $i] :
( q_nil
!= ( cons @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(400,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( cons @ A @ B ) ),
inference(miniscope,[status(thm)],[399]) ).
thf(401,plain,
! [B: $i,A: $i] :
( q_nil
!= ( cons @ A @ B ) ),
inference(cnf,[status(esa)],[400]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( cons @ A @ B )
!= q_nil ),
inference(lifteq,[status(thm)],[401]) ).
thf(2030,plain,
! [B: $i,A: $i] :
( ( ( queue @ ( host @ sk2 ) )
!= q_nil )
| ( ( cons @ ( m_Down @ sk3 ) @ sk1 )
!= ( cons @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[135,402]) ).
thf(2031,plain,
( ( queue @ ( host @ sk2 ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2030:[bind(A,$thf( m_Down @ sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(35,axiom,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( snoc @ ( init @ A ) @ ( last @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(308,plain,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( snoc @ ( init @ A ) @ ( last @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(309,plain,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( snoc @ ( init @ A ) @ ( last @ A ) ) ) ),
inference(cnf,[status(esa)],[308]) ).
thf(310,plain,
! [A: $i] :
( ( A = q_nil )
| ( ( snoc @ ( init @ A ) @ ( last @ A ) )
= A ) ),
inference(lifteq,[status(thm)],[309]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( elem @ A @ ( snoc @ C @ B ) )
<=> ( ( A = B )
| ( elem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(359,plain,
! [A: $i,B: $i,C: $i] :
( ( ( elem @ A @ ( snoc @ C @ B ) )
=> ( ( A = B )
| ( elem @ A @ C ) ) )
& ( ( ( A = B )
| ( elem @ A @ C ) )
=> ( elem @ A @ ( snoc @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(360,plain,
( ! [A: $i,B: $i,C: $i] :
( ( elem @ A @ ( snoc @ C @ B ) )
=> ( ( A = B )
| ( elem @ A @ C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( elem @ A @ C ) )
=> ( elem @ A @ ( snoc @ C @ B ) ) ) ),
inference(miniscope,[status(thm)],[359]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( elem @ A @ ( snoc @ C @ B ) ) ),
inference(cnf,[status(esa)],[360]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( elem @ A @ ( snoc @ C @ B ) ) ),
inference(lifteq,[status(thm)],[361]) ).
thf(365,plain,
! [B: $i,A: $i] : ( elem @ A @ ( snoc @ B @ A ) ),
inference(simp,[status(thm)],[364]) ).
thf(11203,plain,
! [C: $i,B: $i,A: $i] :
( ( A = q_nil )
| ( elem @ B @ A )
| ( ( snoc @ ( init @ A ) @ ( last @ A ) )
!= ( snoc @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[310,365]) ).
thf(11204,plain,
! [A: $i] :
( ( A = q_nil )
| ( elem @ ( last @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[11203:[bind(A,$thf( E )),bind(B,$thf( last @ E )),bind(C,$thf( init @ E ))]]) ).
thf(11261,plain,
! [A: $i] :
( ( A = q_nil )
| ( elem @ ( last @ A ) @ A ) ),
inference(simp,[status(thm)],[11204]) ).
thf(92,plain,
leq @ nbr_proc @ ( s @ ( host @ sk10 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(87,plain,
( ( host @ sk6 )
= ( host @ sk10 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(151,plain,
( ( host @ sk10 )
= ( host @ sk6 ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(497,plain,
leq @ nbr_proc @ ( s @ ( host @ sk6 ) ),
inference(rewrite,[status(thm)],[92,151]) ).
thf(83,plain,
( ( host @ sk8 )
= ( s @ ( host @ sk10 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(160,plain,
( ( s @ ( host @ sk10 ) )
= ( host @ sk8 ) ),
inference(lifteq,[status(thm)],[83]) ).
thf(507,plain,
( ( s @ ( host @ sk6 ) )
= ( host @ sk8 ) ),
inference(rewrite,[status(thm)],[160,151]) ).
thf(508,plain,
leq @ nbr_proc @ ( host @ sk8 ),
inference(rewrite,[status(thm)],[497,507]) ).
thf(12188,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( leq @ nbr_proc @ ( host @ q_nil ) )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[11261,508]) ).
thf(12189,plain,
( ( elem @ ( last @ sk8 ) @ sk8 )
| ( leq @ nbr_proc @ ( host @ q_nil ) ) ),
inference(pattern_uni,[status(thm)],[12188:[bind(A,$thf( sk8 ))]]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
| ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(368,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
| ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( leq @ A @ B )
| ( leq @ B @ A ) ),
inference(cnf,[status(esa)],[368]) ).
thf(58,axiom,
! [A: $i] :
~ ( leq @ ( s @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(403,plain,
! [A: $i] :
~ ( leq @ ( s @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(404,plain,
~ ? [A: $i] : ( leq @ ( s @ A ) @ A ),
inference(miniscope,[status(thm)],[403]) ).
thf(405,plain,
! [A: $i] :
~ ( leq @ ( s @ A ) @ A ),
inference(cnf,[status(esa)],[404]) ).
thf(9753,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ A @ B )
| ( ( leq @ B @ A )
!= ( leq @ ( s @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[369,405]) ).
thf(9754,plain,
! [A: $i] : ( leq @ A @ ( s @ A ) ),
inference(pattern_uni,[status(thm)],[9753:[bind(A,$thf( A )),bind(B,$thf( s @ A )),bind(C,$thf( A ))]]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(290,plain,
! [A: $i,B: $i] :
( ( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( leq @ A @ B )
& ( leq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(291,plain,
( ! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( leq @ A @ B )
& ( leq @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[290]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[291]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[292]) ).
thf(296,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[295]) ).
thf(2056,plain,
! [B: $i,A: $i] :
( ( leq @ A @ A )
!= ( leq @ ( s @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[296,405]) ).
thf(2075,plain,
! [B: $i,A: $i] :
( ( A
!= ( s @ B ) )
| ( A != B ) ),
inference(simp,[status(thm)],[2056]) ).
thf(2092,plain,
! [A: $i] :
( ( s @ A )
!= A ),
inference(simp,[status(thm)],[2075]) ).
thf(12591,plain,
! [B: $i,A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( q_nil != B )
| ( A
!= ( s @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11261,2092]) ).
thf(12592,plain,
! [A: $i] :
( ( elem @ ( last @ ( s @ A ) ) @ ( s @ A ) )
| ( q_nil != A ) ),
inference(pattern_uni,[status(thm)],[12591:[bind(A,$thf( s @ C )),bind(B,$thf( C ))]]) ).
thf(13233,plain,
elem @ ( last @ ( s @ q_nil ) ) @ ( s @ q_nil ),
inference(simp,[status(thm)],[12592]) ).
thf(63,axiom,
! [A: $i] :
~ ( elem @ A @ q_nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(419,plain,
! [A: $i] :
~ ( elem @ A @ q_nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(420,plain,
~ ? [A: $i] : ( elem @ A @ q_nil ),
inference(miniscope,[status(thm)],[419]) ).
thf(421,plain,
! [A: $i] :
~ ( elem @ A @ q_nil ),
inference(cnf,[status(esa)],[420]) ).
thf(14129,plain,
! [A: $i] :
( ( elem @ ( last @ ( s @ q_nil ) ) @ ( s @ q_nil ) )
!= ( elem @ A @ q_nil ) ),
inference(paramod_ordered,[status(thm)],[13233,421]) ).
thf(14269,plain,
! [A: $i] :
( ( ( last @ ( s @ q_nil ) )
!= A )
| ( ( s @ q_nil )
!= q_nil ) ),
inference(simp,[status(thm)],[14129]) ).
thf(14305,plain,
( ( s @ q_nil )
!= q_nil ),
inference(simp,[status(thm)],[14269]) ).
thf(74,plain,
setIn @ sk2 @ alive,
inference(cnf,[status(esa)],[70]) ).
thf(12,axiom,
~ ( setIn @ nil @ alive ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(209,plain,
~ ( setIn @ nil @ alive ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(210,plain,
~ ( setIn @ nil @ alive ),
inference(polarity_switch,[status(thm)],[209]) ).
thf(462,plain,
( ( setIn @ sk2 @ alive )
!= ( setIn @ nil @ alive ) ),
inference(paramod_ordered,[status(thm)],[74,210]) ).
thf(465,plain,
( ( sk2 != nil )
| ( alive != alive ) ),
inference(simp,[status(thm)],[462]) ).
thf(468,plain,
sk2 != nil,
inference(simp,[status(thm)],[465]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NotNorm @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(234,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NotNorm @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) )
| ( ( host @ B )
!= ( host @ A ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ A ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ A ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ( B != A )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(1110,plain,
! [A: $i] :
~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ A ) ) ),
inference(simp,[status(thm)],[1075]) ).
thf(93,plain,
( ( host @ sk2 )
!= ( host @ sk10 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(123,plain,
( ( host @ sk10 )
!= ( host @ sk2 ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(481,plain,
( ( host @ sk6 )
!= ( host @ sk2 ) ),
inference(rewrite,[status(thm)],[123,151]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ack @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(352,plain,
! [A: $i,B: $i,C: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ack @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(13,axiom,
leq @ ( s @ zero ) @ nbr_proc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(211,plain,
leq @ ( s @ zero ) @ nbr_proc,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( leq @ ( s @ A ) @ ( s @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(256,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
=> ( leq @ ( s @ A ) @ ( s @ B ) ) )
& ( ( leq @ ( s @ A ) @ ( s @ B ) )
=> ( leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(257,plain,
( ! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ ( s @ A ) @ ( s @ B ) ) )
& ! [A: $i,B: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
=> ( leq @ A @ B ) ) ),
inference(miniscope,[status(thm)],[256]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( leq @ ( s @ A ) @ ( s @ B ) ) ),
inference(cnf,[status(esa)],[257]) ).
thf(21470,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ ( s @ zero ) @ nbr_proc )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[211,259]) ).
thf(21471,plain,
leq @ ( s @ ( s @ zero ) ) @ ( s @ nbr_proc ),
inference(pattern_uni,[status(thm)],[21470:[bind(A,$thf( s @ zero )),bind(B,$thf( nbr_proc ))]]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) )
| ( ( host @ C )
!= ( host @ B ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_2 )
| ( leq @ ( index @ pendack @ ( host @ C ) ) @ ( host @ A ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
!= ( host @ B ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_2 )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) )
| ( leq @ ( index @ pendack @ ( host @ C ) ) @ ( host @ A ) ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
!= ( host @ B ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_2 )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) )
| ( leq @ ( index @ pendack @ ( host @ C ) ) @ ( host @ A ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(20,axiom,
! [A: $i] : ( leq @ ( host @ A ) @ nbr_proc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(232,plain,
! [A: $i] : ( leq @ ( host @ A ) @ nbr_proc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(233,plain,
! [A: $i] : ( leq @ ( host @ A ) @ nbr_proc ),
inference(cnf,[status(esa)],[232]) ).
thf(2051,plain,
! [B: $i,A: $i] :
( ( leq @ ( host @ A ) @ nbr_proc )
!= ( leq @ ( s @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[233,405]) ).
thf(2071,plain,
! [B: $i,A: $i] :
( ( ( host @ A )
!= ( s @ B ) )
| ( nbr_proc != B ) ),
inference(simp,[status(thm)],[2051]) ).
thf(2088,plain,
! [A: $i] :
( ( host @ A )
!= ( s @ nbr_proc ) ),
inference(simp,[status(thm)],[2071]) ).
thf(3889,plain,
! [A: $i] :
( ( ( host @ sk8 )
!= ( host @ A ) )
| ( ( s @ ( host @ sk6 ) )
!= ( s @ nbr_proc ) ) ),
inference(paramod_ordered,[status(thm)],[507,2088]) ).
thf(3904,plain,
! [A: $i] :
( ( sk8 != A )
| ( ( host @ sk6 )
!= nbr_proc ) ),
inference(simp,[status(thm)],[3889]) ).
thf(3905,plain,
( ( host @ sk6 )
!= nbr_proc ),
inference(simp,[status(thm)],[3904]) ).
thf(82,plain,
setIn @ sk7 @ alive,
inference(cnf,[status(esa)],[70]) ).
thf(464,plain,
( ( setIn @ sk7 @ alive )
!= ( setIn @ nil @ alive ) ),
inference(paramod_ordered,[status(thm)],[82,210]) ).
thf(467,plain,
( ( sk7 != nil )
| ( alive != alive ) ),
inference(simp,[status(thm)],[464]) ).
thf(470,plain,
sk7 != nil,
inference(simp,[status(thm)],[467]) ).
thf(12665,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( nil != q_nil )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[11261,470]) ).
thf(12666,plain,
( ( elem @ ( last @ sk7 ) @ sk7 )
| ( nil != q_nil ) ),
inference(pattern_uni,[status(thm)],[12665:[bind(A,$thf( sk7 ))]]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( elem @ A @ ( cons @ B @ C ) )
<=> ( ( A = B )
| ( elem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(271,plain,
! [A: $i,B: $i,C: $i] :
( ( ( elem @ A @ ( cons @ B @ C ) )
=> ( ( A = B )
| ( elem @ A @ C ) ) )
& ( ( ( A = B )
| ( elem @ A @ C ) )
=> ( elem @ A @ ( cons @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(272,plain,
( ! [A: $i,B: $i,C: $i] :
( ( elem @ A @ ( cons @ B @ C ) )
=> ( ( A = B )
| ( elem @ A @ C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( A = B )
| ( elem @ A @ C ) )
=> ( elem @ A @ ( cons @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[271]) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( elem @ A @ ( cons @ B @ C ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( elem @ A @ ( cons @ B @ C ) ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(277,plain,
! [B: $i,A: $i] : ( elem @ A @ ( cons @ A @ B ) ),
inference(simp,[status(thm)],[276]) ).
thf(5706,plain,
! [A: $i] :
( ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ sk6 ) ) )
| ( ( host @ sk10 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,1110]) ).
thf(5707,plain,
~ ( elem @ ( m_Down @ sk10 ) @ ( queue @ ( host @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[5706:[bind(A,$thf( sk10 ))]]) ).
thf(5924,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Down @ sk10 ) @ ( queue @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,5707]) ).
thf(5931,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Down @ sk10 ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ sk6 ) ) ) ),
inference(simp,[status(thm)],[5924]) ).
thf(5982,plain,
! [A: $i] :
( ( cons @ ( m_Down @ sk10 ) @ A )
!= ( queue @ ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[5931]) ).
thf(50,axiom,
! [A: $i] :
( ( pidMsg @ ( m_Down @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(377,plain,
! [A: $i] :
( ( pidMsg @ ( m_Down @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(378,plain,
! [A: $i] :
( ( pidMsg @ ( m_Down @ A ) )
= A ),
inference(cnf,[status(esa)],[377]) ).
thf(379,plain,
! [A: $i] :
( ( pidMsg @ ( m_Down @ A ) )
= A ),
inference(lifteq,[status(thm)],[378]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(202,plain,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
ordered @ q_nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(201,plain,
ordered @ q_nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ldr @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(268,plain,
! [A: $i,B: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ldr @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(269,plain,
! [A: $i] :
( ( ordered @ A )
=> ! [B: $i] : ( ordered @ ( snoc @ A @ ( m_Ldr @ B ) ) ) ),
inference(miniscope,[status(thm)],[268]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ~ ( ordered @ A )
| ( ordered @ ( snoc @ A @ ( m_Ldr @ B ) ) ) ),
inference(cnf,[status(esa)],[269]) ).
thf(23151,plain,
! [B: $i,A: $i] :
( ( ordered @ ( snoc @ A @ ( m_Ldr @ B ) ) )
| ( ( ordered @ q_nil )
!= ( ordered @ A ) ) ),
inference(paramod_ordered,[status(thm)],[201,270]) ).
thf(23152,plain,
! [A: $i] : ( ordered @ ( snoc @ q_nil @ ( m_Ldr @ A ) ) ),
inference(pattern_uni,[status(thm)],[23151:[bind(A,$thf( q_nil ))]]) ).
thf(23183,plain,
! [A: $i] : ( ordered @ ( snoc @ q_nil @ ( m_Ldr @ A ) ) ),
inference(simp,[status(thm)],[23152]) ).
thf(55,axiom,
! [A: $i] :
( ( cons @ A @ q_nil )
= ( snoc @ q_nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(393,plain,
! [A: $i] :
( ( cons @ A @ q_nil )
= ( snoc @ q_nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(394,plain,
! [A: $i] :
( ( cons @ A @ q_nil )
= ( snoc @ q_nil @ A ) ),
inference(cnf,[status(esa)],[393]) ).
thf(395,plain,
! [A: $i] :
( ( snoc @ q_nil @ A )
= ( cons @ A @ q_nil ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(23191,plain,
! [A: $i] : ( ordered @ ( cons @ ( m_Ldr @ A ) @ q_nil ) ),
inference(rewrite,[status(thm)],[23183,395]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) ) )
& ( ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( host @ B )
!= ( host @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive ) ),
inference(cnf,[status(esa)],[70]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( host @ B )
!= ( host @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( host @ B )
!= ( host @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive ) ),
inference(simp,[status(thm)],[119]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( init @ ( snoc @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( init @ ( snoc @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( init @ ( snoc @ B @ A ) )
= B ),
inference(cnf,[status(esa)],[245]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( init @ ( snoc @ B @ A ) )
= B ),
inference(lifteq,[status(thm)],[246]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(384,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( s @ zero ) @ ( sk4 @ D @ C @ B @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ( leq @ ( s @ zero ) @ ( sk4 @ D @ C @ B @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ( leq @ ( s @ zero ) @ ( sk4 @ D @ C @ B @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(2049,plain,
! [A: $i] :
( ~ ( leq @ ( host @ sk8 ) @ A )
| ( ( s @ ( host @ sk6 ) )
!= ( s @ A ) ) ),
inference(paramod_ordered,[status(thm)],[507,405]) ).
thf(2050,plain,
~ ( leq @ ( host @ sk8 ) @ ( host @ sk6 ) ),
inference(pattern_uni,[status(thm)],[2049:[bind(A,$thf( host @ sk6 ))]]) ).
thf(2421,plain,
! [A: $i] :
( ( leq @ A @ A )
!= ( leq @ ( host @ sk8 ) @ ( host @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[296,2050]) ).
thf(2436,plain,
! [A: $i] :
( ( A
!= ( host @ sk8 ) )
| ( A
!= ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[2421]) ).
thf(2454,plain,
( ( host @ sk8 )
!= ( host @ sk6 ) ),
inference(simp,[status(thm)],[2436]) ).
thf(2462,plain,
sk8 != sk6,
inference(simp,[status(thm)],[2454]) ).
thf(12769,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( sk6 != q_nil )
| ( A != sk8 ) ),
inference(paramod_ordered,[status(thm)],[11261,2462]) ).
thf(12770,plain,
( ( elem @ ( last @ sk8 ) @ sk8 )
| ( sk6 != q_nil ) ),
inference(pattern_uni,[status(thm)],[12769:[bind(A,$thf( sk8 ))]]) ).
thf(24266,plain,
! [A: $i] :
( ( sk6 != q_nil )
| ( ( elem @ ( last @ sk8 ) @ sk8 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12770,421]) ).
thf(24368,plain,
! [A: $i] :
( ( sk6 != q_nil )
| ( ( last @ sk8 )
!= A )
| ( sk8 != q_nil ) ),
inference(simp,[status(thm)],[24266]) ).
thf(24430,plain,
( ( sk6 != q_nil )
| ( sk8 != q_nil ) ),
inference(simp,[status(thm)],[24368]) ).
thf(11666,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( A
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11261,2031]) ).
thf(11667,plain,
elem @ ( last @ ( queue @ ( host @ sk2 ) ) ) @ ( queue @ ( host @ sk2 ) ),
inference(pattern_uni,[status(thm)],[11666:[bind(A,$thf( queue @ ( host @ sk2 ) ))]]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( elem @ ( m_Ldr @ B ) @ ( queue @ ( host @ A ) ) )
| ~ ( leq @ ( host @ A ) @ ( host @ B ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(579,plain,
! [B: $i,A: $i] :
( ~ ( elem @ ( m_Ldr @ B ) @ ( queue @ ( host @ A ) ) )
| ( ( leq @ ( host @ sk2 ) @ ( host @ sk3 ) )
!= ( leq @ ( host @ A ) @ ( host @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[85,91]) ).
thf(580,plain,
~ ( elem @ ( m_Ldr @ sk3 ) @ ( queue @ ( host @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[579:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(14392,plain,
( ( elem @ ( last @ ( queue @ ( host @ sk2 ) ) ) @ ( queue @ ( host @ sk2 ) ) )
!= ( elem @ ( m_Ldr @ sk3 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11667,580]) ).
thf(14427,plain,
( ( ( last @ ( queue @ ( host @ sk2 ) ) )
!= ( m_Ldr @ sk3 ) )
| ( ( queue @ ( host @ sk2 ) )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[14392]) ).
thf(14521,plain,
( ( last @ ( queue @ ( host @ sk2 ) ) )
!= ( m_Ldr @ sk3 ) ),
inference(simp,[status(thm)],[14427]) ).
thf(38,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(320,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(9755,plain,
! [B: $i,A: $i] :
( ( leq @ B @ A )
| ( ( leq @ A @ B )
!= ( leq @ ( host @ sk8 ) @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[369,2050]) ).
thf(9756,plain,
leq @ ( host @ sk6 ) @ ( host @ sk8 ),
inference(pattern_uni,[status(thm)],[9755:[bind(A,$thf( host @ sk8 )),bind(B,$thf( host @ sk6 ))]]) ).
thf(21514,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ ( host @ sk6 ) @ ( host @ sk8 ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9756,259]) ).
thf(21515,plain,
leq @ ( s @ ( host @ sk6 ) ) @ ( s @ ( host @ sk8 ) ),
inference(pattern_uni,[status(thm)],[21514:[bind(A,$thf( host @ sk6 )),bind(B,$thf( host @ sk8 ))]]) ).
thf(22474,plain,
leq @ ( host @ sk8 ) @ ( s @ ( host @ sk8 ) ),
inference(rewrite,[status(thm)],[21515,507]) ).
thf(95,plain,
( ( host @ sk2 )
= ( host @ sk7 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(116,plain,
( ( host @ sk7 )
= ( host @ sk2 ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(5916,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( queue @ ( host @ sk2 ) ) )
| ( ( cons @ ( m_Down @ sk3 ) @ sk1 )
!= ( cons @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[135,277]) ).
thf(5917,plain,
elem @ ( m_Down @ sk3 ) @ ( queue @ ( host @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5916:[bind(A,$thf( m_Down @ sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(6379,plain,
! [B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ A ) )
| ( ( elem @ ( m_Down @ sk3 ) @ ( queue @ ( host @ sk2 ) ) )
!= ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5917,118]) ).
thf(6380,plain,
( ( host @ sk3 )
!= ( host @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6379:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(6435,plain,
( ( host @ sk7 )
!= ( host @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[116,6380]) ).
thf(6446,plain,
sk7 != sk3,
inference(simp,[status(thm)],[6435]) ).
thf(12446,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( sk3 != q_nil )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[11261,6446]) ).
thf(12447,plain,
( ( elem @ ( last @ sk7 ) @ sk7 )
| ( sk3 != q_nil ) ),
inference(pattern_uni,[status(thm)],[12446:[bind(A,$thf( sk7 ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(178,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) ) )
& ( ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(179,plain,
( ! [A: $i,B: $i] :
( ( A != B )
=> ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) )
=> ( A != B ) ) ),
inference(miniscope,[status(thm)],[178]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) ) ),
inference(cnf,[status(esa)],[179]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(185,plain,
! [A: $i] :
( ( sk12 @ ( m_NormQ @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(m_NormQ),[sk12])]) ).
thf(5898,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Ldr @ sk3 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,580]) ).
thf(5926,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk3 ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[5898]) ).
thf(5977,plain,
! [A: $i] :
( ( cons @ ( m_Ldr @ sk3 ) @ A )
!= ( queue @ ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[5926]) ).
thf(37,axiom,
! [A: $i] :
( ( ordered @ ( cons @ A @ q_nil ) )
& ( ordered @ ( snoc @ q_nil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(315,plain,
! [A: $i] :
( ( ordered @ ( cons @ A @ q_nil ) )
& ( ordered @ ( snoc @ q_nil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(316,plain,
( ! [A: $i] : ( ordered @ ( cons @ A @ q_nil ) )
& ! [A: $i] : ( ordered @ ( snoc @ q_nil @ A ) ) ),
inference(miniscope,[status(thm)],[315]) ).
thf(318,plain,
! [A: $i] : ( ordered @ ( cons @ A @ q_nil ) ),
inference(cnf,[status(esa)],[316]) ).
thf(874,plain,
! [A: $i] :
( ( ordered @ ( queue @ ( host @ sk2 ) ) )
| ( ( cons @ ( m_Down @ sk3 ) @ sk1 )
!= ( cons @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[135,318]) ).
thf(875,plain,
! [A: $i] :
( ( ordered @ ( queue @ ( host @ sk2 ) ) )
| ( ( m_Down @ sk3 )
!= A )
| ( sk1 != q_nil ) ),
inference(simp,[status(thm)],[874]) ).
thf(876,plain,
( ( ordered @ ( queue @ ( host @ sk2 ) ) )
| ( sk1 != q_nil ) ),
inference(simp,[status(thm)],[875]) ).
thf(12685,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( ordered @ ( queue @ ( host @ sk2 ) ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[11261,876]) ).
thf(12686,plain,
( ( elem @ ( last @ sk1 ) @ sk1 )
| ( ordered @ ( queue @ ( host @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[12685:[bind(A,$thf( sk1 ))]]) ).
thf(5904,plain,
! [C: $i,B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ C @ q_nil ) ),
inference(paramod_ordered,[status(thm)],[277,421]) ).
thf(5958,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( cons @ A @ B )
!= q_nil ) ),
inference(simp,[status(thm)],[5904]) ).
thf(6009,plain,
! [B: $i,A: $i] :
( ( cons @ B @ A )
!= q_nil ),
inference(simp,[status(thm)],[5958]) ).
thf(32,axiom,
! [A: $i] :
( ( pidElem @ A )
<=> ? [B: $i] :
( ( A
= ( m_Halt @ B ) )
| ( A
= ( m_Down @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(280,plain,
! [A: $i] :
( ( ( pidElem @ A )
=> ? [B: $i] :
( ( A
= ( m_Halt @ B ) )
| ( A
= ( m_Down @ B ) ) ) )
& ( ? [B: $i] :
( ( A
= ( m_Halt @ B ) )
| ( A
= ( m_Down @ B ) ) )
=> ( pidElem @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(281,plain,
( ! [A: $i] :
( ( pidElem @ A )
=> ( ? [B: $i] :
( A
= ( m_Halt @ B ) )
| ? [B: $i] :
( A
= ( m_Down @ B ) ) ) )
& ! [A: $i] :
( ( ? [B: $i] :
( A
= ( m_Halt @ B ) )
| ? [B: $i] :
( A
= ( m_Down @ B ) ) )
=> ( pidElem @ A ) ) ),
inference(miniscope,[status(thm)],[280]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Down @ B ) )
| ( pidElem @ A ) ),
inference(cnf,[status(esa)],[281]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Down @ B ) )
| ( pidElem @ A ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(288,plain,
! [A: $i] : ( pidElem @ ( m_Down @ A ) ),
inference(simp,[status(thm)],[287]) ).
thf(18,axiom,
! [A: $i] : ( leq @ ( s @ zero ) @ ( host @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(226,plain,
! [A: $i] : ( leq @ ( s @ zero ) @ ( host @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(227,plain,
! [A: $i] : ( leq @ ( s @ zero ) @ ( host @ A ) ),
inference(cnf,[status(esa)],[226]) ).
thf(2060,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ zero ) @ ( host @ A ) )
!= ( leq @ ( s @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[227,405]) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ( ( s @ zero )
!= ( s @ B ) )
| ( ( host @ A )
!= B ) ),
inference(simp,[status(thm)],[2060]) ).
thf(2090,plain,
! [A: $i] :
( ( s @ ( host @ A ) )
!= ( s @ zero ) ),
inference(simp,[status(thm)],[2073]) ).
thf(4186,plain,
! [A: $i] :
( ( host @ A )
!= zero ),
inference(simp,[status(thm)],[2090]) ).
thf(4742,plain,
! [A: $i] :
( ( pendack != status )
| ( zero != elec_2 )
| ( ( host @ sk3 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[560,4186]) ).
thf(4743,plain,
( ( pendack != status )
| ( zero != elec_2 ) ),
inference(pattern_uni,[status(thm)],[4742:[bind(A,$thf( sk3 ))]]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( host @ D )
!= ( host @ C ) )
| ~ ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ A ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ A ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( host @ D )
!= ( host @ C ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ A ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ A ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( host @ D )
!= ( host @ C ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ A ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(9798,plain,
! [B: $i,A: $i] :
( ~ ( elem @ ( m_Ldr @ B ) @ ( queue @ ( host @ A ) ) )
| ( ( leq @ ( host @ sk6 ) @ ( host @ sk8 ) )
!= ( leq @ ( host @ A ) @ ( host @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[9756,91]) ).
thf(9799,plain,
~ ( elem @ ( m_Ldr @ sk8 ) @ ( queue @ ( host @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9798:[bind(A,$thf( sk6 )),bind(B,$thf( sk8 ))]]) ).
thf(10521,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Ldr @ sk8 ) @ ( queue @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,9799]) ).
thf(10552,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk8 ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ sk6 ) ) ) ),
inference(simp,[status(thm)],[10521]) ).
thf(10558,plain,
! [A: $i] :
( ( snoc @ A @ ( m_Ldr @ sk8 ) )
!= ( queue @ ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[10552]) ).
thf(11199,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ sk6 ) ) )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ B @ ( m_Ldr @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[395,10558]) ).
thf(11200,plain,
( ( cons @ ( m_Ldr @ sk8 ) @ q_nil )
!= ( queue @ ( host @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[11199:[bind(A,$thf( m_Ldr @ sk8 )),bind(B,$thf( q_nil ))]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_Halt @ A )
!= ( m_Halt @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_Halt @ A )
!= ( m_Halt @ B ) ) )
& ( ( ( m_Halt @ A )
!= ( m_Halt @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(190,plain,
( ! [A: $i,B: $i] :
( ( A != B )
=> ( ( m_Halt @ A )
!= ( m_Halt @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( m_Halt @ A )
!= ( m_Halt @ B ) )
=> ( A != B ) ) ),
inference(miniscope,[status(thm)],[189]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_Halt @ A )
!= ( m_Halt @ B ) ) ),
inference(cnf,[status(esa)],[190]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_Halt @ A )
!= ( m_Halt @ B ) ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(196,plain,
! [A: $i] :
( ( sk13 @ ( m_Halt @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(m_Halt),[sk13])]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ B ) )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ C ) )
!= norm )
| ( ( index @ ldr @ ( host @ C ) )
!= ( host @ B ) )
| ~ ( setIn @ B @ alive )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ B ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ C ) )
!= norm )
| ( ( index @ ldr @ ( host @ C ) )
!= ( host @ B ) )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ B @ alive ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ B ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ C ) )
!= norm )
| ( ( index @ ldr @ ( host @ C ) )
!= ( host @ B ) )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ B @ alive ) ),
inference(simp,[status(thm)],[156]) ).
thf(21478,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ ( host @ sk2 ) @ ( host @ sk3 ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[85,259]) ).
thf(21479,plain,
leq @ ( s @ ( host @ sk2 ) ) @ ( s @ ( host @ sk3 ) ),
inference(pattern_uni,[status(thm)],[21478:[bind(A,$thf( host @ sk2 )),bind(B,$thf( host @ sk3 ))]]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( host @ A )
!= ( host @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(389,plain,
! [A: $i,B: $i] :
( ( ( host @ A )
!= ( host @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( elem @ ( m_Ldr @ C ) @ ( queue @ ( host @ B ) ) )
| ( ( leq @ A @ A )
!= ( leq @ ( host @ B ) @ ( host @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[296,91]) ).
thf(1026,plain,
! [A: $i] :
~ ( elem @ ( m_Ldr @ A ) @ ( queue @ ( host @ A ) ) ),
inference(pattern_uni,[status(thm)],[1025:[bind(A,$thf( host @ D )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(1028,plain,
! [A: $i] :
~ ( elem @ ( m_Ldr @ A ) @ ( queue @ ( host @ A ) ) ),
inference(simp,[status(thm)],[1026]) ).
thf(5014,plain,
! [A: $i] :
( ~ ( elem @ ( m_Ldr @ A ) @ ( queue @ ( host @ sk2 ) ) )
| ( ( host @ sk7 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[116,1028]) ).
thf(5015,plain,
~ ( elem @ ( m_Ldr @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5014:[bind(A,$thf( sk7 ))]]) ).
thf(5919,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Ldr @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,5015]) ).
thf(5959,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk7 ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[5919]) ).
thf(6010,plain,
! [A: $i] :
( ( cons @ ( m_Ldr @ sk7 ) @ A )
!= ( queue @ ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[5959]) ).
thf(4193,plain,
! [A: $i] :
( ( ( s @ zero )
!= ( host @ sk8 ) )
| ( ( s @ ( host @ sk6 ) )
!= ( s @ ( host @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[507,2090]) ).
thf(4194,plain,
( ( s @ zero )
!= ( host @ sk8 ) ),
inference(pattern_uni,[status(thm)],[4193:[bind(A,$thf( sk6 ))]]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( snoc @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(228,plain,
! [A: $i,B: $i] :
( q_nil
!= ( snoc @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5075,plain,
! [C: $i,B: $i,A: $i] :
( ( ( init @ ( cons @ A @ q_nil ) )
= C )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,247]) ).
thf(5076,plain,
! [A: $i] :
( ( init @ ( cons @ A @ q_nil ) )
= q_nil ),
inference(pattern_uni,[status(thm)],[5075:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(261,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( head @ ( cons @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(216,plain,
! [A: $i,B: $i] :
( ( head @ ( cons @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(473,plain,
( ( host @ sk10 )
!= ( host @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[116,123]) ).
thf(475,plain,
sk10 != sk7,
inference(simp,[status(thm)],[473]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NotNorm @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(373,plain,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NotNorm @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(374,plain,
~ ? [A: $i,B: $i] :
( ( m_Ldr @ A )
= ( m_NotNorm @ B ) ),
inference(miniscope,[status(thm)],[373]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( m_Ldr @ A )
!= ( m_NotNorm @ B ) ),
inference(cnf,[status(esa)],[374]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( m_Ldr @ A )
!= ( m_NotNorm @ B ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(89,plain,
leq @ nbr_proc @ ( index @ pendack @ ( host @ sk2 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(547,plain,
leq @ nbr_proc @ ( host @ sk3 ),
inference(rewrite,[status(thm)],[89,132]) ).
thf(2054,plain,
! [A: $i] :
( ( leq @ ( s @ A ) @ A )
!= ( leq @ nbr_proc @ ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[547,405]) ).
thf(2072,plain,
! [A: $i] :
( ( ( s @ A )
!= nbr_proc )
| ( A
!= ( host @ sk3 ) ) ),
inference(simp,[status(thm)],[2054]) ).
thf(2089,plain,
( ( s @ ( host @ sk3 ) )
!= nbr_proc ),
inference(simp,[status(thm)],[2072]) ).
thf(2118,plain,
( ( ( host @ sk8 )
!= nbr_proc )
| ( ( s @ ( host @ sk6 ) )
!= ( s @ ( host @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[507,2089]) ).
thf(2122,plain,
( ( ( host @ sk8 )
!= nbr_proc )
| ( ( host @ sk6 )
!= ( host @ sk3 ) ) ),
inference(simp,[status(thm)],[2118]) ).
thf(22,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(238,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3902,plain,
! [A: $i] :
( ( sk8 != A )
| ( ( s @ ( host @ sk6 ) )
!= ( s @ nbr_proc ) ) ),
inference(simp,[status(thm)],[3889]) ).
thf(3908,plain,
( ( s @ ( host @ sk6 ) )
!= ( s @ nbr_proc ) ),
inference(simp,[status(thm)],[3902]) ).
thf(3973,plain,
( ( s @ nbr_proc )
!= ( host @ sk8 ) ),
inference(rewrite,[status(thm)],[3908,507]) ).
thf(6468,plain,
! [C: $i,B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ C @ q_nil ) ),
inference(paramod_ordered,[status(thm)],[365,421]) ).
thf(6498,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( snoc @ B @ A )
!= q_nil ) ),
inference(simp,[status(thm)],[6468]) ).
thf(6559,plain,
! [B: $i,A: $i] :
( ( snoc @ A @ B )
!= q_nil ),
inference(simp,[status(thm)],[6498]) ).
thf(4191,plain,
! [A: $i] :
( ( ( s @ ( host @ sk2 ) )
!= ( s @ zero ) )
| ( ( host @ sk7 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[116,2090]) ).
thf(4192,plain,
( ( s @ ( host @ sk2 ) )
!= ( s @ zero ) ),
inference(pattern_uni,[status(thm)],[4191:[bind(A,$thf( sk7 ))]]) ).
thf(4686,plain,
( ( host @ sk2 )
!= zero ),
inference(simp,[status(thm)],[4192]) ).
thf(6462,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Ldr @ sk3 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,580]) ).
thf(6501,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk3 ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6462]) ).
thf(6562,plain,
! [A: $i] :
( ( snoc @ A @ ( m_Ldr @ sk3 ) )
!= ( queue @ ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[6501]) ).
thf(78,plain,
elem @ ( m_Down @ sk9 ) @ ( snoc @ ( queue @ ( host @ sk10 ) ) @ ( m_Ldr @ sk2 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(480,plain,
elem @ ( m_Down @ sk9 ) @ ( snoc @ ( queue @ ( host @ sk6 ) ) @ ( m_Ldr @ sk2 ) ),
inference(rewrite,[status(thm)],[78,151]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( last @ ( snoc @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( last @ ( snoc @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( last @ ( snoc @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[219]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( last @ ( snoc @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[220]) ).
thf(229,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( snoc @ B @ A ) ),
inference(miniscope,[status(thm)],[228]) ).
thf(230,plain,
! [B: $i,A: $i] :
( q_nil
!= ( snoc @ B @ A ) ),
inference(cnf,[status(esa)],[229]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( snoc @ B @ A )
!= q_nil ),
inference(lifteq,[status(thm)],[230]) ).
thf(2482,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cons @ A @ q_nil )
!= q_nil )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,231]) ).
thf(2483,plain,
! [A: $i] :
( ( cons @ A @ q_nil )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2482:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(56,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(396,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(206,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( tail @ ( cons @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( tail @ ( cons @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(11852,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( sk7 != q_nil )
| ( A != sk10 ) ),
inference(paramod_ordered,[status(thm)],[11261,475]) ).
thf(11853,plain,
( ( elem @ ( last @ sk10 ) @ sk10 )
| ( sk7 != q_nil ) ),
inference(pattern_uni,[status(thm)],[11852:[bind(A,$thf( sk10 ))]]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_Down @ A )
!= ( m_Down @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
thf(300,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_Down @ A )
!= ( m_Down @ B ) ) )
& ( ( ( m_Down @ A )
!= ( m_Down @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(301,plain,
( ! [A: $i,B: $i] :
( ( A != B )
=> ( ( m_Down @ A )
!= ( m_Down @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( m_Down @ A )
!= ( m_Down @ B ) )
=> ( A != B ) ) ),
inference(miniscope,[status(thm)],[300]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_Down @ A )
!= ( m_Down @ B ) ) ),
inference(cnf,[status(esa)],[301]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_Down @ A )
!= ( m_Down @ B ) ) ),
inference(lifteq,[status(thm)],[303]) ).
thf(307,plain,
! [A: $i] :
( ( sk18 @ ( m_Down @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(m_Down),[sk18])]) ).
thf(3898,plain,
! [A: $i] :
( ( ( s @ nbr_proc )
!= ( host @ sk6 ) )
| ( ( host @ sk10 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,2088]) ).
thf(3899,plain,
( ( s @ nbr_proc )
!= ( host @ sk6 ) ),
inference(pattern_uni,[status(thm)],[3898:[bind(A,$thf( sk10 ))]]) ).
thf(25,axiom,
! [A: $i] :
~ ( setIn @ A @ setEmpty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(248,plain,
! [A: $i] :
~ ( setIn @ A @ setEmpty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NormQ @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(380,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NormQ @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4211,plain,
( ( s @ ( host @ sk6 ) )
!= ( s @ zero ) ),
inference(paramod_ordered,[status(thm)],[507,4194]) ).
thf(4216,plain,
( ( host @ sk6 )
!= zero ),
inference(simp,[status(thm)],[4211]) ).
thf(5028,plain,
! [A: $i] :
( ~ ( elem @ ( m_Ldr @ A ) @ ( queue @ ( host @ sk6 ) ) )
| ( ( host @ sk10 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,1028]) ).
thf(5029,plain,
~ ( elem @ ( m_Ldr @ sk10 ) @ ( queue @ ( host @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[5028:[bind(A,$thf( sk10 ))]]) ).
thf(5922,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Ldr @ sk10 ) @ ( queue @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,5029]) ).
thf(5969,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk10 ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ sk6 ) ) ) ),
inference(simp,[status(thm)],[5922]) ).
thf(6020,plain,
! [A: $i] :
( ( cons @ ( m_Ldr @ sk10 ) @ A )
!= ( queue @ ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[5969]) ).
thf(5692,plain,
! [A: $i] :
( ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ sk2 ) ) )
| ( ( host @ sk7 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[116,1110]) ).
thf(5693,plain,
~ ( elem @ ( m_Down @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5692:[bind(A,$thf( sk7 ))]]) ).
thf(6480,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Down @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,5693]) ).
thf(6510,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Down @ sk7 ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6480]) ).
thf(6571,plain,
! [A: $i] :
( ( snoc @ A @ ( m_Down @ sk7 ) )
!= ( queue @ ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[6510]) ).
thf(6441,plain,
( ( pendack != status )
| ( ( host @ sk2 )
!= elec_2 )
| ( ( host @ sk3 )
!= ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[560,6380]) ).
thf(6442,plain,
( ( pendack != status )
| ( ( host @ sk2 )
!= elec_2 ) ),
inference(pattern_uni,[status(thm)],[6441:[]]) ).
thf(692,plain,
! [A: $i] :
( ( pendack != status )
| ( leq @ elec_2 @ nbr_proc )
| ( ( host @ sk3 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[560,233]) ).
thf(693,plain,
( ( pendack != status )
| ( leq @ elec_2 @ nbr_proc ) ),
inference(pattern_uni,[status(thm)],[692:[bind(A,$thf( sk3 ))]]) ).
thf(2053,plain,
! [A: $i] :
( ( pendack != status )
| ( ( leq @ ( s @ A ) @ A )
!= ( leq @ elec_2 @ nbr_proc ) ) ),
inference(paramod_ordered,[status(thm)],[693,405]) ).
thf(2066,plain,
! [A: $i] :
( ( pendack != status )
| ( ( s @ A )
!= elec_2 )
| ( A != nbr_proc ) ),
inference(simp,[status(thm)],[2053]) ).
thf(2083,plain,
( ( pendack != status )
| ( ( s @ nbr_proc )
!= elec_2 ) ),
inference(simp,[status(thm)],[2066]) ).
thf(6488,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Down @ sk10 ) @ ( queue @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,5707]) ).
thf(6502,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Down @ sk10 ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ sk6 ) ) ) ),
inference(simp,[status(thm)],[6488]) ).
thf(6563,plain,
! [A: $i] :
( ( snoc @ A @ ( m_Down @ sk10 ) )
!= ( queue @ ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[6502]) ).
thf(9687,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ sk6 ) ) )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ B @ ( m_Down @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[395,6563]) ).
thf(9688,plain,
( ( cons @ ( m_Down @ sk10 ) @ q_nil )
!= ( queue @ ( host @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[9687:[bind(A,$thf( m_Down @ sk10 )),bind(B,$thf( q_nil ))]]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( s @ A ) @ ( s @ B ) )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[257]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( leq @ ( s @ A ) @ ( s @ B ) )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[258]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Halt @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(346,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Halt @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(347,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
= ( m_Halt @ C ) ),
inference(miniscope,[status(thm)],[346]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_Halt @ C ) ),
inference(cnf,[status(esa)],[347]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_Halt @ C ) ),
inference(lifteq,[status(thm)],[348]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( tail @ ( cons @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[265]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ( tail @ ( cons @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[266]) ).
thf(5753,plain,
! [B: $i,A: $i] :
( ( ( tail @ ( queue @ ( host @ sk2 ) ) )
= B )
| ( ( cons @ ( m_Down @ sk3 ) @ sk1 )
!= ( cons @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[135,267]) ).
thf(5754,plain,
( ( tail @ ( queue @ ( host @ sk2 ) ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[5753:[bind(A,$thf( m_Down @ sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(71,plain,
! [A: $i] :
( ( ( index @ status @ ( host @ A ) )
!= elec_1 )
| ~ ( setIn @ A @ alive )
| ( ( index @ elid @ ( host @ A ) )
= A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(136,plain,
! [A: $i] :
( ( ( index @ status @ ( host @ A ) )
!= elec_1 )
| ( ( index @ elid @ ( host @ A ) )
= A )
| ~ ( setIn @ A @ alive ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(137,plain,
! [A: $i] :
( ( ( index @ status @ ( host @ A ) )
!= elec_1 )
| ( ( index @ elid @ ( host @ A ) )
= A )
| ~ ( setIn @ A @ alive ) ),
inference(simp,[status(thm)],[136]) ).
thf(21627,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ ( s @ ( s @ zero ) ) @ ( s @ nbr_proc ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21471,259]) ).
thf(21628,plain,
leq @ ( s @ ( s @ ( s @ zero ) ) ) @ ( s @ ( s @ nbr_proc ) ),
inference(pattern_uni,[status(thm)],[21627:[bind(A,$thf( s @ ( s @ zero ) )),bind(B,$thf( s @ nbr_proc ))]]) ).
thf(90,plain,
! [A: $i] :
( ( leq @ ( host @ sk10 ) @ A )
| ~ ( leq @ ( s @ zero ) @ A )
| ( setIn @ A @ ( index @ down @ ( host @ sk10 ) ) )
| ( A
= ( host @ sk9 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(163,plain,
! [A: $i] :
( ( A
= ( host @ sk9 ) )
| ( leq @ ( host @ sk10 ) @ A )
| ~ ( leq @ ( s @ zero ) @ A )
| ( setIn @ A @ ( index @ down @ ( host @ sk10 ) ) ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(164,plain,
! [A: $i] :
( ( A
= ( host @ sk9 ) )
| ( leq @ ( host @ sk10 ) @ A )
| ~ ( leq @ ( s @ zero ) @ A )
| ( setIn @ A @ ( index @ down @ ( host @ sk10 ) ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(14804,plain,
! [A: $i] :
( ( A
= ( host @ sk9 ) )
| ( leq @ ( host @ sk6 ) @ A )
| ~ ( leq @ ( s @ zero ) @ A )
| ( setIn @ A @ ( index @ down @ ( host @ sk6 ) ) ) ),
inference(rewrite,[status(thm)],[164,151]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Ldr @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(458,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Ldr @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(459,plain,
~ ? [A: $i,B: $i] :
( ( m_Down @ A )
= ( m_Ldr @ B ) ),
inference(miniscope,[status(thm)],[458]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_Ldr @ B ) ),
inference(cnf,[status(esa)],[459]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_Ldr @ B ) ),
inference(lifteq,[status(thm)],[460]) ).
thf(5900,plain,
! [C: $i,B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,1110]) ).
thf(5932,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( m_Down @ C ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ C ) ) ) ),
inference(simp,[status(thm)],[5900]) ).
thf(5983,plain,
! [B: $i,A: $i] :
( ( cons @ ( m_Down @ B ) @ A )
!= ( queue @ ( host @ B ) ) ),
inference(simp,[status(thm)],[5932]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_NotNorm @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(197,plain,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_NotNorm @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( head @ ( cons @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[216]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( head @ ( cons @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[217]) ).
thf(3967,plain,
! [B: $i,A: $i] :
( ( ( head @ ( queue @ ( host @ sk2 ) ) )
= A )
| ( ( cons @ ( m_Down @ sk3 ) @ sk1 )
!= ( cons @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[135,218]) ).
thf(3968,plain,
( ( head @ ( queue @ ( host @ sk2 ) ) )
= ( m_Down @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3967:[bind(A,$thf( m_Down @ sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(6349,plain,
( ( elem @ ( m_Down @ sk3 ) @ ( queue @ ( host @ sk2 ) ) )
!= ( elem @ ( m_Ldr @ sk3 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5917,580]) ).
thf(6400,plain,
( ( ( m_Down @ sk3 )
!= ( m_Ldr @ sk3 ) )
| ( ( queue @ ( host @ sk2 ) )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6349]) ).
thf(6413,plain,
( ( m_Down @ sk3 )
!= ( m_Ldr @ sk3 ) ),
inference(simp,[status(thm)],[6400]) ).
thf(21636,plain,
! [A: $i] :
( ( leq @ ( s @ ( s @ zero ) ) @ ( s @ nbr_proc ) )
!= ( leq @ ( s @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[21471,405]) ).
thf(21644,plain,
! [A: $i] :
( ( ( s @ ( s @ zero ) )
!= ( s @ A ) )
| ( ( s @ nbr_proc )
!= A ) ),
inference(simp,[status(thm)],[21636]) ).
thf(21668,plain,
( ( s @ ( s @ nbr_proc ) )
!= ( s @ ( s @ zero ) ) ),
inference(simp,[status(thm)],[21644]) ).
thf(11674,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( nil != q_nil )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[11261,468]) ).
thf(11675,plain,
( ( elem @ ( last @ sk2 ) @ sk2 )
| ( nil != q_nil ) ),
inference(pattern_uni,[status(thm)],[11674:[bind(A,$thf( sk2 ))]]) ).
thf(14618,plain,
! [A: $i] :
( ( nil != q_nil )
| ( ( elem @ ( last @ sk2 ) @ sk2 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[11675,421]) ).
thf(14732,plain,
! [A: $i] :
( ( nil != q_nil )
| ( ( last @ sk2 )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[14618]) ).
thf(14753,plain,
( ( nil != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[14732]) ).
thf(6,axiom,
! [A: $i] :
( ( pidMsg @ ( m_Halt @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(186,plain,
! [A: $i] :
( ( pidMsg @ ( m_Halt @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(187,plain,
! [A: $i] :
( ( pidMsg @ ( m_Halt @ A ) )
= A ),
inference(cnf,[status(esa)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( pidMsg @ ( m_Halt @ A ) )
= A ),
inference(lifteq,[status(thm)],[187]) ).
thf(53,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(386,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(387,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[386]) ).
thf(388,plain,
wait != norm,
inference(lifteq,[status(thm)],[387]) ).
thf(12795,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( ( host @ sk6 )
= ( host @ q_nil ) )
| ( A != sk10 ) ),
inference(paramod_ordered,[status(thm)],[11261,151]) ).
thf(12796,plain,
( ( elem @ ( last @ sk10 ) @ sk10 )
| ( ( host @ sk6 )
= ( host @ q_nil ) ) ),
inference(pattern_uni,[status(thm)],[12795:[bind(A,$thf( sk10 ))]]) ).
thf(10590,plain,
! [B: $i,A: $i] :
( ( leq @ A @ ( s @ A ) )
!= ( leq @ ( s @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[9754,405]) ).
thf(10607,plain,
! [B: $i,A: $i] :
( ( A
!= ( s @ B ) )
| ( ( s @ A )
!= B ) ),
inference(simp,[status(thm)],[10590]) ).
thf(10631,plain,
! [A: $i] :
( ( s @ ( s @ A ) )
!= A ),
inference(simp,[status(thm)],[10607]) ).
thf(12799,plain,
! [B: $i,A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( q_nil != B )
| ( A
!= ( s @ ( s @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11261,10631]) ).
thf(12800,plain,
! [A: $i] :
( ( elem @ ( last @ ( s @ ( s @ A ) ) ) @ ( s @ ( s @ A ) ) )
| ( q_nil != A ) ),
inference(pattern_uni,[status(thm)],[12799:[bind(A,$thf( s @ ( s @ D ) )),bind(B,$thf( D ))]]) ).
thf(13344,plain,
elem @ ( last @ ( s @ ( s @ q_nil ) ) ) @ ( s @ ( s @ q_nil ) ),
inference(simp,[status(thm)],[12800]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( m_NotNorm @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( m_NotNorm @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(167,plain,
~ ? [A: $i,B: $i] :
( ( m_NotNorm @ A )
= ( m_Halt @ B ) ),
inference(miniscope,[status(thm)],[166]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( m_NotNorm @ A )
!= ( m_Halt @ B ) ),
inference(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( m_NotNorm @ A )
!= ( m_Halt @ B ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(2052,plain,
! [A: $i] :
( ( leq @ ( s @ A ) @ A )
!= ( leq @ ( host @ sk2 ) @ ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[85,405]) ).
thf(2067,plain,
! [A: $i] :
( ( ( s @ A )
!= ( host @ sk2 ) )
| ( A
!= ( host @ sk3 ) ) ),
inference(simp,[status(thm)],[2052]) ).
thf(2084,plain,
( ( s @ ( host @ sk3 ) )
!= ( host @ sk2 ) ),
inference(simp,[status(thm)],[2067]) ).
thf(2498,plain,
( ( ( host @ sk8 )
!= ( host @ sk2 ) )
| ( ( s @ ( host @ sk6 ) )
!= ( s @ ( host @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[507,2084]) ).
thf(2505,plain,
( ( sk8 != sk2 )
| ( ( host @ sk6 )
!= ( host @ sk3 ) ) ),
inference(simp,[status(thm)],[2498]) ).
thf(9063,plain,
( ( sk8 != sk2 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[2505]) ).
thf(6430,plain,
sk3 != sk2,
inference(simp,[status(thm)],[6380]) ).
thf(12767,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( sk2 != q_nil )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[11261,6430]) ).
thf(12768,plain,
( ( elem @ ( last @ sk3 ) @ sk3 )
| ( sk2 != q_nil ) ),
inference(pattern_uni,[status(thm)],[12767:[bind(A,$thf( sk3 ))]]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NotNorm @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NotNorm @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(223,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
= ( m_NotNorm @ C ) ),
inference(miniscope,[status(thm)],[222]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_NotNorm @ C ) ),
inference(cnf,[status(esa)],[223]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_NotNorm @ C ) ),
inference(lifteq,[status(thm)],[224]) ).
thf(94,plain,
setIn @ ( host @ sk6 ) @ ( index @ acks @ ( host @ sk2 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(249,plain,
~ ? [A: $i] : ( setIn @ A @ setEmpty ),
inference(miniscope,[status(thm)],[248]) ).
thf(250,plain,
! [A: $i] :
~ ( setIn @ A @ setEmpty ),
inference(cnf,[status(esa)],[249]) ).
thf(599,plain,
! [A: $i] :
( ( setIn @ ( host @ sk6 ) @ ( index @ acks @ ( host @ sk2 ) ) )
!= ( setIn @ A @ setEmpty ) ),
inference(paramod_ordered,[status(thm)],[94,250]) ).
thf(615,plain,
! [A: $i] :
( ( ( host @ sk6 )
!= A )
| ( ( index @ acks @ ( host @ sk2 ) )
!= setEmpty ) ),
inference(simp,[status(thm)],[599]) ).
thf(618,plain,
( ( index @ acks @ ( host @ sk2 ) )
!= setEmpty ),
inference(simp,[status(thm)],[615]) ).
thf(673,plain,
( ( setEmpty != elec_2 )
| ( ( index @ acks @ ( host @ sk2 ) )
!= ( index @ status @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,618]) ).
thf(683,plain,
( ( setEmpty != elec_2 )
| ( acks != status )
| ( ( host @ sk2 )
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[673]) ).
thf(686,plain,
( ( setEmpty != elec_2 )
| ( acks != status ) ),
inference(simp,[status(thm)],[683]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,plain,
setIn @ sk10 @ alive,
inference(cnf,[status(esa)],[70]) ).
thf(471,plain,
sk10 != sk2,
inference(simp,[status(thm)],[123]) ).
thf(6476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ D )
!= ( host @ C ) )
| ( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,118]) ).
thf(6529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D != C )
| ( A
!= ( m_Down @ D ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ C ) ) ) ),
inference(simp,[status(thm)],[6476]) ).
thf(6539,plain,
! [B: $i,A: $i] :
( ( snoc @ A @ ( m_Down @ B ) )
!= ( queue @ ( host @ B ) ) ),
inference(simp,[status(thm)],[6529]) ).
thf(522,plain,
( ( leq @ nbr_proc @ ( host @ sk2 ) )
| ( ( host @ sk8 )
!= ( host @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[116,508]) ).
thf(524,plain,
( ( leq @ nbr_proc @ ( host @ sk2 ) )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[522]) ).
thf(2057,plain,
! [A: $i] :
( ( sk8 != sk7 )
| ( ( leq @ ( s @ A ) @ A )
!= ( leq @ nbr_proc @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[524,405]) ).
thf(2068,plain,
! [A: $i] :
( ( sk8 != sk7 )
| ( ( s @ A )
!= nbr_proc )
| ( A
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[2057]) ).
thf(2085,plain,
( ( sk8 != sk7 )
| ( ( s @ ( host @ sk2 ) )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2068]) ).
thf(675,plain,
( ( ( host @ sk3 )
!= setEmpty )
| ( ( index @ acks @ ( host @ sk2 ) )
!= ( index @ pendack @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[132,618]) ).
thf(682,plain,
( ( ( host @ sk3 )
!= setEmpty )
| ( acks != pendack )
| ( ( host @ sk2 )
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[675]) ).
thf(685,plain,
( ( ( host @ sk3 )
!= setEmpty )
| ( acks != pendack ) ),
inference(simp,[status(thm)],[682]) ).
thf(697,plain,
( ( ( host @ sk6 )
!= setEmpty )
| ( acks != pendack )
| ( ( host @ sk10 )
!= ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[151,685]) ).
thf(701,plain,
( ( ( host @ sk6 )
!= setEmpty )
| ( acks != pendack )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[697]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive )
| ( ( index @ ldr @ ( host @ A ) )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ A ) )
!= norm )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ( B = A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( index @ ldr @ ( host @ A ) )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ A ) )
!= norm )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ( B = A )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( ( index @ ldr @ ( host @ A ) )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ A ) )
!= norm )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ( B = A )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive ) ),
inference(simp,[status(thm)],[128]) ).
thf(3919,plain,
( ( pendack != status )
| ( nbr_proc != elec_2 )
| ( ( host @ sk6 )
!= ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[560,3905]) ).
thf(3920,plain,
( ( pendack != status )
| ( nbr_proc != elec_2 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[3919]) ).
thf(11926,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( setIn @ q_nil @ alive )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[11261,74]) ).
thf(11927,plain,
( ( elem @ ( last @ sk2 ) @ sk2 )
| ( setIn @ q_nil @ alive ) ),
inference(pattern_uni,[status(thm)],[11926:[bind(A,$thf( sk2 ))]]) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( setIn @ ( sk4 @ D @ C @ B @ A ) @ ( index @ down @ ( host @ D ) ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( setIn @ ( sk4 @ D @ C @ B @ A ) @ ( index @ down @ ( host @ D ) ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( setIn @ ( sk4 @ D @ C @ B @ A ) @ ( index @ down @ ( host @ D ) ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Down @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(241,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Down @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(242,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
= ( m_Down @ C ) ),
inference(miniscope,[status(thm)],[241]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_Down @ C ) ),
inference(cnf,[status(esa)],[242]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_Down @ C ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(203,plain,
~ ? [A: $i,B: $i] :
( ( m_NormQ @ A )
= ( m_Halt @ B ) ),
inference(miniscope,[status(thm)],[202]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( m_NormQ @ A )
!= ( m_Halt @ B ) ),
inference(cnf,[status(esa)],[203]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( m_NormQ @ A )
!= ( m_Halt @ B ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(311,plain,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(9715,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ sk2 ) ) )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ B @ ( m_Down @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[395,6571]) ).
thf(9716,plain,
( ( cons @ ( m_Down @ sk7 ) @ q_nil )
!= ( queue @ ( host @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9715:[bind(A,$thf( m_Down @ sk7 )),bind(B,$thf( q_nil ))]]) ).
thf(397,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[396]) ).
thf(398,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[397]) ).
thf(41,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_09) ).
thf(343,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(235,plain,
~ ? [A: $i,B: $i] :
( ( m_Down @ A )
= ( m_NotNorm @ B ) ),
inference(miniscope,[status(thm)],[234]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_NotNorm @ B ) ),
inference(cnf,[status(esa)],[235]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_NotNorm @ B ) ),
inference(lifteq,[status(thm)],[236]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ordered @ ( cons @ ( m_Halt @ B ) @ A ) )
& ( ( host @ B )
= ( host @ C ) )
& ( elem @ ( m_Down @ C ) @ A ) )
=> ( leq @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(412,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ordered @ ( cons @ ( m_Halt @ B ) @ A ) )
& ( ( host @ B )
= ( host @ C ) )
& ( elem @ ( m_Down @ C ) @ A ) )
=> ( leq @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(6481,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Ldr @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,5015]) ).
thf(6500,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk7 ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6481]) ).
thf(6561,plain,
! [A: $i] :
( ( snoc @ A @ ( m_Ldr @ sk7 ) )
!= ( queue @ ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[6500]) ).
thf(108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk4 @ D @ C @ B @ A )
!= ( host @ C ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk4 @ D @ C @ B @ A )
!= ( host @ C ) )
| ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk4 @ D @ C @ B @ A )
!= ( host @ C ) )
| ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(22050,plain,
! [A: $i] :
( ( leq @ ( s @ ( host @ sk2 ) ) @ ( s @ ( host @ sk3 ) ) )
!= ( leq @ ( s @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[21479,405]) ).
thf(22061,plain,
! [A: $i] :
( ( ( s @ ( host @ sk2 ) )
!= ( s @ A ) )
| ( ( s @ ( host @ sk3 ) )
!= A ) ),
inference(simp,[status(thm)],[22050]) ).
thf(22096,plain,
( ( s @ ( s @ ( host @ sk3 ) ) )
!= ( s @ ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[22061]) ).
thf(262,plain,
~ ? [A: $i,B: $i] :
( ( m_Down @ A )
= ( m_Halt @ B ) ),
inference(miniscope,[status(thm)],[261]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_Halt @ B ) ),
inference(cnf,[status(esa)],[262]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_Halt @ B ) ),
inference(lifteq,[status(thm)],[263]) ).
thf(9020,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ sk2 ) ) )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ B @ ( m_Ldr @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[395,6561]) ).
thf(9021,plain,
( ( cons @ ( m_Ldr @ sk7 ) @ q_nil )
!= ( queue @ ( host @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9020:[bind(A,$thf( m_Ldr @ sk7 )),bind(B,$thf( q_nil ))]]) ).
thf(3887,plain,
! [A: $i] :
( ( ( s @ nbr_proc )
!= ( host @ sk2 ) )
| ( ( host @ sk7 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[116,2088]) ).
thf(3888,plain,
( ( s @ nbr_proc )
!= ( host @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3887:[bind(A,$thf( sk7 ))]]) ).
thf(171,plain,
( ! [A: $i,B: $i] :
( ( A != B )
=> ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) )
=> ( A != B ) ) ),
inference(miniscope,[status(thm)],[170]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) ) ),
inference(cnf,[status(esa)],[171]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Halt @ B ) )
| ( pidElem @ A ) ),
inference(cnf,[status(esa)],[281]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Halt @ B ) )
| ( pidElem @ A ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(286,plain,
! [A: $i] : ( pidElem @ ( m_Halt @ A ) ),
inference(simp,[status(thm)],[285]) ).
thf(18860,plain,
! [A: $i] :
( ( sk3 != q_nil )
| ( ( elem @ ( last @ sk7 ) @ sk7 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12447,421]) ).
thf(18953,plain,
! [A: $i] :
( ( sk3 != q_nil )
| ( ( last @ sk7 )
!= A )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[18860]) ).
thf(19000,plain,
( ( sk3 != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[18953]) ).
thf(10544,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Ldr @ sk8 ) @ ( queue @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,9799]) ).
thf(10551,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk8 ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ sk6 ) ) ) ),
inference(simp,[status(thm)],[10544]) ).
thf(10557,plain,
! [A: $i] :
( ( cons @ ( m_Ldr @ sk8 ) @ A )
!= ( queue @ ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[10551]) ).
thf(98,plain,
! [A: $i] :
( ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ~ ( setIn @ A @ alive )
| ( ( index @ elid @ ( host @ A ) )
= A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(143,plain,
! [A: $i] :
( ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ elid @ ( host @ A ) )
= A )
| ~ ( setIn @ A @ alive ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(144,plain,
! [A: $i] :
( ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ elid @ ( host @ A ) )
= A )
| ~ ( setIn @ A @ alive ) ),
inference(simp,[status(thm)],[143]) ).
thf(11918,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( ( host @ sk2 )
= ( host @ q_nil ) )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[11261,116]) ).
thf(11919,plain,
( ( elem @ ( last @ sk7 ) @ sk7 )
| ( ( host @ sk2 )
= ( host @ q_nil ) ) ),
inference(pattern_uni,[status(thm)],[11918:[bind(A,$thf( sk7 ))]]) ).
thf(43,axiom,
! [A: $i] : ( leq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(350,plain,
! [A: $i] : ( leq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9812,plain,
! [A: $i] :
( ( leq @ ( s @ A ) @ A )
!= ( leq @ ( host @ sk6 ) @ ( host @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[9756,405]) ).
thf(9821,plain,
! [A: $i] :
( ( ( s @ A )
!= ( host @ sk6 ) )
| ( A
!= ( host @ sk8 ) ) ),
inference(simp,[status(thm)],[9812]) ).
thf(9835,plain,
( ( s @ ( host @ sk8 ) )
!= ( host @ sk6 ) ),
inference(simp,[status(thm)],[9821]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ A ) ) )
| ( ( index @ status @ ( host @ B ) )
!= elec_2 )
| ( leq @ ( index @ pendack @ ( host @ B ) ) @ ( host @ A ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( ( index @ status @ ( host @ B ) )
!= elec_2 )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ A ) ) )
| ( leq @ ( index @ pendack @ ( host @ B ) ) @ ( host @ A ) ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( ( index @ status @ ( host @ B ) )
!= elec_2 )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ B @ alive )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ A ) ) )
| ( leq @ ( index @ pendack @ ( host @ B ) ) @ ( host @ A ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(106,plain,
elem @ ( m_Down @ sk8 ) @ ( snoc @ ( queue @ ( host @ sk10 ) ) @ ( m_Ldr @ sk2 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(659,plain,
elem @ ( m_Down @ sk8 ) @ ( snoc @ ( queue @ ( host @ sk6 ) ) @ ( m_Ldr @ sk2 ) ),
inference(rewrite,[status(thm)],[106,151]) ).
thf(660,plain,
! [A: $i] :
( ( elem @ ( m_Down @ sk8 ) @ ( snoc @ ( queue @ ( host @ sk6 ) ) @ ( m_Ldr @ sk2 ) ) )
!= ( elem @ A @ q_nil ) ),
inference(paramod_ordered,[status(thm)],[659,421]) ).
thf(666,plain,
! [A: $i] :
( ( ( m_Down @ sk8 )
!= A )
| ( ( snoc @ ( queue @ ( host @ sk6 ) ) @ ( m_Ldr @ sk2 ) )
!= q_nil ) ),
inference(simp,[status(thm)],[660]) ).
thf(672,plain,
( ( snoc @ ( queue @ ( host @ sk6 ) ) @ ( m_Ldr @ sk2 ) )
!= q_nil ),
inference(simp,[status(thm)],[666]) ).
thf(12081,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( setIn @ q_nil @ alive )
| ( A != sk10 ) ),
inference(paramod_ordered,[status(thm)],[11261,109]) ).
thf(12082,plain,
( ( elem @ ( last @ sk10 ) @ sk10 )
| ( setIn @ q_nil @ alive ) ),
inference(pattern_uni,[status(thm)],[12081:[bind(A,$thf( sk10 ))]]) ).
thf(59,axiom,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( cons @ ( head @ A ) @ ( tail @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(406,plain,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( cons @ ( head @ A ) @ ( tail @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( setIn @ ( sk5 @ C @ B @ A ) @ ( index @ down @ ( host @ C ) ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ~ ( setIn @ D @ alive )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm ) ),
inference(cnf,[status(esa)],[70]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ~ ( setIn @ ( sk5 @ C @ B @ A ) @ ( index @ down @ ( host @ C ) ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ~ ( setIn @ ( sk5 @ C @ B @ A ) @ ( index @ down @ ( host @ C ) ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(simp,[status(thm)],[112]) ).
thf(538,plain,
! [A: $i] :
( ( setIn @ sk7 @ alive )
!= ( setIn @ A @ setEmpty ) ),
inference(paramod_ordered,[status(thm)],[82,250]) ).
thf(541,plain,
! [A: $i] :
( ( sk7 != A )
| ( setEmpty != alive ) ),
inference(simp,[status(thm)],[538]) ).
thf(544,plain,
setEmpty != alive,
inference(simp,[status(thm)],[541]) ).
thf(12667,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( q_nil != alive )
| ( A != setEmpty ) ),
inference(paramod_ordered,[status(thm)],[11261,544]) ).
thf(12668,plain,
( ( elem @ ( last @ setEmpty ) @ setEmpty )
| ( q_nil != alive ) ),
inference(pattern_uni,[status(thm)],[12667:[bind(A,$thf( setEmpty ))]]) ).
thf(12790,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( setIn @ q_nil @ alive )
| ( A != sk7 ) ),
inference(paramod_ordered,[status(thm)],[11261,82]) ).
thf(12791,plain,
( ( elem @ ( last @ sk7 ) @ sk7 )
| ( setIn @ q_nil @ alive ) ),
inference(pattern_uni,[status(thm)],[12790:[bind(A,$thf( sk7 ))]]) ).
thf(9046,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ sk2 ) ) )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ B @ ( m_Ldr @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[395,6562]) ).
thf(9047,plain,
( ( cons @ ( m_Ldr @ sk3 ) @ q_nil )
!= ( queue @ ( host @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[9046:[bind(A,$thf( m_Ldr @ sk3 )),bind(B,$thf( q_nil ))]]) ).
thf(207,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[206]) ).
thf(208,plain,
wait != elec_1,
inference(lifteq,[status(thm)],[207]) ).
thf(344,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[343]) ).
thf(345,plain,
norm != elec_2,
inference(lifteq,[status(thm)],[344]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NormQ @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(323,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NormQ @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6387,plain,
( ( elem @ ( m_Down @ sk3 ) @ ( queue @ ( host @ sk2 ) ) )
!= ( elem @ ( m_Ldr @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5917,5015]) ).
thf(6398,plain,
( ( ( m_Down @ sk3 )
!= ( m_Ldr @ sk7 ) )
| ( ( queue @ ( host @ sk2 ) )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6387]) ).
thf(6429,plain,
( ( m_Down @ sk3 )
!= ( m_Ldr @ sk7 ) ),
inference(simp,[status(thm)],[6398]) ).
thf(22117,plain,
! [A: $i] :
( ( q_nil != alive )
| ( ( elem @ ( last @ setEmpty ) @ setEmpty )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12668,421]) ).
thf(22217,plain,
! [A: $i] :
( ( q_nil != alive )
| ( ( last @ setEmpty )
!= A )
| ( setEmpty != q_nil ) ),
inference(simp,[status(thm)],[22117]) ).
thf(22283,plain,
( ( q_nil != alive )
| ( setEmpty != q_nil ) ),
inference(simp,[status(thm)],[22217]) ).
thf(699,plain,
( ( pendack != status )
| ( setEmpty != elec_2 )
| ( acks != pendack )
| ( ( host @ sk3 )
!= ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[560,685]) ).
thf(700,plain,
( ( pendack != status )
| ( setEmpty != elec_2 )
| ( acks != pendack ) ),
inference(pattern_uni,[status(thm)],[699:[]]) ).
thf(239,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[238]) ).
thf(240,plain,
norm != elec_1,
inference(lifteq,[status(thm)],[239]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(251,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( host @ D ) @ ( sk4 @ D @ C @ B @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( leq @ ( host @ D ) @ ( sk4 @ D @ C @ B @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ A ) )
!= elec_2 )
| ( ( index @ status @ ( host @ D ) )
!= elec_1 )
| ~ ( leq @ ( host @ D ) @ ( sk4 @ D @ C @ B @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( leq @ ( host @ A ) @ ( host @ D ) )
| ~ ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ D ) ) )
| ~ ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(21488,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ nbr_proc @ ( host @ sk3 ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[547,259]) ).
thf(21489,plain,
leq @ ( s @ nbr_proc ) @ ( s @ ( host @ sk3 ) ),
inference(pattern_uni,[status(thm)],[21488:[bind(A,$thf( nbr_proc )),bind(B,$thf( host @ sk3 ))]]) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( elem @ A @ C )
| ( elem @ A @ ( cons @ B @ C ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( elem @ A @ C )
| ( elem @ A @ ( cons @ B @ C ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(2048,plain,
! [A: $i] :
( ( leq @ ( s @ zero ) @ nbr_proc )
!= ( leq @ ( s @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[211,405]) ).
thf(2069,plain,
! [A: $i] :
( ( ( s @ zero )
!= ( s @ A ) )
| ( nbr_proc != A ) ),
inference(simp,[status(thm)],[2048]) ).
thf(2086,plain,
( ( s @ nbr_proc )
!= ( s @ zero ) ),
inference(simp,[status(thm)],[2069]) ).
thf(17438,plain,
! [A: $i] :
( ( elem @ ( last @ ( s @ ( s @ q_nil ) ) ) @ ( s @ ( s @ q_nil ) ) )
!= ( elem @ A @ q_nil ) ),
inference(paramod_ordered,[status(thm)],[13344,421]) ).
thf(17588,plain,
! [A: $i] :
( ( ( last @ ( s @ ( s @ q_nil ) ) )
!= A )
| ( ( s @ ( s @ q_nil ) )
!= q_nil ) ),
inference(simp,[status(thm)],[17438]) ).
thf(17647,plain,
( ( s @ ( s @ q_nil ) )
!= q_nil ),
inference(simp,[status(thm)],[17588]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( s @ ( host @ A ) )
= ( host @ B ) )
=> ( ( host @ A )
!= ( host @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_01) ).
thf(455,plain,
! [A: $i,B: $i] :
( ( ( s @ ( host @ A ) )
= ( host @ B ) )
=> ( ( host @ A )
!= ( host @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(5918,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Down @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,5693]) ).
thf(5925,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Down @ sk7 ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[5918]) ).
thf(5976,plain,
! [A: $i] :
( ( cons @ ( m_Down @ sk7 ) @ A )
!= ( queue @ ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[5925]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ ( s @ B ) )
<=> ( ( A
= ( s @ B ) )
| ( leq @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(438,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ ( s @ B ) )
=> ( ( A
= ( s @ B ) )
| ( leq @ A @ B ) ) )
& ( ( ( A
= ( s @ B ) )
| ( leq @ A @ B ) )
=> ( leq @ A @ ( s @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(490,plain,
sk6 != sk2,
inference(simp,[status(thm)],[481]) ).
thf(6386,plain,
( ( elem @ ( m_Down @ sk7 ) @ ( queue @ ( host @ sk2 ) ) )
!= ( elem @ ( m_Down @ sk3 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5917,5693]) ).
thf(6411,plain,
( ( ( m_Down @ sk7 )
!= ( m_Down @ sk3 ) )
| ( ( queue @ ( host @ sk2 ) )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[6386]) ).
thf(6417,plain,
( ( m_Down @ sk7 )
!= ( m_Down @ sk3 ) ),
inference(simp,[status(thm)],[6411]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ C @ B @ A )
!= ( host @ B ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ~ ( setIn @ D @ alive )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm ) ),
inference(cnf,[status(esa)],[70]) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ C @ B @ A )
!= ( host @ B ) )
| ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk5 @ C @ B @ A )
!= ( host @ B ) )
| ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(simp,[status(thm)],[161]) ).
thf(2468,plain,
( ( host @ sk10 )
!= ( host @ sk8 ) ),
inference(paramod_ordered,[status(thm)],[151,2454]) ).
thf(2471,plain,
sk10 != sk8,
inference(simp,[status(thm)],[2468]) ).
thf(598,plain,
( ( setIn @ ( host @ sk6 ) @ elec_2 )
| ( ( index @ acks @ ( host @ sk2 ) )
!= ( index @ status @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,94]) ).
thf(609,plain,
( ( setIn @ ( host @ sk6 ) @ elec_2 )
| ( acks != status )
| ( ( host @ sk2 )
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[598]) ).
thf(617,plain,
( ( setIn @ ( host @ sk6 ) @ elec_2 )
| ( acks != status ) ),
inference(simp,[status(thm)],[609]) ).
thf(14402,plain,
( ( elem @ ( last @ ( queue @ ( host @ sk2 ) ) ) @ ( queue @ ( host @ sk2 ) ) )
!= ( elem @ ( m_Ldr @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11667,5015]) ).
thf(14439,plain,
( ( ( last @ ( queue @ ( host @ sk2 ) ) )
!= ( m_Ldr @ sk7 ) )
| ( ( queue @ ( host @ sk2 ) )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[14402]) ).
thf(14530,plain,
( ( last @ ( queue @ ( host @ sk2 ) ) )
!= ( m_Ldr @ sk7 ) ),
inference(simp,[status(thm)],[14439]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NormQ @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(355,plain,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NormQ @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(6486,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Ldr @ sk10 ) @ ( queue @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,5029]) ).
thf(6496,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ sk10 ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ sk6 ) ) ) ),
inference(simp,[status(thm)],[6486]) ).
thf(6557,plain,
! [A: $i] :
( ( snoc @ A @ ( m_Ldr @ sk10 ) )
!= ( queue @ ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[6496]) ).
thf(252,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( m_Ack @ A @ C )
= ( m_Ack @ B @ D ) ) ),
inference(miniscope,[status(thm)],[251]) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( sk15 @ A @ ( m_Ack @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(m_Ack),[sk15])]) ).
thf(12084,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( sk2 != q_nil )
| ( A != sk10 ) ),
inference(paramod_ordered,[status(thm)],[11261,471]) ).
thf(12085,plain,
( ( elem @ ( last @ sk10 ) @ sk10 )
| ( sk2 != q_nil ) ),
inference(pattern_uni,[status(thm)],[12084:[bind(A,$thf( sk10 ))]]) ).
thf(18278,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( elem @ ( last @ sk10 ) @ sk10 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12085,421]) ).
thf(18360,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( last @ sk10 )
!= A )
| ( sk10 != q_nil ) ),
inference(simp,[status(thm)],[18278]) ).
thf(18434,plain,
( ( sk2 != q_nil )
| ( sk10 != q_nil ) ),
inference(simp,[status(thm)],[18360]) ).
thf(5905,plain,
! [C: $i,B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ B ) )
!= ( elem @ ( m_Ldr @ C ) @ ( queue @ ( host @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[277,1028]) ).
thf(5961,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( m_Ldr @ C ) )
| ( ( cons @ A @ B )
!= ( queue @ ( host @ C ) ) ) ),
inference(simp,[status(thm)],[5905]) ).
thf(6012,plain,
! [B: $i,A: $i] :
( ( cons @ ( m_Ldr @ B ) @ A )
!= ( queue @ ( host @ B ) ) ),
inference(simp,[status(thm)],[5961]) ).
thf(17878,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( elem @ ( last @ sk10 ) @ sk10 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[11853,421]) ).
thf(18011,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( last @ sk10 )
!= A )
| ( sk10 != q_nil ) ),
inference(simp,[status(thm)],[17878]) ).
thf(18060,plain,
( ( sk7 != q_nil )
| ( sk10 != q_nil ) ),
inference(simp,[status(thm)],[18011]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ A ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( host @ D )
!= ( host @ C ) )
| ~ ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ A ) ) )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ C ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ A ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( host @ D )
!= ( host @ C ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ A ) ) )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ C ) ) ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ A ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( host @ D )
!= ( host @ C ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ D ) @ ( queue @ ( host @ A ) ) )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ C ) ) ) ),
inference(simp,[status(thm)],[149]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ordered @ ( cons @ A @ B ) )
<=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ A ) @ ( pidMsg @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_53) ).
thf(327,plain,
! [A: $i,B: $i] :
( ( ( ordered @ ( cons @ A @ B ) )
=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ A ) @ ( pidMsg @ C ) ) ) ) )
& ( ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ A ) @ ( pidMsg @ C ) ) ) )
=> ( ordered @ ( cons @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) )
=> ( ( setIn @ A @ pids )
& ( setIn @ B @ pids ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(409,plain,
! [A: $i,B: $i] :
( ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) )
=> ( ( setIn @ A @ pids )
& ( setIn @ B @ pids ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(22956,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( elem @ ( last @ sk3 ) @ sk3 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12768,421]) ).
thf(23083,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( last @ sk3 )
!= A )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[22956]) ).
thf(23117,plain,
( ( sk2 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[23083]) ).
thf(177,plain,
! [A: $i] :
( ( sk11 @ ( m_NotNorm @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(m_NotNorm),[sk11])]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( snoc @ ( cons @ A @ C ) @ B )
= ( cons @ A @ ( snoc @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(370,plain,
! [A: $i,B: $i,C: $i] :
( ( snoc @ ( cons @ A @ C ) @ B )
= ( cons @ A @ ( snoc @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(76,plain,
( ( index @ status @ ( host @ sk10 ) )
= elec_1 ),
inference(cnf,[status(esa)],[70]) ).
thf(142,plain,
( ( index @ status @ ( host @ sk10 ) )
= elec_1 ),
inference(lifteq,[status(thm)],[76]) ).
thf(502,plain,
( ( index @ status @ ( host @ sk6 ) )
= elec_1 ),
inference(rewrite,[status(thm)],[142,151]) ).
thf(21731,plain,
! [A: $i] :
( ( leq @ ( s @ nbr_proc ) @ ( s @ ( host @ sk3 ) ) )
!= ( leq @ ( s @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[21489,405]) ).
thf(21757,plain,
! [A: $i] :
( ( ( s @ nbr_proc )
!= ( s @ A ) )
| ( ( s @ ( host @ sk3 ) )
!= A ) ),
inference(simp,[status(thm)],[21731]) ).
thf(21779,plain,
( ( s @ ( s @ ( host @ sk3 ) ) )
!= ( s @ nbr_proc ) ),
inference(simp,[status(thm)],[21757]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( leq @ ( host @ C ) @ ( sk5 @ C @ B @ A ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ~ ( setIn @ D @ alive )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm ) ),
inference(cnf,[status(esa)],[70]) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ~ ( leq @ ( host @ C ) @ ( sk5 @ C @ B @ A ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ~ ( leq @ ( host @ C ) @ ( sk5 @ C @ B @ A ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(simp,[status(thm)],[126]) ).
thf(12528,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( sk8 != q_nil )
| ( A != sk10 ) ),
inference(paramod_ordered,[status(thm)],[11261,2471]) ).
thf(12529,plain,
( ( elem @ ( last @ sk10 ) @ sk10 )
| ( sk8 != q_nil ) ),
inference(pattern_uni,[status(thm)],[12528:[bind(A,$thf( sk10 ))]]) ).
thf(12522,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( sk2 != q_nil )
| ( A != sk6 ) ),
inference(paramod_ordered,[status(thm)],[11261,490]) ).
thf(12523,plain,
( ( elem @ ( last @ sk6 ) @ sk6 )
| ( sk2 != q_nil ) ),
inference(pattern_uni,[status(thm)],[12522:[bind(A,$thf( sk6 ))]]) ).
thf(21503,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ nbr_proc @ ( host @ sk8 ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[508,259]) ).
thf(21504,plain,
leq @ ( s @ nbr_proc ) @ ( s @ ( host @ sk8 ) ),
inference(pattern_uni,[status(thm)],[21503:[bind(A,$thf( nbr_proc )),bind(B,$thf( host @ sk8 ))]]) ).
thf(19969,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( elem @ ( last @ sk6 ) @ sk6 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12523,421]) ).
thf(20096,plain,
! [A: $i] :
( ( sk2 != q_nil )
| ( ( last @ sk6 )
!= A )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[19969]) ).
thf(20103,plain,
( ( sk2 != q_nil )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[20096]) ).
thf(312,plain,
~ ? [A: $i,B: $i] :
( ( m_Ldr @ A )
= ( m_Halt @ B ) ),
inference(miniscope,[status(thm)],[311]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( m_Ldr @ A )
!= ( m_Halt @ B ) ),
inference(cnf,[status(esa)],[312]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( m_Ldr @ A )
!= ( m_Halt @ B ) ),
inference(lifteq,[status(thm)],[313]) ).
thf(21820,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ ( s @ nbr_proc ) @ ( s @ ( host @ sk8 ) ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21504,259]) ).
thf(21821,plain,
leq @ ( s @ ( s @ nbr_proc ) ) @ ( s @ ( s @ ( host @ sk8 ) ) ),
inference(pattern_uni,[status(thm)],[21820:[bind(A,$thf( s @ nbr_proc )),bind(B,$thf( s @ ( host @ sk8 ) ))]]) ).
thf(890,plain,
! [A: $i] :
( ( pendack != status )
| ( leq @ ( s @ zero ) @ elec_2 )
| ( ( host @ sk3 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[560,227]) ).
thf(891,plain,
( ( pendack != status )
| ( leq @ ( s @ zero ) @ elec_2 ) ),
inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( sk3 ))]]) ).
thf(21276,plain,
! [A: $i] :
( ( nil != q_nil )
| ( ( elem @ ( last @ sk7 ) @ sk7 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12666,421]) ).
thf(21377,plain,
! [A: $i] :
( ( nil != q_nil )
| ( ( last @ sk7 )
!= A )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[21276]) ).
thf(21411,plain,
( ( nil != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[21377]) ).
thf(11903,plain,
! [B: $i,A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( A
!= ( cons @ B @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[11261,2483]) ).
thf(11904,plain,
! [A: $i] : ( elem @ ( last @ ( cons @ A @ q_nil ) ) @ ( cons @ A @ q_nil ) ),
inference(pattern_uni,[status(thm)],[11903:[bind(A,$thf( cons @ C @ q_nil )),bind(B,$thf( C ))]]) ).
thf(13415,plain,
! [A: $i] : ( elem @ ( last @ ( cons @ A @ q_nil ) ) @ ( cons @ A @ q_nil ) ),
inference(simp,[status(thm)],[11904]) ).
thf(4241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( last @ ( cons @ A @ q_nil ) )
= B )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[395,221]) ).
thf(4242,plain,
! [A: $i] :
( ( last @ ( cons @ A @ q_nil ) )
= A ),
inference(pattern_uni,[status(thm)],[4241:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(18500,plain,
! [A: $i] : ( elem @ A @ ( cons @ A @ q_nil ) ),
inference(rewrite,[status(thm)],[13415,4242]) ).
thf(18512,plain,
! [B: $i,A: $i] :
( ( elem @ A @ ( cons @ A @ q_nil ) )
!= ( elem @ ( m_Ldr @ B ) @ ( queue @ ( host @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[18500,1028]) ).
thf(18588,plain,
! [B: $i,A: $i] :
( ( A
!= ( m_Ldr @ B ) )
| ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ B ) ) ) ),
inference(simp,[status(thm)],[18512]) ).
thf(18662,plain,
! [A: $i] :
( ( cons @ ( m_Ldr @ A ) @ q_nil )
!= ( queue @ ( host @ A ) ) ),
inference(simp,[status(thm)],[18588]) ).
thf(21056,plain,
( ( ( host @ sk8 )
!= nbr_proc )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[2122]) ).
thf(22719,plain,
! [A: $i] :
( ( leq @ ( s @ ( s @ ( s @ zero ) ) ) @ ( s @ ( s @ nbr_proc ) ) )
!= ( leq @ ( s @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[21628,405]) ).
thf(22746,plain,
! [A: $i] :
( ( ( s @ ( s @ ( s @ zero ) ) )
!= ( s @ A ) )
| ( ( s @ ( s @ nbr_proc ) )
!= A ) ),
inference(simp,[status(thm)],[22719]) ).
thf(22760,plain,
( ( s @ ( s @ ( s @ nbr_proc ) ) )
!= ( s @ ( s @ ( s @ zero ) ) ) ),
inference(simp,[status(thm)],[22746]) ).
thf(606,plain,
( ( setIn @ ( host @ sk6 ) @ ( index @ acks @ ( host @ sk2 ) ) )
!= ( setIn @ nil @ alive ) ),
inference(paramod_ordered,[status(thm)],[94,210]) ).
thf(607,plain,
( ( ( host @ sk6 )
!= nil )
| ( ( index @ acks @ ( host @ sk2 ) )
!= alive ) ),
inference(simp,[status(thm)],[606]) ).
thf(1328,plain,
( ( ( host @ sk6 )
!= nil )
| ( elec_2 != alive )
| ( ( index @ acks @ ( host @ sk2 ) )
!= ( index @ status @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,607]) ).
thf(1333,plain,
( ( ( host @ sk6 )
!= nil )
| ( elec_2 != alive )
| ( acks != status )
| ( ( host @ sk2 )
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1341,plain,
( ( ( host @ sk6 )
!= nil )
| ( elec_2 != alive )
| ( acks != status ) ),
inference(simp,[status(thm)],[1333]) ).
thf(21716,plain,
! [B: $i,A: $i] :
( ( leq @ ( s @ A ) @ ( s @ B ) )
| ( ( leq @ ( s @ nbr_proc ) @ ( s @ ( host @ sk3 ) ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21489,259]) ).
thf(21717,plain,
leq @ ( s @ ( s @ nbr_proc ) ) @ ( s @ ( s @ ( host @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[21716:[bind(A,$thf( s @ nbr_proc )),bind(B,$thf( s @ ( host @ sk3 ) ))]]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ B ) )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ C ) )
!= wait )
| ( ( host @ ( index @ elid @ ( host @ C ) ) )
!= ( host @ B ) )
| ~ ( setIn @ B @ alive )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ B ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ C ) )
!= wait )
| ( ( host @ ( index @ elid @ ( host @ C ) ) )
!= ( host @ B ) )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ B @ alive ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
= ( host @ B ) )
| ( ( host @ B )
!= ( host @ A ) )
| ( ( index @ status @ ( host @ C ) )
!= wait )
| ( ( host @ ( index @ elid @ ( host @ C ) ) )
!= ( host @ B ) )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ~ ( setIn @ C @ alive )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ B @ alive ) ),
inference(simp,[status(thm)],[138]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Ldr @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(415,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Ldr @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(416,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
= ( m_Ldr @ C ) ),
inference(miniscope,[status(thm)],[415]) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_Ldr @ C ) ),
inference(cnf,[status(esa)],[416]) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_Ldr @ C ) ),
inference(lifteq,[status(thm)],[417]) ).
thf(526,plain,
( ( leq @ nbr_proc @ elec_2 )
| ( ( index @ pendack @ ( host @ sk2 ) )
!= ( index @ status @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,89]) ).
thf(532,plain,
( ( leq @ nbr_proc @ elec_2 )
| ( pendack != status )
| ( ( host @ sk2 )
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[526]) ).
thf(536,plain,
( ( leq @ nbr_proc @ elec_2 )
| ( pendack != status ) ),
inference(simp,[status(thm)],[532]) ).
thf(2058,plain,
! [A: $i] :
( ( pendack != status )
| ( ( leq @ ( s @ A ) @ A )
!= ( leq @ nbr_proc @ elec_2 ) ) ),
inference(paramod_ordered,[status(thm)],[536,405]) ).
thf(2064,plain,
! [A: $i] :
( ( pendack != status )
| ( ( s @ A )
!= nbr_proc )
| ( A != elec_2 ) ),
inference(simp,[status(thm)],[2058]) ).
thf(2081,plain,
( ( pendack != status )
| ( ( s @ elec_2 )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2064]) ).
thf(18529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ C )
!= ( host @ B ) )
| ( ( elem @ A @ ( cons @ A @ q_nil ) )
!= ( elem @ ( m_Down @ C ) @ ( queue @ ( host @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18500,118]) ).
thf(18609,plain,
! [C: $i,B: $i,A: $i] :
( ( C != B )
| ( A
!= ( m_Down @ C ) )
| ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ B ) ) ) ),
inference(simp,[status(thm)],[18529]) ).
thf(18683,plain,
! [A: $i] :
( ( cons @ ( m_Down @ A ) @ q_nil )
!= ( queue @ ( host @ A ) ) ),
inference(simp,[status(thm)],[18609]) ).
thf(12079,plain,
! [A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( leq @ nbr_proc @ ( host @ q_nil ) )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[11261,547]) ).
thf(12080,plain,
( ( elem @ ( last @ sk3 ) @ sk3 )
| ( leq @ nbr_proc @ ( host @ q_nil ) ) ),
inference(pattern_uni,[status(thm)],[12079:[bind(A,$thf( sk3 ))]]) ).
thf(381,plain,
~ ? [A: $i,B: $i] :
( ( m_Down @ A )
= ( m_NormQ @ B ) ),
inference(miniscope,[status(thm)],[380]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_NormQ @ B ) ),
inference(cnf,[status(esa)],[381]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( m_Down @ A )
!= ( m_NormQ @ B ) ),
inference(lifteq,[status(thm)],[382]) ).
thf(2095,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[2086]) ).
thf(213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(cnf,[status(esa)],[212]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(447,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) ) )
& ( ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(21835,plain,
! [A: $i] :
( ( leq @ ( s @ nbr_proc ) @ ( s @ ( host @ sk8 ) ) )
!= ( leq @ ( s @ A ) @ A ) ),
inference(paramod_ordered,[status(thm)],[21504,405]) ).
thf(21855,plain,
! [A: $i] :
( ( ( s @ nbr_proc )
!= ( s @ A ) )
| ( ( s @ ( host @ sk8 ) )
!= A ) ),
inference(simp,[status(thm)],[21835]) ).
thf(21879,plain,
( ( s @ ( s @ ( host @ sk8 ) ) )
!= ( s @ nbr_proc ) ),
inference(simp,[status(thm)],[21855]) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( leq @ ( s @ zero ) @ ( sk5 @ C @ B @ A ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ~ ( setIn @ D @ alive )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm ) ),
inference(cnf,[status(esa)],[70]) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ( leq @ ( s @ zero ) @ ( sk5 @ C @ B @ A ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( host @ A )
!= ( s @ ( host @ C ) ) )
| ( ( index @ status @ ( host @ C ) )
!= elec_1 )
| ( ( index @ ldr @ ( host @ D ) )
!= ( host @ D ) )
| ( ( index @ status @ ( host @ D ) )
!= norm )
| ( leq @ ( s @ zero ) @ ( sk5 @ C @ B @ A ) )
| ~ ( setIn @ C @ alive )
| ~ ( leq @ nbr_proc @ ( s @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ C ) ) )
| ~ ( elem @ ( m_Down @ A ) @ ( queue @ ( host @ C ) ) )
| ~ ( setIn @ D @ alive ) ),
inference(simp,[status(thm)],[145]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ordered @ ( snoc @ B @ A ) )
<=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ C ) @ ( pidMsg @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_54) ).
thf(422,plain,
! [A: $i,B: $i] :
( ( ( ordered @ ( snoc @ B @ A ) )
=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ C ) @ ( pidMsg @ A ) ) ) ) )
& ( ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ C ) @ ( pidMsg @ A ) ) ) )
=> ( ordered @ ( snoc @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(562,plain,
( ( leq @ nbr_proc @ ( host @ sk6 ) )
| ( ( host @ sk10 )
!= ( host @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[151,547]) ).
thf(564,plain,
( ( leq @ nbr_proc @ ( host @ sk6 ) )
| ( sk10 != sk3 ) ),
inference(simp,[status(thm)],[562]) ).
thf(12705,plain,
! [C: $i,B: $i,A: $i] :
( ( elem @ ( last @ A ) @ A )
| ( A
!= ( snoc @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11261,231]) ).
thf(12706,plain,
! [B: $i,A: $i] : ( elem @ ( last @ ( snoc @ A @ B ) ) @ ( snoc @ A @ B ) ),
inference(pattern_uni,[status(thm)],[12705:[bind(A,$thf( snoc @ D @ E )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(13284,plain,
! [B: $i,A: $i] : ( elem @ ( last @ ( snoc @ A @ B ) ) @ ( snoc @ A @ B ) ),
inference(simp,[status(thm)],[12706]) ).
thf(20838,plain,
! [B: $i,A: $i] : ( elem @ B @ ( snoc @ A @ B ) ),
inference(rewrite,[status(thm)],[13284,221]) ).
thf(324,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
= ( m_NormQ @ C ) ),
inference(miniscope,[status(thm)],[323]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_NormQ @ C ) ),
inference(cnf,[status(esa)],[324]) ).
thf(326,plain,
! [C: $i,B: $i,A: $i] :
( ( m_Ack @ A @ B )
!= ( m_NormQ @ C ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(356,plain,
~ ? [A: $i,B: $i] :
( ( m_Ldr @ A )
= ( m_NormQ @ B ) ),
inference(miniscope,[status(thm)],[355]) ).
thf(357,plain,
! [B: $i,A: $i] :
( ( m_Ldr @ A )
!= ( m_NormQ @ B ) ),
inference(cnf,[status(esa)],[356]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( m_Ldr @ A )
!= ( m_NormQ @ B ) ),
inference(lifteq,[status(thm)],[357]) ).
thf(6469,plain,
! [C: $i,B: $i,A: $i] :
( ( elem @ A @ ( snoc @ B @ A ) )
!= ( elem @ ( m_Ldr @ C ) @ ( queue @ ( host @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[365,1028]) ).
thf(6497,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( m_Ldr @ C ) )
| ( ( snoc @ B @ A )
!= ( queue @ ( host @ C ) ) ) ),
inference(simp,[status(thm)],[6469]) ).
thf(6558,plain,
! [B: $i,A: $i] :
( ( snoc @ A @ ( m_Ldr @ B ) )
!= ( queue @ ( host @ B ) ) ),
inference(simp,[status(thm)],[6497]) ).
thf(2044,plain,
! [A: $i] :
( ( pendack != status )
| ( ( leq @ ( s @ A ) @ A )
!= ( leq @ ( host @ sk2 ) @ elec_2 ) ) ),
inference(paramod_ordered,[status(thm)],[629,405]) ).
thf(2074,plain,
! [A: $i] :
( ( pendack != status )
| ( ( s @ A )
!= ( host @ sk2 ) )
| ( A != elec_2 ) ),
inference(simp,[status(thm)],[2044]) ).
thf(2091,plain,
( ( pendack != status )
| ( ( s @ elec_2 )
!= ( host @ sk2 ) ) ),
inference(simp,[status(thm)],[2074]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( setIn @ B @ alive )
| ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ A ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ~ ( setIn @ B @ alive )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ A ) ) ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( ( index @ status @ ( host @ B ) )
!= norm )
| ( ( index @ ldr @ ( host @ B ) )
!= ( host @ B ) )
| ~ ( setIn @ B @ alive )
| ~ ( setIn @ A @ alive )
| ~ ( setIn @ ( host @ B ) @ ( index @ down @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(4205,plain,
! [A: $i] :
( ( pendack != status )
| ( ( s @ zero )
!= ( s @ elec_2 ) )
| ( ( host @ sk3 )
!= ( host @ A ) ) ),
inference(paramod_ordered,[status(thm)],[560,2090]) ).
thf(4206,plain,
( ( pendack != status )
| ( ( s @ zero )
!= ( s @ elec_2 ) ) ),
inference(pattern_uni,[status(thm)],[4205:[bind(A,$thf( sk3 ))]]) ).
thf(198,plain,
~ ? [A: $i,B: $i] :
( ( m_NormQ @ A )
= ( m_NotNorm @ B ) ),
inference(miniscope,[status(thm)],[197]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( m_NormQ @ A )
!= ( m_NotNorm @ B ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( m_NormQ @ A )
!= ( m_NotNorm @ B ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(14319,plain,
( ( ( host @ sk8 )
!= q_nil )
| ( ( s @ ( host @ sk6 ) )
!= ( s @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[507,14305]) ).
thf(14330,plain,
( ( ( host @ sk8 )
!= q_nil )
| ( ( host @ sk6 )
!= q_nil ) ),
inference(simp,[status(thm)],[14319]) ).
thf(19167,plain,
! [B: $i,A: $i] :
( ( ( queue @ ( host @ sk2 ) )
!= ( queue @ ( host @ B ) ) )
| ( ( cons @ ( m_Down @ sk3 ) @ sk1 )
!= ( cons @ ( m_Down @ B ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[135,5983]) ).
thf(19168,plain,
( ( queue @ ( host @ sk3 ) )
!= ( queue @ ( host @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[19167:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(11127,plain,
! [A: $i] :
( ( ( host @ sk8 )
!= A )
| ( ( s @ ( s @ A ) )
!= ( s @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[507,10631]) ).
thf(11138,plain,
( ( s @ ( s @ ( host @ sk8 ) ) )
!= ( s @ ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[11127]) ).
thf(11144,plain,
( ( s @ ( s @ ( host @ sk8 ) ) )
!= ( host @ sk8 ) ),
inference(rewrite,[status(thm)],[11138,507]) ).
thf(20381,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( elem @ ( last @ sk10 ) @ sk10 )
!= ( elem @ A @ q_nil ) ) ),
inference(paramod_ordered,[status(thm)],[12529,421]) ).
thf(20454,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( last @ sk10 )
!= A )
| ( sk10 != q_nil ) ),
inference(simp,[status(thm)],[20381]) ).
thf(20548,plain,
( ( sk8 != q_nil )
| ( sk10 != q_nil ) ),
inference(simp,[status(thm)],[20454]) ).
thf(321,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[320]) ).
thf(322,plain,
wait != elec_2,
inference(lifteq,[status(thm)],[321]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( setIn @ C @ alive )
| ( ( host @ B )
!= ( host @ C ) )
| ( ( index @ status @ ( host @ C ) )
!= norm )
| ( ( index @ ldr @ ( host @ C ) )
!= ( host @ C ) )
| ~ ( setIn @ A @ alive )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ C ) )
| ( ( index @ status @ ( host @ C ) )
!= norm )
| ( ( index @ ldr @ ( host @ C ) )
!= ( host @ C ) )
| ~ ( setIn @ C @ alive )
| ~ ( setIn @ A @ alive )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( host @ B )
!= ( host @ C ) )
| ( ( index @ status @ ( host @ C ) )
!= norm )
| ( ( index @ ldr @ ( host @ C ) )
!= ( host @ C ) )
| ~ ( setIn @ C @ alive )
| ~ ( setIn @ A @ alive )
| ~ ( elem @ ( m_Down @ B ) @ ( queue @ ( host @ A ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( sk14 @ A @ ( m_Ack @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(m_Ack),[sk14])]) ).
thf(2426,plain,
( ( sk10 != sk3 )
| ( ( leq @ ( host @ sk8 ) @ ( host @ sk6 ) )
!= ( leq @ nbr_proc @ ( host @ sk6 ) ) ) ),
inference(paramod_ordered,[status(thm)],[564,2050]) ).
thf(2435,plain,
( ( sk10 != sk3 )
| ( ( host @ sk8 )
!= nbr_proc )
| ( ( host @ sk6 )
!= ( host @ sk6 ) ) ),
inference(simp,[status(thm)],[2426]) ).
thf(2453,plain,
( ( sk10 != sk3 )
| ( ( host @ sk8 )
!= nbr_proc ) ),
inference(simp,[status(thm)],[2435]) ).
thf(7552,plain,
! [B: $i,A: $i] :
( ( ( cons @ A @ q_nil )
!= ( queue @ ( host @ sk6 ) ) )
| ( ( snoc @ q_nil @ A )
!= ( snoc @ B @ ( m_Ldr @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[395,6557]) ).
thf(7553,plain,
( ( cons @ ( m_Ldr @ sk10 ) @ q_nil )
!= ( queue @ ( host @ sk6 ) ) ),
inference(pattern_uni,[status(thm)],[7552:[bind(A,$thf( m_Ldr @ sk10 )),bind(B,$thf( q_nil ))]]) ).
thf(14389,plain,
( ( elem @ ( last @ ( queue @ ( host @ sk2 ) ) ) @ ( queue @ ( host @ sk2 ) ) )
!= ( elem @ ( m_Down @ sk7 ) @ ( queue @ ( host @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11667,5693]) ).
thf(14440,plain,
( ( ( last @ ( queue @ ( host @ sk2 ) ) )
!= ( m_Down @ sk7 ) )
| ( ( queue @ ( host @ sk2 ) )
!= ( queue @ ( host @ sk2 ) ) ) ),
inference(simp,[status(thm)],[14389]) ).
thf(14531,plain,
( ( last @ ( queue @ ( host @ sk2 ) ) )
!= ( m_Down @ sk7 ) ),
inference(simp,[status(thm)],[14440]) ).
thf(463,plain,
( ( setIn @ sk10 @ alive )
!= ( setIn @ nil @ alive ) ),
inference(paramod_ordered,[status(thm)],[109,210]) ).
thf(466,plain,
( ( sk10 != nil )
| ( alive != alive ) ),
inference(simp,[status(thm)],[463]) ).
thf(469,plain,
sk10 != nil,
inference(simp,[status(thm)],[466]) ).
thf(2055,plain,
! [A: $i] :
( ( leq @ ( s @ A ) @ A )
!= ( leq @ nbr_proc @ ( host @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[508,405]) ).
thf(2070,plain,
! [A: $i] :
( ( ( s @ A )
!= nbr_proc )
| ( A
!= ( host @ sk8 ) ) ),
inference(simp,[status(thm)],[2055]) ).
thf(2087,plain,
( ( s @ ( host @ sk8 ) )
!= nbr_proc ),
inference(simp,[status(thm)],[2070]) ).
thf(492,plain,
( ( host @ sk7 )
!= ( host @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[116,481]) ).
thf(496,plain,
sk7 != sk6,
inference(simp,[status(thm)],[492]) ).
thf(448,plain,
( ! [A: $i,B: $i] :
( ( A != B )
=> ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) )
=> ( A != B ) ) ),
inference(miniscope,[status(thm)],[447]) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) ) ),
inference(cnf,[status(esa)],[448]) ).
thf(453,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) ) ),
inference(lifteq,[status(thm)],[450]) ).
thf(454,plain,
! [A: $i] :
( ( sk21 @ ( m_Ldr @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(m_Ldr),[sk21])]) ).
thf(40828,plain,
$false,
inference(e,[status(thm)],[69,629,2031,12189,9754,14305,468,234,1110,481,352,21471,115,3905,12666,308,5982,379,202,23191,170,120,247,384,153,24430,14521,12770,320,22474,12447,185,5977,12686,6009,288,4743,11667,184,125,11200,196,157,21479,389,6010,189,4194,421,228,5076,261,216,475,2090,376,211,2122,238,3973,6559,4686,6562,480,280,221,2483,132,396,116,507,74,206,265,11853,307,3899,233,248,380,4216,6020,270,13233,6571,6442,85,201,2083,9688,693,165,260,349,5754,137,21628,14804,4192,461,5983,197,3968,6413,21668,14753,403,188,388,12796,13344,169,9063,1028,12768,225,686,547,212,109,471,256,6539,2085,393,701,2505,129,11261,3920,11927,134,244,205,508,311,9716,398,2089,343,237,412,618,6561,166,148,22096,264,9021,3888,296,176,402,286,19000,259,10557,118,4186,144,11919,350,9835,159,672,12082,406,113,219,12668,2084,419,245,318,12791,377,9047,271,208,345,323,91,6429,22283,700,9756,240,251,6446,155,685,399,21489,278,2086,17647,455,226,267,241,135,5976,5693,438,490,6417,162,2471,209,617,14530,355,458,6557,255,18434,6012,18060,580,150,327,409,310,23117,2092,2454,177,5015,370,502,21779,127,470,12529,359,544,12523,10558,21504,386,20103,314,21821,876,891,218,21411,368,250,231,2088,5917,18662,524,21056,22760,1341,186,21717,139,418,2081,18683,12080,2462,18500,383,9799,2095,346,536,82,214,290,6430,151,447,315,405,10631,373,21879,300,146,6563,422,2050,564,20838,210,326,268,358,195,6558,94,415,2091,6380,395,131,4206,200,14330,19168,277,12085,11144,4242,20548,178,369,607,322,11675,122,5707,659,215,560,2453,232,254,227,7553,5029,14531,469,222,2087,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SWV478+1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % Command : run_Leo-III %s %d THM
% 0.12/0.35 % Computer : n020.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Jun 20 20:54:40 EDT 2024
% 0.12/0.35 % CPUTime :
% 1.02/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.52/1.20 % [INFO] Parsing done (206ms).
% 1.52/1.22 % [INFO] Running in sequential loop mode.
% 2.04/1.46 % [INFO] eprover registered as external prover.
% 2.04/1.46 % [INFO] Scanning for conjecture ...
% 2.45/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.59/1.74 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.89/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.92/1.79 % [INFO] Type checking passed.
% 2.92/1.79 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 77.23/19.70 % External prover 'e' found a proof!
% 77.23/19.70 % [INFO] Killing All external provers ...
% 77.23/19.70 % Time passed: 19163ms (effective reasoning time: 18485ms)
% 77.23/19.70 % 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)>
% 77.23/19.71 % 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
% 77.23/19.71 % No. of inferences in proof: 791
% 77.23/19.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19163 ms resp. 18485 ms w/o parsing
% 77.96/19.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.96/19.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------