%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:59:30 AM UTC 2026
% Result : Theorem 11.26s 4.20s
% Output : Refutation 11.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 75
% Syntax : Number of formulae : 207 ( 136 unt; 0 typ; 8 def)
% Number of atoms : 881 ( 481 equ; 0 cnn)
% Maximal formula atoms : 62 ( 4 avg)
% Number of connectives : 3035 ( 389 ~; 115 |; 332 &;1992 @)
% ( 13 <=>; 194 =>; 0 <=; 0 <~>)
% Maximal formula depth : 56 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 25 con; 0-2 aty)
% Number of variables : 491 ( 0 ^; 480 !; 3 ?; 491 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(queue_decl,type,
queue: $i > $i ).
thf(host_decl,type,
host: $i > $i ).
thf(setIn_decl,type,
setIn: $i > $i > $o ).
thf(alive_decl,type,
alive: $i ).
thf(m_Halt_decl,type,
m_Halt: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(down_decl,type,
down: $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(status_decl,type,
status: $i ).
thf(norm_decl,type,
norm: $i ).
thf(wait_decl,type,
wait: $i ).
thf(elid_decl,type,
elid: $i ).
thf(pids_decl,type,
pids: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(m_NotNorm_decl,type,
m_NotNorm: $i > $i ).
thf(m_NormQ_decl,type,
m_NormQ: $i > $i ).
thf(ordered_decl,type,
ordered: $i > $o ).
thf(snoc_decl,type,
snoc: $i > $i > $i ).
thf(m_Ldr_decl,type,
m_Ldr: $i > $i ).
thf(last_decl,type,
last: $i > $i ).
thf(q_nil_decl,type,
q_nil: $i ).
thf(init_decl,type,
init: $i > $i ).
thf(elec_1_decl,type,
elec_1: $i ).
thf(elec_2_decl,type,
elec_2: $i ).
thf(nil_decl,type,
nil: $i ).
thf(nbr_proc_decl,type,
nbr_proc: $i ).
thf(setEmpty_decl,type,
setEmpty: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(pidElem_decl,type,
pidElem: $i > $o ).
thf(pidMsg_decl,type,
pidMsg: $i > $i ).
thf(head_decl,type,
head: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
!= ( zero @ s ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( C @ host )
!= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != C ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != C ) ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( A @ ( H @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( ( B @ host @ queue )
= ( sk1 @ ( C @ m_Down @ cons ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i,F: $i,G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( alive @ ( F @ setIn ) )
& ( alive @ ( D @ setIn ) )
& ( ( F @ host )
!= ( D @ host ) ) )
=> ~ ( ( F @ host @ queue @ ( E @ m_Down @ elem ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( D @ ( E @ leq ) )
& ~ ( alive @ ( D @ setIn ) ) )
=> ~ ( alive @ ( E @ setIn ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ~ ( alive @ ( E @ setIn ) ) ) )
=> ( ( alive @ ( B @ setIn ) )
=> ( ~ ( C @ host @ ( B @ host @ leq ) )
=> ( ( ( ( ( C @ host )
= ( B @ host @ ( elid @ index ) @ host ) )
& ( ( B @ host @ ( status @ index ) )
= wait ) )
| ( ( ( B @ host @ ( status @ index ) )
= norm )
& ( ( B @ host @ ( ldr @ index ) )
= ( C @ host ) ) ) )
=> ( ( ( ( B @ host )
= ( A @ host ) )
& ~ ( pids @ ( A @ setIn ) )
& ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ( A @ ( D @ leq ) ) ) )
=> ( ( ( A @ host )
!= ( zero @ s ) )
=> ! [D: $i] :
( ( ( B @ host )
= ( D @ host ) )
=> ! [E: $i,F: $i] :
( ( ( A @ host )
!= ( F @ host ) )
=> ( ( ( B @ host )
!= ( F @ host ) )
=> ! [G: $i] :
( ( ( ( G @ host )
= ( F @ host ) )
& ( ( E @ host )
= ( D @ host ) )
& ( ( F @ host )
!= ( D @ host ) )
& ( ( F = A )
| ( ( alive @ ( F @ setIn ) )
& ( F != B ) ) )
& ( ( D = A )
| ( ( alive @ ( D @ setIn ) )
& ( D != B ) ) ) )
=> ~ ( ( F @ host @ ( down @ index ) @ ( E @ host @ setIn ) )
& ( sk1 @ ( G @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( ( A @ host @ queue )
= ( sk1 @ ( B @ m_Down @ cons ) ) )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( ( E @ host )
!= ( C @ host ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( alive @ ( E @ setIn ) )
& ( alive @ ( C @ setIn ) )
& ( ( E @ host )
!= ( C @ host ) ) )
=> ~ ( ( E @ host @ queue @ ( D @ m_Down @ elem ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( C @ ( D @ leq ) )
& ~ ( alive @ ( C @ setIn ) ) )
=> ~ ( alive @ ( D @ setIn ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
=> ~ ( E @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ( ( D @ host )
!= ( C @ host ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ~ ( alive @ ( D @ setIn ) ) ) )
=> ( ( alive @ ( A @ setIn ) )
=> ( ~ ( B @ host @ ( A @ host @ leq ) )
=> ( ( ( ( ( B @ host )
= ( A @ host @ ( elid @ index ) @ host ) )
& ( ( A @ host @ ( status @ index ) )
= wait ) )
| ( ( ( A @ host @ ( status @ index ) )
= norm )
& ( ( A @ host @ ( ldr @ index ) )
= ( B @ host ) ) ) )
=> ( ( ( ( A @ host )
= ( sk2 @ host ) )
& ~ ( pids @ ( sk2 @ setIn ) )
& ! [C: $i] :
( ( ( A @ host )
= ( C @ host ) )
=> ( sk2 @ ( C @ leq ) ) ) )
=> ( ( ( sk2 @ host )
!= ( zero @ s ) )
=> ! [C: $i] :
( ( ( A @ host )
= ( C @ host ) )
=> ! [D: $i,E: $i] :
( ( ( sk2 @ host )
!= ( E @ host ) )
=> ( ( ( A @ host )
!= ( E @ host ) )
=> ! [F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( ( D @ host )
= ( C @ host ) )
& ( ( E @ host )
!= ( C @ host ) )
& ( ( E = sk2 )
| ( ( alive @ ( E @ setIn ) )
& ( E != A ) ) )
& ( ( C = sk2 )
| ( ( alive @ ( C @ setIn ) )
& ( C != A ) ) ) )
=> ~ ( ( E @ host @ ( down @ index ) @ ( D @ host @ setIn ) )
& ( sk1 @ ( F @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( ( sk3 @ host @ queue )
= ( sk1 @ ( A @ m_Down @ cons ) ) )
& ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ( ( D @ host )
!= ( B @ host ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i,C: $i,D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( alive @ ( D @ setIn ) )
& ( alive @ ( B @ setIn ) )
& ( ( D @ host )
!= ( B @ host ) ) )
=> ~ ( ( D @ host @ queue @ ( C @ m_Down @ elem ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( B @ ( C @ leq ) )
& ~ ( alive @ ( B @ setIn ) ) )
=> ~ ( alive @ ( C @ setIn ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
=> ~ ( D @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ( ( C @ host )
!= ( B @ host ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ~ ( alive @ ( C @ setIn ) ) ) )
=> ( ( alive @ ( sk3 @ setIn ) )
=> ( ~ ( A @ host @ ( sk3 @ host @ leq ) )
=> ( ( ( ( ( A @ host )
= ( sk3 @ host @ ( elid @ index ) @ host ) )
& ( ( sk3 @ host @ ( status @ index ) )
= wait ) )
| ( ( ( sk3 @ host @ ( status @ index ) )
= norm )
& ( ( sk3 @ host @ ( ldr @ index ) )
= ( A @ host ) ) ) )
=> ( ( ( ( sk3 @ host )
= ( sk2 @ host ) )
& ~ ( pids @ ( sk2 @ setIn ) )
& ! [B: $i] :
( ( ( sk3 @ host )
= ( B @ host ) )
=> ( sk2 @ ( B @ leq ) ) ) )
=> ( ( ( sk2 @ host )
!= ( zero @ s ) )
=> ! [B: $i] :
( ( ( sk3 @ host )
= ( B @ host ) )
=> ! [C: $i,D: $i] :
( ( ( sk2 @ host )
!= ( D @ host ) )
=> ( ( ( sk3 @ host )
!= ( D @ host ) )
=> ! [E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( ( C @ host )
= ( B @ host ) )
& ( ( D @ host )
!= ( B @ host ) )
& ( ( D = sk2 )
| ( ( alive @ ( D @ setIn ) )
& ( D != sk3 ) ) )
& ( ( B = sk2 )
| ( ( alive @ ( B @ setIn ) )
& ( B != sk3 ) ) ) )
=> ~ ( ( D @ host @ ( down @ index ) @ ( C @ host @ setIn ) )
& ( sk1 @ ( E @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk3 @ host )
= ( A @ host ) )
=> ! [B: $i,C: $i] :
( ( ( sk2 @ host )
!= ( C @ host ) )
=> ( ( ( sk3 @ host )
!= ( C @ host ) )
=> ! [D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( ( B @ host )
= ( A @ host ) )
& ( ( C @ host )
!= ( A @ host ) )
& ( ( C = sk2 )
| ( ( alive @ ( C @ setIn ) )
& ( C != sk3 ) ) )
& ( ( A = sk2 )
| ( ( alive @ ( A @ setIn ) )
& ( A != sk3 ) ) ) )
=> ~ ( ( C @ host @ ( down @ index ) @ ( B @ host @ setIn ) )
& ( sk1 @ ( D @ m_Down @ elem ) ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk2 @ host )
!= ( B @ host ) )
=> ( ( ( sk3 @ host )
!= ( B @ host ) )
=> ! [C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( ( A @ host )
= ( sk5 @ host ) )
& ( ( B @ host )
!= ( sk5 @ host ) )
& ( ( B = sk2 )
| ( ( alive @ ( B @ setIn ) )
& ( B != sk3 ) ) )
& ( ( sk5 = sk2 )
| ( ( alive @ ( sk5 @ setIn ) )
& ( sk5 != sk3 ) ) ) )
=> ~ ( ( B @ host @ ( down @ index ) @ ( A @ host @ setIn ) )
& ( sk1 @ ( C @ m_Down @ elem ) ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( sk2 @ host )
!= ( A @ host ) )
=> ( ( ( sk3 @ host )
!= ( A @ host ) )
=> ! [B: $i] :
( ( ( ( B @ host )
= ( A @ host ) )
& ( ( sk6 @ host )
= ( sk5 @ host ) )
& ( ( A @ host )
!= ( sk5 @ host ) )
& ( ( A = sk2 )
| ( ( alive @ ( A @ setIn ) )
& ( A != sk3 ) ) )
& ( ( sk5 = sk2 )
| ( ( alive @ ( sk5 @ setIn ) )
& ( sk5 != sk3 ) ) ) )
=> ~ ( ( A @ host @ ( down @ index ) @ ( sk6 @ host @ setIn ) )
& ( sk1 @ ( B @ m_Down @ elem ) ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( ( ( A @ host )
= ( sk7 @ host ) )
& ( ( sk6 @ host )
= ( sk5 @ host ) )
& ( ( sk7 @ host )
!= ( sk5 @ host ) )
& ( ( sk7 = sk2 )
| ( ( alive @ ( sk7 @ setIn ) )
& ( sk7 != sk3 ) ) )
& ( ( sk5 = sk2 )
| ( ( alive @ ( sk5 @ setIn ) )
& ( sk5 != sk3 ) ) ) )
=> ~ ( ( sk7 @ host @ ( down @ index ) @ ( sk6 @ host @ setIn ) )
& ( sk1 @ ( A @ m_Down @ elem ) ) ) ) ) ) ).
thf(10,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(170,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_01) ).
thf(444,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(64,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(414,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
!= ( zero @ s ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( C @ host )
!= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != C ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != C ) ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( A @ ( H @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
!= ( zero @ s ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( C @ host )
!= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != C ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != C ) ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( A @ ( H @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C @ host @ queue )
= ( A @ ( D @ m_Down @ cons ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( alive @ ( G @ setIn ) )
& ( alive @ ( E @ setIn ) )
& ( ( G @ host )
!= ( E @ host ) ) )
=> ~ ( ( G @ host @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) ) )
=> ( ( alive @ ( C @ setIn ) )
=> ( ~ ( D @ host @ ( C @ host @ leq ) )
=> ( ( ( ( ( D @ host )
= ( C @ host @ ( elid @ index ) @ host ) )
& ( ( C @ host @ ( status @ index ) )
= wait ) )
| ( ( ( C @ host @ ( status @ index ) )
= norm )
& ( ( C @ host @ ( ldr @ index ) )
= ( D @ host ) ) ) )
=> ( ( ( ( C @ host )
= ( B @ host ) )
& ~ ( pids @ ( B @ setIn ) )
& ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ( B @ ( E @ leq ) ) ) )
=> ( ( ( B @ host )
!= ( zero @ s ) )
=> ! [E: $i] :
( ( ( C @ host )
= ( E @ host ) )
=> ! [F: $i,G: $i] :
( ( ( B @ host )
!= ( G @ host ) )
=> ( ( ( C @ host )
!= ( G @ host ) )
=> ! [H: $i] :
( ( ( ( H @ host )
= ( G @ host ) )
& ( ( F @ host )
= ( E @ host ) )
& ( ( G @ host )
!= ( E @ host ) )
& ( ( G = B )
| ( ( alive @ ( G @ setIn ) )
& ( G != C ) ) )
& ( ( E = B )
| ( ( alive @ ( E @ setIn ) )
& ( E != C ) ) ) )
=> ~ ( ( G @ host @ ( down @ index ) @ ( F @ host @ setIn ) )
& ( A @ ( H @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(365,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(70,plain,
! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk7 @ host @ ( down @ index ) @ ( sk6 @ host @ setIn ) )
& ( sk1 @ ( sk8 @ m_Down @ elem ) )
& ( ( sk8 @ host )
= ( sk7 @ host ) )
& ( ( sk6 @ host )
= ( sk5 @ host ) )
& ( ( sk7 @ host )
!= ( sk5 @ host ) )
& ( ( sk7 = sk2 )
| ( alive @ ( sk7 @ setIn ) ) )
& ( ( sk7 = sk2 )
| ( sk7 != sk3 ) )
& ( ( sk5 = sk2 )
| ( alive @ ( sk5 @ setIn ) ) )
& ( ( sk5 = sk2 )
| ( sk5 != sk3 ) )
& ( ( sk3 @ host )
!= ( sk7 @ host ) )
& ( ( sk2 @ host )
!= ( sk7 @ host ) )
& ( ( sk3 @ host )
= ( sk5 @ host ) )
& ( ( sk2 @ host )
!= ( zero @ s ) )
& ( ( sk3 @ host )
= ( sk2 @ host ) )
& ~ ( pids @ ( sk2 @ setIn ) )
& ( ( sk2 @ ( V @ leq ) )
| ( ( sk3 @ host )
!= ( V @ host ) ) )
& ( ( ( sk4 @ host )
= ( sk3 @ host @ ( elid @ index ) @ host ) )
| ( ( sk3 @ host @ ( status @ index ) )
= norm ) )
& ( ( ( sk3 @ host @ ( status @ index ) )
= wait )
| ( ( sk3 @ host @ ( status @ index ) )
= norm ) )
& ( ( ( sk4 @ host )
= ( sk3 @ host @ ( elid @ index ) @ host ) )
| ( ( sk3 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) )
& ( ( ( sk3 @ host @ ( status @ index ) )
= wait )
| ( ( sk3 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) )
& ~ ( sk4 @ host @ ( sk3 @ host @ leq ) )
& ( alive @ ( sk3 @ setIn ) )
& ( ( sk3 @ host @ queue )
= ( sk1 @ ( sk4 @ m_Down @ cons ) ) )
& ( ~ ( T @ host @ ( down @ index ) @ ( S @ host @ setIn ) )
| ~ ( R @ host @ queue @ ( U @ m_Down @ elem ) )
| ( ( U @ host )
!= ( T @ host ) )
| ( ( S @ host )
!= ( R @ host ) )
| ~ ( alive @ ( T @ setIn ) )
| ~ ( alive @ ( R @ setIn ) )
| ( ( T @ host )
= ( R @ host ) ) )
& ( ~ ( P @ host @ queue @ ( O @ m_Down @ elem ) )
| ~ ( N @ host @ queue @ ( Q @ m_Down @ elem ) )
| ( ( Q @ host )
!= ( P @ host ) )
| ( ( O @ host )
!= ( N @ host ) )
| ~ ( alive @ ( P @ setIn ) )
| ~ ( alive @ ( N @ setIn ) )
| ( ( P @ host )
= ( N @ host ) ) )
& ( ~ ( alive @ ( M @ setIn ) )
| ~ ( alive @ ( L @ setIn ) )
| ( ( M @ host )
!= ( L @ host ) )
| ( M = L ) )
& ( ~ ( alive @ ( K @ setIn ) )
| ( ( K @ host )
!= ( J @ host ) )
| ~ ( J @ ( K @ leq ) )
| ( alive @ ( J @ setIn ) ) )
& ( ~ ( I @ host @ ( G @ host @ leq ) )
| ~ ( H @ host @ queue @ ( G @ ( I @ m_Ack ) @ elem ) ) )
& ( ~ ( F @ host @ ( E @ host @ leq ) )
| ~ ( E @ host @ queue @ ( F @ m_Halt @ elem ) ) )
& ( ( ( D @ host )
!= ( C @ host ) )
| ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ( ~ ( alive @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(101,plain,
alive @ ( sk3 @ setIn ),
inference(cnfConj,[status(thm)],[70]) ).
thf(88,plain,
sk1 @ ( sk8 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[70]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(384,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(404,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ ordered )
<=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_54) ).
thf(417,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( A @ ( B @ snoc ) @ ordered ) )
& ( ( A @ ( B @ snoc ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( A @ pidMsg @ ( C @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(320,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(372,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(344,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(97,plain,
( ( sk7 = sk2 )
| ( alive @ ( sk7 @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(116,plain,
( ( alive @ ( sk7 @ setIn ) )
| ( sk7 = sk2 ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(90,plain,
( ( sk2 @ host )
!= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(130,plain,
( ( sk7 @ host )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(516,plain,
sk7 != sk2,
inference(simp,[status(thm)],[130]) ).
thf(606,plain,
alive @ ( sk7 @ setIn ),
inference(simplifyReflect,[status(thm)],[116,516]) ).
thf(26,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(226,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(227,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[226]) ).
thf(228,plain,
elec_1 != norm,
inference(lifteq,[status(thm)],[227]) ).
thf(52,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(374,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(375,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[374]) ).
thf(376,plain,
wait != norm,
inference(lifteq,[status(thm)],[375]) ).
thf(45,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(348,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(353,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( B @ ( C @ snoc ) @ ( A @ elem ) ) )
& ( ( B @ ( C @ snoc ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(86,plain,
~ ( pids @ ( sk2 @ setIn ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(451,plain,
( ( ( alive @ ( sk3 @ setIn ) )
!= ( pids @ ( sk2 @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,86]) ).
thf(452,plain,
( ( alive @ ( sk3 @ setIn ) )
!= ( pids @ ( sk2 @ setIn ) ) ),
inference(simp,[status(thm)],[451]) ).
thf(453,plain,
( ( pids != alive )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[452]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
<=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(265,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(206,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(307,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(28,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(233,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(380,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(201,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(220,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
thf(297,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Down )
!= ( B @ m_Down ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ pidElem )
<=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(275,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) )
=> ( A @ pidElem ) )
& ( ( A @ pidElem )
=> ? [B: $i] :
( ( A
= ( B @ m_Down ) )
| ( A
= ( B @ m_Halt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(15,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(192,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m_Down @ elem ) )
& ( ( B @ host )
= ( C @ host ) )
& ( A @ ( B @ m_Halt @ cons ) @ ordered ) )
=> ( C @ ( B @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(407,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ m_Down @ elem ) )
& ( ( B @ host )
= ( C @ host ) )
& ( A @ ( B @ m_Halt @ cons ) @ ordered ) )
=> ( C @ ( B @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(229,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(195,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(196,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[195]) ).
thf(197,plain,
elec_1 != wait,
inference(lifteq,[status(thm)],[196]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ ordered )
<=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_53) ).
thf(324,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ( A @ cons ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(40,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(317,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(56,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(388,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(75,plain,
~ ( sk4 @ host @ ( sk3 @ host @ leq ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(94,plain,
( ( sk3 @ host )
= ( sk2 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(129,plain,
( ( sk3 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(499,plain,
~ ( sk4 @ host @ ( sk2 @ host @ leq ) ),
inference(rewrite,[status(thm)],[75,129]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(173,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(43,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_09) ).
thf(341,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(342,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[341]) ).
thf(343,plain,
elec_2 != norm,
inference(lifteq,[status(thm)],[342]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(311,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(398,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(93,plain,
( ( sk6 @ host )
= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(111,plain,
( ( sk6 @ host )
= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(100,plain,
( ( sk3 @ host )
= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(132,plain,
( ( sk5 @ host )
= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(528,plain,
( ( sk5 @ host )
= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[132,129]) ).
thf(530,plain,
( ( sk6 @ host )
= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[111,528]) ).
thf(14,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(191,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(286,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) ) )
& ( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(391,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(350,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(377,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ leq ) )
<=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(434,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) )
=> ( B @ s @ ( A @ leq ) ) )
& ( ( B @ s @ ( A @ leq ) )
=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(17,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(198,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(199,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[198]) ).
thf(612,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[606,199]) ).
thf(613,plain,
( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[612]) ).
thf(615,plain,
( ( alive != alive )
| ( sk7 != nil ) ),
inference(simp,[status(thm)],[613]) ).
thf(616,plain,
sk7 != nil,
inference(simp,[status(thm)],[615]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( A @ host @ queue @ ( D @ m_Down @ elem ) )
| ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( D @ host )
!= ( C @ host ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( ( C @ host )
= ( A @ host ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(193,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[192]) ).
thf(194,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[193]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(460,plain,
( ( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,199]) ).
thf(461,plain,
( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[460]) ).
thf(462,plain,
( ( alive != alive )
| ( sk3 != nil ) ),
inference(simp,[status(thm)],[461]) ).
thf(463,plain,
sk3 != nil,
inference(simp,[status(thm)],[462]) ).
thf(78,plain,
( ( sk7 @ host )
!= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(112,plain,
( ( sk7 @ host )
!= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(465,plain,
sk7 != sk5,
inference(simp,[status(thm)],[112]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(363,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(23,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(218,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(368,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(318,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[317]) ).
thf(319,plain,
elec_2 != wait,
inference(lifteq,[status(thm)],[318]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(258,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,plain,
( ( sk8 @ host )
= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(114,plain,
( ( sk8 @ host )
= ( sk7 @ host ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(401,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(96,plain,
( ( sk5 = sk2 )
| ( sk5 != sk3 ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(119,plain,
( ( sk5 = sk2 )
| ( sk5 != sk3 ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(214,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(447,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(410,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(262,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) )
=> ( ( pids @ ( B @ setIn ) )
& ( pids @ ( A @ setIn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( B @ s @ ( A @ s @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( ( B @ s @ ( A @ s @ leq ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( B @ s @ ( A @ s @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(469,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( ( sk5 @ host )
!= ( sk5 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[111,112]) ).
thf(470,plain,
( ( sk7 @ host )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[469]) ).
thf(474,plain,
sk7 != sk6,
inference(simp,[status(thm)],[470]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(395,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(85,plain,
( ( sk3 @ host )
!= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(104,plain,
( ( sk7 @ host )
!= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(464,plain,
sk7 != sk3,
inference(simp,[status(thm)],[104]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(163,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(200,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(76,plain,
( ( sk2 @ host )
!= ( zero @ s ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(122,plain,
( ( zero @ s )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(222,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(988,plain,
$false,
inference(e,[status(thm)],[170,444,414,143,69,365,101,88,384,153,404,417,320,372,344,606,228,376,348,353,453,133,265,206,307,233,248,380,201,220,160,297,275,192,407,229,197,324,317,156,388,499,173,129,73,343,311,398,530,191,286,391,236,181,350,86,377,434,616,103,198,130,226,167,374,516,194,199,177,463,465,363,218,368,319,258,114,401,119,214,447,410,262,210,242,341,195,474,395,464,528,163,200,122,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV456+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.55 % Computer : n009.cluster.edu
% 0.15/0.55 % Model : x86_64 x86_64
% 0.15/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.55 % Memory : 8046.5625MB
% 0.15/0.55 % OS : Linux 6.8.0-71-generic
% 0.15/0.55 % CPULimit : 300
% 0.15/0.55 % WCLimit : 300
% 0.15/0.55 % DateTime : Sat Sep 26 13:54:45 UTC 2026
% 0.15/0.56 % CPUTime :
% 0.15/0.56 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/1.05 % [INFO] Parsing done (173ms).
% 1.13/1.07 % [INFO] Running in sequential loop mode.
% 1.94/1.47 % [INFO] eprover registered as external prover.
% 1.94/1.48 % [INFO] Scanning for conjecture ...
% 2.41/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.64/1.78 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.87/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.87/1.86 % [INFO] Type checking passed.
% 2.87/1.86 % [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 ...
% 11.86/4.19 % External prover 'e' found a proof!
% 11.86/4.19 % [INFO] Killing All external provers ...
% 11.86/4.20 % Time passed: 3541ms (effective reasoning time: 3114ms)
% 11.86/4.20 % 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)>
% 11.26/4.20 % 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
% 11.26/4.20 % No. of inferences in proof: 199
% 11.26/4.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3541 ms resp. 3114 ms w/o parsing
% 11.73/4.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.73/4.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------