%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV452+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:59:29 AM UTC 2026
% Result : Theorem 83.62s 19.24s
% Output : Refutation 85.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 86
% Syntax : Number of formulae : 1389 ( 561 unt; 0 typ; 19 def)
% Number of atoms : 3891 (1918 equ; 0 cnn)
% Maximal formula atoms : 56 ( 2 avg)
% Number of connectives : 12098 (2046 ~;1207 |; 364 &;8249 @)
% ( 13 <=>; 219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 24 con; 0-2 aty)
% Number of variables : 1858 ( 6 ^;1775 !; 58 ?;1858 :)
% ( 0 !>; 0 ?*; 0 @-; 19 @+)
% Comments :
%------------------------------------------------------------------------------
thf(setIn_decl,type,
setIn: $i > $i > $o ).
thf(alive_decl,type,
alive: $i ).
thf(elem_decl,type,
elem: $i > $i > $o ).
thf(m_Down_decl,type,
m_Down: $i > $i ).
thf(queue_decl,type,
queue: $i > $i ).
thf(host_decl,type,
host: $i > $i ).
thf(m_Halt_decl,type,
m_Halt: $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(m_Ack_decl,type,
m_Ack: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(index_decl,type,
index: $i > $i > $i ).
thf(ldr_decl,type,
ldr: $i ).
thf(status_decl,type,
status: $i ).
thf(norm_decl,type,
norm: $i ).
thf(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(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i > $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 @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( 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] :
( ( ( 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 @ queue @ ( F @ m_Down @ elem ) )
& ( 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 @ queue @ ( E @ m_Down @ elem ) )
& ( D @ host @ queue @ ( G @ m_Down @ elem ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( E != D ) )
=> ( ~ ( alive @ ( E @ setIn ) )
| ~ ( alive @ ( D @ setIn ) ) ) )
& ! [D: $i,E: $i] :
( ( ( ( E @ host )
= ( D @ host ) )
& ( D @ ( E @ leq ) )
& ~ ( alive @ ( D @ setIn ) ) )
=> ~ ( alive @ ( E @ setIn ) ) )
& ! [D: $i,E: $i,F: $i] :
( ( E @ host @ queue @ ( D @ ( F @ m_Ack ) @ elem ) )
=> ~ ( F @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Halt @ elem ) )
=> ~ ( E @ host @ ( D @ host @ leq ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ( ( E @ host )
!= ( D @ host ) ) )
& ! [D: $i,E: $i] :
( ( D @ host @ queue @ ( E @ m_Down @ elem ) )
=> ~ ( alive @ ( E @ setIn ) ) )
& ! [D: $i,E: $i] :
( ( alive @ ( E @ setIn ) )
=> ~ ( D @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( 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] :
( ( ( 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 @ queue @ ( E @ m_Down @ elem ) )
& ( 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 @ queue @ ( D @ m_Down @ elem ) )
& ( C @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( D != C ) )
=> ( ~ ( alive @ ( D @ setIn ) )
| ~ ( alive @ ( C @ setIn ) ) ) )
& ! [C: $i,D: $i] :
( ( ( ( D @ host )
= ( C @ host ) )
& ( C @ ( D @ leq ) )
& ~ ( alive @ ( C @ setIn ) ) )
=> ~ ( alive @ ( D @ setIn ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( D @ host @ queue @ ( C @ ( E @ m_Ack ) @ elem ) )
=> ~ ( E @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Halt @ elem ) )
=> ~ ( D @ host @ ( C @ host @ leq ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ( ( D @ host )
!= ( C @ host ) ) )
& ! [C: $i,D: $i] :
( ( C @ host @ queue @ ( D @ m_Down @ elem ) )
=> ~ ( alive @ ( D @ setIn ) ) )
& ! [C: $i,D: $i] :
( ( alive @ ( D @ setIn ) )
=> ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( 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] :
( ( ( 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 @ queue @ ( D @ m_Down @ elem ) )
& ( 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 @ queue @ ( C @ m_Down @ elem ) )
& ( B @ host @ queue @ ( E @ m_Down @ elem ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( C != B ) )
=> ( ~ ( alive @ ( C @ setIn ) )
| ~ ( alive @ ( B @ setIn ) ) ) )
& ! [B: $i,C: $i] :
( ( ( ( C @ host )
= ( B @ host ) )
& ( B @ ( C @ leq ) )
& ~ ( alive @ ( B @ setIn ) ) )
=> ~ ( alive @ ( C @ setIn ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( C @ host @ queue @ ( B @ ( D @ m_Ack ) @ elem ) )
=> ~ ( D @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Halt @ elem ) )
=> ~ ( C @ host @ ( B @ host @ leq ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ( ( C @ host )
!= ( B @ host ) ) )
& ! [B: $i,C: $i] :
( ( B @ host @ queue @ ( C @ m_Down @ elem ) )
=> ~ ( alive @ ( C @ setIn ) ) )
& ! [B: $i,C: $i] :
( ( alive @ ( C @ setIn ) )
=> ~ ( B @ host @ queue @ ( C @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( 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] :
( ( ( 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 @ queue @ ( C @ m_Down @ elem ) )
& ( sk1 @ ( E @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk3 @ host )
= ( A @ host ) )
=> ! [B: $i,C: $i] :
( ( ( 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 @ queue @ ( B @ m_Down @ elem ) )
& ( sk1 @ ( D @ m_Down @ elem ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( 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 @ queue @ ( A @ m_Down @ elem ) )
& ( sk1 @ ( C @ m_Down @ elem ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( 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 @ queue @ ( sk6 @ m_Down @ elem ) )
& ( 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 @ queue @ ( sk6 @ m_Down @ elem ) )
& ( sk1 @ ( A @ m_Down @ elem ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ m_Down ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( ( C @ pidMsg @ host )
= ( B @ pidMsg @ host ) )
& ( C @ pidElem )
& ( B @ pidElem )
& ( A @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( B @ pidMsg @ leq ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( ( C @ pidMsg @ host )
= ( B @ pidMsg @ host ) )
& ( C @ pidElem )
& ( B @ pidElem )
& ( A @ ( C @ elem ) ) )
=> ( B @ pidMsg @ ( C @ pidMsg @ leq ) ) ) ) ) ).
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 @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( 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] :
( ( ( 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 @ queue @ ( F @ m_Down @ elem ) )
& ( 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 @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( 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] :
( ( ( 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 @ queue @ ( F @ m_Down @ elem ) )
& ( 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 @ queue @ ( F @ m_Down @ elem ) )
& ( E @ host @ queue @ ( H @ m_Down @ elem ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( F != E ) )
=> ( ~ ( alive @ ( F @ setIn ) )
| ~ ( alive @ ( E @ setIn ) ) ) )
& ! [E: $i,F: $i] :
( ( ( ( F @ host )
= ( E @ host ) )
& ( E @ ( F @ leq ) )
& ~ ( alive @ ( E @ setIn ) ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( F @ host @ queue @ ( E @ ( G @ m_Ack ) @ elem ) )
=> ~ ( G @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Halt @ elem ) )
=> ~ ( F @ host @ ( E @ host @ leq ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ( ( F @ host )
!= ( E @ host ) ) )
& ! [E: $i,F: $i] :
( ( E @ host @ queue @ ( F @ m_Down @ elem ) )
=> ~ ( alive @ ( F @ setIn ) ) )
& ! [E: $i,F: $i] :
( ( alive @ ( F @ setIn ) )
=> ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) ) )
=> ( ( alive @ ( 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] :
( ( ( 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 @ queue @ ( F @ m_Down @ elem ) )
& ( A @ ( H @ m_Down @ elem ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,plain,
! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
& ( 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 ) )
& ( ( sk3 @ host )
= ( sk5 @ host ) )
& ( ( sk2 @ host )
!= ( zero @ s ) )
& ( ( sk3 @ host )
= ( sk2 @ host ) )
& ~ ( pids @ ( sk2 @ setIn ) )
& ( ( sk2 @ ( T @ leq ) )
| ( ( sk3 @ host )
!= ( T @ 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 ) ) )
& ( ~ ( R @ host @ queue @ ( Q @ m_Down @ elem ) )
| ~ ( P @ host @ queue @ ( S @ m_Down @ elem ) )
| ( ( S @ host )
!= ( R @ host ) )
| ( ( Q @ host )
!= ( P @ host ) )
| ~ ( alive @ ( R @ setIn ) )
| ~ ( alive @ ( P @ setIn ) )
| ( ( R @ host )
= ( P @ host ) ) )
& ( ~ ( alive @ ( O @ setIn ) )
| ~ ( alive @ ( N @ setIn ) )
| ( ( O @ host )
!= ( N @ host ) )
| ( O = N ) )
& ( ~ ( alive @ ( M @ setIn ) )
| ( ( M @ host )
!= ( L @ host ) )
| ~ ( L @ ( M @ leq ) )
| ( alive @ ( L @ setIn ) ) )
& ( ~ ( K @ host @ ( I @ host @ leq ) )
| ~ ( J @ host @ queue @ ( I @ ( K @ m_Ack ) @ elem ) ) )
& ( ~ ( H @ host @ ( G @ host @ leq ) )
| ~ ( G @ host @ queue @ ( H @ m_Halt @ elem ) ) )
& ( ( ( F @ host )
!= ( E @ host ) )
| ~ ( E @ host @ queue @ ( F @ m_Down @ elem ) ) )
& ( ~ ( alive @ ( D @ setIn ) )
| ~ ( C @ host @ queue @ ( D @ m_Down @ elem ) ) )
& ( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(73,plain,
( ( sk3 @ host )
= ( sk2 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(104,plain,
( ( sk3 @ host )
= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(90,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk3 @ host )
!= ( A @ host ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(126,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk3 @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(127,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk3 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(1531,plain,
! [A: $i] :
( ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(rewrite,[status(thm)],[127,104]) ).
thf(1566,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[104,1531]) ).
thf(1567,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1566]) ).
thf(1568,plain,
sk2 @ ( sk3 @ leq ),
inference(pattern_uni,[status(thm)],[1567:[bind(A,$thf( sk3 ))]]) ).
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(283,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(284,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) ) )
& ! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[283]) ).
thf(285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ leq ) )
| ( C != D ) )
& ( ( D @ ( C @ leq ) )
| ( C != D ) )
& ( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[286]) ).
thf(11259,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[1568,289]) ).
thf(11260,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[11259]) ).
thf(11261,plain,
( ~ ( sk3 @ ( sk2 @ leq ) )
| ( sk3 = sk2 ) ),
inference(pattern_uni,[status(thm)],[11260:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(97,plain,
alive @ ( sk3 @ setIn ),
inference(cnfConj,[status(thm)],[70]) ).
thf(17,axiom,
~ ( alive @ ( nil @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(195,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(196,plain,
~ ( alive @ ( nil @ setIn ) ),
inference(polarity_switch,[status(thm)],[195]) ).
thf(451,plain,
( ( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,196]) ).
thf(452,plain,
( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[451]) ).
thf(453,plain,
( ( alive != alive )
| ( sk3 != nil ) ),
inference(simp,[status(thm)],[452]) ).
thf(454,plain,
sk3 != nil,
inference(simp,[status(thm)],[453]) ).
thf(14976,plain,
( ( sk3 != sk3 )
| ( sk2 != nil )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[11261,454]) ).
thf(14977,plain,
( ( sk2 != nil )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[14976:[]]) ).
thf(10,axiom,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(167,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(168,plain,
! [A: $i] :
( ( A
= ( A @ last @ ( A @ init @ snoc ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[168]) ).
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(350,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(351,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( B @ ( C @ snoc ) @ ( A @ elem ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[350]) ).
thf(352,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( F @ snoc ) @ ( D @ elem ) )
| ~ ( F @ ( D @ elem ) ) )
& ( ( E @ ( F @ snoc ) @ ( D @ elem ) )
| ( D != E ) )
& ( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( B @ ( C @ snoc ) @ ( A @ elem ) ) ) ),
inference(cnf,[status(esa)],[351]) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[352]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[354]) ).
thf(358,plain,
! [B: $i,A: $i] : ( A @ ( B @ snoc ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[357]) ).
thf(3100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ last @ ( A @ init @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( A @ ( B @ elem ) )
| ( A = q_nil ) ),
inference(paramod_ordered,[status(thm)],[169,358]) ).
thf(3101,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(pattern_uni,[status(thm)],[3100:[bind(A,$thf( E )),bind(B,$thf( E @ last )),bind(C,$thf( E @ init ))]]) ).
thf(3190,plain,
! [A: $i] :
( ( A @ ( A @ last @ elem ) )
| ( A = q_nil ) ),
inference(simp,[status(thm)],[3101]) ).
thf(88,plain,
( ( sk3 @ host )
= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(101,plain,
( ( sk5 @ host )
= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(462,plain,
( ( sk5 @ host )
= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[101,104]) ).
thf(1559,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[462,1531]) ).
thf(1560,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1561,plain,
sk2 @ ( sk5 @ leq ),
inference(pattern_uni,[status(thm)],[1560:[bind(A,$thf( sk5 ))]]) ).
thf(4187,plain,
! [A: $i] :
( ( A != sk2 )
| ( q_nil @ ( sk5 @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,1561]) ).
thf(4188,plain,
( ( q_nil @ ( sk5 @ leq ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4187:[bind(A,$thf( sk2 ))]]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[287]) ).
thf(291,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[290]) ).
thf(89,plain,
~ ( sk4 @ host @ ( sk3 @ host @ leq ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(518,plain,
~ ( sk4 @ host @ ( sk2 @ host @ leq ) ),
inference(rewrite,[status(thm)],[89,104]) ).
thf(878,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,518]) ).
thf(879,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[878]) ).
thf(883,plain,
! [A: $i] :
( ( A
!= ( sk4 @ host ) )
| ( A
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[879]) ).
thf(885,plain,
( ( sk4 @ host )
!= ( sk2 @ host ) ),
inference(simp,[status(thm)],[883]) ).
thf(886,plain,
sk4 != sk2,
inference(simp,[status(thm)],[885]) ).
thf(4200,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,886]) ).
thf(4201,plain,
( ( sk2 != q_nil )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4200:[bind(A,$thf( sk4 ))]]) ).
thf(893,plain,
( ( ( sk4 @ host )
!= ( sk3 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[104,885]) ).
thf(894,plain,
( ( sk4 @ host )
!= ( sk3 @ host ) ),
inference(simp,[status(thm)],[893]) ).
thf(896,plain,
sk4 != sk3,
inference(simp,[status(thm)],[894]) ).
thf(4093,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk3 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,896]) ).
thf(4094,plain,
( ( sk3 != q_nil )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4093:[bind(A,$thf( sk4 ))]]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(365,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
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(321,plain,
! [A: $i,B: $i] :
( ( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ( A @ cons ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(322,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) )
=> ( B @ ( A @ cons ) @ ordered ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ ordered )
=> ( ! [C: $i] :
( ( ( ( C @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
& ( C @ pidElem )
& ( A @ pidElem )
& ( B @ ( C @ elem ) ) )
=> ( C @ pidMsg @ ( A @ pidMsg @ leq ) ) )
& ( B @ ordered ) ) ) ),
inference(miniscope,[status(thm)],[321]) ).
thf(323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ cons ) @ ordered )
| ~ ( D @ ( E @ sk18 ) @ pidMsg @ ( D @ pidMsg @ leq ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( ( D @ ( E @ sk18 ) @ pidMsg @ host )
= ( D @ pidMsg @ host ) )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ ( E @ sk18 ) @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( D @ pidElem )
| ~ ( E @ ordered ) )
& ( ( E @ ( D @ cons ) @ ordered )
| ( E @ ( D @ ( E @ sk18 ) @ elem ) )
| ~ ( E @ ordered ) )
& ( ( C @ pidMsg @ ( A @ pidMsg @ leq ) )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( B @ ( A @ cons ) @ ordered ) )
& ( ( B @ ordered )
| ~ ( B @ ( A @ cons ) @ ordered ) ) ),
inference(cnf,[status(esa)],[322]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ ( B @ sk18 ) @ pidElem )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ ( B @ sk18 ) @ pidElem )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[330]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(707,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ( B != A ) ),
inference(simp,[status(thm)],[107]) ).
thf(743,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Down @ elem ) ),
inference(simp,[status(thm)],[707]) ).
thf(2426,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[462,743]) ).
thf(2427,plain,
~ ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[2426:[bind(A,$thf( sk5 ))]]) ).
thf(75,plain,
sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[70]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ~ ( alive @ ( B @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[75,80]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(simp,[status(thm)],[470]) ).
thf(472,plain,
~ ( alive @ ( sk6 @ setIn ) ),
inference(pattern_uni,[status(thm)],[471:[bind(A,$thf( sk7 )),bind(B,$thf( sk6 ))]]) ).
thf(478,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( sk3 @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,472]) ).
thf(479,plain,
( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( sk3 @ setIn ) ) ),
inference(simp,[status(thm)],[478]) ).
thf(480,plain,
( ( alive != alive )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[479]) ).
thf(481,plain,
sk6 != sk3,
inference(simp,[status(thm)],[480]) ).
thf(71,plain,
( ( sk6 @ host )
= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(114,plain,
( ( sk6 @ host )
= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(534,plain,
( ( sk6 @ host )
= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[114,462]) ).
thf(87,plain,
( ( sk3 @ host )
!= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(121,plain,
( ( sk7 @ host )
!= ( sk3 @ host ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(491,plain,
( ( sk7 @ host )
!= ( sk2 @ host ) ),
inference(rewrite,[status(thm)],[121,104]) ).
thf(570,plain,
( ( ( sk7 @ host )
!= ( sk6 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[534,491]) ).
thf(571,plain,
( ( sk7 @ host )
!= ( sk6 @ host ) ),
inference(simp,[status(thm)],[570]) ).
thf(576,plain,
sk7 != sk6,
inference(simp,[status(thm)],[571]) ).
thf(4004,plain,
! [A: $i] :
( ( A != sk7 )
| ( sk6 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,576]) ).
thf(4005,plain,
( ( sk6 != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4004:[bind(A,$thf( sk7 ))]]) ).
thf(79,plain,
( ( sk7 = sk2 )
| ( alive @ ( sk7 @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(124,plain,
( ( alive @ ( sk7 @ setIn ) )
| ( sk7 = sk2 ) ),
inference(lifteq,[status(thm)],[79]) ).
thf(492,plain,
sk7 != sk2,
inference(simp,[status(thm)],[491]) ).
thf(613,plain,
alive @ ( sk7 @ setIn ),
inference(simplifyReflect,[status(thm)],[124,492]) ).
thf(92,plain,
( ( sk3 @ host @ queue )
= ( sk1 @ ( sk4 @ m_Down @ cons ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(111,plain,
( ( sk1 @ ( sk4 @ m_Down @ cons ) )
= ( sk3 @ host @ queue ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(756,plain,
( ( sk1 @ ( sk4 @ m_Down @ cons ) )
= ( sk2 @ host @ queue ) ),
inference(rewrite,[status(thm)],[111,104]) ).
thf(98,plain,
sk1 @ ( sk8 @ m_Down @ elem ),
inference(cnfConj,[status(thm)],[70]) ).
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(262,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(263,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ elem ) )
| ( A = B ) )
=> ( C @ ( B @ cons ) @ ( A @ elem ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
=> ( ( C @ ( A @ elem ) )
| ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[262]) ).
thf(264,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ cons ) @ ( D @ elem ) )
| ~ ( F @ ( D @ elem ) ) )
& ( ( F @ ( E @ cons ) @ ( D @ elem ) )
| ( D != E ) )
& ( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[264]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(9547,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,271]) ).
thf(9548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[9547]) ).
thf(9549,plain,
! [A: $i] : ( sk1 @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[9548:[bind(A,$thf( sk8 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(9677,plain,
! [A: $i] : ( sk1 @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[9549]) ).
thf(15678,plain,
! [A: $i] :
( ( ( sk1 @ ( sk4 @ m_Down @ cons ) )
!= ( sk1 @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[756,9677]) ).
thf(15679,plain,
sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[15678:[bind(A,$thf( sk4 @ m_Down ))]]) ).
thf(15883,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ~ ( alive @ ( B @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[15679,80]) ).
thf(15884,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(simp,[status(thm)],[15883]) ).
thf(15885,plain,
~ ( alive @ ( sk8 @ setIn ) ),
inference(pattern_uni,[status(thm)],[15884:[bind(A,$thf( sk2 )),bind(B,$thf( sk8 ))]]) ).
thf(15990,plain,
( ( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( sk7 @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,15885]) ).
thf(15991,plain,
( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( sk7 @ setIn ) ) ),
inference(simp,[status(thm)],[15990]) ).
thf(16006,plain,
( ( alive != alive )
| ( sk8 != sk7 ) ),
inference(simp,[status(thm)],[15991]) ).
thf(16013,plain,
sk8 != sk7,
inference(simp,[status(thm)],[16006]) ).
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(347,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ordered )
=> ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(94,plain,
( ( sk8 @ host )
= ( sk7 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(125,plain,
( ( sk8 @ host )
= ( sk7 @ host ) ),
inference(lifteq,[status(thm)],[94]) ).
thf(503,plain,
( ( ( sk8 @ host )
!= ( sk6 @ host ) )
| ( ( sk7 @ host )
= ( sk5 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[114,125]) ).
thf(512,plain,
( ( sk8 != sk6 )
| ( ( sk7 @ host )
= ( sk5 @ host ) ) ),
inference(simp,[status(thm)],[503]) ).
thf(858,plain,
( ( sk8 != sk6 )
| ( ( sk7 @ host )
= ( sk2 @ host ) ) ),
inference(rewrite,[status(thm)],[512,462]) ).
thf(859,plain,
sk8 != sk6,
inference(simplifyReflect,[status(thm)],[858,491]) ).
thf(4021,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk6 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,859]) ).
thf(4022,plain,
( ( sk6 != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4021:[bind(A,$thf( sk8 ))]]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(388,plain,
! [A: $i,B: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(389,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( B @ ( A @ cons ) ) ),
inference(miniscope,[status(thm)],[388]) ).
thf(390,plain,
! [B: $i,A: $i] :
( q_nil
!= ( B @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[389]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) )
!= q_nil ),
inference(lifteq,[status(thm)],[390]) ).
thf(2019,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[756,391]) ).
thf(2020,plain,
( ( sk2 @ host @ queue )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2019:[bind(A,$thf( sk4 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(3416,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,2020]) ).
thf(3417,plain,
! [A: $i] :
( ( A
!= ( sk2 @ host @ queue ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[3416]) ).
thf(3418,plain,
sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ),
inference(pattern_uni,[status(thm)],[3417:[bind(A,$thf( sk2 @ host @ queue ))]]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( B @ host @ ( A @ host @ leq ) )
| ~ ( A @ host @ queue @ ( B @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(1729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ $true
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[291,128]) ).
thf(1730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( C @ host @ ( B @ host @ leq ) ) )
| ~ ( B @ host @ queue @ ( C @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[1729]) ).
thf(1731,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[1730:[bind(A,$thf( D @ host )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(1771,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( A @ m_Halt @ elem ) ),
inference(simp,[status(thm)],[1731]) ).
thf(2606,plain,
! [A: $i] :
( ( ( sk5 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[462,1771]) ).
thf(2607,plain,
~ ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[2606:[bind(A,$thf( sk5 ))]]) ).
thf(9024,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,2607]) ).
thf(9025,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[9024]) ).
thf(9119,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk5 @ m_Halt ) ) ),
inference(simp,[status(thm)],[9025]) ).
thf(9180,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk5 @ m_Halt ) ),
inference(simp,[status(thm)],[9119]) ).
thf(15510,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk3 @ ( sk2 @ leq ) ) )
| ( sk2 != nil )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,14977]) ).
thf(15511,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk3 @ ( sk2 @ leq ) ) )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[15510]) ).
thf(15565,plain,
! [A: $i] :
( ( A != sk3 )
| ( A != sk2 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[15511]) ).
thf(15573,plain,
( ( sk3 != sk2 )
| ( sk2 != nil ) ),
inference(simp,[status(thm)],[15565]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[264]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(270,plain,
! [B: $i,A: $i] : ( B @ ( A @ cons ) @ ( A @ elem ) ),
inference(simp,[status(thm)],[269]) ).
thf(2896,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( A @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[756,270]) ).
thf(2897,plain,
sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ),
inference(pattern_uni,[status(thm)],[2896:[bind(A,$thf( sk4 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(2992,plain,
( ( ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2897,2427]) ).
thf(2993,plain,
( ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2992]) ).
thf(3064,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk5 @ m_Down )
!= ( sk4 @ m_Down ) ) ),
inference(simp,[status(thm)],[2993]) ).
thf(3072,plain,
( ( sk5 @ m_Down )
!= ( sk4 @ m_Down ) ),
inference(simp,[status(thm)],[3064]) ).
thf(56,axiom,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(385,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(386,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
= ( A @ ( q_nil @ snoc ) ) ),
inference(cnf,[status(esa)],[385]) ).
thf(387,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) )
= ( q_nil @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[386]) ).
thf(2610,plain,
! [A: $i] :
( ( ( sk3 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[104,1771]) ).
thf(2611,plain,
~ ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[2610:[bind(A,$thf( sk3 ))]]) ).
thf(3124,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,2611]) ).
thf(3125,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[3124]) ).
thf(3146,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Halt ) ) ),
inference(simp,[status(thm)],[3125]) ).
thf(3173,plain,
! [A: $i] :
( ( sk3 @ m_Halt @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3146]) ).
thf(3316,plain,
! [B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( sk3 @ m_Halt @ ( B @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) ) ),
inference(paramod_ordered,[status(thm)],[387,3173]) ).
thf(3317,plain,
( ( q_nil @ ( sk3 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(pattern_uni,[status(thm)],[3316:[bind(A,$thf( sk3 @ m_Halt )),bind(B,$thf( q_nil ))]]) ).
thf(891,plain,
( ( ( sk5 @ host )
!= ( sk4 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[462,885]) ).
thf(892,plain,
( ( sk5 @ host )
!= ( sk4 @ host ) ),
inference(simp,[status(thm)],[891]) ).
thf(895,plain,
sk5 != sk4,
inference(simp,[status(thm)],[892]) ).
thf(12319,plain,
! [B: $i,A: $i] :
( ( A != sk5 )
| ( B != sk4 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[289,895]) ).
thf(12320,plain,
! [A: $i] :
( ( A != sk4 )
| ~ ( sk5 @ ( A @ leq ) )
| ~ ( A @ ( sk5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12319:[bind(A,$thf( sk5 ))]]) ).
thf(13520,plain,
( ~ ( sk5 @ ( sk4 @ leq ) )
| ~ ( sk4 @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[12320]) ).
thf(24,axiom,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(217,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
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(308,plain,
! [A: $i] :
( ( A @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(99,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(119,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)],[99]) ).
thf(120,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)],[119]) ).
thf(4018,plain,
! [A: $i] :
( ( A != sk7 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,613]) ).
thf(4019,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4018:[bind(A,$thf( sk7 ))]]) ).
thf(64,axiom,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(411,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(412,plain,
~ ? [A: $i] : ( q_nil @ ( A @ elem ) ),
inference(miniscope,[status(thm)],[411]) ).
thf(413,plain,
! [A: $i] :
~ ( q_nil @ ( A @ elem ) ),
inference(cnf,[status(esa)],[412]) ).
thf(9963,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( alive @ ( q_nil @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[4019,413]) ).
thf(9964,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( alive @ ( q_nil @ setIn ) ) ),
inference(simp,[status(thm)],[9963]) ).
thf(10011,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( sk7 @ last )
!= A )
| ( alive @ ( q_nil @ setIn ) ) ),
inference(simp,[status(thm)],[9964]) ).
thf(10050,plain,
( ( sk7 != q_nil )
| ( alive @ ( q_nil @ setIn ) ) ),
inference(simp,[status(thm)],[10011]) ).
thf(3028,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ $true
| ~ ( alive @ ( B @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[2897,80]) ).
thf(3029,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) )
!= ( A @ host @ queue @ ( B @ m_Down @ elem ) ) )
| ~ ( alive @ ( B @ setIn ) ) ),
inference(simp,[status(thm)],[3028]) ).
thf(3030,plain,
~ ( alive @ ( sk4 @ setIn ) ),
inference(pattern_uni,[status(thm)],[3029:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(10105,plain,
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ~ $true
| ( sk7 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[10050,3030]) ).
thf(10106,plain,
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[10105]) ).
thf(10110,plain,
( ( alive != alive )
| ( sk4 != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[10106]) ).
thf(10125,plain,
( ( sk4 != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[10110]) ).
thf(505,plain,
( ( ( sk8 @ host )
!= ( sk3 @ host ) )
| ( ( sk7 @ host )
= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[125,104]) ).
thf(513,plain,
( ( sk8 != sk3 )
| ( ( sk7 @ host )
= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[505]) ).
thf(977,plain,
sk8 != sk3,
inference(simplifyReflect,[status(thm)],[513,491]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(355,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[352]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ ( C @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(29441,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,359]) ).
thf(29442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[29441]) ).
thf(29443,plain,
! [A: $i] : ( A @ ( sk7 @ host @ queue @ snoc ) @ ( sk6 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[29442:[bind(A,$thf( sk6 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk7 @ host @ queue ))]]) ).
thf(29525,plain,
! [A: $i] : ( A @ ( sk7 @ host @ queue @ snoc ) @ ( sk6 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[29443]) ).
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(431,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(432,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) )
=> ( B @ s @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ s @ ( A @ leq ) )
=> ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ) ) ),
inference(miniscope,[status(thm)],[431]) ).
thf(433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ s @ ( C @ leq ) )
| ~ ( D @ ( C @ leq ) ) )
& ( ( D @ s @ ( C @ leq ) )
| ( C
!= ( D @ s ) ) )
& ( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) )
| ~ ( B @ s @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[432]) ).
thf(436,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[436]) ).
thf(675,plain,
! [A: $i] :
( ( ( sk1 @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,413]) ).
thf(676,plain,
! [A: $i] :
( ( sk1 @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[675]) ).
thf(678,plain,
! [A: $i] :
( ( sk1 != q_nil )
| ( ( sk8 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[676]) ).
thf(680,plain,
sk1 != q_nil,
inference(simp,[status(thm)],[678]) ).
thf(3954,plain,
! [A: $i] :
( ( A != sk1 )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,680]) ).
thf(3955,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[3954]) ).
thf(3956,plain,
sk1 @ ( sk1 @ last @ elem ),
inference(pattern_uni,[status(thm)],[3955:[bind(A,$thf( sk1 ))]]) ).
thf(9594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3956,271]) ).
thf(9595,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[9594]) ).
thf(9596,plain,
! [A: $i] : ( sk1 @ ( A @ cons ) @ ( sk1 @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[9595:[bind(A,$thf( sk1 @ last )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(9687,plain,
! [A: $i] : ( sk1 @ ( A @ cons ) @ ( sk1 @ last @ elem ) ),
inference(simp,[status(thm)],[9596]) ).
thf(16960,plain,
! [A: $i] :
( ( ( sk1 @ ( sk4 @ m_Down @ cons ) )
!= ( sk1 @ ( A @ cons ) ) )
| ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[756,9687]) ).
thf(16961,plain,
sk2 @ host @ queue @ ( sk1 @ last @ elem ),
inference(pattern_uni,[status(thm)],[16960:[bind(A,$thf( sk4 @ m_Down ))]]) ).
thf(17165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16961,271]) ).
thf(17166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[17165]) ).
thf(17167,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk1 @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[17166:[bind(A,$thf( sk1 @ last )),bind(B,$thf( B )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(17253,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk1 @ last @ elem ) ),
inference(simp,[status(thm)],[17167]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(381,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(382,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[381]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[382]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[383]) ).
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(239,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(240,plain,
( ! [A: $i,B: $i] :
( ( B @ s @ ( A @ s @ leq ) )
=> ( B @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ s @ ( A @ s @ leq ) ) ) ),
inference(miniscope,[status(thm)],[239]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ leq ) )
| ~ ( D @ s @ ( C @ s @ leq ) ) )
& ( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(4706,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1568,242]) ).
thf(4707,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4706]) ).
thf(4708,plain,
sk2 @ s @ ( sk3 @ s @ leq ),
inference(pattern_uni,[status(thm)],[4707:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(4789,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk3 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4708,242]) ).
thf(4790,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk3 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4789]) ).
thf(4791,plain,
sk2 @ s @ s @ ( sk3 @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[4790:[bind(A,$thf( sk3 @ s )),bind(B,$thf( sk2 @ s ))]]) ).
thf(5408,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk3 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4791,242]) ).
thf(5409,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk3 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5408]) ).
thf(5410,plain,
sk2 @ s @ s @ s @ ( sk3 @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[5409:[bind(A,$thf( sk3 @ s @ s )),bind(B,$thf( sk2 @ s @ s ))]]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(392,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(393,plain,
~ ? [A: $i] : ( A @ ( A @ s @ leq ) ),
inference(miniscope,[status(thm)],[392]) ).
thf(394,plain,
! [A: $i] :
~ ( A @ ( A @ s @ leq ) ),
inference(cnf,[status(esa)],[393]) ).
thf(21799,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s @ ( sk3 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5410,394]) ).
thf(21800,plain,
! [A: $i] :
( ( sk2 @ s @ s @ s @ ( sk3 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[21799]) ).
thf(21855,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s )
!= A )
| ( ( sk3 @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[21800]) ).
thf(21876,plain,
( ( sk2 @ s @ s @ s @ s )
!= ( sk3 @ s @ s @ s ) ),
inference(simp,[status(thm)],[21855]) ).
thf(887,plain,
( ( ( sk6 @ host )
!= ( sk4 @ host ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[534,885]) ).
thf(888,plain,
( ( sk6 @ host )
!= ( sk4 @ host ) ),
inference(simp,[status(thm)],[887]) ).
thf(900,plain,
sk6 != sk4,
inference(simp,[status(thm)],[888]) ).
thf(3825,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk4 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,900]) ).
thf(3826,plain,
( ( sk4 != q_nil )
| ( sk6 @ ( sk6 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3825:[bind(A,$thf( sk6 ))]]) ).
thf(43,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_09) ).
thf(338,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(339,plain,
elec_2 != norm,
inference(polarity_switch,[status(thm)],[338]) ).
thf(340,plain,
elec_2 != norm,
inference(lifteq,[status(thm)],[339]) ).
thf(18,axiom,
nbr_proc @ ( zero @ s @ leq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(197,plain,
nbr_proc @ ( zero @ s @ leq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4714,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[197,242]) ).
thf(4715,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4714]) ).
thf(4716,plain,
nbr_proc @ s @ ( zero @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[4715:[bind(A,$thf( zero @ s )),bind(B,$thf( nbr_proc ))]]) ).
thf(5190,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4716,242]) ).
thf(5191,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5190]) ).
thf(5192,plain,
nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[5191:[bind(A,$thf( zero @ s @ s )),bind(B,$thf( nbr_proc @ s ))]]) ).
thf(15698,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9677,413]) ).
thf(15699,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[15698]) ).
thf(15773,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ cons ) )
!= q_nil )
| ( ( sk8 @ m_Down )
!= B ) ),
inference(simp,[status(thm)],[15699]) ).
thf(15791,plain,
! [A: $i] :
( ( sk1 @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[15773]) ).
thf(9515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2897,271]) ).
thf(9516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[9515]) ).
thf(9517,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk4 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[9516:[bind(A,$thf( sk4 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(9672,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk4 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[9517]) ).
thf(1548,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk2 @ host )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[534,1531]) ).
thf(1549,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1548]) ).
thf(1550,plain,
sk2 @ ( sk6 @ leq ),
inference(pattern_uni,[status(thm)],[1549:[bind(A,$thf( sk6 ))]]) ).
thf(13315,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[1550,289]) ).
thf(13316,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[13315]) ).
thf(13317,plain,
( ~ ( sk6 @ ( sk2 @ leq ) )
| ( sk6 = sk2 ) ),
inference(pattern_uni,[status(thm)],[13316:[bind(A,$thf( sk6 )),bind(B,$thf( sk2 ))]]) ).
thf(4219,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk2 @ ( q_nil @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,1550]) ).
thf(4220,plain,
( ( sk2 @ ( q_nil @ leq ) )
| ( sk6 @ ( sk6 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4219:[bind(A,$thf( sk6 ))]]) ).
thf(1544,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( sk2 @ host ) )
| ( sk2 @ ( A @ leq ) )
| ( ( sk7 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[125,1531]) ).
thf(1589,plain,
! [A: $i] :
( ( sk8 != sk2 )
| ( sk7 != A )
| ( sk2 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1544]) ).
thf(1611,plain,
( ( sk8 != sk2 )
| ( sk2 @ ( sk7 @ leq ) ) ),
inference(simp,[status(thm)],[1589]) ).
thf(2161,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk7 @ leq ) ) )
| ~ $true
| ( sk8 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[1611,394]) ).
thf(2162,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk7 @ leq ) ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2161]) ).
thf(2175,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk7 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2162]) ).
thf(2184,plain,
( ( ( sk2 @ s )
!= sk7 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2175]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(360,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ leq ) )
| ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[360]) ).
thf(30652,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ~ $true
| ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[361,394]) ).
thf(30653,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ leq ) )
!= ( C @ ( C @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[30652]) ).
thf(30654,plain,
! [A: $i] : ( A @ s @ ( A @ leq ) ),
inference(pattern_uni,[status(thm)],[30653:[bind(A,$thf( A )),bind(B,$thf( A @ s )),bind(C,$thf( A ))]]) ).
thf(30744,plain,
! [B: $i,A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30654,394]) ).
thf(30745,plain,
! [B: $i,A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[30744]) ).
thf(30782,plain,
! [B: $i,A: $i] :
( ( ( A @ s )
!= B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[30745]) ).
thf(30814,plain,
! [A: $i] :
( ( A @ s @ s )
!= A ),
inference(simp,[status(thm)],[30782]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(cnf,[status(esa)],[157]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ last )
= A ),
inference(lifteq,[status(thm)],[158]) ).
thf(2390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) @ last )
= B ) ),
inference(paramod_ordered,[status(thm)],[387,159]) ).
thf(2391,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ last )
= A ),
inference(pattern_uni,[status(thm)],[2390:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(2420,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[534,743]) ).
thf(2421,plain,
~ ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[2420:[bind(A,$thf( sk6 ))]]) ).
thf(9080,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,2421]) ).
thf(9081,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[9080]) ).
thf(9118,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[9081]) ).
thf(9179,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Down ) ),
inference(simp,[status(thm)],[9118]) ).
thf(9218,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk2 @ host @ queue @ last ) )
| ( A
!= ( sk6 @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[2391,9179]) ).
thf(9246,plain,
( ( q_nil @ ( sk6 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[9218]) ).
thf(2156,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,394]) ).
thf(2157,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2156]) ).
thf(2171,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( A
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2157]) ).
thf(2180,plain,
! [A: $i] :
( ( A @ s )
!= A ),
inference(simp,[status(thm)],[2171]) ).
thf(3865,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s ) )
| ( q_nil != B )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,2180]) ).
thf(3866,plain,
! [A: $i] :
( ( q_nil != A )
| ( A @ s @ ( A @ s @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3865:[bind(A,$thf( C @ s )),bind(B,$thf( C ))]]) ).
thf(4456,plain,
q_nil @ s @ ( q_nil @ s @ last @ elem ),
inference(simp,[status(thm)],[3866]) ).
thf(9562,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4456,271]) ).
thf(9563,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[9562]) ).
thf(9564,plain,
! [A: $i] : ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[9563:[bind(A,$thf( q_nil @ s @ last )),bind(B,$thf( B )),bind(C,$thf( q_nil @ s ))]]) ).
thf(9680,plain,
! [A: $i] : ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) ),
inference(simp,[status(thm)],[9564]) ).
thf(38981,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9680,413]) ).
thf(38982,plain,
! [B: $i,A: $i] :
( ( q_nil @ s @ ( A @ cons ) @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[38981]) ).
thf(39053,plain,
! [B: $i,A: $i] :
( ( ( q_nil @ s @ ( A @ cons ) )
!= q_nil )
| ( ( q_nil @ s @ last )
!= B ) ),
inference(simp,[status(thm)],[38982]) ).
thf(39093,plain,
! [A: $i] :
( ( q_nil @ s @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[39053]) ).
thf(2598,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk7 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[125,1771]) ).
thf(2599,plain,
~ ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[2598:[bind(A,$thf( sk8 ))]]) ).
thf(2918,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,2599]) ).
thf(2919,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[2918]) ).
thf(2957,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Halt ) ) ),
inference(simp,[status(thm)],[2919]) ).
thf(2972,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Halt @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[2957]) ).
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(317,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(318,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NormQ ) ),
inference(miniscope,[status(thm)],[317]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(cnf,[status(esa)],[318]) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NormQ ) ),
inference(lifteq,[status(thm)],[319]) ).
thf(218,plain,
! [A: $i] : ( nbr_proc @ ( A @ host @ leq ) ),
inference(cnf,[status(esa)],[217]) ).
thf(4742,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,242]) ).
thf(4743,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[4742]) ).
thf(4744,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[4743:[bind(A,$thf( D )),bind(B,$thf( D @ host )),bind(C,$thf( nbr_proc ))]]) ).
thf(4760,plain,
! [A: $i] : ( nbr_proc @ s @ ( A @ host @ s @ leq ) ),
inference(simp,[status(thm)],[4744]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(404,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(43312,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk7 @ host @ queue @ snoc ) @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29525,413]) ).
thf(43313,plain,
! [B: $i,A: $i] :
( ( A @ ( sk7 @ host @ queue @ snoc ) @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[43312]) ).
thf(43428,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk7 @ host @ queue @ snoc ) )
!= q_nil )
| ( ( sk6 @ m_Down )
!= B ) ),
inference(simp,[status(thm)],[43313]) ).
thf(43485,plain,
! [A: $i] :
( ( A @ ( sk7 @ host @ queue @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[43428]) ).
thf(4751,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1550,242]) ).
thf(4752,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4751]) ).
thf(4753,plain,
sk2 @ s @ ( sk6 @ s @ leq ),
inference(pattern_uni,[status(thm)],[4752:[bind(A,$thf( sk6 )),bind(B,$thf( sk2 ))]]) ).
thf(4852,plain,
! [A: $i] :
( ( ( sk2 @ s @ ( sk6 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4753,394]) ).
thf(4853,plain,
! [A: $i] :
( ( sk2 @ s @ ( sk6 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4852]) ).
thf(4861,plain,
! [A: $i] :
( ( ( sk2 @ s )
!= A )
| ( ( sk6 @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[4853]) ).
thf(4866,plain,
( ( sk2 @ s @ s )
!= ( sk6 @ s ) ),
inference(simp,[status(thm)],[4861]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(401,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(cnf,[status(esa)],[401]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(lifteq,[status(thm)],[402]) ).
thf(3274,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ head )
= A ) ),
inference(paramod_ordered,[status(thm)],[756,403]) ).
thf(3275,plain,
( ( sk2 @ host @ queue @ head )
= ( sk4 @ m_Down ) ),
inference(pattern_uni,[status(thm)],[3274:[bind(A,$thf( sk4 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(74,plain,
( ( sk5 = sk2 )
| ( alive @ ( sk5 @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(110,plain,
( ( alive @ ( sk5 @ setIn ) )
| ( sk5 = sk2 ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(2154,plain,
! [A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[197,394]) ).
thf(2155,plain,
! [A: $i] :
( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[2154]) ).
thf(2176,plain,
! [A: $i] :
( ( nbr_proc != A )
| ( ( zero @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[2155]) ).
thf(2177,plain,
( ( nbr_proc @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2176]) ).
thf(2185,plain,
nbr_proc != zero,
inference(simp,[status(thm)],[2177]) ).
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(341,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(342,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Halt ) ),
inference(miniscope,[status(thm)],[341]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(cnf,[status(esa)],[342]) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Halt ) ),
inference(lifteq,[status(thm)],[343]) ).
thf(2600,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ~ ( sk2 @ host @ queue @ ( A @ m_Halt @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[534,1771]) ).
thf(2601,plain,
~ ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ),
inference(pattern_uni,[status(thm)],[2600:[bind(A,$thf( sk6 ))]]) ).
thf(17136,plain,
( ( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16961,2601]) ).
thf(17137,plain,
( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[17136]) ).
thf(17226,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk1 @ last )
!= ( sk6 @ m_Halt ) ) ),
inference(simp,[status(thm)],[17137]) ).
thf(17270,plain,
( ( sk1 @ last )
!= ( sk6 @ m_Halt ) ),
inference(simp,[status(thm)],[17226]) ).
thf(5084,plain,
! [A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4456,413]) ).
thf(5085,plain,
! [A: $i] :
( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[5084]) ).
thf(5135,plain,
! [A: $i] :
( ( ( q_nil @ s )
!= q_nil )
| ( ( q_nil @ s @ last )
!= A ) ),
inference(simp,[status(thm)],[5085]) ).
thf(5150,plain,
( ( q_nil @ s )
!= q_nil ),
inference(simp,[status(thm)],[5135]) ).
thf(4242,plain,
! [A: $i] :
( ( A != sk3 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,454]) ).
thf(4243,plain,
( ( nil != q_nil )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4242:[bind(A,$thf( sk3 ))]]) ).
thf(48198,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[197,440]) ).
thf(48199,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[48198]) ).
thf(48200,plain,
nbr_proc @ s @ ( zero @ s @ leq ),
inference(pattern_uni,[status(thm)],[48199:[bind(A,$thf( zero @ s )),bind(B,$thf( nbr_proc ))]]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(49325,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ leq ) )
!= ( B @ s @ ( A @ s @ leq ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48200,244]) ).
thf(49326,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ leq ) )
!= ( B @ s @ ( A @ s @ leq ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[49325]) ).
thf(49327,plain,
nbr_proc @ ( zero @ leq ),
inference(pattern_uni,[status(thm)],[49326:[bind(A,$thf( zero )),bind(B,$thf( nbr_proc ))]]) ).
thf(50006,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( zero @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49327,394]) ).
thf(50007,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[50006]) ).
thf(50052,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( ( A @ s )
!= zero ) ),
inference(simp,[status(thm)],[50007]) ).
thf(50083,plain,
( ( nbr_proc @ s )
!= zero ),
inference(simp,[status(thm)],[50052]) ).
thf(15,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(189,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5185,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4716,394]) ).
thf(5186,plain,
! [A: $i] :
( ( nbr_proc @ s @ ( zero @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5185]) ).
thf(5195,plain,
! [A: $i] :
( ( ( nbr_proc @ s )
!= A )
| ( ( zero @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[5186]) ).
thf(5199,plain,
( ( nbr_proc @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[5195]) ).
thf(12767,plain,
! [B: $i,A: $i] :
( ( A != sk8 )
| ( B != sk6 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[289,859]) ).
thf(12768,plain,
! [A: $i] :
( ( A != sk6 )
| ~ ( sk8 @ ( A @ leq ) )
| ~ ( A @ ( sk8 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12767:[bind(A,$thf( sk8 ))]]) ).
thf(13689,plain,
( ~ ( sk8 @ ( sk6 @ leq ) )
| ~ ( sk6 @ ( sk8 @ leq ) ) ),
inference(simp,[status(thm)],[12768]) ).
thf(40632,plain,
( ( ( sk8 @ ( sk6 @ leq ) )
!= ( sk2 @ ( sk6 @ leq ) ) )
| ~ $true
| ~ ( sk6 @ ( sk8 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[1550,13689]) ).
thf(40633,plain,
( ( ( sk8 @ ( sk6 @ leq ) )
!= ( sk2 @ ( sk6 @ leq ) ) )
| ~ ( sk6 @ ( sk8 @ leq ) ) ),
inference(simp,[status(thm)],[40632]) ).
thf(40648,plain,
( ( sk8 != sk2 )
| ( sk6 != sk6 )
| ~ ( sk6 @ ( sk8 @ leq ) ) ),
inference(simp,[status(thm)],[40633]) ).
thf(40747,plain,
( ( sk8 != sk2 )
| ~ ( sk6 @ ( sk8 @ leq ) ) ),
inference(simp,[status(thm)],[40648]) ).
thf(40879,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( sk6 @ ( sk8 @ leq ) ) )
| ( sk8 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30654,40747]) ).
thf(40880,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( sk6 @ ( sk8 @ leq ) ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[40879]) ).
thf(40909,plain,
! [A: $i] :
( ( ( A @ s )
!= sk6 )
| ( A != sk8 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[40880]) ).
thf(40931,plain,
( ( ( sk8 @ s )
!= sk6 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[40909]) ).
thf(17100,plain,
( ( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16961,2427]) ).
thf(17101,plain,
( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[17100]) ).
thf(17211,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk1 @ last )
!= ( sk5 @ m_Down ) ) ),
inference(simp,[status(thm)],[17101]) ).
thf(17264,plain,
( ( sk1 @ last )
!= ( sk5 @ m_Down ) ),
inference(simp,[status(thm)],[17211]) ).
thf(17304,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk5 @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[2391,17264]) ).
thf(17317,plain,
( ( q_nil @ ( sk5 @ m_Down @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[17304]) ).
thf(23,axiom,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(215,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(216,plain,
! [A: $i] : ( A @ host @ ( zero @ s @ leq ) ),
inference(cnf,[status(esa)],[215]) ).
thf(2152,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,394]) ).
thf(2153,plain,
! [B: $i,A: $i] :
( ( A @ host @ ( zero @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2152]) ).
thf(2172,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= B )
| ( ( zero @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2153]) ).
thf(2181,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( zero @ s ) ),
inference(simp,[status(thm)],[2172]) ).
thf(2242,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[534,2181]) ).
thf(2243,plain,
( ( sk2 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[2242:[bind(A,$thf( sk6 ))]]) ).
thf(2301,plain,
( ( sk2 @ host )
!= zero ),
inference(simp,[status(thm)],[2243]) ).
thf(40,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(314,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(315,plain,
elec_2 != wait,
inference(polarity_switch,[status(thm)],[314]) ).
thf(316,plain,
elec_2 != wait,
inference(lifteq,[status(thm)],[315]) ).
thf(17182,plain,
( ( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16961,2421]) ).
thf(17183,plain,
( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[17182]) ).
thf(17227,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk1 @ last )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[17183]) ).
thf(17271,plain,
( ( sk1 @ last )
!= ( sk6 @ m_Down ) ),
inference(simp,[status(thm)],[17227]) ).
thf(17865,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk6 @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[159,17271]) ).
thf(17875,plain,
! [A: $i] :
( ( sk6 @ m_Down @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17865]) ).
thf(17884,plain,
! [A: $i] :
( ( sk6 @ m_Down @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17875]) ).
thf(2522,plain,
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,2421]) ).
thf(2523,plain,
( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2522]) ).
thf(2526,plain,
( ( ( sk7 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk6 @ m_Down )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[2523]) ).
thf(2533,plain,
( ( sk7 @ host @ queue )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2526]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(259,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(lifteq,[status(thm)],[260]) ).
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(150,plain,
! [A: $i,B: $i] :
( ( A @ ordered )
=> ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(151,plain,
! [A: $i] :
( ( A @ ordered )
=> ! [B: $i] : ( B @ m_Ldr @ ( A @ snoc ) @ ordered ) ),
inference(miniscope,[status(thm)],[150]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( B @ m_Ldr @ ( A @ snoc ) @ ordered )
| ~ ( A @ ordered ) ),
inference(cnf,[status(esa)],[151]) ).
thf(541,plain,
( ( ( sk8 @ host )
!= ( sk5 @ host ) )
| ( ( sk7 @ host )
= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[125,462]) ).
thf(549,plain,
( ( sk8 != sk5 )
| ( ( sk7 @ host )
= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(1028,plain,
sk8 != sk5,
inference(simplifyReflect,[status(thm)],[549,491]) ).
thf(3641,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk5 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,1028]) ).
thf(3642,plain,
( ( sk5 != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3641:[bind(A,$thf( sk8 ))]]) ).
thf(20560,plain,
! [A: $i] :
( ( A != sk5 )
| ( q_nil != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3642]) ).
thf(20561,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk8 @ ( sk8 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[20560]) ).
thf(20562,plain,
( ( sk8 @ ( sk8 @ last @ elem ) )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[20561:[bind(A,$thf( sk5 ))]]) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,80]) ).
thf(474,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk3 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[473]) ).
thf(475,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk3 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
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(441,plain,
! [A: $i,B: $i] :
( ( ( A @ host @ s )
= ( B @ host ) )
=> ( ( A @ host )
!= ( B @ host ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(442,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= ( B @ host ) )
| ( ( A @ host @ s )
!= ( B @ host ) ) ),
inference(cnf,[status(esa)],[441]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ( ( A @ host )
!= ( B @ host ) )
| ( ( A @ host @ s )
!= ( B @ host ) ) ),
inference(lifteq,[status(thm)],[442]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(374,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(375,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(cnf,[status(esa)],[374]) ).
thf(376,plain,
! [A: $i] :
( ( A @ m_Down @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[375]) ).
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(211,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(20568,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk5 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3642,413]) ).
thf(20569,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[20568]) ).
thf(20620,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( sk8 @ last )
!= A )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[20569]) ).
thf(20655,plain,
( ( sk8 != q_nil )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[20620]) ).
thf(17110,plain,
( ( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16961,2607]) ).
thf(17111,plain,
( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[17110]) ).
thf(17214,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk1 @ last )
!= ( sk5 @ m_Halt ) ) ),
inference(simp,[status(thm)],[17111]) ).
thf(17266,plain,
( ( sk1 @ last )
!= ( sk5 @ m_Halt ) ),
inference(simp,[status(thm)],[17214]) ).
thf(4784,plain,
! [A: $i] :
( ( ( sk2 @ s @ ( sk3 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4708,394]) ).
thf(4785,plain,
! [A: $i] :
( ( sk2 @ s @ ( sk3 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4784]) ).
thf(4793,plain,
! [A: $i] :
( ( ( sk2 @ s )
!= A )
| ( ( sk3 @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[4785]) ).
thf(4798,plain,
( ( sk2 @ s @ s )
!= ( sk3 @ s ) ),
inference(simp,[status(thm)],[4793]) ).
thf(2167,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk6 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1550,394]) ).
thf(2168,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk6 @ leq ) ) ),
inference(simp,[status(thm)],[2167]) ).
thf(2169,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk6 ) ),
inference(simp,[status(thm)],[2168]) ).
thf(2178,plain,
( ( sk2 @ s )
!= sk6 ),
inference(simp,[status(thm)],[2169]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49942,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49327,440]) ).
thf(49943,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( zero @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[49942]) ).
thf(49944,plain,
nbr_proc @ s @ ( zero @ leq ),
inference(pattern_uni,[status(thm)],[49943:[bind(A,$thf( zero )),bind(B,$thf( nbr_proc ))]]) ).
thf(50224,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( zero @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49944,394]) ).
thf(50225,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( nbr_proc @ s @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[50224]) ).
thf(50297,plain,
! [A: $i] :
( ( A
!= ( nbr_proc @ s ) )
| ( ( A @ s )
!= zero ) ),
inference(simp,[status(thm)],[50225]) ).
thf(50326,plain,
( ( nbr_proc @ s @ s )
!= zero ),
inference(simp,[status(thm)],[50297]) ).
thf(2892,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,2607]) ).
thf(2893,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[2892]) ).
thf(2949,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk5 @ m_Halt ) ) ),
inference(simp,[status(thm)],[2893]) ).
thf(2964,plain,
! [A: $i] :
( ( A @ ( sk5 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2949]) ).
thf(59,axiom,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(395,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(396,plain,
! [A: $i] :
( ( A
= ( A @ tail @ ( A @ head @ cons ) ) )
| ( A = q_nil ) ),
inference(cnf,[status(esa)],[395]) ).
thf(397,plain,
! [A: $i] :
( ( ( A @ tail @ ( A @ head @ cons ) )
= A )
| ( A = q_nil ) ),
inference(lifteq,[status(thm)],[396]) ).
thf(4857,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk6 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4753,242]) ).
thf(4858,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk6 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4857]) ).
thf(4859,plain,
sk2 @ s @ s @ ( sk6 @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[4858:[bind(A,$thf( sk6 @ s )),bind(B,$thf( sk2 @ s ))]]) ).
thf(5490,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk6 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4859,242]) ).
thf(5491,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk6 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5490]) ).
thf(5492,plain,
sk2 @ s @ s @ s @ ( sk6 @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[5491:[bind(A,$thf( sk6 @ s @ s )),bind(B,$thf( sk2 @ s @ s ))]]) ).
thf(22141,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s @ ( sk6 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5492,394]) ).
thf(22142,plain,
! [A: $i] :
( ( sk2 @ s @ s @ s @ ( sk6 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[22141]) ).
thf(22195,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s )
!= A )
| ( ( sk6 @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[22142]) ).
thf(22217,plain,
( ( sk2 @ s @ s @ s @ s )
!= ( sk6 @ s @ s @ s ) ),
inference(simp,[status(thm)],[22195]) ).
thf(3345,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk3 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,481]) ).
thf(3346,plain,
( ( sk3 != q_nil )
| ( sk6 @ ( sk6 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3345:[bind(A,$thf( sk6 ))]]) ).
thf(4626,plain,
! [A: $i] :
( ( A != sk3 )
| ( q_nil != q_nil )
| ( sk6 @ ( sk6 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3346]) ).
thf(4627,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk6 @ ( sk6 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4626]) ).
thf(4628,plain,
( ( sk6 @ ( sk6 @ last @ elem ) )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4627:[bind(A,$thf( sk3 ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(204,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NotNorm )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[203]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( A @ m_NotNorm )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[205]) ).
thf(4081,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,104]) ).
thf(4082,plain,
( ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4081:[bind(A,$thf( sk3 ))]]) ).
thf(673,plain,
! [A: $i] :
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,413]) ).
thf(674,plain,
! [A: $i] :
( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[673]) ).
thf(677,plain,
! [A: $i] :
( ( ( sk7 @ host @ queue )
!= q_nil )
| ( ( sk6 @ m_Down )
!= A ) ),
inference(simp,[status(thm)],[674]) ).
thf(679,plain,
( ( sk7 @ host @ queue )
!= q_nil ),
inference(simp,[status(thm)],[677]) ).
thf(3667,plain,
! [A: $i] :
( ( A
!= ( sk7 @ host @ queue ) )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,679]) ).
thf(3668,plain,
! [A: $i] :
( ( A
!= ( sk7 @ host @ queue ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[3667]) ).
thf(3669,plain,
sk7 @ host @ queue @ ( sk7 @ host @ queue @ last @ elem ),
inference(pattern_uni,[status(thm)],[3668:[bind(A,$thf( sk7 @ host @ queue ))]]) ).
thf(2418,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ~ ( sk7 @ host @ queue @ ( A @ m_Down @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[125,743]) ).
thf(2419,plain,
~ ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[2418:[bind(A,$thf( sk8 ))]]) ).
thf(10454,plain,
( ( ( sk7 @ host @ queue @ ( sk7 @ host @ queue @ last @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3669,2419]) ).
thf(10455,plain,
( ( sk7 @ host @ queue @ ( sk7 @ host @ queue @ last @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[10454]) ).
thf(10562,plain,
( ( ( sk7 @ host @ queue )
!= ( sk7 @ host @ queue ) )
| ( ( sk7 @ host @ queue @ last )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[10455]) ).
thf(10611,plain,
( ( sk7 @ host @ queue @ last )
!= ( sk8 @ m_Down ) ),
inference(simp,[status(thm)],[10562]) ).
thf(14496,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk7 @ host @ queue @ last ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[2391,10611]) ).
thf(14527,plain,
( ( q_nil @ ( sk8 @ m_Down @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[14496]) ).
thf(3493,plain,
! [A: $i] :
( ( A != sk7 )
| ( sk2 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,492]) ).
thf(3494,plain,
( ( sk2 != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3493:[bind(A,$thf( sk7 ))]]) ).
thf(5279,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk2 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3494,413]) ).
thf(5280,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[5279]) ).
thf(5335,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( sk7 @ last )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[5280]) ).
thf(5344,plain,
( ( sk7 != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[5335]) ).
thf(5351,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk7 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,5344]) ).
thf(5352,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk7 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5351]) ).
thf(5353,plain,
( ( sk7 != q_nil )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5352:[bind(A,$thf( sk2 ))]]) ).
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(272,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(273,plain,
( ! [A: $i] :
( ( ? [B: $i] :
( A
= ( B @ m_Down ) )
| ? [B: $i] :
( A
= ( B @ m_Halt ) ) )
=> ( A @ pidElem ) )
& ! [A: $i] :
( ( A @ pidElem )
=> ( ? [B: $i] :
( A
= ( B @ m_Down ) )
| ? [B: $i] :
( A
= ( B @ m_Halt ) ) ) ) ),
inference(miniscope,[status(thm)],[272]) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ pidElem )
| ( B
!= ( D @ m_Down ) ) )
& ( ( B @ pidElem )
| ( B
!= ( C @ m_Halt ) ) )
& ( ( A
= ( A @ sk16 @ m_Down ) )
| ( A
= ( A @ sk15 @ m_Halt ) )
| ~ ( A @ pidElem ) ) ),
inference(cnf,[status(esa)],[273]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(cnfConj,[status(thm)],[274]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Halt ) ) ),
inference(lifteq,[status(thm)],[276]) ).
thf(280,plain,
! [A: $i] : ( A @ m_Halt @ pidElem ),
inference(simp,[status(thm)],[279]) ).
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(233,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(3851,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk1 @ ( q_nil @ m_Down @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,98]) ).
thf(3852,plain,
( ( sk1 @ ( q_nil @ m_Down @ elem ) )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3851:[bind(A,$thf( sk8 ))]]) ).
thf(15115,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5192,394]) ).
thf(15116,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[15115]) ).
thf(15157,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s )
!= A )
| ( ( zero @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[15116]) ).
thf(15179,plain,
( ( nbr_proc @ s @ s @ s )
!= ( zero @ s @ s @ s ) ),
inference(simp,[status(thm)],[15157]) ).
thf(9010,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,2427]) ).
thf(9011,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[9010]) ).
thf(9155,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk5 @ m_Down ) ) ),
inference(simp,[status(thm)],[9011]) ).
thf(9201,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk5 @ m_Down ) ),
inference(simp,[status(thm)],[9155]) ).
thf(9761,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk2 @ host @ queue @ last ) )
| ( A
!= ( sk5 @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[2391,9201]) ).
thf(9785,plain,
( ( q_nil @ ( sk5 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[9761]) ).
thf(22875,plain,
! [A: $i] :
( ( A != sk4 )
| ( q_nil != q_nil )
| ( sk6 @ ( sk6 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3826]) ).
thf(22876,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk6 @ ( sk6 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[22875]) ).
thf(22877,plain,
( ( sk6 @ ( sk6 @ last @ elem ) )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[22876:[bind(A,$thf( sk4 ))]]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(304,plain,
! [A: $i,B: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(305,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[304]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[305]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(9572,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,271]) ).
thf(9573,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[9572]) ).
thf(9574,plain,
! [A: $i] : ( sk7 @ host @ queue @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[9573:[bind(A,$thf( sk6 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk7 @ host @ queue ))]]) ).
thf(9682,plain,
! [A: $i] : ( sk7 @ host @ queue @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[9574]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ( B = A ) ),
inference(simp,[status(thm)],[116]) ).
thf(521,plain,
( ( ( sk8 @ host )
!= ( sk2 @ host ) )
| ~ ( sk4 @ host @ ( sk7 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[125,518]) ).
thf(529,plain,
( ( sk8 != sk2 )
| ~ ( sk4 @ host @ ( sk7 @ host @ leq ) ) ),
inference(simp,[status(thm)],[521]) ).
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(140,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(141,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) ) ) ),
inference(miniscope,[status(thm)],[140]) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_NormQ )
= ( D @ m_NormQ ) ) )
& ( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NormQ )
!= ( B @ m_NormQ ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(146,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NormQ @ A )
= B ),
inference(detectInverse,[status(thm)],[145]) ).
thf(147,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk10 )
= A ),
inference(cnf,[status(esa)],[146]) ).
thf(2232,plain,
! [A: $i] :
( ( A @ m_NormQ @ sk10 )
= A ),
inference(lifteq,[status(thm)],[147]) ).
thf(3079,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( sk4 @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,3030]) ).
thf(3080,plain,
( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( sk4 @ setIn ) ) ),
inference(simp,[status(thm)],[3079]) ).
thf(3083,plain,
( ( alive != alive )
| ( sk7 != sk4 ) ),
inference(simp,[status(thm)],[3080]) ).
thf(3086,plain,
sk7 != sk4,
inference(simp,[status(thm)],[3083]) ).
thf(3794,plain,
! [A: $i] :
( ( A != sk7 )
| ( sk4 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3086]) ).
thf(3795,plain,
( ( sk4 != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3794:[bind(A,$thf( sk7 ))]]) ).
thf(4709,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,242]) ).
thf(4710,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ host @ ( zero @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[4709]) ).
thf(4711,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[4710:[bind(A,$thf( E )),bind(B,$thf( zero @ s )),bind(C,$thf( E @ host ))]]) ).
thf(4759,plain,
! [A: $i] : ( A @ host @ s @ ( zero @ s @ s @ leq ) ),
inference(simp,[status(thm)],[4711]) ).
thf(33178,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4759,394]) ).
thf(33179,plain,
! [B: $i,A: $i] :
( ( A @ host @ s @ ( zero @ s @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[33178]) ).
thf(33243,plain,
! [B: $i,A: $i] :
( ( ( A @ host @ s )
!= B )
| ( ( zero @ s @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[33179]) ).
thf(33282,plain,
! [A: $i] :
( ( A @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(simp,[status(thm)],[33243]) ).
thf(15994,plain,
( ( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ~ $true
| ( sk7 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[10050,15885]) ).
thf(15995,plain,
( ( ( alive @ ( sk8 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[15994]) ).
thf(16004,plain,
( ( alive != alive )
| ( sk8 != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[15995]) ).
thf(16011,plain,
( ( sk8 != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[16004]) ).
thf(48355,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,440]) ).
thf(48356,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[48355]) ).
thf(48357,plain,
sk2 @ s @ ( sk5 @ leq ),
inference(pattern_uni,[status(thm)],[48356:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 ))]]) ).
thf(348,plain,
! [A: $i] :
( ( A @ ordered )
=> ! [B: $i,C: $i] : ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered ) ),
inference(miniscope,[status(thm)],[347]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ m_Ack ) @ ( A @ snoc ) @ ordered )
| ~ ( A @ ordered ) ),
inference(cnf,[status(esa)],[348]) ).
thf(86,plain,
( ( sk7 @ host )
!= ( sk5 @ host ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(115,plain,
( ( sk7 @ host )
!= ( sk5 @ host ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(457,plain,
( ( sk7 @ host )
!= ( sk3 @ host ) ),
inference(rewrite,[status(thm)],[115,101]) ).
thf(459,plain,
( ( ( sk7 @ host )
!= ( sk5 @ host ) )
| ( ( sk3 @ host )
!= ( sk3 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[101,457]) ).
thf(460,plain,
( ( sk7 @ host )
!= ( sk5 @ host ) ),
inference(simp,[status(thm)],[459]) ).
thf(461,plain,
sk7 != sk5,
inference(simp,[status(thm)],[460]) ).
thf(3609,plain,
! [A: $i] :
( ( A != sk7 )
| ( sk5 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,461]) ).
thf(3610,plain,
( ( sk5 != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3609:[bind(A,$thf( sk7 ))]]) ).
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(414,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(415,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: $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 ) ) ) ),
inference(miniscope,[status(thm)],[414]) ).
thf(416,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ snoc ) @ ordered )
| ~ ( D @ pidMsg @ ( D @ ( E @ sk19 ) @ pidMsg @ leq ) )
| ~ ( E @ ordered ) )
& ( ( D @ ( E @ snoc ) @ ordered )
| ( ( D @ ( E @ sk19 ) @ pidMsg @ host )
= ( D @ pidMsg @ host ) )
| ~ ( E @ ordered ) )
& ( ( D @ ( E @ snoc ) @ ordered )
| ( D @ ( E @ sk19 ) @ pidElem )
| ~ ( E @ ordered ) )
& ( ( D @ ( E @ snoc ) @ ordered )
| ( D @ pidElem )
| ~ ( E @ ordered ) )
& ( ( D @ ( E @ snoc ) @ ordered )
| ( E @ ( D @ ( E @ sk19 ) @ elem ) )
| ~ ( E @ ordered ) )
& ( ( A @ pidMsg @ ( C @ pidMsg @ leq ) )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( A @ ( B @ snoc ) @ ordered ) )
& ( ( B @ ordered )
| ~ ( A @ ( B @ snoc ) @ ordered ) ) ),
inference(cnf,[status(esa)],[415]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ( ( A @ ( B @ sk19 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[416]) ).
thf(428,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ~ ( B @ ordered )
| ( ( A @ ( B @ sk19 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) ) ),
inference(lifteq,[status(thm)],[418]) ).
thf(429,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ~ ( B @ ordered )
| ( ( A @ ( B @ sk19 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(29332,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2897,359]) ).
thf(29333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[29332]) ).
thf(29334,plain,
! [A: $i] : ( A @ ( sk2 @ host @ queue @ snoc ) @ ( sk4 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[29333:[bind(A,$thf( sk4 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(29531,plain,
! [A: $i] : ( A @ ( sk2 @ host @ queue @ snoc ) @ ( sk4 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[29334]) ).
thf(39861,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9682,413]) ).
thf(39862,plain,
! [B: $i,A: $i] :
( ( sk7 @ host @ queue @ ( A @ cons ) @ ( sk6 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[39861]) ).
thf(39939,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ host @ queue @ ( A @ cons ) )
!= q_nil )
| ( ( sk6 @ m_Down )
!= B ) ),
inference(simp,[status(thm)],[39862]) ).
thf(39977,plain,
! [A: $i] :
( ( sk7 @ host @ queue @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[39939]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ~ ( A @ ( B @ sk18 ) @ pidMsg @ ( A @ pidMsg @ leq ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ~ ( A @ ( B @ sk18 ) @ pidMsg @ ( A @ pidMsg @ leq ) )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[327]) ).
thf(15813,plain,
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15679,2427]) ).
thf(15814,plain,
( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[15813]) ).
thf(15941,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk8 @ m_Down )
!= ( sk5 @ m_Down ) ) ),
inference(simp,[status(thm)],[15814]) ).
thf(15962,plain,
( ( sk8 @ m_Down )
!= ( sk5 @ m_Down ) ),
inference(simp,[status(thm)],[15941]) ).
thf(586,plain,
( ( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true
| ( sk5 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[110,196]) ).
thf(587,plain,
( ( ( alive @ ( sk5 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[586]) ).
thf(595,plain,
( ( alive != alive )
| ( sk5 != nil )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[587]) ).
thf(598,plain,
( ( sk5 != nil )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[595]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(160,plain,
! [A: $i,B: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2908,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,413]) ).
thf(2909,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[2908]) ).
thf(2954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[2909]) ).
thf(2969,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[2954]) ).
thf(10495,plain,
( ( ( sk7 @ host @ queue @ ( sk7 @ host @ queue @ last @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3669,2599]) ).
thf(10496,plain,
( ( sk7 @ host @ queue @ ( sk7 @ host @ queue @ last @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[10495]) ).
thf(10580,plain,
( ( ( sk7 @ host @ queue )
!= ( sk7 @ host @ queue ) )
| ( ( sk7 @ host @ queue @ last )
!= ( sk8 @ m_Halt ) ) ),
inference(simp,[status(thm)],[10496]) ).
thf(10622,plain,
( ( sk7 @ host @ queue @ last )
!= ( sk8 @ m_Halt ) ),
inference(simp,[status(thm)],[10580]) ).
thf(14575,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk7 @ host @ queue @ last ) )
| ( A
!= ( sk8 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[2391,10622]) ).
thf(14605,plain,
( ( q_nil @ ( sk8 @ m_Halt @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[14575]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ~ ( A @ pidMsg @ ( A @ ( B @ sk19 ) @ pidMsg @ leq ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[416]) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ~ ( A @ pidMsg @ ( A @ ( B @ sk19 ) @ pidMsg @ leq ) )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[417]) ).
thf(3010,plain,
( ( ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2897,2601]) ).
thf(3011,plain,
( ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3010]) ).
thf(3055,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk6 @ m_Halt )
!= ( sk4 @ m_Down ) ) ),
inference(simp,[status(thm)],[3011]) ).
thf(3069,plain,
( ( sk6 @ m_Halt )
!= ( sk4 @ m_Down ) ),
inference(simp,[status(thm)],[3055]) ).
thf(16,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(192,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
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(407,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(619,plain,
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,196]) ).
thf(620,plain,
( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( nil @ setIn ) ) ),
inference(simp,[status(thm)],[619]) ).
thf(627,plain,
( ( alive != alive )
| ( sk7 != nil ) ),
inference(simp,[status(thm)],[620]) ).
thf(630,plain,
sk7 != nil,
inference(simp,[status(thm)],[627]) ).
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(226,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(227,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Down ) ),
inference(miniscope,[status(thm)],[226]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Down ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(2776,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk7 @ host @ leq ) ) )
| ( sk8 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[291,529]) ).
thf(2777,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk7 @ host @ leq ) ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2776]) ).
thf(2797,plain,
! [A: $i] :
( ( A
!= ( sk4 @ host ) )
| ( A
!= ( sk7 @ host ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2777]) ).
thf(2826,plain,
( ( ( sk7 @ host )
!= ( sk4 @ host ) )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[2797]) ).
thf(3039,plain,
( ( ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2897,2421]) ).
thf(3040,plain,
( ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3039]) ).
thf(3044,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk6 @ m_Down )
!= ( sk4 @ m_Down ) ) ),
inference(simp,[status(thm)],[3040]) ).
thf(3065,plain,
( ( sk6 @ m_Down )
!= ( sk4 @ m_Down ) ),
inference(simp,[status(thm)],[3044]) ).
thf(15878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15679,271]) ).
thf(15879,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[15878]) ).
thf(15880,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[15879:[bind(A,$thf( sk8 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(15947,plain,
! [A: $i] : ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[15880]) ).
thf(29399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,359]) ).
thf(29400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[29399]) ).
thf(29401,plain,
! [A: $i] : ( A @ ( sk1 @ snoc ) @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[29400:[bind(A,$thf( sk8 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(29593,plain,
! [A: $i] : ( A @ ( sk1 @ snoc ) @ ( sk8 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[29401]) ).
thf(30697,plain,
! [A: $i] :
( ( ( A @ s @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30654,518]) ).
thf(30698,plain,
! [A: $i] :
( ( A @ s @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[30697]) ).
thf(30771,plain,
! [A: $i] :
( ( ( A @ s )
!= ( sk4 @ host ) )
| ( A
!= ( sk2 @ host ) ) ),
inference(simp,[status(thm)],[30698]) ).
thf(30800,plain,
( ( sk2 @ host @ s )
!= ( sk4 @ host ) ),
inference(simp,[status(thm)],[30771]) ).
thf(193,plain,
elec_1 != wait,
inference(polarity_switch,[status(thm)],[192]) ).
thf(194,plain,
elec_1 != wait,
inference(lifteq,[status(thm)],[193]) ).
thf(12627,plain,
! [B: $i,A: $i] :
( ( A != elec_1 )
| ( B != wait )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[289,194]) ).
thf(12628,plain,
! [A: $i] :
( ( A != wait )
| ~ ( elec_1 @ ( A @ leq ) )
| ~ ( A @ ( elec_1 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12627:[bind(A,$thf( elec_1 ))]]) ).
thf(13639,plain,
( ~ ( elec_1 @ ( wait @ leq ) )
| ~ ( wait @ ( elec_1 @ leq ) ) ),
inference(simp,[status(thm)],[12628]) ).
thf(9276,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk2 @ host @ queue @ last ) )
| ( A
!= ( sk5 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[2391,9180]) ).
thf(9301,plain,
( ( q_nil @ ( sk5 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[9276]) ).
thf(2163,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,394]) ).
thf(2164,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ ( A @ host @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[2163]) ).
thf(2170,plain,
! [B: $i,A: $i] :
( ( nbr_proc != B )
| ( ( A @ host )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[2164]) ).
thf(2179,plain,
! [A: $i] :
( ( A @ host )
!= ( nbr_proc @ s ) ),
inference(simp,[status(thm)],[2170]) ).
thf(3481,plain,
! [A: $i] :
( ( A != sk2 )
| ( q_nil @ ( sk3 @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,1568]) ).
thf(3482,plain,
( ( q_nil @ ( sk3 @ leq ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3481:[bind(A,$thf( sk2 ))]]) ).
thf(18676,plain,
( ( sk6 != sk6 )
| ( sk3 != sk2 )
| ~ ( sk6 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[13317,481]) ).
thf(18677,plain,
( ( sk3 != sk2 )
| ~ ( sk6 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[18676:[]]) ).
thf(14,axiom,
q_nil @ ordered,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(188,plain,
q_nil @ ordered,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(154,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_NormQ )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[153]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[154]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( A @ m_NormQ )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(10067,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ~ $true
| ( sk7 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[10050,472]) ).
thf(10068,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[10067]) ).
thf(10111,plain,
( ( alive != alive )
| ( sk6 != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[10068]) ).
thf(10126,plain,
( ( sk6 != q_nil )
| ( sk7 != q_nil ) ),
inference(simp,[status(thm)],[10111]) ).
thf(76,plain,
( ( ( sk3 @ host @ ( status @ index ) )
= wait )
| ( ( sk3 @ host @ ( status @ index ) )
= norm ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(118,plain,
( ( ( sk3 @ host @ ( status @ index ) )
= wait )
| ( ( sk3 @ host @ ( status @ index ) )
= norm ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(980,plain,
( ( ( sk2 @ host @ ( status @ index ) )
= wait )
| ( ( sk2 @ host @ ( status @ index ) )
= norm ) ),
inference(rewrite,[status(thm)],[118,104]) ).
thf(40840,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk6 @ ( sk8 @ leq ) ) )
| ( sk8 != sk2 )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[1531,40747]) ).
thf(40841,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk6 @ ( sk8 @ leq ) ) )
| ( sk8 != sk2 )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[40840]) ).
thf(40914,plain,
! [A: $i] :
( ( sk6 != sk2 )
| ( A != sk8 )
| ( sk8 != sk2 )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[40841]) ).
thf(40934,plain,
( ( sk6 != sk2 )
| ( sk8 != sk2 ) ),
inference(simp,[status(thm)],[40914]) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( B @ ( C @ snoc ) @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[352]) ).
thf(356,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ~ ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[353]) ).
thf(48735,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ s @ ( sk5 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48357,394]) ).
thf(48736,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ s @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[48735]) ).
thf(48797,plain,
! [A: $i] :
( ( A
!= ( sk2 @ s ) )
| ( ( A @ s )
!= sk5 ) ),
inference(simp,[status(thm)],[48736]) ).
thf(48829,plain,
( ( sk2 @ s @ s )
!= sk5 ),
inference(simp,[status(thm)],[48797]) ).
thf(12727,plain,
! [B: $i,A: $i] :
( ( A != sk7 )
| ( B != sk6 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[289,576]) ).
thf(12728,plain,
! [A: $i] :
( ( A != sk6 )
| ~ ( sk7 @ ( A @ leq ) )
| ~ ( A @ ( sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12727:[bind(A,$thf( sk7 ))]]) ).
thf(13676,plain,
( ~ ( sk7 @ ( sk6 @ leq ) )
| ~ ( sk6 @ ( sk7 @ leq ) ) ),
inference(simp,[status(thm)],[12728]) ).
thf(17340,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk5 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[159,17266]) ).
thf(17352,plain,
! [A: $i] :
( ( sk5 @ m_Halt @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17340]) ).
thf(17357,plain,
! [A: $i] :
( ( sk5 @ m_Halt @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17352]) ).
thf(26,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(223,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(224,plain,
elec_1 != norm,
inference(polarity_switch,[status(thm)],[223]) ).
thf(225,plain,
elec_1 != norm,
inference(lifteq,[status(thm)],[224]) ).
thf(3122,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,2599]) ).
thf(3123,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[3122]) ).
thf(3152,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Halt ) ) ),
inference(simp,[status(thm)],[3123]) ).
thf(3179,plain,
! [A: $i] :
( ( sk8 @ m_Halt @ ( A @ snoc ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[3152]) ).
thf(4748,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,242]) ).
thf(4749,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4748]) ).
thf(4750,plain,
sk2 @ s @ ( sk5 @ s @ leq ),
inference(pattern_uni,[status(thm)],[4749:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 ))]]) ).
thf(522,plain,
( ( ( sk8 @ host )
!= ( sk4 @ host ) )
| ~ ( sk7 @ host @ ( sk2 @ host @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[125,518]) ).
thf(526,plain,
( ( sk8 != sk4 )
| ~ ( sk7 @ host @ ( sk2 @ host @ leq ) ) ),
inference(simp,[status(thm)],[522]) ).
thf(28,axiom,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(230,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(231,plain,
~ ? [A: $i] : ( setEmpty @ ( A @ setIn ) ),
inference(miniscope,[status(thm)],[230]) ).
thf(232,plain,
! [A: $i] :
~ ( setEmpty @ ( A @ setIn ) ),
inference(cnf,[status(esa)],[231]) ).
thf(604,plain,
! [A: $i] :
( ( ( alive @ ( sk3 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,232]) ).
thf(605,plain,
! [A: $i] :
( ( alive @ ( sk3 @ setIn ) )
!= ( setEmpty @ ( A @ setIn ) ) ),
inference(simp,[status(thm)],[604]) ).
thf(607,plain,
! [A: $i] :
( ( setEmpty != alive )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[605]) ).
thf(609,plain,
setEmpty != alive,
inference(simp,[status(thm)],[607]) ).
thf(12299,plain,
! [B: $i,A: $i] :
( ( A != setEmpty )
| ( B != alive )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[289,609]) ).
thf(12300,plain,
! [A: $i] :
( ( A != alive )
| ~ ( setEmpty @ ( A @ leq ) )
| ~ ( A @ ( setEmpty @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12299:[bind(A,$thf( setEmpty ))]]) ).
thf(13512,plain,
( ~ ( setEmpty @ ( alive @ leq ) )
| ~ ( alive @ ( setEmpty @ leq ) ) ),
inference(simp,[status(thm)],[12300]) ).
thf(17339,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk5 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[2391,17266]) ).
thf(17350,plain,
( ( q_nil @ ( sk5 @ m_Halt @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[17339]) ).
thf(15825,plain,
( ( ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15679,2607]) ).
thf(15826,plain,
( ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[15825]) ).
thf(15934,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk5 @ m_Halt )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[15826]) ).
thf(15959,plain,
( ( sk5 @ m_Halt )
!= ( sk8 @ m_Down ) ),
inference(simp,[status(thm)],[15934]) ).
thf(5271,plain,
! [A: $i] :
( ( A != sk2 )
| ( q_nil != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3494]) ).
thf(5272,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5271]) ).
thf(5273,plain,
( ( sk7 @ ( sk7 @ last @ elem ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5272:[bind(A,$thf( sk2 ))]]) ).
thf(3579,plain,
! [A: $i] :
( ( A != sk7 )
| ( nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,630]) ).
thf(3580,plain,
( ( nil != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3579:[bind(A,$thf( sk7 ))]]) ).
thf(5565,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( nil != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3580,413]) ).
thf(5566,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[5565]) ).
thf(5592,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( sk7 @ last )
!= A )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[5566]) ).
thf(5624,plain,
( ( sk7 != q_nil )
| ( nil != q_nil ) ),
inference(simp,[status(thm)],[5592]) ).
thf(5637,plain,
! [A: $i] :
( ( A != nil )
| ( sk7 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,5624]) ).
thf(5638,plain,
! [A: $i] :
( ( A != nil )
| ( sk7 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5637]) ).
thf(5639,plain,
( ( sk7 != q_nil )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5638:[bind(A,$thf( nil ))]]) ).
thf(171,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[170]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[171]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[172]) ).
thf(52,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(371,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(309,plain,
( ! [A: $i] : ( A @ ( q_nil @ snoc ) @ ordered )
& ! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(miniscope,[status(thm)],[308]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( B @ ( q_nil @ snoc ) @ ordered )
& ( q_nil @ ( A @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [A: $i] : ( q_nil @ ( A @ cons ) @ ordered ),
inference(cnfConj,[status(thm)],[310]) ).
thf(18998,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk6 @ ( sk2 @ leq ) ) )
| ( sk3 != sk2 )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[1531,18677]) ).
thf(18999,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk6 @ ( sk2 @ leq ) ) )
| ( sk3 != sk2 )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[18998]) ).
thf(19033,plain,
! [A: $i] :
( ( sk6 != sk2 )
| ( A != sk2 )
| ( sk3 != sk2 )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[18999]) ).
thf(19072,plain,
( ( sk6 != sk2 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[19033]) ).
thf(19088,plain,
( ( sk3 != sk3 )
| ( sk6 != sk2 )
| ( sk2 != sk2 )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[11261,19072]) ).
thf(19089,plain,
( ( sk3 != sk3 )
| ( sk6 != sk2 )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[19088]) ).
thf(19090,plain,
( ( sk6 != sk2 )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[19089:[]]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ host @ ( A @ host @ leq ) )
| ~ ( B @ host @ queue @ ( A @ ( C @ m_Ack ) @ elem ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(2920,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,2611]) ).
thf(2921,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[2920]) ).
thf(2948,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk3 @ m_Halt ) ) ),
inference(simp,[status(thm)],[2921]) ).
thf(2963,plain,
! [A: $i] :
( ( A @ ( sk3 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2948]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(398,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(3347,plain,
! [A: $i] :
( ( A != sk8 )
| ( sk3 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,977]) ).
thf(3348,plain,
( ( sk3 != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3347:[bind(A,$thf( sk8 ))]]) ).
thf(4926,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3348,413]) ).
thf(4927,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[4926]) ).
thf(4961,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( sk8 @ last )
!= A )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[4927]) ).
thf(4985,plain,
( ( sk8 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[4961]) ).
thf(5207,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk8 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,4985]) ).
thf(5208,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk8 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5207]) ).
thf(5209,plain,
( ( sk8 != q_nil )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5208:[bind(A,$thf( sk3 ))]]) ).
thf(5403,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ ( sk3 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4791,394]) ).
thf(5404,plain,
! [A: $i] :
( ( sk2 @ s @ s @ ( sk3 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5403]) ).
thf(5415,plain,
! [A: $i] :
( ( ( sk2 @ s @ s )
!= A )
| ( ( sk3 @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[5404]) ).
thf(5417,plain,
( ( sk2 @ s @ s @ s )
!= ( sk3 @ s @ s ) ),
inference(simp,[status(thm)],[5415]) ).
thf(2220,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk7 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[125,2179]) ).
thf(2221,plain,
( ( nbr_proc @ s )
!= ( sk7 @ host ) ),
inference(pattern_uni,[status(thm)],[2220:[bind(A,$thf( sk8 ))]]) ).
thf(2235,plain,
! [A: $i] :
( ( A @ host )
!= zero ),
inference(simp,[status(thm)],[2181]) ).
thf(4824,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk5 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4750,242]) ).
thf(4825,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk5 @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4824]) ).
thf(4826,plain,
sk2 @ s @ s @ ( sk5 @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[4825:[bind(A,$thf( sk5 @ s )),bind(B,$thf( sk2 @ s ))]]) ).
thf(5450,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk5 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4826,242]) ).
thf(5451,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ s @ ( sk5 @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5450]) ).
thf(5452,plain,
sk2 @ s @ s @ s @ ( sk5 @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[5451:[bind(A,$thf( sk5 @ s @ s )),bind(B,$thf( sk2 @ s @ s ))]]) ).
thf(21969,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s @ ( sk5 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5452,394]) ).
thf(21970,plain,
! [A: $i] :
( ( sk2 @ s @ s @ s @ ( sk5 @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[21969]) ).
thf(22027,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ s )
!= A )
| ( ( sk5 @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[21970]) ).
thf(22032,plain,
( ( sk2 @ s @ s @ s @ s )
!= ( sk5 @ s @ s @ s ) ),
inference(simp,[status(thm)],[22027]) ).
thf(17830,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk6 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[159,17270]) ).
thf(17842,plain,
! [A: $i] :
( ( sk6 @ m_Halt @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17830]) ).
thf(17848,plain,
! [A: $i] :
( ( sk6 @ m_Halt @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17842]) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ pidMsg @ ( C @ pidMsg @ leq ) )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( A @ ( B @ snoc ) @ ordered ) ),
inference(cnfConj,[status(thm)],[416]) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ pidMsg @ ( C @ pidMsg @ leq ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( A @ ( B @ snoc ) @ ordered )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) ) ),
inference(lifteq,[status(thm)],[422]) ).
thf(3870,plain,
! [A: $i] :
( ( A != setEmpty )
| ( q_nil != alive )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,609]) ).
thf(3871,plain,
( ( q_nil != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3870:[bind(A,$thf( setEmpty ))]]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(cnf,[status(esa)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ init )
= B ),
inference(lifteq,[status(thm)],[165]) ).
thf(29449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15679,359]) ).
thf(29450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[29449]) ).
thf(29451,plain,
! [A: $i] : ( A @ ( sk2 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[29450:[bind(A,$thf( sk8 @ m_Down )),bind(B,$thf( B )),bind(C,$thf( sk2 @ host @ queue ))]]) ).
thf(29527,plain,
! [A: $i] : ( A @ ( sk2 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) ),
inference(simp,[status(thm)],[29451]) ).
thf(46855,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29527,413]) ).
thf(46856,plain,
! [B: $i,A: $i] :
( ( A @ ( sk2 @ host @ queue @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[46855]) ).
thf(46932,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= q_nil )
| ( ( sk8 @ m_Down )
!= B ) ),
inference(simp,[status(thm)],[46856]) ).
thf(46997,plain,
! [A: $i] :
( ( A @ ( sk2 @ host @ queue @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[46932]) ).
thf(29465,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3956,359]) ).
thf(29466,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[29465]) ).
thf(29467,plain,
! [A: $i] : ( A @ ( sk1 @ snoc ) @ ( sk1 @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[29466:[bind(A,$thf( sk1 @ last )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(29535,plain,
! [A: $i] : ( A @ ( sk1 @ snoc ) @ ( sk1 @ last @ elem ) ),
inference(simp,[status(thm)],[29467]) ).
thf(15291,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4760,394]) ).
thf(15292,plain,
! [B: $i,A: $i] :
( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( B @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[15291]) ).
thf(15319,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s )
!= B )
| ( ( A @ host @ s )
!= ( B @ s ) ) ),
inference(simp,[status(thm)],[15292]) ).
thf(15341,plain,
! [A: $i] :
( ( A @ host @ s )
!= ( nbr_proc @ s @ s ) ),
inference(simp,[status(thm)],[15319]) ).
thf(20383,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s )
!= ( sk7 @ host @ s ) ) ),
inference(paramod_ordered,[status(thm)],[125,15341]) ).
thf(20384,plain,
( ( nbr_proc @ s @ s )
!= ( sk7 @ host @ s ) ),
inference(pattern_uni,[status(thm)],[20383:[bind(A,$thf( sk8 ))]]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(444,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ( A @ ( B @ sk19 ) @ pidElem )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[416]) ).
thf(425,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ( A @ ( B @ sk19 ) @ pidElem )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[421]) ).
thf(3887,plain,
! [A: $i] :
( ( A != sk5 )
| ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,462]) ).
thf(3888,plain,
( ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3887:[bind(A,$thf( sk5 ))]]) ).
thf(2733,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ m_Down @ cons ) )
!= ( B @ ( A @ cons ) ) )
| ( ( sk2 @ host @ queue @ tail )
= B ) ),
inference(paramod_ordered,[status(thm)],[756,261]) ).
thf(2734,plain,
( ( sk2 @ host @ queue @ tail )
= sk1 ),
inference(pattern_uni,[status(thm)],[2733:[bind(A,$thf( sk4 @ m_Down )),bind(B,$thf( sk1 ))]]) ).
thf(3126,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,2421]) ).
thf(3127,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3126]) ).
thf(3160,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[3127]) ).
thf(3187,plain,
! [A: $i] :
( ( sk6 @ m_Down @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3160]) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( B @ ordered )
| ~ ( A @ ( B @ snoc ) @ ordered ) ),
inference(cnfConj,[status(thm)],[416]) ).
thf(2922,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,2421]) ).
thf(2923,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2922]) ).
thf(2955,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[2923]) ).
thf(2970,plain,
! [A: $i] :
( ( A @ ( sk6 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2955]) ).
thf(190,plain,
elec_1 != elec_2,
inference(polarity_switch,[status(thm)],[189]) ).
thf(191,plain,
elec_2 != elec_1,
inference(lifteq,[status(thm)],[190]) ).
thf(1643,plain,
( ( ( sk4 @ host @ ( sk2 @ host @ leq ) )
!= ( sk2 @ ( sk3 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1568,518]) ).
thf(1644,plain,
( ( sk4 @ host @ ( sk2 @ host @ leq ) )
!= ( sk2 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1643]) ).
thf(1652,plain,
( ( ( sk4 @ host )
!= sk2 )
| ( ( sk2 @ host )
!= sk3 ) ),
inference(simp,[status(thm)],[1644]) ).
thf(9074,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,2611]) ).
thf(9075,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[9074]) ).
thf(9140,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Halt ) ) ),
inference(simp,[status(thm)],[9075]) ).
thf(9189,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk3 @ m_Halt ) ),
inference(simp,[status(thm)],[9140]) ).
thf(161,plain,
~ ? [A: $i,B: $i] :
( q_nil
= ( A @ ( B @ snoc ) ) ),
inference(miniscope,[status(thm)],[160]) ).
thf(162,plain,
! [B: $i,A: $i] :
( q_nil
!= ( A @ ( B @ snoc ) ) ),
inference(cnf,[status(esa)],[161]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) )
!= q_nil ),
inference(lifteq,[status(thm)],[162]) ).
thf(2392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) )
!= q_nil ) ),
inference(paramod_ordered,[status(thm)],[387,163]) ).
thf(2393,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) )
!= q_nil ),
inference(pattern_uni,[status(thm)],[2392:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(29419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4456,359]) ).
thf(29420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( q_nil @ s @ ( q_nil @ s @ last @ elem ) )
!= ( C @ ( A @ elem ) ) )
| ( B @ ( C @ snoc ) @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[29419]) ).
thf(29421,plain,
! [A: $i] : ( A @ ( q_nil @ s @ snoc ) @ ( q_nil @ s @ last @ elem ) ),
inference(pattern_uni,[status(thm)],[29420:[bind(A,$thf( q_nil @ s @ last )),bind(B,$thf( B )),bind(C,$thf( q_nil @ s ))]]) ).
thf(29597,plain,
! [A: $i] : ( A @ ( q_nil @ s @ snoc ) @ ( q_nil @ s @ last @ elem ) ),
inference(simp,[status(thm)],[29421]) ).
thf(4185,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk2 @ ( q_nil @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,1561]) ).
thf(4186,plain,
( ( sk2 @ ( q_nil @ leq ) )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4185:[bind(A,$thf( sk5 ))]]) ).
thf(22883,plain,
! [A: $i] :
( ( ( sk6 @ ( sk6 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk4 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3826,413]) ).
thf(22884,plain,
! [A: $i] :
( ( ( sk6 @ ( sk6 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[22883]) ).
thf(22928,plain,
! [A: $i] :
( ( sk6 != q_nil )
| ( ( sk6 @ last )
!= A )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[22884]) ).
thf(22972,plain,
( ( sk6 != q_nil )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[22928]) ).
thf(3600,plain,
! [A: $i] :
( ( A != sk3 )
| ( alive @ ( q_nil @ setIn ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,97]) ).
thf(3601,plain,
( ( alive @ ( q_nil @ setIn ) )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3600:[bind(A,$thf( sk3 ))]]) ).
thf(9347,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( alive @ ( q_nil @ setIn ) ) ),
inference(paramod_ordered,[status(thm)],[3601,413]) ).
thf(9348,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( alive @ ( q_nil @ setIn ) ) ),
inference(simp,[status(thm)],[9347]) ).
thf(9395,plain,
! [A: $i] :
( ( sk3 != q_nil )
| ( ( sk3 @ last )
!= A )
| ( alive @ ( q_nil @ setIn ) ) ),
inference(simp,[status(thm)],[9348]) ).
thf(9438,plain,
( ( sk3 != q_nil )
| ( alive @ ( q_nil @ setIn ) ) ),
inference(simp,[status(thm)],[9395]) ).
thf(9485,plain,
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[9438,3030]) ).
thf(9486,plain,
( ( ( alive @ ( sk4 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9485]) ).
thf(9493,plain,
( ( alive != alive )
| ( sk4 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9486]) ).
thf(9506,plain,
( ( sk4 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9493]) ).
thf(234,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ~ ? [C: $i,D: $i] :
( ( C @ ( A @ m_Ack ) )
= ( D @ ( B @ m_Ack ) ) ) ),
inference(miniscope,[status(thm)],[233]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[234]) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[235]) ).
thf(78,plain,
( ( ( sk4 @ host )
= ( sk3 @ host @ ( elid @ index ) @ host ) )
| ( ( sk3 @ host @ ( status @ index ) )
= norm ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(109,plain,
( ( ( sk3 @ host @ ( elid @ index ) @ host )
= ( sk4 @ host ) )
| ( ( sk3 @ host @ ( status @ index ) )
= norm ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(764,plain,
( ( ( sk2 @ host @ ( elid @ index ) @ host )
= ( sk4 @ host ) )
| ( ( sk2 @ host @ ( status @ index ) )
= norm ) ),
inference(rewrite,[status(thm)],[109,104]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(377,plain,
! [A: $i,B: $i] :
( ( ( A @ host )
!= ( B @ host ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1534,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk2 @ host @ leq ) ) )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[1531,518]) ).
thf(1535,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( sk4 @ host @ ( sk2 @ host @ leq ) ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[1534]) ).
thf(1577,plain,
! [A: $i] :
( ( ( sk4 @ host )
!= sk2 )
| ( A
!= ( sk2 @ host ) )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[1535]) ).
thf(1603,plain,
( ( ( sk4 @ host )
!= sk2 )
| ( ( sk2 @ host )
!= sk2 ) ),
inference(simp,[status(thm)],[1577]) ).
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(362,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(31,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(245,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(91,plain,
~ ( pids @ ( sk2 @ setIn ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(9465,plain,
( ( ( pids @ ( sk2 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[9438,91]) ).
thf(9466,plain,
( ( ( pids @ ( sk2 @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9465]) ).
thf(9491,plain,
( ( pids != alive )
| ( sk2 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9466]) ).
thf(582,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( sk5 @ setIn ) ) )
| ~ $true
| ( sk5 = sk2 ) ),
inference(paramod_ordered,[status(thm)],[110,472]) ).
thf(583,plain,
( ( ( alive @ ( sk6 @ setIn ) )
!= ( alive @ ( sk5 @ setIn ) ) )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[582]) ).
thf(596,plain,
( ( alive != alive )
| ( sk6 != sk5 )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[583]) ).
thf(599,plain,
( ( sk6 != sk5 )
| ( sk5 = sk2 ) ),
inference(simp,[status(thm)],[596]) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ leq ) )
| ~ ( A @ ( C @ m_Down @ elem ) )
| ( ( B @ host )
!= ( C @ host ) )
| ~ ( A @ ( B @ m_Halt @ cons ) @ ordered ) ),
inference(cnf,[status(esa)],[404]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ leq ) )
| ~ ( A @ ( C @ m_Down @ elem ) )
| ~ ( A @ ( B @ m_Halt @ cons ) @ ordered )
| ( ( B @ host )
!= ( C @ host ) ) ),
inference(lifteq,[status(thm)],[405]) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,80]) ).
thf(615,plain,
! [B: $i,A: $i] :
( ( ( alive @ ( sk7 @ setIn ) )
!= ( alive @ ( B @ setIn ) ) )
| ~ ( A @ host @ queue @ ( B @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[614]) ).
thf(616,plain,
! [A: $i] :
~ ( A @ host @ queue @ ( sk7 @ m_Down @ elem ) ),
inference(pattern_uni,[status(thm)],[615:[bind(A,$thf( A )),bind(B,$thf( sk7 ))]]) ).
thf(3035,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2897,2611]) ).
thf(3036,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3035]) ).
thf(3046,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Halt )
!= ( sk4 @ m_Down ) ) ),
inference(simp,[status(thm)],[3036]) ).
thf(3066,plain,
( ( sk3 @ m_Halt )
!= ( sk4 @ m_Down ) ),
inference(simp,[status(thm)],[3046]) ).
thf(45,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(345,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4819,plain,
! [A: $i] :
( ( ( sk2 @ s @ ( sk5 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4750,394]) ).
thf(4820,plain,
! [A: $i] :
( ( sk2 @ s @ ( sk5 @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[4819]) ).
thf(4830,plain,
! [A: $i] :
( ( ( sk2 @ s )
!= A )
| ( ( sk5 @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[4820]) ).
thf(4833,plain,
( ( sk2 @ s @ s )
!= ( sk5 @ s ) ),
inference(simp,[status(thm)],[4830]) ).
thf(85,plain,
( ( sk2 @ host )
!= ( zero @ s ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(103,plain,
( ( zero @ s )
!= ( sk2 @ host ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(237,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[236]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk13 ) )
= A ),
inference(cnf,[status(esa)],[237]) ).
thf(3298,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( B @ sk13 ) )
= A ),
inference(lifteq,[status(thm)],[238]) ).
thf(458,plain,
sk7 != sk3,
inference(simp,[status(thm)],[457]) ).
thf(3970,plain,
! [A: $i] :
( ( A != sk7 )
| ( sk3 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,458]) ).
thf(3971,plain,
( ( sk3 != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3970:[bind(A,$thf( sk7 ))]]) ).
thf(2240,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( sk7 @ host @ s )
!= ( zero @ s ) ) ),
inference(paramod_ordered,[status(thm)],[125,2181]) ).
thf(2241,plain,
( ( sk7 @ host @ s )
!= ( zero @ s ) ),
inference(pattern_uni,[status(thm)],[2240:[bind(A,$thf( sk8 ))]]) ).
thf(2252,plain,
( ( sk7 @ host )
!= zero ),
inference(simp,[status(thm)],[2241]) ).
thf(34787,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3971,413]) ).
thf(34788,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[34787]) ).
thf(34859,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( sk7 @ last )
!= A )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[34788]) ).
thf(34899,plain,
( ( sk7 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[34859]) ).
thf(2165,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk5 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,394]) ).
thf(2166,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[2165]) ).
thf(2173,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk5 ) ),
inference(simp,[status(thm)],[2166]) ).
thf(2182,plain,
( ( sk2 @ s )
!= sk5 ),
inference(simp,[status(thm)],[2173]) ).
thf(3102,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,2419]) ).
thf(3103,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3102]) ).
thf(3131,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[3103]) ).
thf(3192,plain,
! [A: $i] :
( ( sk8 @ m_Down @ ( A @ snoc ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[3131]) ).
thf(15890,plain,
( ( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15679,2611]) ).
thf(15891,plain,
( ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[15890]) ).
thf(15939,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk3 @ m_Halt )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[15891]) ).
thf(15961,plain,
( ( sk3 @ m_Halt )
!= ( sk8 @ m_Down ) ),
inference(simp,[status(thm)],[15939]) ).
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(198,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(3875,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk4 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,895]) ).
thf(3876,plain,
( ( sk4 != q_nil )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3875:[bind(A,$thf( sk5 ))]]) ).
thf(32533,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk4 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3876,413]) ).
thf(32534,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[32533]) ).
thf(32593,plain,
! [A: $i] :
( ( sk5 != q_nil )
| ( ( sk5 @ last )
!= A )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[32534]) ).
thf(32641,plain,
( ( sk5 != q_nil )
| ( sk4 != q_nil ) ),
inference(simp,[status(thm)],[32593]) ).
thf(2448,plain,
( ( ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,2419]) ).
thf(2449,plain,
( ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2448]) ).
thf(2456,plain,
( ( ( sk7 @ host @ queue )
!= ( sk7 @ host @ queue ) )
| ( ( sk8 @ m_Down )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[2449]) ).
thf(2461,plain,
( ( sk8 @ m_Down )
!= ( sk6 @ m_Down ) ),
inference(simp,[status(thm)],[2456]) ).
thf(2900,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,2419]) ).
thf(2901,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2900]) ).
thf(2926,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) )
| ( A
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[2901]) ).
thf(2974,plain,
! [A: $i] :
( ( A @ ( sk8 @ m_Down @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[2926]) ).
thf(93,plain,
( ( sk5 = sk2 )
| ( sk5 != sk3 ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(108,plain,
( ( sk5 = sk2 )
| ( sk5 != sk3 ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(5445,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ ( sk5 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4826,394]) ).
thf(5446,plain,
! [A: $i] :
( ( sk2 @ s @ s @ ( sk5 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5445]) ).
thf(5458,plain,
! [A: $i] :
( ( ( sk2 @ s @ s )
!= A )
| ( ( sk5 @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[5446]) ).
thf(5459,plain,
( ( sk2 @ s @ s @ s )
!= ( sk5 @ s @ s ) ),
inference(simp,[status(thm)],[5458]) ).
thf(3479,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk2 @ ( q_nil @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,1568]) ).
thf(3480,plain,
( ( sk2 @ ( q_nil @ leq ) )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3479:[bind(A,$thf( sk3 ))]]) ).
thf(15851,plain,
( ( ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15679,2601]) ).
thf(15852,plain,
( ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[15851]) ).
thf(15937,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk6 @ m_Halt )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[15852]) ).
thf(15960,plain,
( ( sk6 @ m_Halt )
!= ( sk8 @ m_Down ) ),
inference(simp,[status(thm)],[15937]) ).
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(178,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(179,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) ) ) ),
inference(miniscope,[status(thm)],[178]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Ldr )
= ( D @ m_Ldr ) ) )
& ( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[179]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[180]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Ldr )
!= ( B @ m_Ldr ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(184,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Ldr @ A )
= B ),
inference(detectInverse,[status(thm)],[183]) ).
thf(185,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk11 )
= A ),
inference(cnf,[status(esa)],[184]) ).
thf(2350,plain,
! [A: $i] :
( ( A @ m_Ldr @ sk11 )
= A ),
inference(lifteq,[status(thm)],[185]) ).
thf(15682,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9677,2419]) ).
thf(15683,plain,
! [A: $i] :
( ( sk1 @ ( A @ cons ) @ ( sk8 @ m_Down @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[15682]) ).
thf(15753,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) )
| ( ( sk8 @ m_Down )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[15683]) ).
thf(15782,plain,
! [A: $i] :
( ( sk1 @ ( A @ cons ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[15753]) ).
thf(275,plain,
! [A: $i] :
( ( A
= ( A @ sk16 @ m_Down ) )
| ( A
= ( A @ sk15 @ m_Halt ) )
| ~ ( A @ pidElem ) ),
inference(cnfConj,[status(thm)],[274]) ).
thf(278,plain,
! [A: $i] :
( ~ ( A @ pidElem )
| ( ( A @ sk16 @ m_Down )
= A )
| ( ( A @ sk15 @ m_Halt )
= A ) ),
inference(lifteq,[status(thm)],[275]) ).
thf(15300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4760,242]) ).
thf(15301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( nbr_proc @ s @ ( A @ host @ s @ leq ) )
!= ( C @ ( B @ leq ) ) )
| ( C @ s @ ( B @ s @ leq ) ) ),
inference(simp,[status(thm)],[15300]) ).
thf(15302,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(pattern_uni,[status(thm)],[15301:[bind(A,$thf( E )),bind(B,$thf( E @ host @ s )),bind(C,$thf( nbr_proc @ s ))]]) ).
thf(15326,plain,
! [A: $i] : ( nbr_proc @ s @ s @ ( A @ host @ s @ s @ leq ) ),
inference(simp,[status(thm)],[15302]) ).
thf(30919,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ s @ s ) )
| ( q_nil != B )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,30814]) ).
thf(30920,plain,
! [A: $i] :
( ( q_nil != A )
| ( A @ s @ s @ ( A @ s @ s @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[30919:[bind(A,$thf( D @ s @ s )),bind(B,$thf( D ))]]) ).
thf(30935,plain,
q_nil @ s @ s @ ( q_nil @ s @ s @ last @ elem ),
inference(simp,[status(thm)],[30920]) ).
thf(38595,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk4 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9672,413]) ).
thf(38596,plain,
! [B: $i,A: $i] :
( ( sk2 @ host @ queue @ ( A @ cons ) @ ( sk4 @ m_Down @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[38595]) ).
thf(38682,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ host @ queue @ ( A @ cons ) )
!= q_nil )
| ( ( sk4 @ m_Down )
!= B ) ),
inference(simp,[status(thm)],[38596]) ).
thf(38719,plain,
! [A: $i] :
( ( sk2 @ host @ queue @ ( A @ cons ) )
!= q_nil ),
inference(simp,[status(thm)],[38682]) ).
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(130,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(131,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) ) ) ),
inference(miniscope,[status(thm)],[130]) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_NotNorm )
= ( D @ m_NotNorm ) ) )
& ( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[132]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( A @ m_NotNorm )
!= ( B @ m_NotNorm ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[133]) ).
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(294,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(295,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Down )
!= ( B @ m_Down ) ) ) ),
inference(miniscope,[status(thm)],[294]) ).
thf(296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Down )
= ( D @ m_Down ) ) )
& ( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[296]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Down )
!= ( B @ m_Down ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(2898,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,2601]) ).
thf(2899,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[2898]) ).
thf(2936,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Halt ) ) ),
inference(simp,[status(thm)],[2899]) ).
thf(2984,plain,
! [A: $i] :
( ( A @ ( sk6 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2936]) ).
thf(22713,plain,
! [A: $i] :
( ( A != sk4 )
| ( q_nil != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3795]) ).
thf(22714,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[22713]) ).
thf(22715,plain,
( ( sk7 @ ( sk7 @ last @ elem ) )
| ( sk4 @ ( sk4 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[22714:[bind(A,$thf( sk4 ))]]) ).
thf(17829,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk6 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[2391,17270]) ).
thf(17840,plain,
( ( q_nil @ ( sk6 @ m_Halt @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[17829]) ).
thf(1617,plain,
( ( ( sk4 @ host @ ( sk2 @ host @ leq ) )
!= ( sk2 @ ( sk6 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1550,518]) ).
thf(1618,plain,
( ( sk4 @ host @ ( sk2 @ host @ leq ) )
!= ( sk2 @ ( sk6 @ leq ) ) ),
inference(simp,[status(thm)],[1617]) ).
thf(1626,plain,
( ( ( sk4 @ host )
!= sk2 )
| ( ( sk2 @ host )
!= sk6 ) ),
inference(simp,[status(thm)],[1618]) ).
thf(3098,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,2601]) ).
thf(3099,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[3098]) ).
thf(3132,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk6 @ m_Halt ) ) ),
inference(simp,[status(thm)],[3099]) ).
thf(3193,plain,
! [A: $i] :
( ( sk6 @ m_Halt @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3132]) ).
thf(420,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ( B @ ( A @ ( B @ sk19 ) @ elem ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[416]) ).
thf(426,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ( B @ ( A @ ( B @ sk19 ) @ elem ) )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[420]) ).
thf(48181,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1568,440]) ).
thf(48182,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[48181]) ).
thf(48183,plain,
sk2 @ s @ ( sk3 @ leq ),
inference(pattern_uni,[status(thm)],[48182:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(48468,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48183,440]) ).
thf(48469,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ s @ ( sk3 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[48468]) ).
thf(48470,plain,
sk2 @ s @ s @ ( sk3 @ leq ),
inference(pattern_uni,[status(thm)],[48469:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 @ s ))]]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(255,plain,
! [A: $i,B: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
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(207,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(208,plain,
! [B: $i,A: $i] :
( ( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) )
& ( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ) ),
inference(cnf,[status(esa)],[207]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( pids @ ( A @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(48545,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ s @ ( sk3 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48183,394]) ).
thf(48546,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ s @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[48545]) ).
thf(48626,plain,
! [A: $i] :
( ( A
!= ( sk2 @ s ) )
| ( ( A @ s )
!= sk3 ) ),
inference(simp,[status(thm)],[48546]) ).
thf(48646,plain,
( ( sk2 @ s @ s )
!= sk3 ),
inference(simp,[status(thm)],[48626]) ).
thf(448,plain,
( ( ( alive @ ( sk3 @ setIn ) )
!= ( pids @ ( sk2 @ setIn ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,91]) ).
thf(449,plain,
( ( alive @ ( sk3 @ setIn ) )
!= ( pids @ ( sk2 @ setIn ) ) ),
inference(simp,[status(thm)],[448]) ).
thf(450,plain,
( ( pids != alive )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[449]) ).
thf(14932,plain,
( ( sk3 != sk3 )
| ( pids != alive )
| ( sk2 != sk2 )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[11261,450]) ).
thf(14933,plain,
( ( sk3 != sk3 )
| ( pids != alive )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[14932]) ).
thf(14934,plain,
( ( pids != alive )
| ~ ( sk3 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[14933:[]]) ).
thf(36419,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( sk2 @ host @ s @ s )
!= ( zero @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[534,33282]) ).
thf(36420,plain,
( ( sk2 @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(pattern_uni,[status(thm)],[36419:[bind(A,$thf( sk6 ))]]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) )
| ~ ( A @ ( B @ leq ) )
| ( alive @ ( A @ setIn ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( A @ ( B @ leq ) )
| ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(lifteq,[status(thm)],[82]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ ( alive @ ( B @ setIn ) )
| ~ ( A @ ( B @ leq ) )
| ( alive @ ( A @ setIn ) )
| ( ( B @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(9032,plain,
( ( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3418,2601]) ).
thf(9033,plain,
( ( sk2 @ host @ queue @ ( sk2 @ host @ queue @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk6 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[9032]) ).
thf(9156,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Halt ) ) ),
inference(simp,[status(thm)],[9033]) ).
thf(9202,plain,
( ( sk2 @ host @ queue @ last )
!= ( sk6 @ m_Halt ) ),
inference(simp,[status(thm)],[9156]) ).
thf(20405,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s @ s )
!= ( sk2 @ host @ s ) ) ),
inference(paramod_ordered,[status(thm)],[534,15341]) ).
thf(20406,plain,
( ( nbr_proc @ s @ s )
!= ( sk2 @ host @ s ) ),
inference(pattern_uni,[status(thm)],[20405:[bind(A,$thf( sk6 ))]]) ).
thf(5485,plain,
! [A: $i] :
( ( ( sk2 @ s @ s @ ( sk6 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4859,394]) ).
thf(5486,plain,
! [A: $i] :
( ( sk2 @ s @ s @ ( sk6 @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[5485]) ).
thf(5493,plain,
! [A: $i] :
( ( ( sk2 @ s @ s )
!= A )
| ( ( sk6 @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[5486]) ).
thf(5499,plain,
( ( sk2 @ s @ s @ s )
!= ( sk6 @ s @ s ) ),
inference(simp,[status(thm)],[5493]) ).
thf(4920,plain,
! [A: $i] :
( ( A != sk3 )
| ( q_nil != q_nil )
| ( sk8 @ ( sk8 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3348]) ).
thf(4921,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk8 @ ( sk8 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4920]) ).
thf(4922,plain,
( ( sk8 @ ( sk8 @ last @ elem ) )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4921:[bind(A,$thf( sk3 ))]]) ).
thf(29667,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk1 @ snoc ) @ ( sk1 @ last @ elem ) )
!= ( q_nil @ ( B @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29535,413]) ).
thf(29668,plain,
! [B: $i,A: $i] :
( ( A @ ( sk1 @ snoc ) @ ( sk1 @ last @ elem ) )
!= ( q_nil @ ( B @ elem ) ) ),
inference(simp,[status(thm)],[29667]) ).
thf(29723,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk1 @ snoc ) )
!= q_nil )
| ( ( sk1 @ last )
!= B ) ),
inference(simp,[status(thm)],[29668]) ).
thf(29765,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[29723]) ).
thf(15120,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5192,242]) ).
thf(15121,plain,
! [B: $i,A: $i] :
( ( ( nbr_proc @ s @ s @ ( zero @ s @ s @ s @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[15120]) ).
thf(15122,plain,
nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ),
inference(pattern_uni,[status(thm)],[15121:[bind(A,$thf( zero @ s @ s @ s )),bind(B,$thf( nbr_proc @ s @ s ))]]) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ~ $true
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(paramod_ordered,[status(thm)],[1531,394]) ).
thf(2159,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ leq ) )
!= ( B @ ( B @ s @ leq ) ) )
| ( ( sk2 @ host )
!= ( A @ host ) ) ),
inference(simp,[status(thm)],[2158]) ).
thf(2160,plain,
( ( sk2 @ s @ host )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[2159:[bind(A,$thf( sk2 @ s )),bind(B,$thf( sk2 ))]]) ).
thf(17178,plain,
( ( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16961,2611]) ).
thf(17179,plain,
( ( sk2 @ host @ queue @ ( sk1 @ last @ elem ) )
!= ( sk2 @ host @ queue @ ( sk3 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[17178]) ).
thf(17225,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk1 @ last )
!= ( sk3 @ m_Halt ) ) ),
inference(simp,[status(thm)],[17179]) ).
thf(17269,plain,
( ( sk1 @ last )
!= ( sk3 @ m_Halt ) ),
inference(simp,[status(thm)],[17225]) ).
thf(17375,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk3 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[159,17269]) ).
thf(17385,plain,
! [A: $i] :
( ( sk3 @ m_Halt @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17375]) ).
thf(17393,plain,
! [A: $i] :
( ( sk3 @ m_Halt @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17385]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(cnfConj,[status(thm)],[274]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( A @ pidElem )
| ( A
!= ( B @ m_Down ) ) ),
inference(lifteq,[status(thm)],[277]) ).
thf(282,plain,
! [A: $i] : ( A @ m_Down @ pidElem ),
inference(simp,[status(thm)],[281]) ).
thf(175,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Ldr )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[174]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[175]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( A @ m_Ldr )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ pidMsg @ ( A @ pidMsg @ leq ) )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( B @ ( A @ cons ) @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ pidMsg @ ( A @ pidMsg @ leq ) )
| ~ ( C @ pidElem )
| ~ ( A @ pidElem )
| ~ ( B @ ( C @ elem ) )
| ~ ( B @ ( A @ cons ) @ ordered )
| ( ( C @ pidMsg @ host )
!= ( A @ pidMsg @ host ) ) ),
inference(lifteq,[status(thm)],[325]) ).
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(369,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(370,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ leq ) )
| ~ ( C @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnf,[status(esa)],[369]) ).
thf(4221,plain,
! [A: $i] :
( ( A != sk2 )
| ( q_nil @ ( sk6 @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,1550]) ).
thf(4222,plain,
( ( q_nil @ ( sk6 @ leq ) )
| ( sk2 @ ( sk2 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4221:[bind(A,$thf( sk2 ))]]) ).
thf(29154,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( q_nil != alive ) ),
inference(paramod_ordered,[status(thm)],[3871,413]) ).
thf(29155,plain,
! [A: $i] :
( ( ( setEmpty @ ( setEmpty @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[29154]) ).
thf(29218,plain,
! [A: $i] :
( ( setEmpty != q_nil )
| ( ( setEmpty @ last )
!= A )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[29155]) ).
thf(29258,plain,
( ( setEmpty != q_nil )
| ( q_nil != alive ) ),
inference(simp,[status(thm)],[29218]) ).
thf(37476,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15122,394]) ).
thf(37477,plain,
! [A: $i] :
( ( nbr_proc @ s @ s @ s @ ( zero @ s @ s @ s @ s @ leq ) )
!= ( A @ ( A @ s @ leq ) ) ),
inference(simp,[status(thm)],[37476]) ).
thf(37540,plain,
! [A: $i] :
( ( ( nbr_proc @ s @ s @ s )
!= A )
| ( ( zero @ s @ s @ s @ s )
!= ( A @ s ) ) ),
inference(simp,[status(thm)],[37477]) ).
thf(37583,plain,
( ( nbr_proc @ s @ s @ s @ s )
!= ( zero @ s @ s @ s @ s ) ),
inference(simp,[status(thm)],[37540]) ).
thf(35956,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk2 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4201,413]) ).
thf(35957,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[35956]) ).
thf(36027,plain,
! [A: $i] :
( ( sk4 != q_nil )
| ( ( sk4 @ last )
!= A )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[35957]) ).
thf(36063,plain,
( ( sk4 != q_nil )
| ( sk2 != q_nil ) ),
inference(simp,[status(thm)],[36027]) ).
thf(17864,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk6 @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[2391,17271]) ).
thf(17877,plain,
( ( q_nil @ ( sk6 @ m_Down @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[17864]) ).
thf(3088,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,2427]) ).
thf(3089,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3088]) ).
thf(3147,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk5 @ m_Down ) ) ),
inference(simp,[status(thm)],[3089]) ).
thf(3174,plain,
! [A: $i] :
( ( sk5 @ m_Down @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3147]) ).
thf(9449,plain,
( ( ( alive @ ( nil @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[9438,196]) ).
thf(9450,plain,
( ( ( alive @ ( nil @ setIn ) )
!= ( alive @ ( q_nil @ setIn ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9449]) ).
thf(9492,plain,
( ( alive != alive )
| ( nil != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9450]) ).
thf(9505,plain,
( ( nil != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[9492]) ).
thf(35453,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk6 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[4022,413]) ).
thf(35454,plain,
! [A: $i] :
( ( ( sk8 @ ( sk8 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[35453]) ).
thf(35531,plain,
! [A: $i] :
( ( sk8 != q_nil )
| ( ( sk8 @ last )
!= A )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[35454]) ).
thf(35569,plain,
( ( sk8 != q_nil )
| ( sk6 != q_nil ) ),
inference(simp,[status(thm)],[35531]) ).
thf(17305,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk5 @ m_Down ) ) ),
inference(paramod_ordered,[status(thm)],[159,17264]) ).
thf(17315,plain,
! [A: $i] :
( ( sk5 @ m_Down @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17305]) ).
thf(17320,plain,
! [A: $i] :
( ( sk5 @ m_Down @ ( A @ snoc ) )
!= sk1 ),
inference(simp,[status(thm)],[17315]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( ( A @ ( B @ sk18 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ~ ( B @ ordered )
| ( ( A @ ( B @ sk18 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) ) ),
inference(lifteq,[status(thm)],[329]) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ~ ( B @ ordered )
| ( ( A @ ( B @ sk18 ) @ pidMsg @ host )
= ( A @ pidMsg @ host ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(3110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,413]) ).
thf(3111,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( q_nil @ ( C @ elem ) ) ),
inference(simp,[status(thm)],[3110]) ).
thf(3141,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= q_nil )
| ( A != C ) ),
inference(simp,[status(thm)],[3111]) ).
thf(3168,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ snoc ) )
!= q_nil ),
inference(simp,[status(thm)],[3141]) ).
thf(246,plain,
( ! [A: $i,B: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
=> ( A != B ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ m_Halt )
!= ( B @ m_Halt ) ) ) ),
inference(miniscope,[status(thm)],[245]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C != D )
| ( ( C @ m_Halt )
= ( D @ m_Halt ) ) )
& ( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ) ),
inference(cnf,[status(esa)],[246]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[247]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( ( A @ m_Halt )
!= ( B @ m_Halt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[248]) ).
thf(2443,plain,
( ( ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk1 @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,2419]) ).
thf(2444,plain,
( ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) )
!= ( sk1 @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2443]) ).
thf(2450,plain,
( ( ( sk7 @ host @ queue )
!= sk1 )
| ( ( sk8 @ m_Down )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[2444]) ).
thf(2458,plain,
( ( sk7 @ host @ queue )
!= sk1 ),
inference(simp,[status(thm)],[2450]) ).
thf(3588,plain,
! [A: $i] :
( ( A != nbr_proc )
| ( q_nil @ ( zero @ s @ leq ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,197]) ).
thf(3589,plain,
( ( q_nil @ ( zero @ s @ leq ) )
| ( nbr_proc @ ( nbr_proc @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3588:[bind(A,$thf( nbr_proc ))]]) ).
thf(3004,plain,
( ( ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2897,2607]) ).
thf(3005,plain,
( ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) )
!= ( sk2 @ host @ queue @ ( sk4 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[3004]) ).
thf(3049,plain,
( ( ( sk2 @ host @ queue )
!= ( sk2 @ host @ queue ) )
| ( ( sk5 @ m_Halt )
!= ( sk4 @ m_Down ) ) ),
inference(simp,[status(thm)],[3005]) ).
thf(3067,plain,
( ( sk5 @ m_Halt )
!= ( sk4 @ m_Down ) ),
inference(simp,[status(thm)],[3049]) ).
thf(40942,plain,
( ( sk6 != sk6 )
| ( sk2 != sk2 )
| ( sk8 != sk2 )
| ~ ( sk6 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[13317,40934]) ).
thf(40943,plain,
( ( sk6 != sk6 )
| ( sk8 != sk2 )
| ~ ( sk6 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[40942]) ).
thf(40944,plain,
( ( sk8 != sk2 )
| ~ ( sk6 @ ( sk2 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[40943:[]]) ).
thf(3094,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,2607]) ).
thf(3095,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Halt @ elem ) ) ),
inference(simp,[status(thm)],[3094]) ).
thf(3161,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ snoc ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk5 @ m_Halt ) ) ),
inference(simp,[status(thm)],[3095]) ).
thf(3188,plain,
! [A: $i] :
( ( sk5 @ m_Halt @ ( A @ snoc ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[3161]) ).
thf(136,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_NotNorm @ A )
= B ),
inference(detectInverse,[status(thm)],[135]) ).
thf(137,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk9 )
= A ),
inference(cnf,[status(esa)],[136]) ).
thf(2215,plain,
! [A: $i] :
( ( A @ m_NotNorm @ sk9 )
= A ),
inference(lifteq,[status(thm)],[137]) ).
thf(366,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NormQ ) ),
inference(miniscope,[status(thm)],[365]) ).
thf(367,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(cnf,[status(esa)],[366]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NormQ ) ),
inference(lifteq,[status(thm)],[367]) ).
thf(100,plain,
( ( ( sk4 @ host )
= ( sk3 @ host @ ( elid @ index ) @ host ) )
| ( ( sk3 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(129,plain,
( ( ( sk3 @ host @ ( elid @ index ) @ host )
= ( sk4 @ host ) )
| ( ( sk3 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(1807,plain,
( ( ( sk2 @ host @ ( elid @ index ) @ host )
= ( sk4 @ host ) )
| ( ( sk2 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) ),
inference(rewrite,[status(thm)],[129,104]) ).
thf(2187,plain,
( ( sk2 @ s )
!= sk2 ),
inference(simp,[status(thm)],[2160]) ).
thf(2405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( q_nil @ snoc ) )
!= ( B @ ( C @ snoc ) ) )
| ( ( q_nil @ ( A @ cons ) @ init )
= C ) ),
inference(paramod_ordered,[status(thm)],[387,166]) ).
thf(2406,plain,
! [A: $i] :
( ( q_nil @ ( A @ cons ) @ init )
= q_nil ),
inference(pattern_uni,[status(thm)],[2405:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( q_nil ))]]) ).
thf(256,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Halt ) ),
inference(miniscope,[status(thm)],[255]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(cnf,[status(esa)],[256]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Halt ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(12587,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != q_nil )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[289,680]) ).
thf(12588,plain,
! [A: $i] :
( ( A != q_nil )
| ~ ( sk1 @ ( A @ leq ) )
| ~ ( A @ ( sk1 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12587:[bind(A,$thf( sk1 ))]]) ).
thf(13627,plain,
( ~ ( sk1 @ ( q_nil @ leq ) )
| ~ ( q_nil @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[12588]) ).
thf(2886,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,2427]) ).
thf(2887,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( A @ elem ) )
!= ( sk2 @ host @ queue @ ( sk5 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2886]) ).
thf(2940,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cons ) )
!= ( sk2 @ host @ queue ) )
| ( A
!= ( sk5 @ m_Down ) ) ),
inference(simp,[status(thm)],[2887]) ).
thf(2988,plain,
! [A: $i] :
( ( A @ ( sk5 @ m_Down @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[2940]) ).
thf(48358,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1550,440]) ).
thf(48359,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk6 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ s @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[48358]) ).
thf(48360,plain,
sk2 @ s @ ( sk6 @ leq ),
inference(pattern_uni,[status(thm)],[48359:[bind(A,$thf( sk6 )),bind(B,$thf( sk2 ))]]) ).
thf(48926,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ s @ ( sk6 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48360,394]) ).
thf(48927,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ s @ ( sk6 @ leq ) ) ),
inference(simp,[status(thm)],[48926]) ).
thf(49009,plain,
! [A: $i] :
( ( A
!= ( sk2 @ s ) )
| ( ( A @ s )
!= sk6 ) ),
inference(simp,[status(thm)],[48927]) ).
thf(49027,plain,
( ( sk2 @ s @ s )
!= sk6 ),
inference(simp,[status(thm)],[49009]) ).
thf(12583,plain,
! [B: $i,A: $i] :
( ( A != sk7 )
| ( B != sk3 )
| ~ ( A @ ( B @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[289,458]) ).
thf(12584,plain,
! [A: $i] :
( ( A != sk3 )
| ~ ( sk7 @ ( A @ leq ) )
| ~ ( A @ ( sk7 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12583:[bind(A,$thf( sk7 ))]]) ).
thf(13625,plain,
( ~ ( sk7 @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( sk7 @ leq ) ) ),
inference(simp,[status(thm)],[12584]) ).
thf(31158,plain,
! [A: $i] :
( ( ( q_nil @ s @ s @ ( q_nil @ s @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30935,413]) ).
thf(31159,plain,
! [A: $i] :
( ( q_nil @ s @ s @ ( q_nil @ s @ s @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) ),
inference(simp,[status(thm)],[31158]) ).
thf(31244,plain,
! [A: $i] :
( ( ( q_nil @ s @ s )
!= q_nil )
| ( ( q_nil @ s @ s @ last )
!= A ) ),
inference(simp,[status(thm)],[31159]) ).
thf(31266,plain,
( ( q_nil @ s @ s )
!= q_nil ),
inference(simp,[status(thm)],[31244]) ).
thf(251,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Halt @ A )
= B ),
inference(detectInverse,[status(thm)],[250]) ).
thf(252,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(cnf,[status(esa)],[251]) ).
thf(2384,plain,
! [A: $i] :
( ( A @ m_Halt @ sk14 )
= A ),
inference(lifteq,[status(thm)],[252]) ).
thf(10739,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk5 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3610,413]) ).
thf(10740,plain,
! [A: $i] :
( ( ( sk7 @ ( sk7 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[10739]) ).
thf(10785,plain,
! [A: $i] :
( ( sk7 != q_nil )
| ( ( sk7 @ last )
!= A )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[10740]) ).
thf(10828,plain,
( ( sk7 != q_nil )
| ( sk5 != q_nil ) ),
inference(simp,[status(thm)],[10785]) ).
thf(2150,plain,
! [A: $i] :
( ( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk3 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1568,394]) ).
thf(2151,plain,
! [A: $i] :
( ( A @ ( A @ s @ leq ) )
!= ( sk2 @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2150]) ).
thf(2174,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( A @ s )
!= sk3 ) ),
inference(simp,[status(thm)],[2151]) ).
thf(2183,plain,
( ( sk2 @ s )
!= sk3 ),
inference(simp,[status(thm)],[2174]) ).
thf(212,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[211]) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(cnf,[status(esa)],[212]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(1629,plain,
( ( ( sk4 @ host @ ( sk2 @ host @ leq ) )
!= ( sk2 @ ( sk5 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1561,518]) ).
thf(1630,plain,
( ( sk4 @ host @ ( sk2 @ host @ leq ) )
!= ( sk2 @ ( sk5 @ leq ) ) ),
inference(simp,[status(thm)],[1629]) ).
thf(1642,plain,
( ( ( sk4 @ host )
!= sk2 )
| ( ( sk2 @ host )
!= sk5 ) ),
inference(simp,[status(thm)],[1630]) ).
thf(445,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_Ldr ) ),
inference(miniscope,[status(thm)],[444]) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(cnf,[status(esa)],[445]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_Ldr ) ),
inference(lifteq,[status(thm)],[446]) ).
thf(372,plain,
norm != wait,
inference(polarity_switch,[status(thm)],[371]) ).
thf(373,plain,
wait != norm,
inference(lifteq,[status(thm)],[372]) ).
thf(300,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ m_Down @ A )
= B ),
inference(detectInverse,[status(thm)],[299]) ).
thf(301,plain,
! [A: $i] :
( ( A @ m_Down @ sk17 )
= A ),
inference(cnf,[status(esa)],[300]) ).
thf(2385,plain,
! [A: $i] :
( ( A @ m_Down @ sk17 )
= A ),
inference(lifteq,[status(thm)],[301]) ).
thf(408,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( A @ m_Ack ) )
= ( C @ m_Ldr ) ),
inference(miniscope,[status(thm)],[407]) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(cnf,[status(esa)],[408]) ).
thf(410,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) )
!= ( C @ m_Ldr ) ),
inference(lifteq,[status(thm)],[409]) ).
thf(10731,plain,
! [A: $i] :
( ( A != sk5 )
| ( q_nil != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3610]) ).
thf(10732,plain,
! [A: $i] :
( ( A != sk5 )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[10731]) ).
thf(10733,plain,
( ( sk7 @ ( sk7 @ last @ elem ) )
| ( sk5 @ ( sk5 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[10732:[bind(A,$thf( sk5 ))]]) ).
thf(13205,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[1561,289]) ).
thf(13206,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ ( A @ ( B @ leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[13205]) ).
thf(13207,plain,
( ~ ( sk5 @ ( sk2 @ leq ) )
| ( sk5 = sk2 ) ),
inference(pattern_uni,[status(thm)],[13206:[bind(A,$thf( sk5 )),bind(B,$thf( sk2 ))]]) ).
thf(5557,plain,
! [A: $i] :
( ( A != nil )
| ( q_nil != q_nil )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3580]) ).
thf(5558,plain,
! [A: $i] :
( ( A != nil )
| ( sk7 @ ( sk7 @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[5557]) ).
thf(5559,plain,
( ( sk7 @ ( sk7 @ last @ elem ) )
| ( nil @ ( nil @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[5558:[bind(A,$thf( nil ))]]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( pids @ ( B @ setIn ) )
| ~ ( A @ host @ queue @ ( B @ ( A @ m_Ack ) @ elem ) ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ( A = B )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) ) ),
inference(cnfConj,[status(thm)],[264]) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ elem ) )
| ~ ( C @ ( B @ cons ) @ ( A @ elem ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(434,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( A
= ( B @ s ) )
| ~ ( B @ s @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[433]) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ s @ ( A @ leq ) )
| ( A
= ( B @ s ) ) ),
inference(lifteq,[status(thm)],[434]) ).
thf(399,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(cnf,[status(esa)],[398]) ).
thf(400,plain,
! [A: $i] :
( ( A @ m_Halt @ pidMsg )
= A ),
inference(lifteq,[status(thm)],[399]) ).
thf(2222,plain,
! [A: $i] :
( ( ( sk6 @ host )
!= ( A @ host ) )
| ( ( nbr_proc @ s )
!= ( sk2 @ host ) ) ),
inference(paramod_ordered,[status(thm)],[534,2179]) ).
thf(2223,plain,
( ( nbr_proc @ s )
!= ( sk2 @ host ) ),
inference(pattern_uni,[status(thm)],[2222:[bind(A,$thf( sk6 ))]]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( B @ ordered )
| ~ ( B @ ( A @ cons ) @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ m_Ack ) )
!= ( D @ ( B @ m_Ack ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(201,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ m_Ack ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[200]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk12 ) )
= B ),
inference(cnf,[status(esa)],[201]) ).
thf(2731,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ m_Ack ) @ ( A @ sk12 ) )
= B ),
inference(lifteq,[status(thm)],[202]) ).
thf(328,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[328]) ).
thf(419,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[416]) ).
thf(427,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ snoc ) @ ordered )
| ( A @ pidElem )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[419]) ).
thf(96,plain,
( ( ( sk3 @ host @ ( status @ index ) )
= wait )
| ( ( sk3 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(113,plain,
( ( ( sk3 @ host @ ( status @ index ) )
= wait )
| ( ( sk3 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(860,plain,
( ( ( sk2 @ host @ ( status @ index ) )
= wait )
| ( ( sk2 @ host @ ( ldr @ index ) )
= ( sk4 @ host ) ) ),
inference(rewrite,[status(thm)],[113,104]) ).
thf(29899,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29593,2419]) ).
thf(29900,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) @ ( sk8 @ m_Down @ elem ) )
!= ( sk7 @ host @ queue @ ( sk8 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[29899]) ).
thf(29999,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ snoc ) )
!= ( sk7 @ host @ queue ) )
| ( ( sk8 @ m_Down )
!= ( sk8 @ m_Down ) ) ),
inference(simp,[status(thm)],[29900]) ).
thf(30031,plain,
! [A: $i] :
( ( A @ ( sk1 @ snoc ) )
!= ( sk7 @ host @ queue ) ),
inference(simp,[status(thm)],[29999]) ).
thf(9819,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk2 @ host @ queue @ last ) )
| ( A
!= ( sk6 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[2391,9202]) ).
thf(9848,plain,
( ( q_nil @ ( sk6 @ m_Halt @ cons ) )
!= ( sk2 @ host @ queue ) ),
inference(simp,[status(thm)],[9819]) ).
thf(4632,plain,
! [A: $i] :
( ( ( sk6 @ ( sk6 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ~ $true
| ( sk3 != q_nil ) ),
inference(paramod_ordered,[status(thm)],[3346,413]) ).
thf(4633,plain,
! [A: $i] :
( ( ( sk6 @ ( sk6 @ last @ elem ) )
!= ( q_nil @ ( A @ elem ) ) )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[4632]) ).
thf(4682,plain,
! [A: $i] :
( ( sk6 != q_nil )
| ( ( sk6 @ last )
!= A )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[4633]) ).
thf(4691,plain,
( ( sk6 != q_nil )
| ( sk3 != q_nil ) ),
inference(simp,[status(thm)],[4682]) ).
thf(4874,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk6 != q_nil )
| ( q_nil != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,4691]) ).
thf(4875,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk6 != q_nil )
| ( A @ ( A @ last @ elem ) ) ),
inference(simp,[status(thm)],[4874]) ).
thf(4876,plain,
( ( sk6 != q_nil )
| ( sk3 @ ( sk3 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[4875:[bind(A,$thf( sk3 ))]]) ).
thf(29147,plain,
! [A: $i] :
( ( q_nil != q_nil )
| ( A != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,3871]) ).
thf(29148,plain,
! [A: $i] :
( ( A != alive )
| ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[29147:[]]) ).
thf(29274,plain,
( ( setEmpty @ ( setEmpty @ last @ elem ) )
| ( alive @ ( alive @ last @ elem ) ) ),
inference(simp,[status(thm)],[29148]) ).
thf(36403,plain,
! [A: $i] :
( ( ( sk8 @ host )
!= ( A @ host ) )
| ( ( sk7 @ host @ s @ s )
!= ( zero @ s @ s ) ) ),
inference(paramod_ordered,[status(thm)],[125,33282]) ).
thf(36404,plain,
( ( sk7 @ host @ s @ s )
!= ( zero @ s @ s ) ),
inference(pattern_uni,[status(thm)],[36403:[bind(A,$thf( sk8 ))]]) ).
thf(2628,plain,
( ( ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) )
!= ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[75,2599]) ).
thf(2629,plain,
( ( sk7 @ host @ queue @ ( sk8 @ m_Halt @ elem ) )
!= ( sk7 @ host @ queue @ ( sk6 @ m_Down @ elem ) ) ),
inference(simp,[status(thm)],[2628]) ).
thf(2636,plain,
( ( ( sk7 @ host @ queue )
!= ( sk7 @ host @ queue ) )
| ( ( sk8 @ m_Halt )
!= ( sk6 @ m_Down ) ) ),
inference(simp,[status(thm)],[2629]) ).
thf(2640,plain,
( ( sk8 @ m_Halt )
!= ( sk6 @ m_Down ) ),
inference(simp,[status(thm)],[2636]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( B @ ( A @ ( B @ sk18 ) @ elem ) )
| ~ ( B @ ordered ) ),
inference(cnfConj,[status(thm)],[323]) ).
thf(337,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ordered )
| ( B @ ( A @ ( B @ sk18 ) @ elem ) )
| ~ ( B @ ordered ) ),
inference(simp,[status(thm)],[324]) ).
thf(17374,plain,
! [A: $i] :
( ( ( q_nil @ ( A @ cons ) @ last )
!= ( sk1 @ last ) )
| ( A
!= ( sk3 @ m_Halt ) ) ),
inference(paramod_ordered,[status(thm)],[2391,17269]) ).
thf(17387,plain,
( ( q_nil @ ( sk3 @ m_Halt @ cons ) )
!= sk1 ),
inference(simp,[status(thm)],[17374]) ).
thf(3442,plain,
! [A: $i] :
( ( A != sk8 )
| ( ( sk7 @ host )
= ( q_nil @ host ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,125]) ).
thf(3443,plain,
( ( ( sk7 @ host )
= ( q_nil @ host ) )
| ( sk8 @ ( sk8 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3442:[bind(A,$thf( sk8 ))]]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(cnf,[status(esa)],[362]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ cons ) @ snoc ) )
= ( B @ ( C @ snoc ) @ ( A @ cons ) ) ),
inference(lifteq,[status(thm)],[363]) ).
thf(220,plain,
~ ? [A: $i,B: $i] :
( ( A @ m_Down )
= ( B @ m_NotNorm ) ),
inference(miniscope,[status(thm)],[219]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(cnf,[status(esa)],[220]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( A @ m_Down )
!= ( B @ m_NotNorm ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(40787,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk6 @ ( sk8 @ leq ) ) )
| ( sk8 != sk2 )
| ~ $true
| ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[361,40747]) ).
thf(40788,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ leq ) )
!= ( sk6 @ ( sk8 @ leq ) ) )
| ( sk8 != sk2 )
| ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[40787]) ).
thf(40789,plain,
( ( sk8 != sk2 )
| ( sk8 @ ( sk6 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[40788:[bind(A,$thf( sk8 )),bind(B,$thf( sk6 ))]]) ).
thf(3552,plain,
! [A: $i] :
( ( A != sk6 )
| ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( A @ ( A @ last @ elem ) ) ),
inference(paramod_ordered,[status(thm)],[3190,534]) ).
thf(3553,plain,
( ( ( sk2 @ host )
= ( q_nil @ host ) )
| ( sk6 @ ( sk6 @ last @ elem ) ) ),
inference(pattern_uni,[status(thm)],[3552:[bind(A,$thf( sk6 ))]]) ).
thf(52148,plain,
$false,
inference(e,[status(thm)],[69,14977,4188,4201,4094,365,333,2427,481,4005,16013,347,4022,9180,15573,518,3072,3317,13520,217,308,120,10125,977,170,29525,440,17253,385,384,21876,472,3826,340,5192,15791,9672,2607,13317,4220,2184,30814,15885,153,9246,39093,2972,2020,885,320,4760,174,404,43485,4866,3275,110,2185,2897,196,125,344,17270,5150,4243,157,50083,189,5199,40931,17317,289,2301,316,17884,2533,261,152,1568,20562,475,756,443,321,376,211,20655,17266,9680,4798,2178,216,492,164,50326,40747,2964,397,22217,411,4628,206,4082,14527,5353,280,233,4753,3852,15179,381,9785,22877,307,9682,117,270,529,534,2232,3418,3795,2601,33282,16011,48357,349,392,3610,429,29531,39977,334,15962,598,160,2969,14605,424,3069,192,407,630,229,197,361,2826,3065,97,461,2181,15947,5492,29593,30800,13639,9301,2179,3482,317,18677,17264,188,388,156,10126,403,980,40934,49944,356,48829,169,13676,17357,1028,225,3179,4750,526,13512,17350,679,2419,15959,5273,5639,2243,9201,173,11261,371,128,360,311,3173,19090,105,244,2963,398,5209,3190,5417,2221,2235,22032,17271,17848,430,2391,9677,3871,166,46997,29535,20384,444,425,4708,3888,2734,3187,423,2970,191,1652,743,291,9189,259,413,2393,3086,391,10611,29597,4186,22972,9506,9687,236,350,159,764,4716,219,377,1603,230,362,245,1771,29527,9491,599,900,406,98,616,271,3066,2180,345,4833,103,609,140,4985,91,895,3298,3971,2252,462,34899,2182,387,3192,15961,198,32641,2461,2974,108,5410,5459,3480,15960,2350,15782,278,15326,30935,38719,223,135,299,226,3348,431,80,2984,22715,130,17840,394,3876,167,1626,3193,426,48470,374,255,209,4859,48646,458,14934,680,4456,36420,123,9202,194,145,5452,20406,150,414,5499,4922,29765,15122,1531,2160,17393,5624,282,1611,3642,177,331,441,370,4222,29258,338,576,2599,37583,36063,49327,17877,3174,359,9505,613,48200,314,35569,859,17320,336,3168,250,2458,450,3589,3067,203,9438,40944,3188,2215,2611,218,368,16961,1807,104,2187,3346,48183,896,2406,304,258,15341,13627,9179,10050,17269,2988,4791,49027,13625,401,31266,75,2384,10828,2183,272,4759,207,214,2421,1642,447,3601,183,373,2385,15679,410,10733,262,13207,5559,210,294,341,268,358,195,437,1561,400,3030,2223,48360,10622,283,886,326,107,3956,239,242,395,2241,2731,332,427,860,30031,9848,4876,1550,29274,200,163,36404,4019,178,4691,3494,13689,369,5344,4826,2640,3580,337,17387,19072,215,3443,491,454,364,232,2177,3669,30654,222,40789,3553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV452+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
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 13:54:06 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.44/1.24 % [INFO] Parsing done (247ms).
% 1.44/1.25 % [INFO] Running in sequential loop mode.
% 2.32/1.64 % [INFO] eprover registered as external prover.
% 2.32/1.64 % [INFO] Scanning for conjecture ...
% 2.73/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.98/1.94 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.98/2.01 % [INFO] Problem is first-order (TPTP FOF).
% 2.98/2.02 % [INFO] Type checking passed.
% 3.30/2.03 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 83.62/19.23 % External prover 'e' found a proof!
% 83.62/19.23 % [INFO] Killing All external provers ...
% 83.62/19.23 % Time passed: 18689ms (effective reasoning time: 17973ms)
% 83.62/19.23 % 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)>
% 83.62/19.23 % 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
% 83.62/19.23 % No. of inferences in proof: 1370
% 83.62/19.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18689 ms resp. 17973 ms w/o parsing
% 85.08/19.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 85.48/19.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------