TSTP Solution File: SWV473+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV473+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:16:00 EDT 2023
% Result : Theorem 5.86s 2.46s
% Output : Refutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 105
% Syntax : Number of formulae : 174 ( 81 unt; 38 typ; 0 def)
% Number of atoms : 465 ( 247 equ; 0 cnn)
% Maximal formula atoms : 67 ( 3 avg)
% Number of connectives : 1619 ( 160 ~; 30 |; 182 &;1130 @)
% ( 13 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 38 usr; 17 con; 0-2 aty)
% Number of variables : 352 ( 0 ^; 349 !; 3 ?; 352 :)
% Comments :
%------------------------------------------------------------------------------
thf(elem_type,type,
elem: $i > $i > $o ).
thf(m_Ldr_type,type,
m_Ldr: $i > $i ).
thf(queue_type,type,
queue: $i > $i ).
thf(host_type,type,
host: $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(m_Down_type,type,
m_Down: $i > $i ).
thf(nbr_proc_type,type,
nbr_proc: $i ).
thf(m_NotNorm_type,type,
m_NotNorm: $i > $i ).
thf(setIn_type,type,
setIn: $i > $i > $o ).
thf(alive_type,type,
alive: $i ).
thf(index_type,type,
index: $i > $i > $i ).
thf(status_type,type,
status: $i ).
thf(elec_1_type,type,
elec_1: $i ).
thf(elec_2_type,type,
elec_2: $i ).
thf(elid_type,type,
elid: $i ).
thf(norm_type,type,
norm: $i ).
thf(ldr_type,type,
ldr: $i ).
thf(wait_type,type,
wait: $i ).
thf(down_type,type,
down: $i ).
thf(s_type,type,
s: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(m_Ack_type,type,
m_Ack: $i > $i > $i ).
thf(pendack_type,type,
pendack: $i ).
thf(pidMsg_type,type,
pidMsg: $i > $i ).
thf(m_Halt_type,type,
m_Halt: $i > $i ).
thf(m_NormQ_type,type,
m_NormQ: $i > $i ).
thf(last_type,type,
last: $i > $i ).
thf(snoc_type,type,
snoc: $i > $i > $i ).
thf(q_nil_type,type,
q_nil: $i ).
thf(init_type,type,
init: $i > $i ).
thf(ordered_type,type,
ordered: $i > $o ).
thf(nil_type,type,
nil: $i ).
thf(pids_type,type,
pids: $i ).
thf(setEmpty_type,type,
setEmpty: $i ).
thf(tail_type,type,
tail: $i > $i ).
thf(pidElem_type,type,
pidElem: $i > $o ).
thf(head_type,type,
head: $i > $i ).
thf(59,axiom,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( cons @ ( head @ A ) @ ( tail @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(372,plain,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( cons @ ( head @ A ) @ ( tail @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NotNorm @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(339,plain,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NotNorm @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(50,axiom,
! [A: $i] :
( ( pidMsg @ ( m_Down @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(343,plain,
! [A: $i] :
( ( pidMsg @ ( m_Down @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( init @ ( snoc @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( init @ ( snoc @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(55,axiom,
! [A: $i] :
( ( cons @ A @ q_nil )
= ( snoc @ q_nil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(359,plain,
! [A: $i] :
( ( cons @ A @ q_nil )
= ( snoc @ q_nil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) ) )
& ( ( ( m_NotNorm @ A )
!= ( m_NotNorm @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(41,axiom,
elec_2 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_09) ).
thf(309,plain,
elec_2 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( elem @ ( m_Ldr @ F ) @ ( queue @ ( host @ E ) ) )
=> ~ ( leq @ ( host @ E ) @ ( host @ F ) ) )
& ! [E: $i,F: $i] :
( ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) )
=> ( ( host @ F )
!= ( host @ E ) ) )
& ! [E: $i,F: $i] :
( ( ( host @ F )
= nbr_proc )
=> ~ ( elem @ ( m_NotNorm @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i] :
( ( ( F != E )
& ( ( host @ F )
= ( host @ E ) ) )
=> ( ~ ( setIn @ E @ alive )
| ~ ( setIn @ F @ alive ) ) )
& ! [E: $i] :
( ( ( ( ( index @ status @ ( host @ E ) )
= elec_1 )
| ( ( index @ status @ ( host @ E ) )
= elec_2 ) )
& ( setIn @ E @ alive ) )
=> ( ( index @ elid @ ( host @ E ) )
= E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( ( host @ G )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= norm )
& ( ( index @ ldr @ ( host @ G ) )
= ( host @ F ) ) )
=> ~ ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( ( host @ G )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= wait )
& ( ( host @ ( index @ elid @ ( host @ G ) ) )
= ( host @ F ) ) )
=> ~ ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ H ) ) )
& ( ( host @ H )
= nbr_proc )
& ( ( host @ H )
= ( host @ F ) )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) )
& ( ( queue @ ( host @ C ) )
= ( cons @ ( m_Ack @ B @ D ) @ A ) ) )
=> ( ( setIn @ C @ alive )
=> ( ~ ( ( ( index @ elid @ ( host @ C ) )
= B )
& ( ( index @ status @ ( host @ C ) )
= elec_2 )
& ( ( host @ D )
= ( index @ pendack @ ( host @ C ) ) ) )
=> ! [E: $i] :
( ( ( host @ C )
!= ( host @ E ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( host @ C )
= ( host @ H ) )
=> ( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( elem @ ( m_Down @ G ) @ A )
& ( ( host @ H )
= ( host @ F ) )
& ( ( host @ H )
= nbr_proc )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( elem @ ( m_Ldr @ F ) @ ( queue @ ( host @ E ) ) )
=> ~ ( leq @ ( host @ E ) @ ( host @ F ) ) )
& ! [E: $i,F: $i] :
( ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) )
=> ( ( host @ F )
!= ( host @ E ) ) )
& ! [E: $i,F: $i] :
( ( ( host @ F )
= nbr_proc )
=> ~ ( elem @ ( m_NotNorm @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i] :
( ( ( F != E )
& ( ( host @ F )
= ( host @ E ) ) )
=> ( ~ ( setIn @ E @ alive )
| ~ ( setIn @ F @ alive ) ) )
& ! [E: $i] :
( ( ( ( ( index @ status @ ( host @ E ) )
= elec_1 )
| ( ( index @ status @ ( host @ E ) )
= elec_2 ) )
& ( setIn @ E @ alive ) )
=> ( ( index @ elid @ ( host @ E ) )
= E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( ( host @ G )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= norm )
& ( ( index @ ldr @ ( host @ G ) )
= ( host @ F ) ) )
=> ~ ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( ( host @ G )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= wait )
& ( ( host @ ( index @ elid @ ( host @ G ) ) )
= ( host @ F ) ) )
=> ~ ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ H ) ) )
& ( ( host @ H )
= nbr_proc )
& ( ( host @ H )
= ( host @ F ) )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) )
& ( ( queue @ ( host @ C ) )
= ( cons @ ( m_Ack @ B @ D ) @ A ) ) )
=> ( ( setIn @ C @ alive )
=> ( ~ ( ( ( index @ elid @ ( host @ C ) )
= B )
& ( ( index @ status @ ( host @ C ) )
= elec_2 )
& ( ( host @ D )
= ( index @ pendack @ ( host @ C ) ) ) )
=> ! [E: $i] :
( ( ( host @ C )
!= ( host @ E ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( host @ C )
= ( host @ H ) )
=> ( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( elem @ ( m_Down @ G ) @ A )
& ( ( host @ H )
= ( host @ F ) )
& ( ( host @ H )
= nbr_proc )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(69,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i] :
( ( elem @ ( m_Ldr @ F ) @ ( queue @ ( host @ E ) ) )
=> ~ ( leq @ ( host @ E ) @ ( host @ F ) ) )
& ! [E: $i,F: $i] :
( ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) )
=> ( ( host @ F )
!= ( host @ E ) ) )
& ! [E: $i,F: $i] :
( ( ( host @ F )
= nbr_proc )
=> ~ ( elem @ ( m_NotNorm @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i] :
( ( ( F != E )
& ( ( host @ F )
= ( host @ E ) ) )
=> ( ~ ( setIn @ E @ alive )
| ~ ( setIn @ F @ alive ) ) )
& ! [E: $i] :
( ( ( ( ( index @ status @ ( host @ E ) )
= elec_1 )
| ( ( index @ status @ ( host @ E ) )
= elec_2 ) )
& ( setIn @ E @ alive ) )
=> ( ( index @ elid @ ( host @ E ) )
= E ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( ( host @ G )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= norm )
& ( ( index @ ldr @ ( host @ G ) )
= ( host @ F ) ) )
=> ~ ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i] :
( ( ( ( host @ G )
!= ( host @ F ) )
& ( setIn @ G @ alive )
& ( ( host @ G )
= ( host @ E ) )
& ( ( index @ status @ ( host @ G ) )
= wait )
& ( ( host @ ( index @ elid @ ( host @ G ) ) )
= ( host @ F ) ) )
=> ~ ( elem @ ( m_Down @ E ) @ ( queue @ ( host @ F ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ( ( host @ G )
!= ( host @ E ) )
& ( setIn @ E @ alive )
& ( setIn @ G @ alive )
& ( ( host @ F )
= ( host @ E ) )
& ( ( host @ H )
= ( host @ G ) ) )
=> ~ ( ( elem @ ( m_Down @ H ) @ ( queue @ ( host @ E ) ) )
& ( setIn @ ( host @ F ) @ ( index @ down @ ( host @ G ) ) ) ) )
& ! [E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( elem @ ( m_Down @ G ) @ ( queue @ ( host @ H ) ) )
& ( ( host @ H )
= nbr_proc )
& ( ( host @ H )
= ( host @ F ) )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) )
& ( ( queue @ ( host @ C ) )
= ( cons @ ( m_Ack @ B @ D ) @ A ) ) )
=> ( ( setIn @ C @ alive )
=> ( ~ ( ( ( index @ elid @ ( host @ C ) )
= B )
& ( ( index @ status @ ( host @ C ) )
= elec_2 )
& ( ( host @ D )
= ( index @ pendack @ ( host @ C ) ) ) )
=> ! [E: $i] :
( ( ( host @ C )
!= ( host @ E ) )
=> ! [F: $i,G: $i,H: $i] :
( ( ( host @ C )
= ( host @ H ) )
=> ( ( ! [I: $i] :
( ( ~ ( leq @ ( host @ H ) @ I )
& ( leq @ ( s @ zero ) @ I ) )
=> ( ( setIn @ I @ ( index @ down @ ( host @ H ) ) )
| ( I
= ( host @ G ) ) ) )
& ( elem @ ( m_Down @ G ) @ A )
& ( ( host @ H )
= ( host @ F ) )
& ( ( host @ H )
= nbr_proc )
& ( ( index @ status @ ( host @ H ) )
= elec_1 ) )
=> ~ ( ( setIn @ E @ alive )
& ( elem @ ( m_Down @ F ) @ ( queue @ ( host @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( cons @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(365,plain,
! [A: $i,B: $i] :
( q_nil
!= ( cons @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(53,axiom,
norm != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(352,plain,
norm != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_Down @ A )
!= ( m_Down @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
thf(269,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_Down @ A )
!= ( m_Down @ B ) ) )
& ( ( ( m_Down @ A )
!= ( m_Down @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NotNorm @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(202,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NotNorm @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
! [A: $i] :
~ ( elem @ A @ q_nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(385,plain,
! [A: $i] :
~ ( elem @ A @ q_nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_Halt @ A )
!= ( m_Halt @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_Halt @ A )
!= ( m_Halt @ B ) ) )
& ( ( ( m_Halt @ A )
!= ( m_Halt @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
leq @ ( s @ zero ) @ nbr_proc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_03) ).
thf(174,plain,
leq @ ( s @ zero ) @ nbr_proc,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ ( s @ B ) )
<=> ( ( A
= ( s @ B ) )
| ( leq @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(404,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ ( s @ B ) )
=> ( ( A
= ( s @ B ) )
| ( leq @ A @ B ) ) )
& ( ( ( A
= ( s @ B ) )
| ( leq @ A @ B ) )
=> ( leq @ A @ ( s @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( s @ ( host @ A ) )
= ( host @ B ) )
=> ( ( host @ A )
!= ( host @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_01) ).
thf(421,plain,
! [A: $i,B: $i] :
( ( ( s @ ( host @ A ) )
= ( host @ B ) )
=> ( ( host @ A )
!= ( host @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( elem @ A @ ( snoc @ C @ B ) )
<=> ( ( A = B )
| ( elem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(325,plain,
! [A: $i,B: $i,C: $i] :
( ( ( elem @ A @ ( snoc @ C @ B ) )
=> ( ( A = B )
| ( elem @ A @ C ) ) )
& ( ( ( A = B )
| ( elem @ A @ C ) )
=> ( elem @ A @ ( snoc @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NormQ @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(289,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NormQ @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(43,axiom,
! [A: $i] : ( leq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(316,plain,
! [A: $i] : ( leq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(216,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A != B )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
ordered @ q_nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(164,plain,
ordered @ q_nil,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( m_NotNorm @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( m_NotNorm @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NormQ @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(321,plain,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_NormQ @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( leq @ ( s @ A ) @ ( s @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
=> ( leq @ ( s @ A ) @ ( s @ B ) ) )
& ( ( leq @ ( s @ A ) @ ( s @ B ) )
=> ( leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ordered @ ( cons @ A @ B ) )
<=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ A ) @ ( pidMsg @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_53) ).
thf(293,plain,
! [A: $i,B: $i] :
( ( ( ordered @ ( cons @ A @ B ) )
=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ A ) @ ( pidMsg @ C ) ) ) ) )
& ( ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ A ) @ ( pidMsg @ C ) ) ) )
=> ( ordered @ ( cons @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3,axiom,
! [A: $i] :
( ( pidMsg @ ( m_Halt @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(132,plain,
! [A: $i] :
( ( pidMsg @ ( m_Halt @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_NotNorm @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_NotNorm @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Halt @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(312,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Halt @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(23,axiom,
elec_1 != norm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_07) ).
thf(206,plain,
elec_1 != norm,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ldr @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ldr @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Ldr @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(381,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Ldr @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
| ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(334,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
| ( leq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Ldr @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(424,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Ldr @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( m_NormQ @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ordered @ ( snoc @ B @ A ) )
<=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ C ) @ ( pidMsg @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_54) ).
thf(388,plain,
! [A: $i,B: $i] :
( ( ( ordered @ ( snoc @ B @ A ) )
=> ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ C ) @ ( pidMsg @ A ) ) ) ) )
& ( ( ( ordered @ B )
& ! [C: $i] :
( ( ( elem @ C @ B )
& ( pidElem @ A )
& ( pidElem @ C )
& ( ( host @ ( pidMsg @ C ) )
= ( host @ ( pidMsg @ A ) ) ) )
=> ( leq @ ( pidMsg @ C ) @ ( pidMsg @ A ) ) ) )
=> ( ordered @ ( snoc @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(12,axiom,
elec_1 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_06) ).
thf(169,plain,
elec_1 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( snoc @ ( init @ A ) @ ( last @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(161,plain,
! [A: $i] :
( ( A = q_nil )
| ( A
= ( snoc @ ( init @ A ) @ ( last @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( head @ ( cons @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( head @ ( cons @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(38,axiom,
elec_2 != wait,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_08) ).
thf(286,plain,
elec_2 != wait,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(37,axiom,
! [A: $i] :
( ( ordered @ ( cons @ A @ q_nil ) )
& ( ordered @ ( snoc @ q_nil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(281,plain,
! [A: $i] :
( ( ordered @ ( cons @ A @ q_nil ) )
& ( ordered @ ( snoc @ q_nil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(413,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) ) )
& ( ( ( m_Ldr @ A )
!= ( m_Ldr @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( elem @ A @ ( cons @ B @ C ) )
<=> ( ( A = B )
| ( elem @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( elem @ A @ ( cons @ B @ C ) )
=> ( ( A = B )
| ( elem @ A @ C ) ) )
& ( ( ( A = B )
| ( elem @ A @ C ) )
=> ( elem @ A @ ( cons @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(350,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(13,axiom,
~ ( setIn @ nil @ alive ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(172,plain,
~ ( setIn @ nil @ alive ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( tail @ ( cons @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(230,plain,
! [A: $i,B: $i] :
( ( tail @ ( cons @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(56,axiom,
elec_1 != elec_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_05) ).
thf(362,plain,
elec_1 != elec_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(32,axiom,
! [A: $i] :
( ( pidElem @ A )
<=> ? [B: $i] :
( ( A
= ( m_Halt @ B ) )
| ( A
= ( m_Down @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(245,plain,
! [A: $i] :
( ( ( pidElem @ A )
=> ? [B: $i] :
( ( A
= ( m_Halt @ B ) )
| ( A
= ( m_Down @ B ) ) ) )
& ( ? [B: $i] :
( ( A
= ( m_Halt @ B ) )
| ( A
= ( m_Down @ B ) ) )
=> ( pidElem @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ack @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(318,plain,
! [A: $i,B: $i,C: $i] :
( ( ordered @ A )
=> ( ordered @ ( snoc @ A @ ( m_Ack @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(25,axiom,
! [A: $i] :
~ ( setIn @ A @ setEmpty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(213,plain,
! [A: $i] :
~ ( setIn @ A @ setEmpty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(20,axiom,
! [A: $i] : ( leq @ ( s @ zero ) @ ( host @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_02) ).
thf(198,plain,
! [A: $i] : ( leq @ ( s @ zero ) @ ( host @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) ) )
& ( ( ( m_NormQ @ A )
!= ( m_NormQ @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(255,plain,
! [A: $i,B: $i] :
( ( ( ( leq @ A @ B )
& ( leq @ B @ A ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( leq @ A @ B )
& ( leq @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Down @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(209,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_Down @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( host @ A )
!= ( host @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(355,plain,
! [A: $i,B: $i] :
( ( ( host @ A )
!= ( host @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NotNorm @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(194,plain,
! [A: $i,B: $i,C: $i] :
( ( m_Ack @ A @ B )
!= ( m_NotNorm @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( snoc @ ( cons @ A @ C ) @ B )
= ( cons @ A @ ( snoc @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( snoc @ ( cons @ A @ C ) @ B )
= ( cons @ A @ ( snoc @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(175,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C != D )
=> ( ( m_Ack @ A @ C )
!= ( m_Ack @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( last @ ( snoc @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( last @ ( snoc @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ordered @ ( cons @ ( m_Halt @ B ) @ A ) )
& ( ( host @ B )
= ( host @ C ) )
& ( elem @ ( m_Down @ C ) @ A ) )
=> ( leq @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(378,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ordered @ ( cons @ ( m_Halt @ B ) @ A ) )
& ( ( host @ B )
= ( host @ C ) )
& ( elem @ ( m_Down @ C ) @ A ) )
=> ( leq @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NormQ @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(346,plain,
! [A: $i,B: $i] :
( ( m_Down @ A )
!= ( m_NormQ @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( q_nil
!= ( snoc @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(146,plain,
! [A: $i,B: $i] :
( q_nil
!= ( snoc @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) )
=> ( ( setIn @ A @ pids )
& ( setIn @ B @ pids ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(183,plain,
! [A: $i,B: $i] :
( ( elem @ ( m_Ack @ A @ B ) @ ( queue @ ( host @ A ) ) )
=> ( ( setIn @ A @ pids )
& ( setIn @ B @ pids ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: $i] : ( leq @ ( host @ A ) @ nbr_proc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_04) ).
thf(200,plain,
! [A: $i] : ( leq @ ( host @ A ) @ nbr_proc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_Halt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(277,plain,
! [A: $i,B: $i] :
( ( m_Ldr @ A )
!= ( m_Halt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(58,axiom,
! [A: $i] :
~ ( leq @ ( s @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(369,plain,
! [A: $i] :
~ ( leq @ ( s @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(445,plain,
$false,
inference(cvc4,[status(thm)],[372,339,343,150,359,186,309,69,365,352,269,202,385,153,174,404,421,325,289,316,216,164,179,321,221,293,132,265,312,206,233,381,334,424,165,388,169,161,375,286,281,413,236,350,172,230,362,245,318,213,198,135,226,255,209,355,194,336,175,143,378,346,146,183,200,277,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV473+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:33:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.91/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.05 % [INFO] Parsing done (164ms).
% 1.24/1.05 % [INFO] Running in sequential loop mode.
% 1.86/1.25 % [INFO] eprover registered as external prover.
% 1.86/1.26 % [INFO] cvc4 registered as external prover.
% 1.86/1.26 % [INFO] Scanning for conjecture ...
% 2.32/1.38 % [INFO] Found a conjecture and 66 axioms. Running axiom selection ...
% 2.53/1.45 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.53/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.53/1.50 % [INFO] Type checking passed.
% 2.53/1.50 % [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 ...
% 5.86/2.46 % External prover 'cvc4' found a proof!
% 5.86/2.46 % [INFO] Killing All external provers ...
% 5.86/2.46 % Time passed: 1936ms (effective reasoning time: 1401ms)
% 5.86/2.46 % 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)>
% 5.86/2.46 % 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
% 5.86/2.46 % No. of inferences in proof: 136
% 5.86/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1936 ms resp. 1401 ms w/o parsing
% 6.16/2.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.16/2.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------