%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP055^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n019.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 : Wed Sep 30 08:06:34 AM UTC 2026
% Result : Theorem 18.87s 5.55s
% Output : Refutation 19.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 176
% Syntax : Number of formulae : 354 ( 174 unt; 0 typ; 0 def)
% Number of atoms : 692 ( 410 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 3198 ( 216 ~; 14 |; 40 &;2398 @)
% ( 0 <=>; 530 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 586 ( 586 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 11 con; 0-4 aty)
% Number of variables : 1222 ( 4 ^;1166 !; 52 ?;1222 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_l1584713811t_unit_type,type,
list_l1584713811t_unit: $tType ).
thf(list_l611321411t_unit_type,type,
list_l611321411t_unit: $tType ).
thf(list_c1059388851t_unit_type,type,
list_c1059388851t_unit: $tType ).
thf(config256849571t_unit_type,type,
config256849571t_unit: $tType ).
thf(list_l1341496881ge_p_v_type,type,
list_l1341496881ge_p_v: $tType ).
thf(list_l1619404459ge_p_v_type,type,
list_l1619404459ge_p_v: $tType ).
thf(list_message_p_v_type,type,
list_message_p_v: $tType ).
thf(message_p_v_type,type,
message_p_v: $tType ).
thf(messageValue_v_type,type,
messageValue_v: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(s_type,type,
s: $tType ).
thf(p_type,type,
p: $tType ).
thf(fLPThe9398366_p_s_v_decl,type,
fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
thf(fLPThe1519354920_p_v_s_decl,type,
fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
thf(fLPThe536531371_p_v_s_decl,type,
fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(prefix1615116500t_unit_decl,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(gen_le193291088t_unit_decl,type,
gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
thf(insert1308755079t_unit_decl,type,
insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(cons_c1162654829t_unit_decl,type,
cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(cons_message_p_v_decl,type,
cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
thf(nil_co1338500125t_unit_decl,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(nil_message_p_v_decl,type,
nil_message_p_v: list_message_p_v ).
thf(nil_li307996205t_unit_decl,type,
nil_li307996205t_unit: list_l611321411t_unit ).
thf(nil_list_message_p_v_decl,type,
nil_list_message_p_v: list_l1619404459ge_p_v ).
thf(list_e1598815642t_unit_decl,type,
list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(nths_c890550943t_unit_decl,type,
nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
thf(suc_decl,type,
suc: nat > nat ).
thf(semiri1382578993at_nat_decl,type,
semiri1382578993at_nat: nat > nat ).
thf(size_s1406904903t_unit_decl,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(size_s503142615t_unit_decl,type,
size_s503142615t_unit: list_l611321411t_unit > nat ).
thf(size_s1809856791ge_p_v_decl,type,
size_s1809856791ge_p_v: list_l1619404459ge_p_v > nat ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(member_nat_decl,type,
member_nat: nat > set_nat > $o ).
thf(cfg_decl,type,
cfg: config256849571t_unit ).
thf(fe_decl,type,
fe: nat > list_c1059388851t_unit ).
thf(m_decl,type,
m: nat ).
thf(n_decl,type,
n: nat ).
thf(na_decl,type,
na: nat ).
thf(137,axiom,
! [A: config256849571t_unit > $o] :
~ ( list_e1598815642t_unit @ A @ nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_list__ex1__simps_I1_J) ).
thf(892,plain,
! [A: config256849571t_unit > $o] :
~ ( list_e1598815642t_unit @ A @ nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(29,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_infiniteExecutionMsg_Osimps_I2_J) ).
thf(347,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(14,axiom,
! [A: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,B: message_p_v > message_p_v > $o,C: list_message_p_v] :
( ! [D: message_p_v > message_p_v > $o] : ( A @ D @ nil_message_p_v )
=> ( ! [D: message_p_v > message_p_v > $o,E: message_p_v,F: list_message_p_v] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_message_p_v @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_sorted__wrt_Oinduct) ).
thf(247,plain,
! [A: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,B: message_p_v > message_p_v > $o,C: list_message_p_v] :
( ! [D: message_p_v > message_p_v > $o] : ( A @ D @ nil_message_p_v )
=> ( ! [D: message_p_v > message_p_v > $o,E: message_p_v,F: list_message_p_v] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_message_p_v @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_linorder__neqE__nat) ).
thf(861,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(135,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_old_Onat_Oinducts) ).
thf(878,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(53,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_less__Suc0) ).
thf(440,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Suc__less__SucD) ).
thf(511,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(38,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_verit__comp__simplify1_I1_J) ).
thf(385,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(67,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Zero__neq__Suc) ).
thf(500,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(113,axiom,
! [A: nat,B: config256849571t_unit,C: list_c1059388851t_unit] :
( ( gen_le193291088t_unit @ A @ ( cons_c1162654829t_unit @ B @ C ) )
= ( gen_le193291088t_unit @ ( suc @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_gen__length__code_I2_J) ).
thf(747,plain,
! [A: nat,B: config256849571t_unit,C: list_c1059388851t_unit] :
( ( gen_le193291088t_unit @ A @ ( cons_c1162654829t_unit @ B @ C ) )
= ( gen_le193291088t_unit @ ( suc @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(125,axiom,
! [A: list_c1059388851t_unit,B: nat] :
( ( ( size_s1406904903t_unit @ A )
= ( suc @ B ) )
= ( ? [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( A
= ( cons_c1162654829t_unit @ C @ D ) )
& ( ( size_s1406904903t_unit @ D )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_length__Suc__conv) ).
thf(829,plain,
! [A: list_c1059388851t_unit,B: nat] :
( ( ( size_s1406904903t_unit @ A )
= ( suc @ B ) )
= ( ? [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( A
= ( cons_c1162654829t_unit @ C @ D ) )
& ( ( size_s1406904903t_unit @ D )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Nat_OlessE) ).
thf(565,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(97,axiom,
! [A: list_l611321411t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s503142615t_unit @ A ) )
= ( A != nil_li307996205t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_length__greater__0__conv) ).
thf(651,plain,
! [A: list_l611321411t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s503142615t_unit @ A ) )
= ( A != nil_li307996205t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(174,axiom,
( ( fe @ zero_zero_nat )
= ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_FE_I1_J) ).
thf(1055,plain,
( ( fe @ zero_zero_nat )
= ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(107,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_gr0__conv__Suc) ).
thf(719,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(68,axiom,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
= ( ? [B: config256849571t_unit,C: list_c1059388851t_unit] :
( A
= ( cons_c1162654829t_unit @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_neq__Nil__conv) ).
thf(504,plain,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
= ( ? [B: config256849571t_unit,C: list_c1059388851t_unit] :
( A
= ( cons_c1162654829t_unit @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(82,axiom,
! [A: nat] :
( ( gen_le193291088t_unit @ A @ nil_co1338500125t_unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_gen__length__code_I1_J) ).
thf(587,plain,
! [A: nat] :
( ( gen_le193291088t_unit @ A @ nil_co1338500125t_unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(28,axiom,
! [A: list_l611321411t_unit] :
( ( ( size_s503142615t_unit @ A )
= zero_zero_nat )
= ( A = nil_li307996205t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_length__0__conv) ).
thf(344,plain,
! [A: list_l611321411t_unit] :
( ( ( size_s503142615t_unit @ A )
= zero_zero_nat )
= ( A = nil_li307996205t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(142,axiom,
! [A: nat] :
( ( semiri1382578993at_nat @ ( suc @ A ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_of__nat__neq__0) ).
thf(917,plain,
! [A: nat] :
( ( semiri1382578993at_nat @ ( suc @ A ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(105,axiom,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(702,plain,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(56,axiom,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe1519354920_p_v_s @ D @ E @ F @ zero_zero_nat )
= ( cons_c1162654829t_unit @ D @ nil_co1338500125t_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J) ).
thf(448,plain,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe1519354920_p_v_s @ D @ E @ F @ zero_zero_nat )
= ( cons_c1162654829t_unit @ D @ nil_co1338500125t_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(23,axiom,
! [A: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ A ) )
= ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_of__nat__0__eq__iff) ).
thf(316,plain,
! [A: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ A ) )
= ( zero_zero_nat = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(3,axiom,
! [A: message_p_v,B: list_message_p_v] :
( nil_message_p_v
!= ( cons_message_p_v @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_list_Odistinct_I1_J) ).
thf(179,plain,
! [A: message_p_v,B: list_message_p_v] :
( nil_message_p_v
!= ( cons_message_p_v @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_less__numeral__extra_I4_J) ).
thf(443,plain,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(173,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ( ( A = nil_co1338500125t_unit )
=> ! [C: config256849571t_unit,D: list_c1059388851t_unit] :
( B
!= ( cons_c1162654829t_unit @ C @ D ) ) )
=> ~ ! [C: list_c1059388851t_unit,D: list_c1059388851t_unit,E: config256849571t_unit] :
( ( A
= ( cons_c1162654829t_unit @ E @ C ) )
=> ( ( B
= ( cons_c1162654829t_unit @ E @ D ) )
=> ~ ( prefix1615116500t_unit @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_prefixList_Ocases) ).
thf(1040,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ( ( A = nil_co1338500125t_unit )
=> ! [C: config256849571t_unit,D: list_c1059388851t_unit] :
( B
!= ( cons_c1162654829t_unit @ C @ D ) ) )
=> ~ ! [C: list_c1059388851t_unit,D: list_c1059388851t_unit,E: config256849571t_unit] :
( ( A
= ( cons_c1162654829t_unit @ E @ C ) )
=> ( ( B
= ( cons_c1162654829t_unit @ E @ D ) )
=> ~ ( prefix1615116500t_unit @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(31,axiom,
! [A: list_l1619404459ge_p_v] :
( ( ( size_s1809856791ge_p_v @ A )
= zero_zero_nat )
= ( A = nil_list_message_p_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_length__0__conv) ).
thf(353,plain,
! [A: list_l1619404459ge_p_v] :
( ( ( size_s1809856791ge_p_v @ A )
= zero_zero_nat )
= ( A = nil_list_message_p_v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Suc__mono) ).
thf(956,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(42,axiom,
! [A: list_c1059388851t_unit,B: set_nat] :
( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( member_nat @ C @ B ) )
=> ( ( nths_c890550943t_unit @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_nths__all) ).
thf(396,plain,
! [A: list_c1059388851t_unit,B: set_nat] :
( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( member_nat @ C @ B ) )
=> ( ( nths_c890550943t_unit @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(69,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Suc__neq__Zero) ).
thf(507,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(73,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_infinite__descent0) ).
thf(527,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(57,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_not__less__zero) ).
thf(452,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(17,axiom,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ~ ! [B: message_p_v,C: list_message_p_v] :
( A
!= ( cons_message_p_v @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_list_Oexhaust) ).
thf(270,plain,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ~ ! [B: message_p_v,C: list_message_p_v] :
( A
!= ( cons_message_p_v @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(100,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_neq0__conv) ).
thf(661,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(115,axiom,
! [A: list_l1619404459ge_p_v] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1809856791ge_p_v @ A ) )
= ( A != nil_list_message_p_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_length__greater__0__conv) ).
thf(761,plain,
! [A: list_l1619404459ge_p_v] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1809856791ge_p_v @ A ) )
= ( A != nil_list_message_p_v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(123,axiom,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit] : ( A @ ( cons_c1162654829t_unit @ C @ nil_co1338500125t_unit ) )
=> ( ! [C: config256849571t_unit,D: config256849571t_unit,E: list_c1059388851t_unit] :
( ( ( C = D )
=> ( A @ ( cons_c1162654829t_unit @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) ) )
=> ( A @ ( cons_c1162654829t_unit @ C @ ( cons_c1162654829t_unit @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_remdups__adj_Oinduct) ).
thf(810,plain,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit] : ( A @ ( cons_c1162654829t_unit @ C @ nil_co1338500125t_unit ) )
=> ( ! [C: config256849571t_unit,D: config256849571t_unit,E: list_c1059388851t_unit] :
( ( ( C = D )
=> ( A @ ( cons_c1162654829t_unit @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) ) )
=> ( A @ ( cons_c1162654829t_unit @ C @ ( cons_c1162654829t_unit @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(37,axiom,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe536531371_p_v_s @ D @ E @ F @ ( suc @ G ) )
= ( F @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ G ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J) ).
thf(381,plain,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe536531371_p_v_s @ D @ E @ F @ ( suc @ G ) )
= ( F @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ G ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Suc__lessE) ).
thf(714,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(175,axiom,
ord_less_nat @ m @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_MLessN) ).
thf(1057,plain,
ord_less_nat @ m @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_less__SucI) ).
thf(910,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(166,axiom,
( prefix1615116500t_unit
= ( ^ [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ? [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( A = nil_co1338500125t_unit )
& ( B
= ( cons_c1162654829t_unit @ C @ D ) ) )
| ? [C: list_c1059388851t_unit,D: list_c1059388851t_unit,E: config256849571t_unit] :
( ( A
= ( cons_c1162654829t_unit @ E @ C ) )
& ( B
= ( cons_c1162654829t_unit @ E @ D ) )
& ( prefix1615116500t_unit @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_prefixList_Osimps) ).
thf(1021,plain,
( prefix1615116500t_unit
= ( ^ [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ? [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( A = nil_co1338500125t_unit )
& ( B
= ( cons_c1162654829t_unit @ C @ D ) ) )
| ? [C: list_c1059388851t_unit,D: list_c1059388851t_unit,E: config256849571t_unit] :
( ( A
= ( cons_c1162654829t_unit @ E @ C ) )
& ( B
= ( cons_c1162654829t_unit @ E @ D ) )
& ( prefix1615116500t_unit @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(111,axiom,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat,H: list_c1059388851t_unit] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( ( fLPThe1519354920_p_v_s @ D @ E @ F @ G )
= H )
=> ( ( ( G = zero_zero_nat )
=> ( H
!= ( cons_c1162654829t_unit @ D @ nil_co1338500125t_unit ) ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( E @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ I ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims) ).
thf(729,plain,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat,H: list_c1059388851t_unit] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( ( fLPThe1519354920_p_v_s @ D @ E @ F @ G )
= H )
=> ( ( ( G = zero_zero_nat )
=> ( H
!= ( cons_c1162654829t_unit @ D @ nil_co1338500125t_unit ) ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( E @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ I ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_old_Onat_Oinject) ).
thf(407,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_less__Suc__eq__0__disj) ).
thf(630,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(62,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_gr0I) ).
thf(467,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(34,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat,E: list_message_p_v] :
( ( ( fLPThe536531371_p_v_s @ A @ B @ C @ D )
= E )
=> ( ( ( D = zero_zero_nat )
=> ( E != nil_message_p_v ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ F ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_infiniteExecutionMsg_Oelims) ).
thf(361,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat,E: list_message_p_v] :
( ( ( fLPThe536531371_p_v_s @ A @ B @ C @ D )
= E )
=> ( ( ( D = zero_zero_nat )
=> ( E != nil_message_p_v ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ F ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(27,axiom,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat,H: list_message_p_v] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( ( fLPThe536531371_p_v_s @ D @ E @ F @ G )
= H )
=> ( ( ( G = zero_zero_nat )
=> ( H != nil_message_p_v ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( F @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ I ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims) ).
thf(329,plain,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat,H: list_message_p_v] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( ( fLPThe536531371_p_v_s @ D @ E @ F @ G )
= H )
=> ( ( ( G = zero_zero_nat )
=> ( H != nil_message_p_v ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( F @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ I ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(136,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_verit__comp__simplify1_I1_J) ).
thf(889,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Suc__less__eq2) ).
thf(461,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(65,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_size__neq__size__imp__neq) ).
thf(493,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(11,axiom,
! [A: list_message_p_v,B: list_message_p_v > $o] :
( ( A != nil_message_p_v )
=> ( ! [C: message_p_v] : ( B @ ( cons_message_p_v @ C @ nil_message_p_v ) )
=> ( ! [C: message_p_v,D: list_message_p_v] :
( ( D != nil_message_p_v )
=> ( ( B @ D )
=> ( B @ ( cons_message_p_v @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_list__nonempty__induct) ).
thf(224,plain,
! [A: list_message_p_v,B: list_message_p_v > $o] :
( ( A != nil_message_p_v )
=> ( ! [C: message_p_v] : ( B @ ( cons_message_p_v @ C @ nil_message_p_v ) )
=> ( ! [C: message_p_v,D: list_message_p_v] :
( ( D != nil_message_p_v )
=> ( ( B @ D )
=> ( B @ ( cons_message_p_v @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(169,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit] : ( prefix1615116500t_unit @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_prefixList_Ointros_I1_J) ).
thf(1032,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit] : ( prefix1615116500t_unit @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(15,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ zero_zero_nat )
= nil_message_p_v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_infiniteExecutionMsg_Osimps_I1_J) ).
thf(252,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ zero_zero_nat )
= nil_message_p_v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(134,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_nat_Odistinct_I1_J) ).
thf(874,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Suc__inject) ).
thf(615,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(109,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_lessI) ).
thf(725,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(39,axiom,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_of__nat__0) ).
thf(388,plain,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_of__nat__less__imp__less) ).
thf(356,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_less__Suc__induct) ).
thf(593,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(172,axiom,
ord_less_nat @ m @ ( suc @ na ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_IA_I2_J) ).
thf(1039,plain,
ord_less_nat @ m @ ( suc @ na ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(75,axiom,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( A @ D )
=> ( A @ ( cons_c1162654829t_unit @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_list_Oinducts) ).
thf(547,plain,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( A @ D )
=> ( A @ ( cons_c1162654829t_unit @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(164,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Ex__less__Suc2) ).
thf(1016,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(83,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_of__nat__0__less__iff) ).
thf(590,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ A ) )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(41,axiom,
! [A: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_of__nat__less__0__iff) ).
thf(393,plain,
! [A: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(96,axiom,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ~ ! [B: config256849571t_unit,C: list_c1059388851t_unit] :
( A
!= ( cons_c1162654829t_unit @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_list_Oexhaust) ).
thf(647,plain,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ~ ! [B: config256849571t_unit,C: list_c1059388851t_unit] :
( A
!= ( cons_c1162654829t_unit @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(72,axiom,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(515,plain,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_nat__neq__iff) ).
thf(654,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(157,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Ex__less__Suc) ).
thf(984,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(89,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit] :
( ( cons_c1162654829t_unit @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__Cons__self2) ).
thf(622,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit] :
( ( cons_c1162654829t_unit @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(127,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_All__less__Suc2) ).
thf(837,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(92,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_bot__nat__0_Oextremum__strict) ).
thf(633,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(22,axiom,
! [A: list_message_p_v > list_c1059388851t_unit > $o,B: list_message_p_v,C: list_c1059388851t_unit] :
( ( A @ nil_message_p_v @ nil_co1338500125t_unit )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ ( cons_message_p_v @ D @ E ) @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ nil_message_p_v @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( ! [D: message_p_v,E: list_message_p_v,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ E @ G )
=> ( A @ ( cons_message_p_v @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_list__induct2_H) ).
thf(311,plain,
! [A: list_message_p_v > list_c1059388851t_unit > $o,B: list_message_p_v,C: list_c1059388851t_unit] :
( ( A @ nil_message_p_v @ nil_co1338500125t_unit )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ ( cons_message_p_v @ D @ E ) @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ nil_message_p_v @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( ! [D: message_p_v,E: list_message_p_v,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ E @ G )
=> ( A @ ( cons_message_p_v @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(143,axiom,
! [A: list_c1059388851t_unit,B: config256849571t_unit,C: list_c1059388851t_unit] :
( ( A
= ( cons_c1162654829t_unit @ B @ C ) )
=> ( A != nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_list_OdiscI) ).
thf(921,plain,
! [A: list_c1059388851t_unit,B: config256849571t_unit,C: list_c1059388851t_unit] :
( ( A
= ( cons_c1162654829t_unit @ B @ C ) )
=> ( A != nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(99,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_neq__if__length__neq) ).
thf(657,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(76,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Zero__not__Suc) ).
thf(558,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(168,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( C @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( ! [D: list_c1059388851t_unit,E: list_c1059388851t_unit,F: config256849571t_unit] :
( ( prefix1615116500t_unit @ D @ E )
=> ( ( C @ D @ E )
=> ( C @ ( cons_c1162654829t_unit @ F @ D ) @ ( cons_c1162654829t_unit @ F @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prefixList_Oinducts) ).
thf(1026,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( C @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( ! [D: list_c1059388851t_unit,E: list_c1059388851t_unit,F: config256849571t_unit] :
( ( prefix1615116500t_unit @ D @ E )
=> ( ( C @ D @ E )
=> ( C @ ( cons_c1162654829t_unit @ F @ D ) @ ( cons_c1162654829t_unit @ F @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Suc__less__eq) ).
thf(953,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(144,axiom,
! [A: list_c1059388851t_unit > list_c1059388851t_unit > $o,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] : ( A @ nil_co1338500125t_unit @ D )
=> ( ! [D: list_c1059388851t_unit] : ( A @ D @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ E @ ( cons_c1162654829t_unit @ F @ G ) )
=> ( ( A @ ( cons_c1162654829t_unit @ D @ E ) @ G )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_shuffles_Oinduct) ).
thf(926,plain,
! [A: list_c1059388851t_unit > list_c1059388851t_unit > $o,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] : ( A @ nil_co1338500125t_unit @ D )
=> ( ! [D: list_c1059388851t_unit] : ( A @ D @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ E @ ( cons_c1162654829t_unit @ F @ G ) )
=> ( ( A @ ( cons_c1162654829t_unit @ D @ E ) @ G )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(114,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zero__induct) ).
thf(750,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_of__nat__less__iff) ).
thf(375,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(85,axiom,
! [A: set_nat] :
( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A )
= nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_nths__nil) ).
thf(601,plain,
! [A: set_nat] :
( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A )
= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(71,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_less__numeral__extra_I3_J) ).
thf(513,plain,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(50,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_lift__Suc__mono__less__iff) ).
thf(430,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_less__Suc__eq) ).
thf(584,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(77,axiom,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_length__0__conv) ).
thf(562,plain,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_gr__implies__not0) ).
thf(1007,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(43,axiom,
! [A: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,B: config256849571t_unit > config256849571t_unit > $o,C: list_c1059388851t_unit] :
( ! [D: config256849571t_unit > config256849571t_unit > $o] : ( A @ D @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit > config256849571t_unit > $o,E: config256849571t_unit,F: list_c1059388851t_unit] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_c1162654829t_unit @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_sorted__wrt_Oinduct) ).
thf(402,plain,
! [A: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,B: config256849571t_unit > config256849571t_unit > $o,C: list_c1059388851t_unit] :
( ! [D: config256849571t_unit > config256849571t_unit > $o] : ( A @ D @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit > config256849571t_unit > $o,E: config256849571t_unit,F: list_c1059388851t_unit] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_c1162654829t_unit @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(129,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
=> ( ( C @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ E )
= ( size_s1406904903t_unit @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_list__induct2) ).
thf(843,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
=> ( ( C @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ E )
= ( size_s1406904903t_unit @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_less__SucE) ).
thf(958,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(94,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit,C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( ( cons_c1162654829t_unit @ A @ B )
= ( cons_c1162654829t_unit @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list_Oinject) ).
thf(641,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit,C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( ( cons_c1162654829t_unit @ A @ B )
= ( cons_c1162654829t_unit @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(118,axiom,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Ex__list__of__length) ).
thf(787,plain,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(176,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ( prefix1615116500t_unit @ B @ C )
=> ( prefix1615116500t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_PrefixListTransitive) ).
thf(1058,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ( prefix1615116500t_unit @ B @ C )
=> ( prefix1615116500t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(30,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe1519354920_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( B @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_infiniteExecutionCfg_Osimps_I2_J) ).
thf(350,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe1519354920_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( B @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_nat_Oinject) ).
thf(445,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(146,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_not0__implies__Suc) ).
thf(936,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(10,axiom,
! [A: list_message_p_v,B: message_p_v,C: list_message_p_v] :
( ( A
= ( cons_message_p_v @ B @ C ) )
=> ( A != nil_message_p_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_list_OdiscI) ).
thf(219,plain,
! [A: list_message_p_v,B: message_p_v,C: list_message_p_v] :
( ( A
= ( cons_message_p_v @ B @ C ) )
=> ( A != nil_message_p_v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ( ! [B: message_p_v] :
( A
!= ( cons_message_p_v @ B @ nil_message_p_v ) )
=> ~ ! [B: message_p_v,C: message_p_v,D: list_message_p_v] :
( A
!= ( cons_message_p_v @ B @ ( cons_message_p_v @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_remdups__adj_Ocases) ).
thf(274,plain,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ( ! [B: message_p_v] :
( A
!= ( cons_message_p_v @ B @ nil_message_p_v ) )
=> ~ ! [B: message_p_v,C: message_p_v,D: list_message_p_v] :
( A
!= ( cons_message_p_v @ B @ ( cons_message_p_v @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(117,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_zero__less__iff__neq__zero) ).
thf(784,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(159,axiom,
! [A: list_c1059388851t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ A ) )
= ( A != nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_length__greater__0__conv) ).
thf(990,plain,
! [A: list_c1059388851t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ A ) )
= ( A != nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(51,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__irrefl__nat) ).
thf(434,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_strict__inc__induct) ).
thf(764,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_nat_OdiscI) ).
thf(979,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(86,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit,D: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
=> ( ( ( size_s1406904903t_unit @ B )
= ( size_s1406904903t_unit @ C ) )
=> ( ( D @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [E: config256849571t_unit,F: list_c1059388851t_unit,G: config256849571t_unit,H: list_c1059388851t_unit,I: config256849571t_unit,J: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ F )
= ( size_s1406904903t_unit @ H ) )
=> ( ( ( size_s1406904903t_unit @ H )
= ( size_s1406904903t_unit @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons_c1162654829t_unit @ E @ F ) @ ( cons_c1162654829t_unit @ G @ H ) @ ( cons_c1162654829t_unit @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_list__induct3) ).
thf(604,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit,D: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
=> ( ( ( size_s1406904903t_unit @ B )
= ( size_s1406904903t_unit @ C ) )
=> ( ( D @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [E: config256849571t_unit,F: list_c1059388851t_unit,G: config256849571t_unit,H: list_c1059388851t_unit,I: config256849571t_unit,J: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ F )
= ( size_s1406904903t_unit @ H ) )
=> ( ( ( size_s1406904903t_unit @ H )
= ( size_s1406904903t_unit @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons_c1162654829t_unit @ E @ F ) @ ( cons_c1162654829t_unit @ G @ H ) @ ( cons_c1162654829t_unit @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(162,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__not__refl) ).
thf(1011,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_less__trans__Suc) ).
thf(419,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(25,axiom,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe1519354920_p_v_s @ D @ E @ F @ ( suc @ G ) )
= ( E @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ G ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J) ).
thf(323,plain,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v,G: nat] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe1519354920_p_v_s @ D @ E @ F @ ( suc @ G ) )
= ( E @ ( fLPThe1519354920_p_v_s @ D @ E @ F @ G ) @ ( fLPThe536531371_p_v_s @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__not__refl2) ).
thf(799,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(138,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_old_Onat_Odistinct_I1_J) ).
thf(895,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(155,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ zero_zero_nat )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_NatPredicateTippingPoint) ).
thf(964,plain,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ zero_zero_nat )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(90,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_old_Onat_Oexhaust) ).
thf(626,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(148,axiom,
! [A: config256849571t_unit] :
( ( insert1308755079t_unit @ A @ nil_co1338500125t_unit )
= ( cons_c1162654829t_unit @ A @ nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insert__Nil) ).
thf(943,plain,
! [A: config256849571t_unit] :
( ( insert1308755079t_unit @ A @ nil_co1338500125t_unit )
= ( cons_c1162654829t_unit @ A @ nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(6,axiom,
! [A: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,B: message_p_v > message_p_v > $o,C: list_message_p_v] :
( ! [D: message_p_v > message_p_v > $o] : ( A @ D @ nil_message_p_v )
=> ( ! [D: message_p_v > message_p_v > $o,E: message_p_v] : ( A @ D @ ( cons_message_p_v @ E @ nil_message_p_v ) )
=> ( ! [D: message_p_v > message_p_v > $o,E: message_p_v,F: message_p_v,G: list_message_p_v] :
( ( A @ D @ ( cons_message_p_v @ F @ G ) )
=> ( A @ D @ ( cons_message_p_v @ E @ ( cons_message_p_v @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_successively_Oinduct) ).
thf(198,plain,
! [A: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,B: message_p_v > message_p_v > $o,C: list_message_p_v] :
( ! [D: message_p_v > message_p_v > $o] : ( A @ D @ nil_message_p_v )
=> ( ! [D: message_p_v > message_p_v > $o,E: message_p_v] : ( A @ D @ ( cons_message_p_v @ E @ nil_message_p_v ) )
=> ( ! [D: message_p_v > message_p_v > $o,E: message_p_v,F: message_p_v,G: list_message_p_v] :
( ( A @ D @ ( cons_message_p_v @ F @ G ) )
=> ( A @ D @ ( cons_message_p_v @ E @ ( cons_message_p_v @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(145,axiom,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ( ! [B: config256849571t_unit] :
( A
!= ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) )
=> ~ ! [B: config256849571t_unit,C: config256849571t_unit,D: list_c1059388851t_unit] :
( A
!= ( cons_c1162654829t_unit @ B @ ( cons_c1162654829t_unit @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_remdups__adj_Ocases) ).
thf(932,plain,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ( ! [B: config256849571t_unit] :
( A
!= ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) )
=> ~ ! [B: config256849571t_unit,C: config256849571t_unit,D: list_c1059388851t_unit] :
( A
!= ( cons_c1162654829t_unit @ B @ ( cons_c1162654829t_unit @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(177,axiom,
ord_less_nat @ m @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062m_A_060_An_092_060close_062) ).
thf(1061,plain,
ord_less_nat @ m @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(141,axiom,
! [A: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,B: config256849571t_unit > config256849571t_unit > $o,C: list_c1059388851t_unit] :
( ! [D: config256849571t_unit > config256849571t_unit > $o] : ( A @ D @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit > config256849571t_unit > $o,E: config256849571t_unit] : ( A @ D @ ( cons_c1162654829t_unit @ E @ nil_co1338500125t_unit ) )
=> ( ! [D: config256849571t_unit > config256849571t_unit > $o,E: config256849571t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ D @ ( cons_c1162654829t_unit @ F @ G ) )
=> ( A @ D @ ( cons_c1162654829t_unit @ E @ ( cons_c1162654829t_unit @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_successively_Oinduct) ).
thf(912,plain,
! [A: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,B: config256849571t_unit > config256849571t_unit > $o,C: list_c1059388851t_unit] :
( ! [D: config256849571t_unit > config256849571t_unit > $o] : ( A @ D @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit > config256849571t_unit > $o,E: config256849571t_unit] : ( A @ D @ ( cons_c1162654829t_unit @ E @ nil_co1338500125t_unit ) )
=> ( ! [D: config256849571t_unit > config256849571t_unit > $o,E: config256849571t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ D @ ( cons_c1162654829t_unit @ F @ G ) )
=> ( A @ D @ ( cons_c1162654829t_unit @ E @ ( cons_c1162654829t_unit @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Suc__lessD) ).
thf(827,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(93,axiom,
! [A: list_c1059388851t_unit > list_c1059388851t_unit > $o,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] : ( A @ nil_co1338500125t_unit @ D )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: list_c1059388851t_unit] :
( ( A @ F @ E )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_splice_Oinduct) ).
thf(636,plain,
! [A: list_c1059388851t_unit > list_c1059388851t_unit > $o,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] : ( A @ nil_co1338500125t_unit @ D )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: list_c1059388851t_unit] :
( ( A @ F @ E )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(58,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_gr0__implies__Suc) ).
thf(455,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(19,axiom,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ( A @ nil_message_p_v )
=> ( ! [C: message_p_v] : ( A @ ( cons_message_p_v @ C @ nil_message_p_v ) )
=> ( ! [C: message_p_v,D: message_p_v,E: list_message_p_v] :
( ( ( C = D )
=> ( A @ ( cons_message_p_v @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_message_p_v @ D @ E ) ) )
=> ( A @ ( cons_message_p_v @ C @ ( cons_message_p_v @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_remdups__adj_Oinduct) ).
thf(278,plain,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ( A @ nil_message_p_v )
=> ( ! [C: message_p_v] : ( A @ ( cons_message_p_v @ C @ nil_message_p_v ) )
=> ( ! [C: message_p_v,D: message_p_v,E: list_message_p_v] :
( ( ( C = D )
=> ( A @ ( cons_message_p_v @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_message_p_v @ D @ E ) ) )
=> ( A @ ( cons_message_p_v @ C @ ( cons_message_p_v @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(132,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_bot__nat__0_Onot__eq__extremum) ).
thf(868,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(108,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_gr__zeroI) ).
thf(722,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(170,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: config256849571t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( prefix1615116500t_unit @ ( cons_c1162654829t_unit @ C @ A ) @ ( cons_c1162654829t_unit @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_prefixList_Ointros_I2_J) ).
thf(1034,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: config256849571t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( prefix1615116500t_unit @ ( cons_c1162654829t_unit @ C @ A ) @ ( cons_c1162654829t_unit @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(16,axiom,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ( A @ nil_message_p_v )
=> ( ! [C: message_p_v] : ( A @ ( cons_message_p_v @ C @ nil_message_p_v ) )
=> ( ! [C: message_p_v,D: message_p_v,E: list_message_p_v] :
( ( A @ E )
=> ( ( A @ ( cons_message_p_v @ D @ E ) )
=> ( A @ ( cons_message_p_v @ C @ ( cons_message_p_v @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_induct__list012) ).
thf(255,plain,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ( A @ nil_message_p_v )
=> ( ! [C: message_p_v] : ( A @ ( cons_message_p_v @ C @ nil_message_p_v ) )
=> ( ! [C: message_p_v,D: message_p_v,E: list_message_p_v] :
( ( A @ E )
=> ( ( A @ ( cons_message_p_v @ D @ E ) )
=> ( A @ ( cons_message_p_v @ C @ ( cons_message_p_v @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > $o,B: message_p_v > config256849571t_unit,C: list_message_p_v,D: list_c1059388851t_unit] :
( ! [E: message_p_v > config256849571t_unit,F: list_c1059388851t_unit] : ( A @ E @ nil_message_p_v @ F )
=> ( ! [E: message_p_v > config256849571t_unit,F: message_p_v,G: list_message_p_v,H: list_c1059388851t_unit] :
( ( A @ E @ G @ ( cons_c1162654829t_unit @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_message_p_v @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_map__tailrec__rev_Oinduct) ).
thf(209,plain,
! [A: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > $o,B: message_p_v > config256849571t_unit,C: list_message_p_v,D: list_c1059388851t_unit] :
( ! [E: message_p_v > config256849571t_unit,F: list_c1059388851t_unit] : ( A @ E @ nil_message_p_v @ F )
=> ( ! [E: message_p_v > config256849571t_unit,F: message_p_v,G: list_message_p_v,H: list_c1059388851t_unit] :
( ( A @ E @ G @ ( cons_c1162654829t_unit @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_message_p_v @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(147,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_n__not__Suc__n) ).
thf(939,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(59,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_not__less0) ).
thf(458,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(5,axiom,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe536531371_p_v_s @ D @ E @ F @ zero_zero_nat )
= nil_message_p_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J) ).
thf(194,plain,
! [A: p > s > messageValue_v > s,B: p > s > messageValue_v > message_p_v > nat,C: p > s,D: config256849571t_unit,E: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,F: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe9398366_p_s_v @ A @ B @ C )
=> ( ( fLPThe536531371_p_v_s @ D @ E @ F @ zero_zero_nat )
= nil_message_p_v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(80,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit] :
( nil_co1338500125t_unit
!= ( cons_c1162654829t_unit @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_list_Odistinct_I1_J) ).
thf(580,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit] :
( nil_co1338500125t_unit
!= ( cons_c1162654829t_unit @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(20,axiom,
! [A: list_message_p_v > list_message_p_v > $o,B: list_message_p_v,C: list_message_p_v] :
( ! [D: list_message_p_v] : ( A @ nil_message_p_v @ D )
=> ( ! [D: message_p_v,E: list_message_p_v,F: list_message_p_v] :
( ( A @ F @ E )
=> ( A @ ( cons_message_p_v @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_splice_Oinduct) ).
thf(295,plain,
! [A: list_message_p_v > list_message_p_v > $o,B: list_message_p_v,C: list_message_p_v] :
( ! [D: list_message_p_v] : ( A @ nil_message_p_v @ D )
=> ( ! [D: message_p_v,E: list_message_p_v,F: list_message_p_v] :
( ( A @ F @ E )
=> ( A @ ( cons_message_p_v @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(46,axiom,
! [A: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o,B: config256849571t_unit > config256849571t_unit,C: list_c1059388851t_unit,D: list_c1059388851t_unit] :
( ! [E: config256849571t_unit > config256849571t_unit,F: list_c1059388851t_unit] : ( A @ E @ nil_co1338500125t_unit @ F )
=> ( ! [E: config256849571t_unit > config256849571t_unit,F: config256849571t_unit,G: list_c1059388851t_unit,H: list_c1059388851t_unit] :
( ( A @ E @ G @ ( cons_c1162654829t_unit @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_c1162654829t_unit @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_map__tailrec__rev_Oinduct) ).
thf(414,plain,
! [A: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o,B: config256849571t_unit > config256849571t_unit,C: list_c1059388851t_unit,D: list_c1059388851t_unit] :
( ! [E: config256849571t_unit > config256849571t_unit,F: list_c1059388851t_unit] : ( A @ E @ nil_co1338500125t_unit @ F )
=> ( ! [E: config256849571t_unit > config256849571t_unit,F: config256849571t_unit,G: list_c1059388851t_unit,H: list_c1059388851t_unit] :
( ( A @ E @ G @ ( cons_c1162654829t_unit @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_c1162654829t_unit @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_less__imp__of__nat__less) ).
thf(327,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( semiri1382578993at_nat @ A ) @ ( semiri1382578993at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(160,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat,E: list_c1059388851t_unit] :
( ( ( fLPThe1519354920_p_v_s @ A @ B @ C @ D )
= E )
=> ( ( ( D = zero_zero_nat )
=> ( E
!= ( cons_c1162654829t_unit @ A @ nil_co1338500125t_unit ) ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( B @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ F ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_infiniteExecutionCfg_Oelims) ).
thf(993,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat,E: list_c1059388851t_unit] :
( ( ( fLPThe1519354920_p_v_s @ A @ B @ C @ D )
= E )
=> ( ( ( D = zero_zero_nat )
=> ( E
!= ( cons_c1162654829t_unit @ A @ nil_co1338500125t_unit ) ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( B @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ F ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(102,axiom,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit] : ( A @ ( cons_c1162654829t_unit @ C @ nil_co1338500125t_unit ) )
=> ( ! [C: config256849571t_unit,D: config256849571t_unit,E: list_c1059388851t_unit] :
( ( A @ E )
=> ( ( A @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( A @ ( cons_c1162654829t_unit @ C @ ( cons_c1162654829t_unit @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_induct__list012) ).
thf(673,plain,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit] : ( A @ ( cons_c1162654829t_unit @ C @ nil_co1338500125t_unit ) )
=> ( ! [C: config256849571t_unit,D: config256849571t_unit,E: list_c1059388851t_unit] :
( ( A @ E )
=> ( ( A @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( A @ ( cons_c1162654829t_unit @ C @ ( cons_c1162654829t_unit @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(128,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_not__less__less__Suc__eq) ).
thf(840,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(63,axiom,
! [A: set_nat,B: config256849571t_unit] :
( ( ( member_nat @ zero_zero_nat @ A )
=> ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) @ A )
= ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) ) )
& ( ~ ( member_nat @ zero_zero_nat @ A )
=> ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) @ A )
= nil_co1338500125t_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_nths__singleton) ).
thf(470,plain,
! [A: set_nat,B: config256849571t_unit] :
( ( ( member_nat @ zero_zero_nat @ A )
=> ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) @ A )
= ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) ) )
& ( ~ ( member_nat @ zero_zero_nat @ A )
=> ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ B @ nil_co1338500125t_unit ) @ A )
= nil_co1338500125t_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(74,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ ( cons_c1162654829t_unit @ A @ B ) )
= ( suc @ ( size_s1406904903t_unit @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_length__Cons) ).
thf(544,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ ( cons_c1162654829t_unit @ A @ B ) )
= ( suc @ ( size_s1406904903t_unit @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(112,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_not__gr__zero) ).
thf(744,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(167,axiom,
( ( m = na )
| ( ord_less_nat @ m @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062) ).
thf(1023,plain,
( ( m = na )
| ( ord_less_nat @ m @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__not__refl3) ).
thf(864,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(110,axiom,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_list_Osize_I3_J) ).
thf(727,plain,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(79,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_nat__less__induct) ).
thf(571,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(66,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_int @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_lift__Suc__mono__less) ).
thf(497,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_int @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(7,axiom,
! [A: list_message_p_v > list_message_p_v > $o,B: list_message_p_v,C: list_message_p_v] :
( ! [D: list_message_p_v] : ( A @ nil_message_p_v @ D )
=> ( ! [D: list_message_p_v] : ( A @ D @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v,F: message_p_v,G: list_message_p_v] :
( ( A @ E @ ( cons_message_p_v @ F @ G ) )
=> ( ( A @ ( cons_message_p_v @ D @ E ) @ G )
=> ( A @ ( cons_message_p_v @ D @ E ) @ ( cons_message_p_v @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_shuffles_Oinduct) ).
thf(203,plain,
! [A: list_message_p_v > list_message_p_v > $o,B: list_message_p_v,C: list_message_p_v] :
( ! [D: list_message_p_v] : ( A @ nil_message_p_v @ D )
=> ( ! [D: list_message_p_v] : ( A @ D @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v,F: message_p_v,G: list_message_p_v] :
( ( A @ E @ ( cons_message_p_v @ F @ G ) )
=> ( ( A @ ( cons_message_p_v @ D @ E ) @ G )
=> ( A @ ( cons_message_p_v @ D @ E ) @ ( cons_message_p_v @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(103,axiom,
! [A: list_c1059388851t_unit > list_c1059388851t_unit > $o,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ ( cons_c1162654829t_unit @ D @ E ) @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ E @ G )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_list__induct2_H) ).
thf(688,plain,
! [A: list_c1059388851t_unit > list_c1059388851t_unit > $o,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ( A @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ ( cons_c1162654829t_unit @ D @ E ) @ nil_co1338500125t_unit )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ D @ E ) )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: config256849571t_unit,G: list_c1059388851t_unit] :
( ( A @ E @ G )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_c1162654829t_unit @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(104,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_lift__Suc__mono__less) ).
thf(699,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(154,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe1519354920_p_v_s @ A @ B @ C @ zero_zero_nat )
= ( cons_c1162654829t_unit @ A @ nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_infiniteExecutionCfg_Osimps_I1_J) ).
thf(961,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe1519354920_p_v_s @ A @ B @ C @ zero_zero_nat )
= ( cons_c1162654829t_unit @ A @ nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(24,axiom,
! [A: message_p_v,B: list_message_p_v] :
( ( cons_message_p_v @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__Cons__self2) ).
thf(319,plain,
! [A: message_p_v,B: list_message_p_v] :
( ( cons_message_p_v @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(149,axiom,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_lift__Suc__mono__less__iff) ).
thf(946,plain,
! [A: nat > int,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_int @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_int @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_less__antisym) ).
thf(390,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(36,axiom,
! [A: message_p_v,B: list_message_p_v,C: message_p_v,D: list_message_p_v] :
( ( ( cons_message_p_v @ A @ B )
= ( cons_message_p_v @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_list_Oinject) ).
thf(378,plain,
! [A: message_p_v,B: list_message_p_v,C: message_p_v,D: list_message_p_v] :
( ( ( cons_message_p_v @ A @ B )
= ( cons_message_p_v @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(64,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit > $o] :
( ( A != nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit] : ( B @ ( cons_c1162654829t_unit @ C @ nil_co1338500125t_unit ) )
=> ( ! [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( D != nil_co1338500125t_unit )
=> ( ( B @ D )
=> ( B @ ( cons_c1162654829t_unit @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_list__nonempty__induct) ).
thf(478,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit > $o] :
( ( A != nil_co1338500125t_unit )
=> ( ! [C: config256849571t_unit] : ( B @ ( cons_c1162654829t_unit @ C @ nil_co1338500125t_unit ) )
=> ( ! [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( D != nil_co1338500125t_unit )
=> ( ( B @ D )
=> ( B @ ( cons_c1162654829t_unit @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(139,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nat__induct) ).
thf(899,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(126,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_diff__induct) ).
thf(832,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(9,axiom,
! [A: list_c1059388851t_unit > list_message_p_v > $o,B: list_c1059388851t_unit,C: list_message_p_v] :
( ( A @ nil_co1338500125t_unit @ nil_message_p_v )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ ( cons_c1162654829t_unit @ D @ E ) @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ nil_co1338500125t_unit @ ( cons_message_p_v @ D @ E ) )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: message_p_v,G: list_message_p_v] :
( ( A @ E @ G )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_message_p_v @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_list__induct2_H) ).
thf(214,plain,
! [A: list_c1059388851t_unit > list_message_p_v > $o,B: list_c1059388851t_unit,C: list_message_p_v] :
( ( A @ nil_co1338500125t_unit @ nil_message_p_v )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit] : ( A @ ( cons_c1162654829t_unit @ D @ E ) @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ nil_co1338500125t_unit @ ( cons_message_p_v @ D @ E ) )
=> ( ! [D: config256849571t_unit,E: list_c1059388851t_unit,F: message_p_v,G: list_message_p_v] :
( ( A @ E @ G )
=> ( A @ ( cons_c1162654829t_unit @ D @ E ) @ ( cons_message_p_v @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
! [A: list_message_p_v > list_message_p_v > $o,B: list_message_p_v,C: list_message_p_v] :
( ( A @ nil_message_p_v @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ ( cons_message_p_v @ D @ E ) @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ nil_message_p_v @ ( cons_message_p_v @ D @ E ) )
=> ( ! [D: message_p_v,E: list_message_p_v,F: message_p_v,G: list_message_p_v] :
( ( A @ E @ G )
=> ( A @ ( cons_message_p_v @ D @ E ) @ ( cons_message_p_v @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_list__induct2_H) ).
thf(300,plain,
! [A: list_message_p_v > list_message_p_v > $o,B: list_message_p_v,C: list_message_p_v] :
( ( A @ nil_message_p_v @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ ( cons_message_p_v @ D @ E ) @ nil_message_p_v )
=> ( ! [D: message_p_v,E: list_message_p_v] : ( A @ nil_message_p_v @ ( cons_message_p_v @ D @ E ) )
=> ( ! [D: message_p_v,E: list_message_p_v,F: message_p_v,G: list_message_p_v] :
( ( A @ E @ G )
=> ( A @ ( cons_message_p_v @ D @ E ) @ ( cons_message_p_v @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(88,axiom,
( size_s1406904903t_unit
= ( gen_le193291088t_unit @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_length__code) ).
thf(620,plain,
( size_s1406904903t_unit
= ( gen_le193291088t_unit @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(45,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_old_Onat_Odistinct_I2_J) ).
thf(410,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(150,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_not__gr0) ).
thf(950,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(4,axiom,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ( A @ nil_message_p_v )
=> ( ! [C: message_p_v,D: list_message_p_v] :
( ( A @ D )
=> ( A @ ( cons_message_p_v @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_list_Oinducts) ).
thf(183,plain,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ( A @ nil_message_p_v )
=> ( ! [C: message_p_v,D: list_message_p_v] :
( ( A @ D )
=> ( A @ ( cons_message_p_v @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,axiom,
! [A: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > $o,B: config256849571t_unit > message_p_v,C: list_c1059388851t_unit,D: list_message_p_v] :
( ! [E: config256849571t_unit > message_p_v,F: list_message_p_v] : ( A @ E @ nil_co1338500125t_unit @ F )
=> ( ! [E: config256849571t_unit > message_p_v,F: config256849571t_unit,G: list_c1059388851t_unit,H: list_message_p_v] :
( ( A @ E @ G @ ( cons_message_p_v @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_c1162654829t_unit @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_map__tailrec__rev_Oinduct) ).
thf(422,plain,
! [A: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > $o,B: config256849571t_unit > message_p_v,C: list_c1059388851t_unit,D: list_message_p_v] :
( ! [E: config256849571t_unit > message_p_v,F: list_message_p_v] : ( A @ E @ nil_co1338500125t_unit @ F )
=> ( ! [E: config256849571t_unit > message_p_v,F: config256849571t_unit,G: list_c1059388851t_unit,H: list_message_p_v] :
( ( A @ E @ G @ ( cons_message_p_v @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_c1162654829t_unit @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(119,axiom,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ! [C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ D ) @ ( size_s1406904903t_unit @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_length__induct) ).
thf(790,plain,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ! [C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ D ) @ ( size_s1406904903t_unit @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(52,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_less__zeroE) ).
thf(437,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(101,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_infinite__descent) ).
thf(664,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(12,axiom,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
= ( ? [B: message_p_v,C: list_message_p_v] :
( A
= ( cons_message_p_v @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_neq__Nil__conv) ).
thf(239,plain,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
= ( ? [B: message_p_v,C: list_message_p_v] :
( A
= ( cons_message_p_v @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > $o,B: message_p_v > message_p_v,C: list_message_p_v,D: list_message_p_v] :
( ! [E: message_p_v > message_p_v,F: list_message_p_v] : ( A @ E @ nil_message_p_v @ F )
=> ( ! [E: message_p_v > message_p_v,F: message_p_v,G: list_message_p_v,H: list_message_p_v] :
( ( A @ E @ G @ ( cons_message_p_v @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_message_p_v @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_map__tailrec__rev_Oinduct) ).
thf(242,plain,
! [A: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > $o,B: message_p_v > message_p_v,C: list_message_p_v,D: list_message_p_v] :
( ! [E: message_p_v > message_p_v,F: list_message_p_v] : ( A @ E @ nil_message_p_v @ F )
=> ( ! [E: message_p_v > message_p_v,F: message_p_v,G: list_message_p_v,H: list_message_p_v] :
( ( A @ E @ G @ ( cons_message_p_v @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_message_p_v @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(33,axiom,
! [A: nat] :
( ( ( semiri1382578993at_nat @ A )
= zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_of__nat__eq__0__iff) ).
thf(358,plain,
! [A: nat] :
( ( ( semiri1382578993at_nat @ A )
= zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(122,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_All__less__Suc) ).
thf(807,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(158,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__nat__zero__code) ).
thf(987,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_not__less__eq) ).
thf(464,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(49,axiom,
! [A: nat,B: list_c1059388851t_unit] :
( ( ( suc @ A )
= ( size_s1406904903t_unit @ B ) )
= ( ? [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( B
= ( cons_c1162654829t_unit @ C @ D ) )
& ( ( size_s1406904903t_unit @ D )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Suc__length__conv) ).
thf(427,plain,
! [A: nat,B: list_c1059388851t_unit] :
( ( ( suc @ A )
= ( size_s1406904903t_unit @ B ) )
= ( ? [C: config256849571t_unit,D: list_c1059388851t_unit] :
( ( B
= ( cons_c1162654829t_unit @ C @ D ) )
& ( ( size_s1406904903t_unit @ D )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(165,axiom,
( ( ord_less_nat @ m @ na )
=> ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_IA_I1_J) ).
thf(1019,plain,
( ( ord_less_nat @ m @ na )
=> ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Suc__lessI) ).
thf(644,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1,conjecture,
prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(178,plain,
~ ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(133,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_zero__reorient) ).
thf(871,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(121,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_gr__implies__not__zero) ).
thf(803,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(171,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ord_less_nat @ ( size_s1406904903t_unit @ A ) @ ( size_s1406904903t_unit @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_PrefixListMonotonicity) ).
thf(1037,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ord_less_nat @ ( size_s1406904903t_unit @ A ) @ ( size_s1406904903t_unit @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(163,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_zero__less__Suc) ).
thf(1014,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1069,plain,
$false,
inference(e,[status(thm)],[892,347,247,861,878,440,511,385,500,747,829,565,651,1055,719,504,587,344,917,702,448,316,179,443,1040,353,956,396,507,527,452,270,661,761,810,381,714,1057,910,1021,729,407,630,467,361,329,889,461,493,224,1032,252,874,615,725,388,356,593,1039,547,1016,590,393,647,515,654,984,622,837,633,311,921,657,558,1026,953,926,750,375,601,513,430,584,562,1007,402,843,958,641,787,1058,350,445,936,219,274,784,990,434,764,979,604,1011,419,323,799,895,964,626,943,198,932,1061,912,827,636,455,278,868,722,1034,255,209,939,458,194,580,295,414,327,993,673,840,470,544,744,1023,864,727,571,497,203,688,699,961,319,946,390,378,478,899,832,214,300,620,410,950,183,422,790,437,664,239,242,358,807,987,464,427,1019,644,178,871,803,1037,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP055^1 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.10/0.22 % Computer : n019.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 19:44:18 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.99/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.98/1.18 % [INFO] Parsing done (372ms).
% 1.98/1.19 % [INFO] Running in sequential loop mode.
% 3.10/1.58 % [INFO] eprover registered as external prover.
% 3.10/1.59 % [INFO] Scanning for conjecture ...
% 3.47/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 341 axioms. Running axiom selection ...
% 3.71/1.86 % [INFO] Axiom selection finished. Selected 175 axioms (removed 166 axioms).
% 4.42/2.07 % [INFO] Problem is higher-order (TPTP THF).
% 4.42/2.09 % [INFO] Type checking passed.
% 4.42/2.10 % [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 ...
% 18.87/5.54 % External prover 'e' found a proof!
% 18.87/5.54 % [INFO] Killing All external provers ...
% 18.87/5.54 % Time passed: 5195ms (effective reasoning time: 4347ms)
% 18.87/5.54 % 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)>
% 18.87/5.55 % Axioms used in derivation (175): fact_91_bot__nat__0_Oextremum__strict, fact_180_length__Suc__conv, fact_14_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_179_Ex__less__Suc2, fact_227_gen__length__code_I1_J, fact_157_list__induct2_H, fact_37_length__greater__0__conv, fact_66_less__not__refl3, fact_248_of__nat__neq__0, fact_164_list_Oexhaust, fact_42_less__Suc0, fact_109_less__SucI, fact_96_not__gr0, fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062, fact_104_Suc__less__eq2, fact_1_MLessN, fact_88_old_Onat_Odistinct_I1_J, fact_250_less__imp__of__nat__less, fact_160_neq__Nil__conv, fact_82_Zero__neq__Suc, fact_32_NatPredicateTippingPoint, fact_60_n__not__Suc__n, fact_136_remdups__adj_Oinduct, fact_244_of__nat__less__iff, fact_165_list_Oexhaust, fact_218_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J, fact_139_sorted__wrt_Oinduct, fact_163_list_Oinducts, fact_216_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J, fact_198_infiniteExecutionMsg_Osimps_I2_J, fact_257_list__ex1__simps_I1_J, fact_158_list__induct2_H, fact_110_less__SucE, fact_6_PrefixListTransitive, fact_108_Ex__less__Suc, fact_113_Suc__lessD, fact_132_successively_Oinduct, fact_102_Suc__less__SucD, fact_233_of__nat__0__less__iff, fact_83_Suc__neq__Zero, fact_106_not__less__eq, fact_208_zero__less__iff__neq__zero, fact_135_remdups__adj_Oinduct, fact_0__092_060open_062m_A_060_An_092_060close_062, fact_86_nat__induct, fact_65_less__irrefl__nat, fact_101_less__trans__Suc, fact_54_old_Onat_Oinject, fact_79_old_Onat_Oinducts, fact_50_list_Oinject, fact_203_zero__reorient, fact_225_length__code, fact_80_old_Onat_Oexhaust, fact_75_neq__if__length__neq, fact_166_list_OdiscI, fact_285_verit__comp__simplify1_I1_J, fact_175_less__Suc__eq__0__disj, fact_78_not0__implies__Suc, fact_34_length__greater__0__conv, fact_89_old_Onat_Odistinct_I2_J, fact_128_list__nonempty__induct, fact_67_less__not__refl2, fact_205_gr__zeroI, fact_41_length__0__conv, fact_171_lift__Suc__mono__less__iff, fact_81_Zero__not__Suc, fact_238_of__nat__0, fact_199_infiniteExecutionCfg_Osimps_I2_J, fact_92_infinite__descent0, fact_206_not__less__zero, fact_45_Suc__mono, fact_156_list__induct2_H, fact_98_not__less__less__Suc__eq, fact_217_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J, fact_107_less__Suc__eq, fact_167_list_OdiscI, fact_284_verit__comp__simplify1_I1_J, fact_161_neq__Nil__conv, fact_151_shuffles_Oinduct, fact_39_length__0__conv, fact_87_nat_OdiscI, fact_105_All__less__Suc, fact_38_length__0__conv, fact_85_diff__induct, fact_7_FE_I1_J, fact_236_nths__nil, fact_201_not__gr__zero, fact_215_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J, fact_99_strict__inc__induct, fact_70_less__not__refl, fact_232_nths__singleton, fact_62_linorder__neqE__nat, fact_246_of__nat__less__0__iff, fact_172_lift__Suc__mono__less__iff, fact_176_gr0__implies__Suc, fact_254_nths__all, fact_152_induct__list012, fact_31_prefixList_Oinducts, fact_2_IA_I1_J, fact_202_length__Cons, fact_117_map__tailrec__rev_Oinduct, fact_226_gen__length__code_I2_J, fact_200_infiniteExecutionMsg_Osimps_I1_J, fact_131_successively_Oinduct, fact_150_shuffles_Oinduct, fact_97_gr0I, fact_219_less__numeral__extra_I3_J, fact_95_not__less0, fact_240_of__nat__0__eq__iff, fact_4_IA_I2_J, fact_94_less__zeroE, fact_90_nat_Odistinct_I1_J, fact_46_Suc__less__eq, fact_55_nat_Oinject, fact_197_infiniteExecutionMsg_Oelims, fact_59_not__Cons__self2, fact_114_Nat_OlessE, fact_162_list_Oinducts, fact_84_zero__induct, fact_242_of__nat__eq__0__iff, fact_196_infiniteExecutionCfg_Oelims, fact_112_Suc__lessE, fact_170_length__induct, fact_207_gr__implies__not__zero, fact_183_list_Osize_I3_J, fact_13_PrefixListMonotonicity, fact_159_list__induct2_H, fact_178_gr0__conv__Suc, fact_64_nat__less__induct, fact_195_list__induct2, fact_27_prefixList_Osimps, fact_61_Suc__inject, fact_177_All__less__Suc2, fact_77_Ex__list__of__length, fact_43_zero__less__Suc, fact_56_not__Cons__self2, fact_143_remdups__adj_Ocases, fact_191_list__induct3, fact_140_sorted__wrt_Oinduct, fact_173_lift__Suc__mono__less, fact_63_infinite__descent, fact_335_less__numeral__extra_I4_J, fact_211_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims, fact_49_bot__nat__0_Onot__eq__extremum, fact_44_lessI, fact_100_less__Suc__induct, fact_47_neq0__conv, fact_23_prefixList_Ocases, fact_103_less__antisym, fact_230_insert__Nil, fact_252_of__nat__less__imp__less, fact_127_list__nonempty__induct, fact_15_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_19_prefixList_Ointros_I1_J, fact_11_prefixList_Ointros_I2_J, fact_93_gr__implies__not0, fact_144_remdups__adj_Ocases, fact_168_list_Odistinct_I1_J, fact_33_infiniteExecutionCfg_Osimps_I1_J, fact_181_Suc__length__conv, fact_153_induct__list012, fact_154_splice_Oinduct, fact_169_list_Odistinct_I1_J, fact_115_map__tailrec__rev_Oinduct, fact_155_splice_Oinduct, fact_111_Suc__lessI, fact_116_map__tailrec__rev_Oinduct, fact_174_lift__Suc__mono__less, fact_214_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims, fact_35_length__greater__0__conv, fact_71_nat__neq__iff, fact_48_less__nat__zero__code, fact_120_map__tailrec__rev_Oinduct, fact_53_list_Oinject, fact_73_size__neq__size__imp__neq
% 18.87/5.55 % No. of inferences in proof: 354
% 18.87/5.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5195 ms resp. 4347 ms w/o parsing
% 19.94/5.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.94/5.76 % [INFO] Killing All external provers ...
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