TSTP Solution File: ITP186^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP186^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:38 EDT 2024
% Result : Theorem 27.63s 7.96s
% Output : Refutation 28.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 453
% Syntax : Number of formulae : 782 ( 364 unt; 126 typ; 0 def)
% Number of atoms : 2170 ( 657 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 10765 ( 331 ~; 30 |; 86 &;8474 @)
% ( 0 <=>;1844 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 10 avg)
% Number of types : 17 ( 16 usr)
% Number of type conns : 1512 (1512 >; 0 *; 0 +; 0 <<)
% Number of symbols : 113 ( 110 usr; 15 con; 0-12 aty)
% Number of variables : 3912 ( 100 ^3778 !; 34 ?;3912 :)
% Comments :
%------------------------------------------------------------------------------
thf(noptio751120898ion_pi_type,type,
noptio751120898ion_pi: $tType ).
thf(noptio2087446135ion_pi_type,type,
noptio2087446135ion_pi: $tType ).
thf(noptio570777408ubject_type,type,
noptio570777408ubject: $tType ).
thf(noptio435234344reeRes_type,type,
noptio435234344reeRes: $tType ).
thf(noptio1926134715n_name_type,type,
noptio1926134715n_name: $tType ).
thf(noptio354675977ion_pi_type,type,
noptio354675977ion_pi: $tType ).
thf(noption_Late_subject_type,type,
noption_Late_subject: $tType ).
thf(noption_Late_freeRes_type,type,
noption_Late_freeRes: $tType ).
thf(noption_name_type,type,
noption_name: $tType ).
thf(noption_pi_type,type,
noption_pi: $tType ).
thf(set_name_type,type,
set_name: $tType ).
thf(late_residual_type,type,
late_residual: $tType ).
thf(late_subject_type,type,
late_subject: $tType ).
thf(late_freeRes_type,type,
late_freeRes: $tType ).
thf(name_type,type,
name: $tType ).
thf(pi_type,type,
pi: $tType ).
thf(bang_type,type,
bang: pi > pi ).
thf(input_type,type,
input: name > name > pi > pi ).
thf(match_type,type,
match: name > name > pi > pi ).
thf(mismatch_type,type,
mismatch: name > name > pi > pi ).
thf(output_type,type,
output: name > name > pi > pi ).
thf(par_type,type,
par: pi > pi > pi ).
thf(piNil_type,type,
piNil: pi ).
thf(res_type,type,
res: name > pi > pi ).
thf(sum_type,type,
sum: pi > pi > pi ).
thf(tau_type,type,
tau: pi > pi ).
thf(pi_rec_pi_type,type,
pi_rec_pi: pi > ( name > name > pi > pi > pi ) > ( pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( name > pi > pi > pi ) > ( pi > pi > pi ) > pi > pi ).
thf(pi_rec802206470ion_pi_type,type,
pi_rec802206470ion_pi: ( name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( pi > ( name > noption_pi ) > name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > ( pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi ) > ( pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi ) > ( name > pi > ( name > noption_pi ) > name > noption_pi ) > ( pi > ( name > noption_pi ) > name > noption_pi ) > pi > ( name > noption_pi ) > $o ).
thf(pi_rec_set_name_type,type,
pi_rec_set_name: name > ( name > name > pi > name > name ) > ( pi > name > name ) > ( name > name > pi > name > name ) > ( name > name > pi > name > name ) > ( name > name > pi > name > name ) > ( pi > pi > name > name > name ) > ( pi > pi > name > name > name ) > ( name > pi > name > name ) > ( pi > name > name ) > pi > name > $o ).
thf(pi_rec_set_pi_type,type,
pi_rec_set_pi: pi > ( name > name > pi > pi > pi ) > ( pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( name > pi > pi > pi ) > ( pi > pi > pi ) > pi > pi > $o ).
thf(pi_rec1156860983reeRes_type,type,
pi_rec1156860983reeRes: late_freeRes > ( name > name > pi > late_freeRes > late_freeRes ) > ( pi > late_freeRes > late_freeRes ) > ( name > name > pi > late_freeRes > late_freeRes ) > ( name > name > pi > late_freeRes > late_freeRes ) > ( name > name > pi > late_freeRes > late_freeRes ) > ( pi > pi > late_freeRes > late_freeRes > late_freeRes ) > ( pi > pi > late_freeRes > late_freeRes > late_freeRes ) > ( name > pi > late_freeRes > late_freeRes ) > ( pi > late_freeRes > late_freeRes ) > pi > late_freeRes > $o ).
thf(pi_rec232630607ubject_type,type,
pi_rec232630607ubject: late_subject > ( name > name > pi > late_subject > late_subject ) > ( pi > late_subject > late_subject ) > ( name > name > pi > late_subject > late_subject ) > ( name > name > pi > late_subject > late_subject ) > ( name > name > pi > late_subject > late_subject ) > ( pi > pi > late_subject > late_subject > late_subject ) > ( pi > pi > late_subject > late_subject > late_subject ) > ( name > pi > late_subject > late_subject ) > ( pi > late_subject > late_subject ) > pi > late_subject > $o ).
thf(subs_type,type,
subs: pi > name > name > pi ).
thf(subst_name_type,type,
subst_name: name > name > name > name ).
thf(finite_finite_name_type,type,
finite_finite_name: set_name > $o ).
thf(if_name_type,type,
if_name: $o > name > name > name ).
thf(late_bangPred_type,type,
late_bangPred: pi > pi > $o ).
thf(late_OutputR_type,type,
late_OutputR: name > name > late_freeRes ).
thf(late_TauR_type,type,
late_TauR: late_freeRes ).
thf(late_BoundR_type,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(late_FreeR_type,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(late_r1174711868c_name_type,type,
late_r1174711868c_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name ).
thf(late_residual_rec_pi_type,type,
late_residual_rec_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi ).
thf(late_r124702629reeRes_type,type,
late_r124702629reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes ).
thf(late_r1347955901ubject_type,type,
late_r1347955901ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject ).
thf(late_r1742481968t_name_type,type,
late_r1742481968t_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name > $o ).
thf(late_r1261898622set_pi_type,type,
late_r1261898622set_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi > $o ).
thf(late_r1613948593reeRes_type,type,
late_r1613948593reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes > $o ).
thf(late_r689718217ubject_type,type,
late_r689718217ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject > $o ).
thf(late_BoundOutputS_type,type,
late_BoundOutputS: name > late_subject ).
thf(late_InputS_type,type,
late_InputS: name > late_subject ).
thf(late_transitions_type,type,
late_transitions: pi > late_residual > $o ).
thf(sup_sup_set_name_type,type,
sup_sup_set_name: set_name > set_name > set_name ).
thf(abs_fun_name_name_type,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(abs_fun_name_pi_type,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(abs_fu681348580reeRes_type,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(abs_fu1904601852ubject_type,type,
abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
thf(fresh_1093033124n_name_type,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(fresh_543891186ion_pi_type,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(fresh_785364841reeRes_type,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(fresh_728038529ubject_type,type,
fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
thf(fresh_1030632537i_name_type,type,
fresh_1030632537i_name: name > ( late_freeRes > pi > name ) > $o ).
thf(fresh_1011532071_pi_pi_type,type,
fresh_1011532071_pi_pi: name > ( late_freeRes > pi > pi ) > $o ).
thf(fresh_256112244reeRes_type,type,
fresh_256112244reeRes: name > ( late_freeRes > pi > late_freeRes ) > $o ).
thf(fresh_198785932ubject_type,type,
fresh_198785932ubject: name > ( late_freeRes > pi > late_subject ) > $o ).
thf(fresh_621211324i_name_type,type,
fresh_621211324i_name: name > ( late_subject > name > pi > name ) > $o ).
thf(fresh_1438126218_pi_pi_type,type,
fresh_1438126218_pi_pi: name > ( late_subject > name > pi > pi ) > $o ).
thf(fresh_660367079reeRes_type,type,
fresh_660367079reeRes: name > ( late_subject > name > pi > late_freeRes ) > $o ).
thf(fresh_795910143ubject_type,type,
fresh_795910143ubject: name > ( late_subject > name > pi > late_subject ) > $o ).
thf(fresh_name_name_type,type,
fresh_name_name: name > name > $o ).
thf(fresh_name_pi_type,type,
fresh_name_pi: name > pi > $o ).
thf(fresh_1641682979reeRes_type,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(fresh_81631222sidual_type,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(fresh_717452603ubject_type,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(supp_n1987783534i_name_type,type,
supp_n1987783534i_name: ( name > name > pi > ( name > noption_pi ) > name > noption_pi ) > set_name ).
thf(supp_n612431512e_name_type,type,
supp_n612431512e_name: ( name > name > pi > name > name ) > set_name ).
thf(supp_n1977765016i_name_type,type,
supp_n1977765016i_name: ( name > name > pi > pi > pi ) > set_name ).
thf(supp_n337505932s_name_type,type,
supp_n337505932s_name: ( name > name > pi > late_freeRes > late_freeRes ) > set_name ).
thf(supp_n200783964t_name_type,type,
supp_n200783964t_name: ( name > name > pi > late_subject > late_subject ) > set_name ).
thf(supp_n52582513i_name_type,type,
supp_n52582513i_name: ( name > pi > ( name > noption_pi ) > name > noption_pi ) > set_name ).
thf(supp_n116460699e_name_type,type,
supp_n116460699e_name: ( name > pi > name > name ) > set_name ).
thf(supp_n96533147i_name_type,type,
supp_n96533147i_name: ( name > pi > pi > pi ) > set_name ).
thf(supp_n1410452111s_name_type,type,
supp_n1410452111s_name: ( name > pi > late_freeRes > late_freeRes ) > set_name ).
thf(supp_n122125407t_name_type,type,
supp_n122125407t_name: ( name > pi > late_subject > late_subject ) > set_name ).
thf(supp_n468628396i_name_type,type,
supp_n468628396i_name: ( name > noption_pi ) > set_name ).
thf(supp_p1320058820i_name_type,type,
supp_p1320058820i_name: ( pi > ( name > noption_pi ) > name > noption_pi ) > set_name ).
thf(supp_p1239856366e_name_type,type,
supp_p1239856366e_name: ( pi > name > name ) > set_name ).
thf(supp_p1592910632i_name_type,type,
supp_p1592910632i_name: ( pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi ) > set_name ).
thf(supp_p1618090470e_name_type,type,
supp_p1618090470e_name: ( pi > pi > name > name > name ) > set_name ).
thf(supp_p812767768i_name_type,type,
supp_p812767768i_name: ( pi > pi > pi > pi > pi ) > set_name ).
thf(supp_p1358344533s_name_type,type,
supp_p1358344533s_name: ( pi > pi > late_freeRes > late_freeRes > late_freeRes ) > set_name ).
thf(supp_p1221108749t_name_type,type,
supp_p1221108749t_name: ( pi > pi > late_subject > late_subject > late_subject ) > set_name ).
thf(supp_pi_pi_pi_name_type,type,
supp_pi_pi_pi_name: ( pi > pi > pi ) > set_name ).
thf(supp_p71246050s_name_type,type,
supp_p71246050s_name: ( pi > late_freeRes > late_freeRes ) > set_name ).
thf(supp_p742701746t_name_type,type,
supp_p742701746t_name: ( pi > late_subject > late_subject ) > set_name ).
thf(supp_L926407557e_name_type,type,
supp_L926407557e_name: ( late_freeRes > pi > name ) > set_name ).
thf(supp_L2052723895i_name_type,type,
supp_L2052723895i_name: ( late_freeRes > pi > pi ) > set_name ).
thf(supp_L381160156s_name_type,type,
supp_L381160156s_name: ( late_freeRes > pi > late_freeRes ) > set_name ).
thf(supp_L1759672260t_name_type,type,
supp_L1759672260t_name: ( late_freeRes > pi > late_subject ) > set_name ).
thf(supp_L538372628e_name_type,type,
supp_L538372628e_name: ( late_subject > name > pi > name ) > set_name ).
thf(supp_L729745222i_name_type,type,
supp_L729745222i_name: ( late_subject > name > pi > pi ) > set_name ).
thf(supp_L1178477943s_name_type,type,
supp_L1178477943s_name: ( late_subject > name > pi > late_freeRes ) > set_name ).
thf(supp_L1144036959t_name_type,type,
supp_L1144036959t_name: ( late_subject > name > pi > late_subject ) > set_name ).
thf(supp_name_name_type,type,
supp_name_name: name > set_name ).
thf(supp_pi_name_type,type,
supp_pi_name: pi > set_name ).
thf(supp_L1228270395s_name_type,type,
supp_L1228270395s_name: late_freeRes > set_name ).
thf(supp_L1174042202l_name_type,type,
supp_L1174042202l_name: late_residual > set_name ).
thf(supp_L1174290467t_name_type,type,
supp_L1174290467t_name: late_subject > set_name ).
thf(suppor1289515356ion_pi_type,type,
suppor1289515356ion_pi: set_name > ( name > noption_pi ) > $o ).
thf(supports_name_name_type,type,
supports_name_name: set_name > name > $o ).
thf(supports_name_pi_type,type,
supports_name_pi: set_name > pi > $o ).
thf(suppor1556658829reeRes_type,type,
suppor1556658829reeRes: set_name > late_freeRes > $o ).
thf(suppor632428453ubject_type,type,
suppor632428453ubject: set_name > late_subject > $o ).
thf(collect_name_type,type,
collect_name: ( name > $o ) > set_name ).
thf(member_name_type,type,
member_name: name > set_name > $o ).
thf(p_type,type,
p: pi ).
thf(pqr_type,type,
pqr: pi ).
thf(p2_type,type,
p2: pi ).
thf(q_type,type,
q: pi ).
thf(qr_type,type,
qr: pi ).
thf(q2_type,type,
q2: pi ).
thf(r_type,type,
r: pi ).
thf(alpha_type,type,
alpha: late_freeRes ).
thf(a_type,type,
a: name ).
thf(b_type,type,
b: name ).
thf(x_type,type,
x: name ).
thf(209,axiom,
! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_resInputFreeTrans) ).
thf(1411,plain,
! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(274,axiom,
! [A: pi > $o,B: pi] :
( ( A @ piNil )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( output @ C @ D @ E ) ) )
=> ( ! [C: pi] :
( ( A @ C )
=> ( A @ ( tau @ C ) ) )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( input @ C @ D @ E ) ) )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( match @ C @ D @ E ) ) )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( mismatch @ C @ D @ E ) ) )
=> ( ! [C: pi,D: pi] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( sum @ C @ D ) ) ) )
=> ( ! [C: pi,D: pi] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( par @ C @ D ) ) ) )
=> ( ! [C: name,D: pi] :
( ( A @ D )
=> ( A @ ( res @ C @ D ) ) )
=> ( ! [C: pi] :
( ( A @ C )
=> ( A @ ( bang @ C ) ) )
=> ( A @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_pi_Oinducts) ).
thf(1823,plain,
! [A: pi > $o,B: pi] :
( ( A @ piNil )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( output @ C @ D @ E ) ) )
=> ( ! [C: pi] :
( ( A @ C )
=> ( A @ ( tau @ C ) ) )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( input @ C @ D @ E ) ) )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( match @ C @ D @ E ) ) )
=> ( ! [C: name,D: name,E: pi] :
( ( A @ E )
=> ( A @ ( mismatch @ C @ D @ E ) ) )
=> ( ! [C: pi,D: pi] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( sum @ C @ D ) ) ) )
=> ( ! [C: pi,D: pi] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( par @ C @ D ) ) ) )
=> ( ! [C: name,D: pi] :
( ( A @ D )
=> ( A @ ( res @ C @ D ) ) )
=> ( ! [C: pi] :
( ( A @ C )
=> ( A @ ( bang @ C ) ) )
=> ( A @ B ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(179,axiom,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_residual_Ostrong__induct) ).
thf(1168,plain,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(317,axiom,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Par1F) ).
thf(2031,plain,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(230,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_pi_Odistinct_I43_J) ).
thf(1633,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(308,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: name,D: late_subject > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_795910143ubject @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_name_name @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_717452603ubject @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_residual_Orecs_I2_J) ).
thf(1995,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: name,D: late_subject > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_795910143ubject @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_name_name @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_717452603ubject @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(118,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_residual,D: pi,E: name] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( late_r1261898622set_pi @ A @ B @ C @ D )
=> ( ! [F: pi] :
( ( late_r1261898622set_pi @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_1438126218_pi_pi @ E @ A )
=> ( ( fresh_1011532071_pi_pi @ E @ B )
=> ( fresh_name_pi @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_residual_Orec__fresh) ).
thf(846,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_residual,D: pi,E: name] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( late_r1261898622set_pi @ A @ B @ C @ D )
=> ( ! [F: pi] :
( ( late_r1261898622set_pi @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_1438126218_pi_pi @ E @ A )
=> ( ( fresh_1011532071_pi_pi @ E @ B )
=> ( fresh_name_pi @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(4,axiom,
! [A: name,B: name > $o] :
( ( member_name @ A @ ( collect_name @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mem__Collect__eq) ).
thf(333,plain,
! [A: name,B: name > $o] :
( ( member_name @ A @ ( collect_name @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(286,axiom,
! [A: pi,B: pi] :
( ( supp_pi_name @ ( par @ A @ B ) )
= ( sup_sup_set_name @ ( supp_pi_name @ A ) @ ( supp_pi_name @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_pi_Osupp_I8_J) ).
thf(1899,plain,
! [A: pi,B: pi] :
( ( supp_pi_name @ ( par @ A @ B ) )
= ( sup_sup_set_name @ ( supp_pi_name @ A ) @ ( supp_pi_name @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(193,axiom,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_pi_Ostrong__inducts) ).
thf(1315,plain,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(39,axiom,
( supp_L1228270395s_name
= ( ^ [A: late_freeRes] :
( collect_name
@ ^ [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_supp__fresh__iff) ).
thf(468,plain,
( supp_L1228270395s_name
= ( ^ [A: late_freeRes] :
( collect_name
@ ^ [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(273,axiom,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_residual_Ostrong__inducts) ).
thf(1818,plain,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(301,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_sumCases) ).
thf(1956,plain,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(217,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Late__Semantics_OComm1) ).
thf(1554,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(59,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_residual,D: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( late_r1261898622set_pi @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_pi_name @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_residual_Orec__fin__supp) ).
thf(582,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_residual,D: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( late_r1261898622set_pi @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_pi_name @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(294,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( B != C )
=> ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Open) ).
thf(1924,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( B != C )
=> ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(92,axiom,
( subst_name
= ( ^ [A: name,B: name,C: name] : ( if_name @ ( A = B ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_subst__name__def) ).
thf(730,plain,
( subst_name
= ( ^ [A: name,B: name,C: name] : ( if_name @ ( A = B ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(163,axiom,
! [A: late_freeRes] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_exists__fresh) ).
thf(1068,plain,
! [A: late_freeRes] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(327,axiom,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( tau @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( tau @ A )
= ( tau @ C ) )
=> ( B
!= ( late_FreeR @ late_TauR @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_tauCases_H) ).
thf(2062,plain,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( tau @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( tau @ A )
= ( tau @ C ) )
=> ( B
!= ( late_FreeR @ late_TauR @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(225,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_zeroTrans) ).
thf(1618,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(206,axiom,
fresh_name_pi @ x @ q,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_cComm2_Ohyps_I8_J) ).
thf(1401,plain,
fresh_name_pi @ x @ q,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(296,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_pi_Odistinct_I65_J) ).
thf(1939,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(190,axiom,
! [A: pi,B: pi,C: pi > pi > $o] :
( ( late_bangPred @ A @ B )
=> ( ! [D: pi] : ( C @ D @ ( bang @ D ) )
=> ( ! [D: pi] : ( C @ D @ ( par @ D @ ( bang @ D ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_bangPred_Oinducts) ).
thf(1269,plain,
! [A: pi,B: pi,C: pi > pi > $o] :
( ( late_bangPred @ A @ B )
=> ( ! [D: pi] : ( C @ D @ ( bang @ D ) )
=> ( ! [D: pi] : ( C @ D @ ( par @ D @ ( bang @ D ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(46,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_freeRes,D: late_subject > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_795910143ubject @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_717452603ubject @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ F )
& ! [G: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_residual_Orec__unique) ).
thf(511,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_freeRes,D: late_subject > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_795910143ubject @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_717452603ubject @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ F )
& ! [G: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(243,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_fresh__fact1) ).
thf(1692,plain,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(180,axiom,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_outputBoundTrans) ).
thf(1173,plain,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(268,axiom,
! [A: pi,B: late_freeRes,C: pi,D: late_freeRes > pi > $o] :
( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ B @ C ) )
=> ( ( ( B = late_TauR )
=> ( ( A = C )
=> ( D @ late_TauR @ A ) ) )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_tauCases) ).
thf(1788,plain,
! [A: pi,B: late_freeRes,C: pi,D: late_freeRes > pi > $o] :
( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ B @ C ) )
=> ( ( ( B = late_TauR )
=> ( ( A = C )
=> ( D @ late_TauR @ A ) ) )
=> ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(22,axiom,
! [A: pi] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_exists__fresh) ).
thf(385,plain,
! [A: pi] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(252,axiom,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_pi_Ostrong__induct) ).
thf(1735,plain,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(83,axiom,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_pi_Odistinct_I15_J) ).
thf(698,plain,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(260,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Late__Semantics_OClose2) ).
thf(1761,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(232,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_name_pi @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_freshFreeDerivative_I2_J) ).
thf(1640,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_name_pi @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(50,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_pi_Oinject_I6_J) ).
thf(538,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(132,axiom,
( fresh_717452603ubject
= ( ^ [A: name,B: late_subject] :
~ ( member_name @ A @ ( supp_L1174290467t_name @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_fresh__def) ).
thf(930,plain,
( fresh_717452603ubject
= ( ^ [A: name,B: late_subject] :
~ ( member_name @ A @ ( supp_L1174290467t_name @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(214,axiom,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_pi_Ostrong__inducts) ).
thf(1497,plain,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(245,axiom,
! [A: pi] : ( late_bangPred @ A @ ( par @ A @ ( bang @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_aux2) ).
thf(1705,plain,
! [A: pi] : ( late_bangPred @ A @ ( par @ A @ ( bang @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(256,axiom,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_resZeroTrans) ).
thf(1746,plain,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(266,axiom,
alpha = late_TauR,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_cComm2_Ohyps_I9_J) ).
thf(1782,plain,
alpha = late_TauR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(103,axiom,
! [A: name,B: name,C: pi] :
( ( fresh_name_pi @ A @ ( res @ B @ C ) )
= ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_pi_Ofresh_I9_J) ).
thf(782,plain,
! [A: name,B: name,C: pi] :
( ( fresh_name_pi @ A @ ( res @ B @ C ) )
= ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(143,axiom,
! [A: late_freeRes] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ? [B: name] : ( fresh_1641682979reeRes @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_exists__fresh_H) ).
thf(973,plain,
! [A: late_freeRes] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ? [B: name] : ( fresh_1641682979reeRes @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(220,axiom,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Par2F) ).
thf(1601,plain,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(328,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_substRes2) ).
thf(2067,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(117,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: name,D: late_subject > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_795910143ubject @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_name_name @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_717452603ubject @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ F )
& ! [G: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_residual_Orec__unique) ).
thf(829,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: name,D: late_subject > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_795910143ubject @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_name_name @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_717452603ubject @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ F )
& ! [G: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(28,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_freeRes,D: name > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_621211324i_name @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_name @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: name] :
( ( late_r1742481968t_name @ A @ B @ E @ F )
& ! [G: name] :
( ( late_r1742481968t_name @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_residual_Orec__unique) ).
thf(404,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_freeRes,D: name > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_621211324i_name @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_name @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: name] :
( ( late_r1742481968t_name @ A @ B @ E @ F )
& ! [G: name] :
( ( late_r1742481968t_name @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_name__exists__fresh) ).
thf(436,plain,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(271,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_subject,D: late_freeRes > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_660367079reeRes @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_1641682979reeRes @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_residual_Orecs_I2_J) ).
thf(1803,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_subject,D: late_freeRes > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_660367079reeRes @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_1641682979reeRes @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(55,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( input @ A @ B @ C )
!= ( bang @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pi_Odistinct_I59_J) ).
thf(570,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( input @ A @ B @ C )
!= ( bang @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(89,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( bang @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_pi_Odistinct_I33_J) ).
thf(719,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( bang @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(104,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( mismatch @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_pi_Odistinct_I9_J) ).
thf(785,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( mismatch @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(18,axiom,
! [A: name,B: name,C: name] :
( ( ( abs_fun_name_name @ A @ B )
= ( abs_fun_name_name @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_abs__fun__eq1) ).
thf(372,plain,
! [A: name,B: name,C: name] :
( ( ( abs_fun_name_name @ A @ B )
= ( abs_fun_name_name @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(276,axiom,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_residual_Ostrong__inducts) ).
thf(1860,plain,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(84,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( input @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_pi_Odistinct_I21_J) ).
thf(702,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( input @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(109,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( match @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_pi_Odistinct_I61_J) ).
thf(802,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( match @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(170,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_pi_Odistinct_I23_J) ).
thf(1087,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(185,axiom,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( match @ C @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Match) ).
thf(1247,plain,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( match @ C @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(314,axiom,
fresh_name_pi @ x @ ( par @ q @ r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_cComm2_Ohyps_I4_J) ).
thf(2024,plain,
fresh_name_pi @ x @ ( par @ q @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(272,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Late__Semantics_OPar2B) ).
thf(1815,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(279,axiom,
x != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cComm2_Ohyps_I5_J) ).
thf(1875,plain,
x != a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(29,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_pi_Odistinct_I39_J) ).
thf(421,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(283,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_pi_Odistinct_I73_J) ).
thf(1890,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(309,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ B @ A @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_forget) ).
thf(2007,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ B @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(105,axiom,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Late__Semantics1_Osubject_Oinject_I1_J) ).
thf(789,plain,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(68,axiom,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_pi_Odistinct_I3_J) ).
thf(623,plain,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(318,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Output) ).
thf(2034,plain,
! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(110,axiom,
! [A: name,B: name,C: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ C @ A ) )
= ( ( B = C )
| ( fresh_name_name @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_abs__fresh_I2_J) ).
thf(806,plain,
! [A: name,B: name,C: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ C @ A ) )
= ( ( B = C )
| ( fresh_name_name @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(158,axiom,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( output @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( sup_sup_set_name @ ( supp_name_name @ B ) @ ( supp_pi_name @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_pi_Osupp_I2_J) ).
thf(1051,plain,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( output @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( sup_sup_set_name @ ( supp_name_name @ B ) @ ( supp_pi_name @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(9,axiom,
! [A: name > noption_pi] :
( ( finite_finite_name @ ( supp_n468628396i_name @ A ) )
=> ? [B: name] : ( fresh_543891186ion_pi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_exists__fresh_H) ).
thf(348,plain,
! [A: name > noption_pi] :
( ( finite_finite_name @ ( supp_n468628396i_name @ A ) )
=> ? [B: name] : ( fresh_543891186ion_pi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(56,axiom,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_pi_Odistinct_I45_J) ).
thf(574,plain,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
( fresh_543891186ion_pi
= ( ^ [A: name,B: name > noption_pi] :
~ ( member_name @ A @ ( supp_n468628396i_name @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_fresh__def) ).
thf(353,plain,
( fresh_543891186ion_pi
= ( ^ [A: name,B: name > noption_pi] :
~ ( member_name @ A @ ( supp_n468628396i_name @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(141,axiom,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_subject_Oexhaust) ).
thf(966,plain,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(146,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_subject,D: pi > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_1438126218_pi_pi @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_pi @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_1438126218_pi_pi @ E @ A )
=> ( ( fresh_1011532071_pi_pi @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_residual_Orecs_I1_J) ).
thf(981,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_subject,D: pi > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_1438126218_pi_pi @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_pi @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_1438126218_pi_pi @ E @ A )
=> ( ( fresh_1011532071_pi_pi @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(326,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
thf(2058,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(26,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( output @ A @ B @ C )
= ( output @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_pi_Oinject_I1_J) ).
thf(397,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( output @ A @ B @ C )
= ( output @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(200,axiom,
! [A: name,B: pi,C: late_freeRes,D: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ E ) )
=> ( ( ( late_FreeR @ C @ D )
= ( late_FreeR @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
=> ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_resCasesF_H) ).
thf(1377,plain,
! [A: name,B: pi,C: late_freeRes,D: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ E ) )
=> ( ( ( late_FreeR @ C @ D )
= ( late_FreeR @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
=> ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(71,axiom,
! [A: set_name,B: late_subject,C: name] :
( ( suppor632428453ubject @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_717452603ubject @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_supports__fresh) ).
thf(634,plain,
! [A: set_name,B: late_subject,C: name] :
( ( suppor632428453ubject @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_717452603ubject @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(285,axiom,
! [A: pi,B: name,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_tauOutputTrans) ).
thf(1896,plain,
! [A: pi,B: name,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(208,axiom,
! [A: late_freeRes > $o,B: late_freeRes] :
( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
=> ( ( A @ late_TauR )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_freeRes_Oinducts) ).
thf(1405,plain,
! [A: late_freeRes > $o,B: late_freeRes] :
( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
=> ( ( A @ late_TauR )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(297,axiom,
fresh_name_pi @ x @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062) ).
thf(1943,plain,
fresh_name_pi @ x @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(244,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( input @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = F )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ G ) ) )
=> ( ( D
= ( late_BoundR @ ( late_InputS @ F ) @ E @ G ) )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_inputCases_H) ).
thf(1696,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( input @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = F )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ G ) ) )
=> ( ( D
= ( late_BoundR @ ( late_InputS @ F ) @ E @ G ) )
=> ( E = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(305,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_freeRes,D: late_freeRes > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_660367079reeRes @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_1641682979reeRes @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_residual_Orecs_I2_J) ).
thf(1975,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_freeRes,D: late_freeRes > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_660367079reeRes @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_1641682979reeRes @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(235,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_inputFreeTrans) ).
thf(1651,plain,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(310,axiom,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( par @ A @ ( bang @ A ) ) @ B )
=> ( late_transitions @ ( bang @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Bang) ).
thf(2011,plain,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( par @ A @ ( bang @ A ) ) @ B )
=> ( late_transitions @ ( bang @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(129,axiom,
! [A: pi,B: pi] :
( ( supp_pi_name @ ( sum @ A @ B ) )
= ( sup_sup_set_name @ ( supp_pi_name @ A ) @ ( supp_pi_name @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_pi_Osupp_I7_J) ).
thf(920,plain,
! [A: pi,B: pi] :
( ( supp_pi_name @ ( sum @ A @ B ) )
= ( sup_sup_set_name @ ( supp_pi_name @ A ) @ ( supp_pi_name @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(80,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_subject,D: late_subject > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_795910143ubject @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_717452603ubject @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_residual_Orecs_I1_J) ).
thf(678,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_subject,D: late_subject > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_795910143ubject @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_717452603ubject @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(77,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_subject,D: late_freeRes > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_660367079reeRes @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_1641682979reeRes @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_residual_Orecs_I1_J) ).
thf(661,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_subject,D: late_freeRes > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_660367079reeRes @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_1641682979reeRes @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(97,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(761,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(111,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( mismatch @ A @ B @ C )
= ( mismatch @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_pi_Oinject_I5_J) ).
thf(810,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( mismatch @ A @ B @ C )
= ( mismatch @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(21,axiom,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_pi_Odistinct_I11_J) ).
thf(381,plain,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(323,axiom,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_residual_Ostrong__inducts) ).
thf(2047,plain,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(16,axiom,
! [A: name > noption_pi] :
( ( finite_finite_name @ ( supp_n468628396i_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_543891186ion_pi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_exists__fresh) ).
thf(366,plain,
! [A: name > noption_pi] :
( ( finite_finite_name @ ( supp_n468628396i_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_543891186ion_pi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(165,axiom,
! [A: name > noption_pi,B: name > name > pi > ( name > noption_pi ) > name > noption_pi,C: pi > ( name > noption_pi ) > name > noption_pi,D: name > name > pi > ( name > noption_pi ) > name > noption_pi,E: name > name > pi > ( name > noption_pi ) > name > noption_pi,F: name > name > pi > ( name > noption_pi ) > name > noption_pi,G: pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi,H: pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi,I: name > pi > ( name > noption_pi ) > name > noption_pi,J: pi > ( name > noption_pi ) > name > noption_pi,K: pi,L: name > noption_pi] :
( ( finite_finite_name @ ( supp_n468628396i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p1320058820i_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1592910632i_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1592910632i_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n52582513i_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p1320058820i_name @ J ) )
=> ( ( pi_rec802206470ion_pi @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_n468628396i_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_pi_Orec__fin__supp) ).
thf(1074,plain,
! [A: name > noption_pi,B: name > name > pi > ( name > noption_pi ) > name > noption_pi,C: pi > ( name > noption_pi ) > name > noption_pi,D: name > name > pi > ( name > noption_pi ) > name > noption_pi,E: name > name > pi > ( name > noption_pi ) > name > noption_pi,F: name > name > pi > ( name > noption_pi ) > name > noption_pi,G: pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi,H: pi > pi > ( name > noption_pi ) > ( name > noption_pi ) > name > noption_pi,I: name > pi > ( name > noption_pi ) > name > noption_pi,J: pi > ( name > noption_pi ) > name > noption_pi,K: pi,L: name > noption_pi] :
( ( finite_finite_name @ ( supp_n468628396i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p1320058820i_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n1987783534i_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1592910632i_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1592910632i_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n52582513i_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p1320058820i_name @ J ) )
=> ( ( pi_rec802206470ion_pi @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_n468628396i_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(221,axiom,
! [A: pi,B: name,C: name] :
( ( subs @ ( tau @ A ) @ B @ C )
= ( tau @ ( subs @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_simps_I2_J) ).
thf(1604,plain,
! [A: pi,B: name,C: name] :
( ( subs @ ( tau @ A ) @ B @ C )
= ( tau @ ( subs @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(136,axiom,
( fresh_1641682979reeRes
= ( ^ [A: name,B: late_freeRes] :
~ ( member_name @ A @ ( supp_L1228270395s_name @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_fresh__def) ).
thf(942,plain,
( fresh_1641682979reeRes
= ( ^ [A: name,B: late_freeRes] :
~ ( member_name @ A @ ( supp_L1228270395s_name @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(34,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: name,D: late_freeRes > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_660367079reeRes @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_name_name @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_1641682979reeRes @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ F )
& ! [G: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_residual_Orec__unique) ).
thf(439,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: name,D: late_freeRes > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_660367079reeRes @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_name_name @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_1641682979reeRes @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ F )
& ! [G: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(262,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_sumCases_H) ).
thf(1768,plain,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(87,axiom,
( fresh_name_pi
= ( ^ [A: name,B: pi] :
~ ( member_name @ A @ ( supp_pi_name @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_fresh__def) ).
thf(714,plain,
( fresh_name_pi
= ( ^ [A: name,B: pi] :
~ ( member_name @ A @ ( supp_pi_name @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(250,axiom,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_BoundR @ ( late_InputS @ E ) @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_resOutputInputTrans) ).
thf(1730,plain,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_BoundR @ ( late_InputS @ E ) @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(160,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_pi_Odistinct_I81_J) ).
thf(1057,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(248,axiom,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( par @ A @ B ) @ C @ D )
= ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_simps_I8_J) ).
thf(1723,plain,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( par @ A @ B ) @ C @ D )
= ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(171,axiom,
! [A: name,B: name,C: pi,D: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_outputTauTrans) ).
thf(1091,plain,
! [A: name,B: name,C: pi,D: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(194,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( par @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_pi_Ofresh_I8_J) ).
thf(1355,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( par @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(240,axiom,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_residual_Ostrong__induct) ).
thf(1676,plain,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(64,axiom,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_name__exists__fresh) ).
thf(598,plain,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(237,axiom,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_subst__identity) ).
thf(1666,plain,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(70,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_pi_Odistinct_I25_J) ).
thf(630,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(128,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_pi_Odistinct_I51_J) ).
thf(916,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(154,axiom,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_name__exists__fresh) ).
thf(1032,plain,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(14,axiom,
( supp_n468628396i_name
= ( ^ [A: name > noption_pi] :
( collect_name
@ ^ [B: name] :
~ ( fresh_543891186ion_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_supp__fresh__iff) ).
thf(361,plain,
( supp_n468628396i_name
= ( ^ [A: name > noption_pi] :
( collect_name
@ ^ [B: name] :
~ ( fresh_543891186ion_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(292,axiom,
! [A: late_residual > $o,B: late_residual] :
( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_residual_Oinducts) ).
thf(1920,plain,
! [A: late_residual > $o,B: late_residual] :
( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1,conjecture,
late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(329,plain,
~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(227,axiom,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ~ ( fresh_717452603ubject @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_inputIneqTrans) ).
thf(1624,plain,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ~ ( fresh_717452603ubject @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(167,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_subject_Ofresh_I2_J) ).
thf(1079,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(203,axiom,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_fresh__fact2) ).
thf(1392,plain,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(86,axiom,
! [A: pi,B: pi,C: pi] :
( ( sum @ A @ B )
!= ( bang @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_pi_Odistinct_I83_J) ).
thf(710,plain,
! [A: pi,B: pi,C: pi] :
( ( sum @ A @ B )
!= ( bang @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(35,axiom,
! [A: name,B: pi] :
( ( supp_pi_name @ ( res @ A @ B ) )
= ( supp_n468628396i_name @ ( abs_fun_name_pi @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_pi_Osupp_I9_J) ).
thf(456,plain,
! [A: name,B: pi] :
( ( supp_pi_name @ ( res @ A @ B ) )
= ( supp_n468628396i_name @ ( abs_fun_name_pi @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(254,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Late__Semantics_OComm2) ).
thf(1740,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(289,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_resTrans_I2_J) ).
thf(1910,plain,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(207,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Late__Semantics_OPar1B) ).
thf(1402,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(57,axiom,
( supp_L1174290467t_name
= ( ^ [A: late_subject] :
( collect_name
@ ^ [B: name] :
~ ( fresh_717452603ubject @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_supp__fresh__iff) ).
thf(578,plain,
( supp_L1174290467t_name
= ( ^ [A: late_subject] :
( collect_name
@ ^ [B: name] :
~ ( fresh_717452603ubject @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(239,axiom,
! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_BoundR @ A @ B @ C )
!= ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_residual_Odistinct_I1_J) ).
thf(1672,plain,
! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_BoundR @ A @ B @ C )
!= ( late_FreeR @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(247,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ~ ( ( fresh_1641682979reeRes @ A @ D )
| ( fresh_1641682979reeRes @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_outputFreshTrans) ).
thf(1719,plain,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ~ ( ( fresh_1641682979reeRes @ A @ D )
| ( fresh_1641682979reeRes @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(205,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_pi_Odistinct_I55_J) ).
thf(1397,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(23,axiom,
! [A: pi] : ( late_bangPred @ A @ ( bang @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_aux1) ).
thf(388,plain,
! [A: pi] : ( late_bangPred @ A @ ( bang @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(280,axiom,
! [A: pi,B: name,C: name] :
( ( subs @ ( bang @ A ) @ B @ C )
= ( bang @ ( subs @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_simps_I10_J) ).
thf(1878,plain,
! [A: pi,B: name,C: name] :
( ( subs @ ( bang @ A ) @ B @ C )
= ( bang @ ( subs @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(196,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Sum2) ).
thf(1361,plain,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(6,axiom,
! [A: name,B: late_subject,C: late_subject] :
( ( ( abs_fu1904601852ubject @ A @ B )
= ( abs_fu1904601852ubject @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_abs__fun__eq1) ).
thf(339,plain,
! [A: name,B: late_subject,C: late_subject] :
( ( ( abs_fu1904601852ubject @ A @ B )
= ( abs_fu1904601852ubject @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(253,axiom,
late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Free_Ohyps) ).
thf(1739,plain,
late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(126,axiom,
! [A: late_freeRes,B: name > name > pi > late_freeRes > late_freeRes,C: pi > late_freeRes > late_freeRes,D: name > name > pi > late_freeRes > late_freeRes,E: name > name > pi > late_freeRes > late_freeRes,F: name > name > pi > late_freeRes > late_freeRes,G: pi > pi > late_freeRes > late_freeRes > late_freeRes,H: pi > pi > late_freeRes > late_freeRes > late_freeRes,I: name > pi > late_freeRes > late_freeRes,J: pi > late_freeRes > late_freeRes,K: pi,L: late_freeRes] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p71246050s_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1358344533s_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1358344533s_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n1410452111s_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p71246050s_name @ J ) )
=> ( ( pi_rec1156860983reeRes @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_L1228270395s_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_pi_Orec__fin__supp) ).
thf(901,plain,
! [A: late_freeRes,B: name > name > pi > late_freeRes > late_freeRes,C: pi > late_freeRes > late_freeRes,D: name > name > pi > late_freeRes > late_freeRes,E: name > name > pi > late_freeRes > late_freeRes,F: name > name > pi > late_freeRes > late_freeRes,G: pi > pi > late_freeRes > late_freeRes > late_freeRes,H: pi > pi > late_freeRes > late_freeRes > late_freeRes,I: name > pi > late_freeRes > late_freeRes,J: pi > late_freeRes > late_freeRes,K: pi,L: late_freeRes] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p71246050s_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n337505932s_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1358344533s_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1358344533s_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n1410452111s_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p71246050s_name @ J ) )
=> ( ( pi_rec1156860983reeRes @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_L1228270395s_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(210,axiom,
( subs
= ( ^ [A: pi,B: name,C: name] :
( pi_rec_pi @ piNil
@ ^ [D: name,E: name,F: pi] : ( output @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
@ ^ [D: pi] : tau
@ ^ [D: name,E: name,F: pi] : ( input @ ( subst_name @ D @ B @ C ) @ E )
@ ^ [D: name,E: name,F: pi] : ( match @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
@ ^ [D: name,E: name,F: pi] : ( mismatch @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
@ ^ [D: pi,E: pi] : sum
@ ^ [D: pi,E: pi] : par
@ ^ [D: name,E: pi] : ( res @ D )
@ ^ [D: pi] : bang
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subs__def) ).
thf(1414,plain,
( subs
= ( ^ [A: pi,B: name,C: name] :
( pi_rec_pi @ piNil
@ ^ [D: name,E: name,F: pi] : ( output @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
@ ^ [D: pi] : tau
@ ^ [D: name,E: name,F: pi] : ( input @ ( subst_name @ D @ B @ C ) @ E )
@ ^ [D: name,E: name,F: pi] : ( match @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
@ ^ [D: name,E: name,F: pi] : ( mismatch @ ( subst_name @ D @ B @ C ) @ ( subst_name @ E @ B @ C ) )
@ ^ [D: pi,E: pi] : sum
@ ^ [D: pi,E: pi] : par
@ ^ [D: name,E: pi] : ( res @ D )
@ ^ [D: pi] : bang
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(72,axiom,
! [A: name] : ( finite_finite_name @ ( supp_name_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_fs__name1) ).
thf(637,plain,
! [A: name] : ( finite_finite_name @ ( supp_name_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(175,axiom,
( late_bangPred
= ( ^ [A: pi,B: pi] :
( ? [C: pi] :
( ( A = C )
& ( B
= ( bang @ C ) ) )
| ? [C: pi] :
( ( A = C )
& ( B
= ( par @ C @ ( bang @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_bangPred_Osimps) ).
thf(1155,plain,
( late_bangPred
= ( ^ [A: pi,B: pi] :
( ? [C: pi] :
( ( A = C )
& ( B
= ( bang @ C ) ) )
| ? [C: pi] :
( ( A = C )
& ( B
= ( par @ C @ ( bang @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(85,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(706,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(153,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( match @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_pi_Odistinct_I37_J) ).
thf(1028,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( match @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(168,axiom,
( fresh_name_name
= ( ^ [A: name,B: name] :
~ ( member_name @ A @ ( supp_name_name @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_fresh__def) ).
thf(1082,plain,
( fresh_name_name
= ( ^ [A: name,B: name] :
~ ( member_name @ A @ ( supp_name_name @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(157,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: name,D: late_freeRes > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_660367079reeRes @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_name_name @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_1641682979reeRes @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_residual_Orecs_I1_J) ).
thf(1039,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: name,D: late_freeRes > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_660367079reeRes @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_name_name @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_1641682979reeRes @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(142,axiom,
! [A: name] :
( ( supp_L1174290467t_name @ ( late_BoundOutputS @ A ) )
= ( supp_name_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_subject_Osupp_I2_J) ).
thf(970,plain,
! [A: name] :
( ( supp_L1174290467t_name @ ( late_BoundOutputS @ A ) )
= ( supp_name_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(174,axiom,
! [A: name,B: pi,C: late_residual] :
( ( late_transitions @ ( res @ A @ B ) @ C )
=> ( ! [D: pi,E: name,F: name] :
( ( ( res @ A @ B )
= ( res @ F @ D ) )
=> ! [G: pi] :
( ( C
= ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
=> ( E = F ) ) ) )
=> ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ D ) )
=> ( ( C
= ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_717452603ubject @ H @ E )
=> ( ( H != F )
=> ( ( fresh_name_pi @ F @ D )
=> ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
=> ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
( ( ( res @ A @ B )
= ( res @ G @ D ) )
=> ( ( C
= ( late_FreeR @ E @ ( res @ G @ F ) ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
=> ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_resCases_H) ).
thf(1099,plain,
! [A: name,B: pi,C: late_residual] :
( ( late_transitions @ ( res @ A @ B ) @ C )
=> ( ! [D: pi,E: name,F: name] :
( ( ( res @ A @ B )
= ( res @ F @ D ) )
=> ! [G: pi] :
( ( C
= ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
=> ( E = F ) ) ) )
=> ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ D ) )
=> ( ( C
= ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_717452603ubject @ H @ E )
=> ( ( H != F )
=> ( ( fresh_name_pi @ F @ D )
=> ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
=> ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
( ( ( res @ A @ B )
= ( res @ G @ D ) )
=> ( ( C
= ( late_FreeR @ E @ ( res @ G @ F ) ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
=> ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(189,axiom,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( match @ A @ B @ C ) @ D @ E )
= ( match @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_simps_I5_J) ).
thf(1266,plain,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( match @ A @ B @ C ) @ D @ E )
= ( match @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(270,axiom,
! [A: name,B: name,C: name,D: name,E: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( A != D )
=> ( ( subs @ ( input @ B @ A @ E ) @ C @ D )
= ( input @ ( subst_name @ B @ C @ D ) @ A @ ( subs @ E @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_simps_I4_J) ).
thf(1799,plain,
! [A: name,B: name,C: name,D: name,E: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( A != D )
=> ( ( subs @ ( input @ B @ A @ E ) @ C @ D )
= ( input @ ( subst_name @ B @ C @ D ) @ A @ ( subs @ E @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(278,axiom,
late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ a @ b ) @ p2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_cComm2_Ohyps_I1_J) ).
thf(1874,plain,
late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ a @ b ) @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(324,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Sum1) ).
thf(2052,plain,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(102,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( match @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_pi_Ofresh_I5_J) ).
thf(779,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( match @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(228,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Late__Semantics_OInput) ).
thf(1627,plain,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(264,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ A @ C ) ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_resOutputOutputTrans) ).
thf(1776,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ A @ C ) ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(188,axiom,
! [A: name,B: name,C: name,D: pi,E: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_FreeR @ late_TauR @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_resOutputTauTrans) ).
thf(1263,plain,
! [A: name,B: name,C: name,D: pi,E: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_FreeR @ late_TauR @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(148,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_subject,D: pi > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_1438126218_pi_pi @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_pi @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ F )
& ! [G: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_residual_Orec__unique) ).
thf(997,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_subject,D: pi > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_1438126218_pi_pi @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_pi @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ F )
& ! [G: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(275,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_inputBoundOutputTrans) ).
thf(1857,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(106,axiom,
! [A: set_name,B: name,C: name] :
( ( supports_name_name @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_name_name @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_supports__fresh) ).
thf(792,plain,
! [A: set_name,B: name,C: name] :
( ( supports_name_name @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_name_name @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(183,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_transitions_OPar2B) ).
thf(1241,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(265,axiom,
! [A: pi,B: late_subject,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_tauBoundTrans) ).
thf(1779,plain,
! [A: pi,B: late_subject,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(51,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Late__Semantics_OfreeRes_Oinject) ).
thf(541,plain,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(159,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_residual,D: name] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( late_r1742481968t_name @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_name_name @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_residual_Orec__fin__supp) ).
thf(1054,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_residual,D: name] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( late_r1742481968t_name @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_name_name @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(155,axiom,
( fresh_name_name
= ( != @ name ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_name__fresh) ).
thf(1035,plain,
( fresh_name_name
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(164,axiom,
! [A: late_subject,B: name,C: pi] :
( ( supp_L1174042202l_name @ ( late_BoundR @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_L1174290467t_name @ A ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_residual_Osupp_I1_J) ).
thf(1071,plain,
! [A: late_subject,B: name,C: pi] :
( ( supp_L1174042202l_name @ ( late_BoundR @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_L1174290467t_name @ A ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(322,axiom,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_pi_Ostrong__inducts) ).
thf(2043,plain,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(45,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( output @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_pi_Ofresh_I2_J) ).
thf(508,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( output @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(288,axiom,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_pi_Ostrong__inducts) ).
thf(1906,plain,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(30,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_residual,D: late_subject,E: name] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( late_r689718217ubject @ A @ B @ C @ D )
=> ( ! [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( fresh_717452603ubject @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_residual_Orec__fresh) ).
thf(425,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_residual,D: late_subject,E: name] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( late_r689718217ubject @ A @ B @ C @ D )
=> ( ! [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( fresh_717452603ubject @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(31,axiom,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( bang @ B ) )
= ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_pi_Ofresh_I10_J) ).
thf(430,plain,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( bang @ B ) )
= ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(295,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_subject,D: name > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_621211324i_name @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_name @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_residual_Orecs_I2_J) ).
thf(1927,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_subject,D: name > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_621211324i_name @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_name @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(121,axiom,
! [A: set_name,B: late_freeRes,C: name] :
( ( suppor1556658829reeRes @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_1641682979reeRes @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_supports__fresh) ).
thf(856,plain,
! [A: set_name,B: late_freeRes,C: name] :
( ( suppor1556658829reeRes @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_1641682979reeRes @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(316,axiom,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_resInputBoundOutputTrans) ).
thf(2028,plain,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(199,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_nilCases_H) ).
thf(1374,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(19,axiom,
! [A: name,B: late_freeRes,C: late_freeRes] :
( ( ( abs_fu681348580reeRes @ A @ B )
= ( abs_fu681348580reeRes @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_abs__fun__eq1) ).
thf(375,plain,
! [A: name,B: late_freeRes,C: late_freeRes] :
( ( ( abs_fu681348580reeRes @ A @ B )
= ( abs_fu681348580reeRes @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(65,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_subject,D: late_subject > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_795910143ubject @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_717452603ubject @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ F )
& ! [G: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_residual_Orec__unique) ).
thf(601,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_subject,D: late_subject > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_795910143ubject @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_717452603ubject @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ F )
& ! [G: late_subject] :
( ( late_r689718217ubject @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(66,axiom,
! [A: late_subject] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ? [B: name] : ( fresh_717452603ubject @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_exists__fresh_H) ).
thf(618,plain,
! [A: late_subject] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ? [B: name] : ( fresh_717452603ubject @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(261,axiom,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( bang @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( bang @ A )
= ( bang @ C ) )
=> ~ ( late_transitions @ ( par @ C @ ( bang @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_bangCases) ).
thf(1764,plain,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( bang @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( bang @ A )
= ( bang @ C ) )
=> ~ ( late_transitions @ ( par @ C @ ( bang @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(114,axiom,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( mismatch @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( sup_sup_set_name @ ( supp_name_name @ B ) @ ( supp_pi_name @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_pi_Osupp_I6_J) ).
thf(819,plain,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( mismatch @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( sup_sup_set_name @ ( supp_name_name @ B ) @ ( supp_pi_name @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(82,axiom,
! [A: name,B: pi,C: pi] :
( ( res @ A @ B )
!= ( bang @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_pi_Odistinct_I89_J) ).
thf(694,plain,
! [A: name,B: pi,C: pi] :
( ( res @ A @ B )
!= ( bang @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(312,axiom,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( output @ A @ B @ C ) @ D @ E )
= ( output @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_simps_I3_J) ).
thf(2016,plain,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( output @ A @ B @ C ) @ D @ E )
= ( output @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(116,axiom,
! [A: name,B: name > name > pi > name > name,C: pi > name > name,D: name > name > pi > name > name,E: name > name > pi > name > name,F: name > name > pi > name > name,G: pi > pi > name > name > name,H: pi > pi > name > name > name,I: name > pi > name > name,J: pi > name > name,K: pi,L: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p1239856366e_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1618090470e_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1618090470e_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n116460699e_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p1239856366e_name @ J ) )
=> ( ( pi_rec_set_name @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_name_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_pi_Orec__fin__supp) ).
thf(826,plain,
! [A: name,B: name > name > pi > name > name,C: pi > name > name,D: name > name > pi > name > name,E: name > name > pi > name > name,F: name > name > pi > name > name,G: pi > pi > name > name > name,H: pi > pi > name > name > name,I: name > pi > name > name,J: pi > name > name,K: pi,L: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p1239856366e_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n612431512e_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1618090470e_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1618090470e_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n116460699e_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p1239856366e_name @ J ) )
=> ( ( pi_rec_set_name @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_name_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(269,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_pi_Odistinct_I85_J) ).
thf(1795,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(127,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_freeRes,D: late_freeRes > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_660367079reeRes @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_1641682979reeRes @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_residual_Orecs_I1_J) ).
thf(904,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_freeRes,D: late_freeRes > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_660367079reeRes @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_1641682979reeRes @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(144,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( input @ A @ B @ C )
= ( input @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_pi_Oinject_I3_J) ).
thf(975,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( input @ A @ B @ C )
= ( input @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(93,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_pi_Odistinct_I19_J) ).
thf(732,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(282,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) )
=> ~ ( ( A != D )
| ( B != E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_outputIneqTrans) ).
thf(1884,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) )
=> ~ ( ( A != D )
| ( B != E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(224,axiom,
! [A: pi,B: pi] :
( ( late_bangPred @ A @ B )
=> ( ( B
!= ( bang @ A ) )
=> ( B
= ( par @ A @ ( bang @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_bangPred_Ocases) ).
thf(1615,plain,
! [A: pi,B: pi] :
( ( late_bangPred @ A @ B )
=> ( ( B
!= ( bang @ A ) )
=> ( B
= ( par @ A @ ( bang @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(267,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( res @ C @ B ) @ C @ A )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_substRes3) ).
thf(1784,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( res @ C @ B ) @ C @ A )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(202,axiom,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( sum @ A @ B ) @ C @ D )
= ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_simps_I7_J) ).
thf(1389,plain,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( sum @ A @ B ) @ C @ D )
= ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(238,axiom,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_residual_Oinject_I2_J) ).
thf(1669,plain,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(134,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_pi_Odistinct_I27_J) ).
thf(936,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(246,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_freeRes,D: pi > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_1438126218_pi_pi @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_pi @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_residual_Orecs_I2_J) ).
thf(1707,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_freeRes,D: pi > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_1438126218_pi_pi @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_pi @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(192,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( fresh_717452603ubject @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_freshBoundDerivative_I1_J) ).
thf(1312,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( fresh_717452603ubject @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(277,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( output @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = E )
& ( B = F )
& ( C = G ) )
=> ( D
!= ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_outputCases_H) ).
thf(1865,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( output @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = E )
& ( B = F )
& ( C = G ) )
=> ( D
!= ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(251,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_freeRes_Ofresh_I2_J) ).
thf(1733,plain,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(325,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_transitions_OPar1B) ).
thf(2055,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(138,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_pi_Ofresh_I6_J) ).
thf(947,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(10,axiom,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_abs__fresh_I1_J) ).
thf(350,plain,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(74,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(641,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(212,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_subject,D: late_subject > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_795910143ubject @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_717452603ubject @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_residual_Orecs_I2_J) ).
thf(1428,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_subject,D: late_subject > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_795910143ubject @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_717452603ubject @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(98,axiom,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_pi_Oinject_I2_J) ).
thf(764,plain,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(284,axiom,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Tau) ).
thf(1894,plain,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(94,axiom,
! [A: pi] :
( piNil
!= ( bang @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_pi_Odistinct_I17_J) ).
thf(736,plain,
! [A: pi] :
( piNil
!= ( bang @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(123,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_freeRes,D: pi > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_1438126218_pi_pi @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_pi @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ F )
& ! [G: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_residual_Orec__unique) ).
thf(863,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_freeRes,D: pi > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_1438126218_pi_pi @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_pi @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ F )
& ! [G: pi] :
( ( late_r1261898622set_pi @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(124,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_subject,D: late_freeRes > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_660367079reeRes @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_1641682979reeRes @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ F )
& ! [G: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_residual_Orec__unique) ).
thf(880,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_subject,D: late_freeRes > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_660367079reeRes @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_1641682979reeRes @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ F )
& ! [G: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(76,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_subject,D: name > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_621211324i_name @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_name @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_621211324i_name @ E @ A )
=> ( ( fresh_1030632537i_name @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_residual_Orecs_I1_J) ).
thf(649,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_subject,D: name > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_621211324i_name @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_717452603ubject @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_name @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_621211324i_name @ E @ A )
=> ( ( fresh_1030632537i_name @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(315,axiom,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_simps_I1_J) ).
thf(2025,plain,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(49,axiom,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_name__fresh__abs) ).
thf(535,plain,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(113,axiom,
! [A: name,B: pi,C: name,D: pi] :
( ( ( res @ A @ B )
= ( res @ C @ D ) )
= ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_pi_Oinject_I8_J) ).
thf(816,plain,
! [A: name,B: pi,C: name,D: pi] :
( ( ( res @ A @ B )
= ( res @ C @ D ) )
= ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(63,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_pi_Odistinct_I1_J) ).
thf(594,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(108,axiom,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_pi_Ofresh_I3_J) ).
thf(799,plain,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(151,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_pi_Ofresh_I7_J) ).
thf(1022,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(3,axiom,
! [A: name > $o,B: name > $o] :
( ! [C: name] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_name @ A )
= ( collect_name @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Collect__cong) ).
thf(330,plain,
! [A: name > $o,B: name > $o] :
( ! [C: name] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_name @ A )
= ( collect_name @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_abs__fresh_I1_J) ).
thf(345,plain,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(218,axiom,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_pi_Ostrong__induct) ).
thf(1557,plain,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(37,axiom,
! [A: pi] :
( ( supp_pi_name @ ( bang @ A ) )
= ( supp_pi_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_pi_Osupp_I10_J) ).
thf(462,plain,
! [A: pi] :
( ( supp_pi_name @ ( bang @ A ) )
= ( supp_pi_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(133,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_pi_Odistinct_I53_J) ).
thf(932,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(161,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( match @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_pi_Odistinct_I67_J) ).
thf(1061,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( match @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(300,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_pi_Odistinct_I79_J) ).
thf(1952,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(204,axiom,
fresh_name_pi @ x @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_cComm2_Ohyps_I3_J) ).
thf(1396,plain,
fresh_name_pi @ x @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(233,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( ( E != C )
=> ( fresh_name_pi @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_freshBoundDerivative_I2_J) ).
thf(1643,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( ( E != C )
=> ( fresh_name_pi @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(181,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: name,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ F ) )
=> ! [I: pi] :
( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
=> ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
=> ( G = H ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
( ( ( res @ A @ B )
= ( res @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_717452603ubject @ J @ G )
=> ( ( J != H )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_resCasesB_H) ).
thf(1176,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: name,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ F ) )
=> ! [I: pi] :
( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
=> ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
=> ( G = H ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
( ( ( res @ A @ B )
= ( res @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_717452603ubject @ J @ G )
=> ( ( J != H )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(25,axiom,
! [A: set_name,B: pi,C: name] :
( ( supports_name_pi @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_name_pi @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_supports__fresh) ).
thf(394,plain,
! [A: set_name,B: pi,C: name] :
( ( supports_name_pi @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_name_pi @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(119,axiom,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( match @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( sup_sup_set_name @ ( supp_name_name @ B ) @ ( supp_pi_name @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_pi_Osupp_I5_J) ).
thf(851,plain,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( match @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( sup_sup_set_name @ ( supp_name_name @ B ) @ ( supp_pi_name @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(44,axiom,
! [A: pi,B: name > name > pi > pi > pi,C: pi > pi > pi,D: name > name > pi > pi > pi,E: name > name > pi > pi > pi,F: name > name > pi > pi > pi,G: pi > pi > pi > pi > pi,H: pi > pi > pi > pi > pi,I: name > pi > pi > pi,J: pi > pi > pi,K: pi,L: pi] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_pi_pi_pi_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p812767768i_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p812767768i_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n96533147i_name @ I ) )
=> ( ( finite_finite_name @ ( supp_pi_pi_pi_name @ J ) )
=> ( ( pi_rec_set_pi @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_pi_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_pi_Orec__fin__supp) ).
thf(505,plain,
! [A: pi,B: name > name > pi > pi > pi,C: pi > pi > pi,D: name > name > pi > pi > pi,E: name > name > pi > pi > pi,F: name > name > pi > pi > pi,G: pi > pi > pi > pi > pi,H: pi > pi > pi > pi > pi,I: name > pi > pi > pi,J: pi > pi > pi,K: pi,L: pi] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_pi_pi_pi_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n1977765016i_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p812767768i_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p812767768i_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n96533147i_name @ I ) )
=> ( ( finite_finite_name @ ( supp_pi_pi_pi_name @ J ) )
=> ( ( pi_rec_set_pi @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_pi_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(249,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( C != B )
=> ( ( C != F )
=> ( ( fresh_name_pi @ C @ G )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_transitions_OComm1) ).
thf(1726,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( C != B )
=> ( ( C != F )
=> ( ( fresh_name_pi @ C @ G )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(197,axiom,
! [A: pi,B: pi,C: pi] :
( ( par @ A @ B )
!= ( bang @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_pi_Odistinct_I87_J) ).
thf(1364,plain,
! [A: pi,B: pi,C: pi] :
( ( par @ A @ B )
!= ( bang @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(186,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_freeRes,D: name > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_621211324i_name @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_name @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_residual_Orecs_I2_J) ).
thf(1250,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_freeRes,D: name > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_621211324i_name @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_name @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(299,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_transitions_OResB) ).
thf(1948,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(107,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( mismatch @ A @ B @ C )
!= ( bang @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_pi_Odistinct_I77_J) ).
thf(795,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( mismatch @ A @ B @ C )
!= ( bang @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(41,axiom,
! [A: late_subject] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_exists__fresh) ).
thf(487,plain,
! [A: late_subject] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(307,axiom,
! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ( ! [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( E @ ( res @ A @ F ) ) ) )
=> ( E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_resCasesF) ).
thf(1990,plain,
! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ( ! [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( E @ ( res @ A @ F ) ) ) )
=> ( E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(7,axiom,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_name__fresh__abs) ).
thf(342,plain,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: name,D: late_subject > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_795910143ubject @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_name_name @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_717452603ubject @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_residual_Orecs_I1_J) ).
thf(490,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: name,D: late_subject > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_795910143ubject @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_name_name @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_717452603ubject @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(79,axiom,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_name__exists__fresh) ).
thf(675,plain,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(48,axiom,
! [A: pi,B: name,C: name] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ C @ A ) )
= ( ( B = C )
| ( fresh_name_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_abs__fresh_I2_J) ).
thf(531,plain,
! [A: pi,B: name,C: name] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ C @ A ) )
= ( ( B = C )
| ( fresh_name_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(137,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_subject_Ofresh_I1_J) ).
thf(944,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(131,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_residual,D: late_subject] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( late_r689718217ubject @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_L1174290467t_name @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_residual_Orec__fin__supp) ).
thf(927,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_residual,D: late_subject] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( late_r689718217ubject @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_L1174290467t_name @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(320,axiom,
x != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cComm2_Ohyps_I6_J) ).
thf(2037,plain,
x != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(302,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_resTauBoundTrans) ).
thf(1958,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(12,axiom,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_abs__fresh_I1_J) ).
thf(355,plain,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(216,axiom,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A != B )
=> ( E @ A @ B ) ) )
=> ( E @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_mismatchCases) ).
thf(1547,plain,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A != B )
=> ( E @ A @ B ) ) )
=> ( E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(263,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ~ ! [E: pi] :
( ( ( B = A )
& ( C = E ) )
=> ~ ( late_transitions @ E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_matchCases_H) ).
thf(1770,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ~ ! [E: pi] :
( ( ( B = A )
& ( C = E ) )
=> ~ ( late_transitions @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(58,axiom,
! [A: late_freeRes] : ( finite_finite_name @ ( supp_L1228270395s_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_fs__name1) ).
thf(580,plain,
! [A: late_freeRes] : ( finite_finite_name @ ( supp_L1228270395s_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(81,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( match @ A @ B @ C )
!= ( bang @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_pi_Odistinct_I69_J) ).
thf(690,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( match @ A @ B @ C )
!= ( bang @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(303,axiom,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_residual_Ostrong__induct) ).
thf(1961,plain,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(152,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_pi_Ofresh_I4_J) ).
thf(1025,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(223,axiom,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_transitions_OInput) ).
thf(1611,plain,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(255,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_resTrans_I1_J) ).
thf(1743,plain,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(234,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_matchTrans) ).
thf(1647,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(140,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_freeRes,D: name > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_621211324i_name @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_name @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_621211324i_name @ E @ A )
=> ( ( fresh_1030632537i_name @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_residual_Orecs_I1_J) ).
thf(954,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_freeRes,D: name > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_621211324i_name @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_name @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_621211324i_name @ E @ A )
=> ( ( fresh_1030632537i_name @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1174711868c_name @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(198,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( ( fresh_name_pi @ D @ B )
=> ( ! [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ G @ B ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ A @ G ) ) )
=> ( F @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_parCasesB) ).
thf(1368,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( ( fresh_name_pi @ D @ B )
=> ( ! [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ G @ B ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ A @ G ) ) )
=> ( F @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(258,axiom,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_freeRes_Oexhaust) ).
thf(1753,plain,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(173,axiom,
late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_cComm2_Ohyps_I2_J) ).
thf(1098,plain,
late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(147,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( input @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_pi_Odistinct_I57_J) ).
thf(993,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( input @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(78,axiom,
! [A: pi] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ? [B: name] : ( fresh_name_pi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_exists__fresh_H) ).
thf(673,plain,
! [A: pi] :
( ( finite_finite_name @ ( supp_pi_name @ A ) )
=> ? [B: name] : ( fresh_name_pi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(306,axiom,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_residual_Ofresh_I2_J) ).
thf(1987,plain,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(231,axiom,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( mismatch @ A @ B @ C ) @ D @ E )
= ( mismatch @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_simps_I6_J) ).
thf(1637,plain,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( mismatch @ A @ B @ C ) @ D @ E )
= ( mismatch @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(60,axiom,
! [A: pi,B: pi] :
( ( ( bang @ A )
= ( bang @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_pi_Oinject_I9_J) ).
thf(585,plain,
! [A: pi,B: pi] :
( ( ( bang @ A )
= ( bang @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(43,axiom,
! [A: late_subject,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( ( late_BoundR @ A @ B @ C )
= ( late_BoundR @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_residual_Oinject_I1_J) ).
thf(502,plain,
! [A: late_subject,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( ( late_BoundR @ A @ B @ C )
= ( late_BoundR @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(187,axiom,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062) ).
thf(1262,plain,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( par @ p2 @ ( subs @ q2 @ x @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(40,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_subject,D: name > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_621211324i_name @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_name @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: name] :
( ( late_r1742481968t_name @ A @ B @ E @ F )
& ! [G: name] :
( ( late_r1742481968t_name @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_residual_Orec__unique) ).
thf(470,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_subject,D: name > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_621211324i_name @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_717452603ubject @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_name_name @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: name] :
( ( late_r1742481968t_name @ A @ B @ E @ F )
& ! [G: name] :
( ( late_r1742481968t_name @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_freeRes,D: late_subject > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_795910143ubject @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_717452603ubject @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_residual_Orecs_I1_J) ).
thf(544,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_freeRes,D: late_subject > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_795910143ubject @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_717452603ubject @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_795910143ubject @ E @ A )
=> ( ( fresh_198785932ubject @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(195,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Late__Semantics_OClose1) ).
thf(1358,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(96,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_freeRes,D: late_freeRes > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_660367079reeRes @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_1641682979reeRes @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ F )
& ! [G: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_residual_Orec__unique) ).
thf(744,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_freeRes,D: late_freeRes > $o,E: late_residual] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [F: late_subject,G: name,H: pi] : ( D @ ( A @ F @ G @ H ) )
=> ( ! [F: late_freeRes,G: pi] : ( D @ ( B @ F @ G ) )
=> ( ! [F: late_subject,G: name] :
( ( fresh_660367079reeRes @ G @ A )
=> ( ( fresh_717452603ubject @ G @ F )
=> ( ( fresh_1641682979reeRes @ G @ C )
=> ! [H: pi] :
( ( D @ ( A @ F @ G @ H ) )
=> ( fresh_1641682979reeRes @ G @ ( A @ F @ G @ H ) ) ) ) ) )
=> ? [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ F )
& ! [G: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ E @ G )
=> ( G = F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(5,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_name__fresh__abs) ).
thf(336,plain,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(257,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != C )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_transitions_OClose2) ).
thf(1749,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != C )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(91,axiom,
! [A: name,B: name] :
( ( supp_L1228270395s_name @ ( late_OutputR @ A @ B ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( supp_name_name @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_freeRes_Osupp_I1_J) ).
thf(727,plain,
! [A: name,B: name] :
( ( supp_L1228270395s_name @ ( late_OutputR @ A @ B ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( supp_name_name @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(122,axiom,
! [A: late_freeRes,B: name,C: name] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ C @ A ) )
= ( ( B = C )
| ( fresh_1641682979reeRes @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_abs__fresh_I2_J) ).
thf(859,plain,
! [A: late_freeRes,B: name,C: name] :
( ( finite_finite_name @ ( supp_L1228270395s_name @ A ) )
=> ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ C @ A ) )
= ( ( B = C )
| ( fresh_1641682979reeRes @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(172,axiom,
! [A: pi,B: late_residual,C: name,D: name] :
( ( late_transitions @ A @ B )
=> ( ( C != D )
=> ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Mismatch) ).
thf(1094,plain,
! [A: pi,B: late_residual,C: name,D: name] :
( ( late_transitions @ A @ B )
=> ( ( C != D )
=> ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(145,axiom,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( input @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_pi_Osupp_I4_J) ).
thf(978,plain,
! [A: name,B: name,C: pi] :
( ( supp_pi_name @ ( input @ A @ B @ C ) )
= ( sup_sup_set_name @ ( supp_name_name @ A ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(281,axiom,
! [A: late_freeRes,B: pi] :
( ( supp_L1174042202l_name @ ( late_FreeR @ A @ B ) )
= ( sup_sup_set_name @ ( supp_L1228270395s_name @ A ) @ ( supp_pi_name @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_residual_Osupp_I2_J) ).
thf(1881,plain,
! [A: late_freeRes,B: pi] :
( ( supp_L1174042202l_name @ ( late_FreeR @ A @ B ) )
= ( sup_sup_set_name @ ( supp_L1228270395s_name @ A ) @ ( supp_pi_name @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(191,axiom,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_pi_Ostrong__induct) ).
thf(1272,plain,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(69,axiom,
! [A: name,B: pi,C: pi] :
( ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_abs__fun__eq1) ).
thf(627,plain,
! [A: name,B: pi,C: pi] :
( ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(169,axiom,
! [A: late_subject > $o,B: late_subject] :
( ! [C: name] : ( A @ ( late_InputS @ C ) )
=> ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_subject_Oinducts) ).
thf(1084,plain,
! [A: late_subject > $o,B: late_subject] :
( ! [C: name] : ( A @ ( late_InputS @ C ) )
=> ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(242,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi,F: late_freeRes > pi > $o] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ( ( ( D
= ( late_OutputR @ A @ B ) )
=> ( ( C = E )
=> ( F @ ( late_OutputR @ A @ B ) @ C ) ) )
=> ( F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_outputCases) ).
thf(1685,plain,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi,F: late_freeRes > pi > $o] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ( ( ( D
= ( late_OutputR @ A @ B ) )
=> ( ( C = E )
=> ( F @ ( late_OutputR @ A @ B ) @ C ) ) )
=> ( F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(236,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: name,D: late_freeRes > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_660367079reeRes @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_name_name @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_1641682979reeRes @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_residual_Orecs_I2_J) ).
thf(1654,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: name,D: late_freeRes > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( finite_finite_name @ ( supp_name_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_660367079reeRes @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_name_name @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_1641682979reeRes @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r124702629reeRes @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(100,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_pi_Odistinct_I5_J) ).
thf(771,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(311,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( par @ A @ B )
= ( par @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_pi_Oinject_I7_J) ).
thf(2013,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( par @ A @ B )
= ( par @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(38,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Late__Semantics1_OfreeRes_Oinject) ).
thf(465,plain,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(304,axiom,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A = B )
=> ( E @ A @ A ) ) )
=> ( E @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_matchCases) ).
thf(1966,plain,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A = B )
=> ( E @ A @ A ) ) )
=> ( E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(15,axiom,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_name__fresh__abs) ).
thf(363,plain,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(53,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_freeRes,D: pi > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_1438126218_pi_pi @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_pi @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_1438126218_pi_pi @ E @ A )
=> ( ( fresh_1011532071_pi_pi @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_residual_Orecs_I1_J) ).
thf(556,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_freeRes,D: pi > $o,E: name,F: late_subject,G: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [H: late_subject,I: name,J: pi] : ( D @ ( A @ H @ I @ J ) )
=> ( ! [H: late_freeRes,I: pi] : ( D @ ( B @ H @ I ) )
=> ( ! [H: late_subject,I: name,J: pi] :
( ( fresh_1438126218_pi_pi @ I @ A )
=> ( ( fresh_717452603ubject @ I @ H )
=> ( ( fresh_1641682979reeRes @ I @ C )
=> ( ( D @ ( A @ H @ I @ J ) )
=> ( fresh_name_pi @ I @ ( A @ H @ I @ J ) ) ) ) ) )
=> ( ( fresh_1438126218_pi_pi @ E @ A )
=> ( ( fresh_1011532071_pi_pi @ E @ B )
=> ( ( fresh_717452603ubject @ E @ F )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_BoundR @ F @ E @ G ) )
= ( A @ F @ E @ G ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(176,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( F != B )
=> ( ( F != C )
=> ( ( fresh_name_pi @ F @ D )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_transitions_OComm2) ).
thf(1157,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( F != B )
=> ( ( F != C )
=> ( ( fresh_name_pi @ F @ D )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(290,axiom,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_pi_Odistinct_I13_J) ).
thf(1913,plain,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(61,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_pi_Odistinct_I35_J) ).
thf(588,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(112,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( match @ A @ B @ C )
= ( match @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_pi_Oinject_I4_J) ).
thf(813,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( match @ A @ B @ C )
= ( match @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(24,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_pi_Odistinct_I75_J) ).
thf(390,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(229,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_pi_Odistinct_I29_J) ).
thf(1629,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(184,axiom,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( ( fresh_name_pi @ C @ A )
=> ( fresh_81631222sidual @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_freshResidual) ).
thf(1244,plain,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( ( fresh_name_pi @ C @ A )
=> ( fresh_81631222sidual @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(54,axiom,
( supp_pi_name
= ( ^ [A: pi] :
( collect_name
@ ^ [B: name] :
~ ( fresh_name_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_supp__fresh__iff) ).
thf(568,plain,
( supp_pi_name
= ( ^ [A: pi] :
( collect_name
@ ^ [B: name] :
~ ( fresh_name_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(20,axiom,
! [A: late_subject,B: name > name > pi > late_subject > late_subject,C: pi > late_subject > late_subject,D: name > name > pi > late_subject > late_subject,E: name > name > pi > late_subject > late_subject,F: name > name > pi > late_subject > late_subject,G: pi > pi > late_subject > late_subject > late_subject,H: pi > pi > late_subject > late_subject > late_subject,I: name > pi > late_subject > late_subject,J: pi > late_subject > late_subject,K: pi,L: late_subject] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p742701746t_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1221108749t_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1221108749t_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n122125407t_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p742701746t_name @ J ) )
=> ( ( pi_rec232630607ubject @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_L1174290467t_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_pi_Orec__fin__supp) ).
thf(378,plain,
! [A: late_subject,B: name > name > pi > late_subject > late_subject,C: pi > late_subject > late_subject,D: name > name > pi > late_subject > late_subject,E: name > name > pi > late_subject > late_subject,F: name > name > pi > late_subject > late_subject,G: pi > pi > late_subject > late_subject > late_subject,H: pi > pi > late_subject > late_subject > late_subject,I: name > pi > late_subject > late_subject,J: pi > late_subject > late_subject,K: pi,L: late_subject] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_p742701746t_name @ C ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ D ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ E ) )
=> ( ( finite_finite_name @ ( supp_n200783964t_name @ F ) )
=> ( ( finite_finite_name @ ( supp_p1221108749t_name @ G ) )
=> ( ( finite_finite_name @ ( supp_p1221108749t_name @ H ) )
=> ( ( finite_finite_name @ ( supp_n122125407t_name @ I ) )
=> ( ( finite_finite_name @ ( supp_p742701746t_name @ J ) )
=> ( ( pi_rec232630607ubject @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L )
=> ( finite_finite_name @ ( supp_L1174290467t_name @ L ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(32,axiom,
! [A: name,B: late_subject,C: name,D: pi] :
( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_residual_Ofresh_I1_J) ).
thf(433,plain,
! [A: name,B: late_subject,C: name,D: pi] :
( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(213,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ F @ J ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ F )
=> ( ( fresh_name_pi @ H @ J )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ J )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_parCasesB_H) ).
thf(1440,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ F @ J ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ F )
=> ( ( fresh_name_pi @ H @ J )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ J )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(166,axiom,
! [A: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ? [B: name] : ( fresh_name_name @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_exists__fresh_H) ).
thf(1077,plain,
! [A: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ? [B: name] : ( fresh_name_name @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(222,axiom,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_pi_Ostrong__induct) ).
thf(1607,plain,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(319,axiom,
late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_cPar1_Ohyps) ).
thf(2036,plain,
late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(313,axiom,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_residual_Ostrong__induct) ).
thf(2019,plain,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(88,axiom,
! [A: pi] :
( ( supp_pi_name @ ( tau @ A ) )
= ( supp_pi_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_pi_Osupp_I3_J) ).
thf(716,plain,
! [A: pi] :
( ( supp_pi_name @ ( tau @ A ) )
= ( supp_pi_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(177,axiom,
! [A: name,B: name,C: name,D: name,E: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( subs @ ( input @ D @ A @ E ) @ B @ C )
= ( input @ ( subst_name @ D @ B @ C ) @ A @ ( subs @ E @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_substInput) ).
thf(1161,plain,
! [A: name,B: name,C: name,D: name,E: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( subs @ ( input @ D @ A @ E ) @ B @ C )
= ( input @ ( subst_name @ D @ B @ C ) @ A @ ( subs @ E @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(67,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_residual,D: late_freeRes] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( late_r1613948593reeRes @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_L1228270395s_name @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_residual_Orec__fin__supp) ).
thf(620,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_residual,D: late_freeRes] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( late_r1613948593reeRes @ A @ B @ C @ D )
=> ( finite_finite_name @ ( supp_L1228270395s_name @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(139,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_pi_Odistinct_I71_J) ).
thf(950,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(182,axiom,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_subject,D: pi > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_1438126218_pi_pi @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_pi @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_residual_Orecs_I2_J) ).
thf(1229,plain,
! [A: late_subject > name > pi > pi,B: late_freeRes > pi > pi,C: late_subject,D: pi > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L729745222i_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L2052723895i_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1174290467t_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_1438126218_pi_pi @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_717452603ubject @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_name_pi @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_residual_rec_pi @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(120,axiom,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_pi_Ofresh_I1_J) ).
thf(854,plain,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(259,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
= ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_substTrans) ).
thf(1757,plain,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
= ( subs @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(13,axiom,
! [A: set_name] :
( ( collect_name
@ ^ [B: name] : ( member_name @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Collect__mem__eq) ).
thf(358,plain,
! [A: set_name] :
( ( collect_name
@ ^ [B: name] : ( member_name @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( output @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_pi_Odistinct_I31_J) ).
thf(400,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( output @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(162,axiom,
! [A: name] :
( ( supp_L1174290467t_name @ ( late_InputS @ A ) )
= ( supp_name_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_subject_Osupp_I1_J) ).
thf(1065,plain,
! [A: name] :
( ( supp_L1174290467t_name @ ( late_InputS @ A ) )
= ( supp_name_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(321,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_1641682979reeRes @ D @ B )
=> ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ResF) ).
thf(2040,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_1641682979reeRes @ D @ B )
=> ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(178,axiom,
! [A: name,B: pi,C: name,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_resTauOutputTrans) ).
thf(1165,plain,
! [A: name,B: pi,C: name,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(125,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( match @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_pi_Odistinct_I7_J) ).
thf(897,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( match @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(99,axiom,
! [A: pi,B: pi] :
( ( tau @ A )
!= ( bang @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_pi_Odistinct_I47_J) ).
thf(767,plain,
! [A: pi,B: pi] :
( ( tau @ A )
!= ( bang @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(95,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_pi_Odistinct_I63_J) ).
thf(740,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(150,axiom,
! [A: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_name_name @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_exists__fresh) ).
thf(1019,plain,
! [A: name] :
( ( finite_finite_name @ ( supp_name_name @ A ) )
=> ~ ! [B: name] :
~ ( fresh_name_name @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(47,axiom,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_abs__fresh_I1_J) ).
thf(528,plain,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(75,axiom,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_residual,D: late_freeRes,E: name] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( late_r1613948593reeRes @ A @ B @ C @ D )
=> ( ! [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( fresh_1641682979reeRes @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_residual_Orec__fresh) ).
thf(644,plain,
! [A: late_subject > name > pi > late_freeRes,B: late_freeRes > pi > late_freeRes,C: late_residual,D: late_freeRes,E: name] :
( ( finite_finite_name @ ( supp_L1178477943s_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L381160156s_name @ B ) )
=> ( ( late_r1613948593reeRes @ A @ B @ C @ D )
=> ( ! [F: late_freeRes] :
( ( late_r1613948593reeRes @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_660367079reeRes @ E @ A )
=> ( ( fresh_256112244reeRes @ E @ B )
=> ( fresh_1641682979reeRes @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(36,axiom,
! [A: name,B: name,C: name] :
( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_freeRes_Ofresh_I1_J) ).
thf(459,plain,
! [A: name,B: name,C: name] :
( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(115,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_pi_Odistinct_I41_J) ).
thf(822,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(219,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Late__Semantics_OfreeRes_Odistinct_I1_J) ).
thf(1597,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(287,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != F )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_transitions_OClose1) ).
thf(1902,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != F )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(226,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_1641682979reeRes @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_freshFreeDerivative_I1_J) ).
thf(1621,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_1641682979reeRes @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(17,axiom,
! [A: set_name,B: name > noption_pi,C: name] :
( ( suppor1289515356ion_pi @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_543891186ion_pi @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_supports__fresh) ).
thf(369,plain,
! [A: set_name,B: name > noption_pi,C: name] :
( ( suppor1289515356ion_pi @ A @ B )
=> ( ( finite_finite_name @ A )
=> ( ~ ( member_name @ C @ A )
=> ( fresh_543891186ion_pi @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(201,axiom,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_residual_Ostrong__inducts) ).
thf(1384,plain,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(215,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ~ ! [E: pi,F: name,G: name] :
( ( ( A = F )
& ( B = G )
& ( C = E ) )
=> ( ( late_transitions @ E @ D )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_mismatchCases_H) ).
thf(1537,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ~ ! [E: pi,F: name,G: name] :
( ( ( A = F )
& ( B = G )
& ( C = E ) )
=> ( ( late_transitions @ E @ D )
=> ( F = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(293,axiom,
fresh_name_pi @ x @ p2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_cComm2_Ohyps_I7_J) ).
thf(1923,plain,
fresh_name_pi @ x @ p2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(90,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_pi_Odistinct_I49_J) ).
thf(723,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(130,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Late__Semantics1_Osubject_Odistinct_I1_J) ).
thf(923,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(241,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( subs @ ( res @ A @ D ) @ B @ C )
= ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_simps_I9_J) ).
thf(1681,plain,
! [A: name,B: name,C: name,D: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( subs @ ( res @ A @ D ) @ B @ C )
= ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(211,axiom,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_freeRes,D: late_subject > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_795910143ubject @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_717452603ubject @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_residual_Orecs_I2_J) ).
thf(1416,plain,
! [A: late_subject > name > pi > late_subject,B: late_freeRes > pi > late_subject,C: late_freeRes,D: late_subject > $o,E: late_freeRes,F: pi] :
( ( finite_finite_name @ ( supp_L1144036959t_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L1759672260t_name @ B ) )
=> ( ( finite_finite_name @ ( supp_L1228270395s_name @ C ) )
=> ( ! [G: late_subject,H: name,I: pi] : ( D @ ( A @ G @ H @ I ) )
=> ( ! [G: late_freeRes,H: pi] : ( D @ ( B @ G @ H ) )
=> ( ! [G: late_subject,H: name,I: pi] :
( ( fresh_795910143ubject @ H @ A )
=> ( ( fresh_717452603ubject @ H @ G )
=> ( ( fresh_1641682979reeRes @ H @ C )
=> ( ( D @ ( A @ G @ H @ I ) )
=> ( fresh_717452603ubject @ H @ ( A @ G @ H @ I ) ) ) ) ) )
=> ( ( late_r1347955901ubject @ A @ B @ ( late_FreeR @ E @ F ) )
= ( B @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(73,axiom,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_freshRes) ).
thf(639,plain,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(291,axiom,
! [A: name,B: pi,C: late_residual] :
~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_mismatchTrans) ).
thf(1917,plain,
! [A: name,B: pi,C: late_residual] :
~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(62,axiom,
! [A: pi] : ( finite_finite_name @ ( supp_pi_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_fs__name1) ).
thf(592,plain,
! [A: pi] : ( finite_finite_name @ ( supp_pi_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(149,axiom,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_residual,D: name,E: name] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( late_r1742481968t_name @ A @ B @ C @ D )
=> ( ! [F: name] :
( ( late_r1742481968t_name @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_621211324i_name @ E @ A )
=> ( ( fresh_1030632537i_name @ E @ B )
=> ( fresh_name_name @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_residual_Orec__fresh) ).
thf(1014,plain,
! [A: late_subject > name > pi > name,B: late_freeRes > pi > name,C: late_residual,D: name,E: name] :
( ( finite_finite_name @ ( supp_L538372628e_name @ A ) )
=> ( ( finite_finite_name @ ( supp_L926407557e_name @ B ) )
=> ( ( late_r1742481968t_name @ A @ B @ C @ D )
=> ( ! [F: name] :
( ( late_r1742481968t_name @ A @ B @ C @ F )
=> ( F = D ) )
=> ( ( fresh_81631222sidual @ E @ C )
=> ( ( fresh_621211324i_name @ E @ A )
=> ( ( fresh_1030632537i_name @ E @ B )
=> ( fresh_name_name @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(298,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Late__Semantics_OResB) ).
thf(1944,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(135,axiom,
( supp_name_name
= ( ^ [A: name] :
( collect_name
@ ^ [B: name] :
~ ( fresh_name_name @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_supp__fresh__iff) ).
thf(940,plain,
( supp_name_name
= ( ^ [A: name] :
( collect_name
@ ^ [B: name] :
~ ( fresh_name_name @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(156,axiom,
! [A: late_subject] : ( finite_finite_name @ ( supp_L1174290467t_name @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_fs__name1) ).
thf(1037,plain,
! [A: late_subject] : ( finite_finite_name @ ( supp_L1174290467t_name @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(101,axiom,
! [A: late_subject,B: name,C: name] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ C @ A ) )
= ( ( B = C )
| ( fresh_717452603ubject @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_abs__fresh_I2_J) ).
thf(775,plain,
! [A: late_subject,B: name,C: name] :
( ( finite_finite_name @ ( supp_L1174290467t_name @ A ) )
=> ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ C @ A ) )
= ( ( B = C )
| ( fresh_717452603ubject @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(2209,plain,
$false,
inference(cvc4,[status(thm)],[1411,1823,1168,2031,1633,1995,846,333,1899,1315,468,1818,1956,1554,582,1924,730,1068,2062,1618,1401,1939,1269,511,1692,1173,1788,385,1735,698,1761,1640,538,930,1497,1705,1746,1782,782,973,1601,2067,829,404,436,1803,570,719,785,372,1860,702,802,1087,1247,2024,1815,1875,421,1890,2007,789,623,2034,806,1051,348,574,353,966,981,2058,397,1377,634,1896,1405,1943,1696,1975,1651,2011,920,678,661,761,810,381,2047,366,1074,1604,942,439,1768,714,1730,1057,1723,1091,1355,1676,598,1666,630,916,1032,361,1920,329,1624,1079,1392,710,456,1740,1910,1402,578,1672,1719,1397,388,1878,1361,339,1739,901,1414,637,1155,706,1028,1082,1039,970,1099,1266,1799,1874,2052,779,1627,1776,1263,997,1857,792,1241,1779,541,1054,1035,1071,2043,508,1906,425,430,1927,856,2028,1374,375,601,618,1764,819,694,2016,826,1795,904,975,732,1884,1615,1784,1389,1669,936,1707,1312,1865,1733,2055,947,350,641,1428,764,1894,736,863,880,649,2025,535,816,594,799,1022,330,345,1557,462,932,1061,1952,1396,1643,1176,394,851,505,1726,1364,1250,1948,795,487,1990,342,490,675,531,944,927,2037,1958,355,1547,1770,580,690,1961,1025,1611,1743,1647,954,1368,1753,1098,993,673,1987,1637,585,502,1262,470,544,1358,744,336,1749,727,859,1094,978,1881,1272,627,1084,1685,1654,771,2013,465,1966,363,556,1157,1913,588,813,390,1629,1244,568,378,433,1440,1077,1607,2036,2019,716,1161,620,950,1229,854,1757,358,400,1065,2040,1165,897,767,740,1019,528,644,459,822,1597,1902,1621,369,1384,1537,1923,723,923,1681,1416,639,1917,592,1014,1944,940,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP186^1 : TPTP v8.1.2. Released v7.5.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 14:45:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.84/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.72/1.14 % [INFO] Parsing done (288ms).
% 1.72/1.15 % [INFO] Running in sequential loop mode.
% 2.63/1.36 % [INFO] eprover registered as external prover.
% 2.63/1.36 % [INFO] cvc4 registered as external prover.
% 2.63/1.36 % [INFO] Scanning for conjecture ...
% 3.01/1.48 % [INFO] Found a conjecture and 352 axioms. Running axiom selection ...
% 3.27/1.59 % [INFO] Axiom selection finished. Selected 326 axioms (removed 26 axioms).
% 4.35/1.89 % [INFO] Problem is higher-order (TPTP THF).
% 4.59/1.91 % [INFO] Type checking passed.
% 4.59/1.91 % [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 ...
% 27.63/7.96 % External prover 'cvc4' found a proof!
% 27.63/7.96 % [INFO] Killing All external provers ...
% 27.63/7.96 % Time passed: 7444ms (effective reasoning time: 6806ms)
% 27.63/7.96 % 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)>
% 27.63/7.96 % Axioms used in derivation (326): fact_180_abs__fun__eq1, fact_199_Sum1, fact_251_exists__fresh_H, fact_339_pi_Orec__fin__supp, fact_319_residual_Orec__unique, fact_50_freeRes_Oinducts, fact_152_simps_I6_J, fact_5_cComm2_Ohyps_I8_J, fact_36_residual_Ostrong__induct, fact_142_name__fresh__abs, fact_161_Match, fact_126_Late__Semantics_OInput, fact_189_pi_Ofresh_I10_J, fact_304_residual_Orecs_I1_J, fact_168_pi_Oinject_I4_J, fact_185_pi_Ostrong__induct, fact_172_pi_Odistinct_I23_J, fact_160_mismatchCases_H, fact_225_pi_Odistinct_I9_J, fact_1_cComm2_Ohyps_I5_J, fact_16_cComm2_Ohyps_I2_J, fact_240_abs__fresh_I2_J, fact_9_cComm2_Ohyps_I1_J, fact_317_residual_Orec__unique, fact_239_abs__fresh_I2_J, fact_140_residual_Oinject_I1_J, fact_237_abs__fresh_I2_J, fact_272_supp__fresh__iff, fact_29_name__exists__fresh, fact_17_residual_Oinject_I2_J, fact_285_pi_Osupp_I10_J, fact_158_mismatchCases, fact_30_name__exists__fresh, fact_178_abs__fun__eq1, fact_340_pi_Orec__fin__supp, fact_176_abs__fun__eq1, fact_333_pi_Osupp_I8_J, fact_208_zeroTrans, fact_222_pi_Odistinct_I71_J, fact_162_Mismatch, fact_83_pi_Odistinct_I85_J, fact_61_Tau, fact_297_residual_Orecs_I2_J, fact_321_residual_Orec__unique, fact_236_subs__def, fact_219_pi_Odistinct_I1_J, fact_155_matchCases, fact_154_pi_Ofresh_I6_J, fact_24_pi_Ofresh_I3_J, fact_64_freeRes_Oexhaust, fact_332_pi_Osupp_I7_J, fact_324_residual_Orec__unique, fact_105_resOutputOutputTrans, fact_203_pi_Odistinct_I81_J, fact_214_pi_Oinject_I6_J, fact_169_pi_Oinject_I5_J, fact_14_subst__identity, fact_147_abs__fresh_I1_J, fact_10_simps_I8_J, fact_284_subject_Osupp_I1_J, fact_124_outputFreshTrans, fact_97_resTauBoundTrans, fact_218_pi_Odistinct_I3_J, fact_54_Collect__cong, fact_49_pi_Odistinct_I43_J, fact_258_exists__fresh, fact_89_Late__Semantics_Osubject_Odistinct_I1_J, fact_127_transitions_OInput, fact_198_sumCases_H, fact_122_resTrans_I1_J, fact_90_resCasesB_H, fact_63_Late__Semantics1_OfreeRes_Oinject, fact_85_pi_Odistinct_I45_J, fact_157_matchCases_H, fact_322_residual_Orec__unique, fact_207_nilCases_H, fact_177_abs__fun__eq1, fact_316_residual_Orec__unique, fact_106_resInputBoundOutputTrans, fact_20_tauCases_H, fact_174_pi_Odistinct_I39_J, fact_19_tauCases, fact_276_fresh__def, fact_175_pi_Odistinct_I37_J, fact_220_pi_Odistinct_I5_J, fact_337_pi_Osupp_I6_J, fact_166_pi_Odistinct_I67_J, fact_27_freshBoundDerivative_I2_J, fact_134_substInput, fact_65_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_306_residual_Orecs_I1_J, fact_217_pi_Odistinct_I87_J, fact_274_supp__fresh__iff, fact_196_pi_Odistinct_I33_J, fact_94_Open, fact_111_pi_Ofresh_I2_J, fact_278_fresh__def, fact_150_pi_Oinject_I3_J, fact_40_residual_Ostrong__inducts, fact_101_resTauOutputTrans, fact_39_residual_Ostrong__inducts, fact_261_exists__fresh, fact_79_Late__Semantics_OResB, fact_302_residual_Orecs_I1_J, fact_159_mismatchTrans, fact_100_transitions_OPar2B, fact_282_pi_Osupp_I3_J, fact_292_residual_Orecs_I2_J, fact_228_bangCases, fact_213_pi_Odistinct_I83_J, fact_257_exists__fresh, fact_296_residual_Orecs_I2_J, fact_211_pi_Odistinct_I11_J, fact_130_Output, fact_330_pi_Osupp_I4_J, fact_53_Collect__mem__eq, fact_286_fs__name1, fact_173_pi_Odistinct_I25_J, fact_137_pi_Ofresh_I9_J, fact_75_subject_Ofresh_I1_J, fact_209_pi_Odistinct_I13_J, fact_279_fresh__def, fact_318_residual_Orec__unique, fact_182_pi_Ostrong__inducts, fact_336_pi_Osupp_I2_J, fact_305_residual_Orecs_I1_J, fact_118_pi_Odistinct_I35_J, fact_151_simps_I5_J, fact_223_pi_Odistinct_I69_J, fact_192_pi_Ofresh_I1_J, fact_204_pi_Odistinct_I53_J, fact_342_pi_Orec__fin__supp, fact_299_residual_Orecs_I2_J, fact_247_exists__fresh_H, fact_181_pi_Ostrong__inducts, fact_82_ResF, fact_338_pi_Osupp_I5_J, fact_283_subject_Osupp_I2_J, fact_194_simps_I1_J, fact_326_residual_Orec__fin__supp, fact_165_pi_Odistinct_I75_J, fact_188_pi_Ostrong__induct, fact_102_Late__Semantics_OClose1, fact_238_abs__fresh_I2_J, fact_153_pi_Ofresh_I5_J, fact_72_freeRes_Ofresh_I2_J, fact_221_pi_Odistinct_I77_J, fact_22_pi_Ofresh_I8_J, fact_0_cComm2_Ohyps_I9_J, fact_35_residual_Ostrong__induct, fact_74_simps_I9_J, fact_345_supports__fresh, fact_287_fs__name1, fact_70_Late__Semantics_Osubject_Oinject_I2_J, fact_86_resCases_H, fact_128_inputBoundOutputTrans, fact_290_residual_Orecs_I2_J, fact_248_exists__fresh_H, fact_312_residual_Orec__fresh, fact_37_residual_Ostrong__inducts, fact_119_pi_Odistinct_I19_J, fact_110_name__fresh, fact_93_substRes2, fact_212_pi_Odistinct_I17_J, fact_335_residual_Osupp_I2_J, fact_28_name__exists__fresh, fact_234_aux1, fact_133_simps_I3_J, fact_80_resCasesF, fact_197_sumCases, fact_112_pi_Odistinct_I21_J, fact_191_simps_I10_J, fact_66_transitions_OClose2, fact_69_freeRes_Ofresh_I1_J, fact_331_residual_Osupp_I1_J, fact_55_tauOutputTrans, fact_113_pi_Oinject_I1_J, fact_348_supports__fresh, fact_34_residual_Ostrong__induct, fact_116_pi_Odistinct_I29_J, fact_294_residual_Orecs_I2_J, fact_45_forget, fact_273_supp__fresh__iff, fact_8_cComm2_Ohyps_I4_J, fact_301_residual_Orecs_I1_J, fact_115_pi_Odistinct_I57_J, fact_334_freeRes_Osupp_I1_J, fact_295_residual_Orecs_I2_J, fact_56_transitions_OComm2, fact_87_transitions_OResB, fact_343_pi_Orec__fin__supp, fact_43_fresh__fact2, fact_202_pi_Odistinct_I79_J, fact_57_transitions_OComm1, fact_46_parCasesB, fact_271_supp__fresh__iff, fact_107_outputTauTrans, fact_11_Par1F, fact_131_outputIneqTrans, fact_146_abs__fresh_I1_J, fact_81_resCasesF_H, fact_230_pi_Oinducts, fact_308_residual_Orecs_I1_J, fact_260_exists__fresh, fact_347_supports__fresh, fact_171_pi_Odistinct_I51_J, fact_48_Late__Semantics_OPar1B, fact_67_transitions_OClose1, fact_186_pi_Ostrong__induct, fact_42_residual_Odistinct_I1_J, fact_327_residual_Orec__fin__supp, fact_307_residual_Orecs_I1_J, fact_129_inputIneqTrans, fact_184_pi_Ostrong__inducts, fact_3__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_H_091x_058_058_061b_093_092_060close_062, fact_156_matchTrans, fact_227_Bang, fact_149_abs__fresh_I1_J, fact_96_freshBoundDerivative_I1_J, fact_235_bangPred_Oinducts, fact_232_bangPred_Ocases, fact_141_subst__name__def, fact_51_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_277_fresh__def, fact_231_aux2, fact_201_pi_Odistinct_I47_J, fact_71_Late__Semantics1_Osubject_Oinject_I2_J, fact_4_Free_Ohyps, fact_58_freshFreeDerivative_I2_J, fact_303_residual_Orecs_I1_J, fact_13__092_060open_062x_A_092_060sharp_062_AR_092_060close_062, fact_95_freshFreeDerivative_I1_J, fact_143_name__fresh__abs, fact_325_residual_Orec__fin__supp, fact_32_tauBoundTrans, fact_145_name__fresh__abs, fact_187_pi_Ostrong__induct, fact_139_pi_Oinject_I8_J, fact_311_residual_Orec__fresh, fact_59_Late__Semantics_OComm2, fact_313_residual_Orec__fresh, fact_98_parCasesB_H, fact_289_fs__name1, fact_164_pi_Odistinct_I65_J, fact_7_cComm2_Ohyps_I7_J, fact_281_pi_Osupp_I9_J, fact_275_supp__fresh__iff, fact_15_cPar1_Ohyps, fact_328_residual_Orec__fin__supp, fact_117_pi_Odistinct_I31_J, fact_41_residual_Oinducts, fact_103_resOutputTauTrans, fact_38_residual_Ostrong__inducts, fact_206_pi_Odistinct_I41_J, fact_99_transitions_OPar1B, fact_31_name__exists__fresh, fact_68_Late__Semantics_OClose2, fact_195_pi_Odistinct_I59_J, fact_91_freshResidual, fact_44_fresh__fact1, fact_250_exists__fresh_H, fact_148_abs__fresh_I1_J, fact_77_subject_Oexhaust, fact_144_name__fresh__abs, fact_62_Late__Semantics1_Osubject_Oinject_I1_J, fact_108_outputCases, fact_341_pi_Orec__fin__supp, fact_167_pi_Odistinct_I61_J, fact_25_simps_I2_J, fact_104_resOutputInputTrans, fact_109_outputCases_H, fact_233_bangPred_Osimps, fact_21_Late__Semantics_OfreeRes_Oinject, fact_47_Late__Semantics_OPar2B, fact_249_exists__fresh_H, fact_76_subject_Ofresh_I2_J, fact_114_pi_Odistinct_I55_J, fact_224_pi_Odistinct_I63_J, fact_73_residual_Ofresh_I2_J, fact_18_pi_Oinject_I7_J, fact_132_residual_Ofresh_I1_J, fact_216_pi_Odistinct_I89_J, fact_136_inputCases_H, fact_300_residual_Orecs_I1_J, fact_120_resTrans_I2_J, fact_344_supports__fresh, fact_200_Sum2, fact_183_pi_Ostrong__inducts, fact_163_pi_Odistinct_I73_J, fact_78_Late__Semantics1_Osubject_Odistinct_I1_J, fact_60_Late__Semantics_OComm1, fact_293_residual_Orecs_I2_J, fact_2_cComm2_Ohyps_I6_J, fact_26_pi_Oinject_I2_J, fact_310_residual_Orec__fresh, fact_135_simps_I4_J, fact_88_subject_Oinducts, fact_288_fs__name1, fact_170_pi_Odistinct_I49_J, fact_205_pi_Odistinct_I27_J, fact_280_fresh__def, fact_190_pi_Ofresh_I7_J, fact_92_substRes3, fact_33_residual_Ostrong__induct, fact_84_freshRes, fact_259_exists__fresh, fact_12_Par2F, fact_210_pi_Odistinct_I15_J, fact_323_residual_Orec__unique, fact_309_residual_Orecs_I1_J, fact_291_residual_Orecs_I2_J, fact_138_pi_Ofresh_I4_J, fact_226_pi_Odistinct_I7_J, fact_229_resZeroTrans, fact_193_simps_I7_J, fact_23_substTrans, fact_52_mem__Collect__eq, fact_298_residual_Orecs_I2_J, fact_315_residual_Orec__unique, fact_320_residual_Orec__unique, fact_215_pi_Oinject_I9_J, fact_346_supports__fresh, fact_125_resInputFreeTrans, fact_123_outputBoundTrans, fact_6_cComm2_Ohyps_I3_J, fact_121_inputFreeTrans
% 27.63/7.96 % No. of inferences in proof: 656
% 27.63/7.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7444 ms resp. 6806 ms w/o parsing
% 28.36/8.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 28.36/8.17 % [INFO] Killing All external provers ...
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