TSTP Solution File: ITP182^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP182^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 07:48:36 EDT 2024
% Result : Theorem 16.74s 5.14s
% Output : Refutation 17.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 542
% Syntax : Number of formulae : 902 ( 439 unt; 184 typ; 0 def)
% Number of atoms : 1653 ( 763 equ; 4 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 7027 ( 223 ~; 1 |; 98 &;6053 @)
% ( 0 <=>; 652 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 47 ( 46 usr)
% Number of type conns : 437 ( 437 >; 0 *; 0 +; 0 <<)
% Number of symbols : 143 ( 138 usr; 17 con; 0-5 aty)
% Number of variables : 2355 ( 20 ^2307 !; 28 ?;2355 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1872410278e_name_type,type,
produc1872410278e_name: $tType ).
thf(produc890461031e_name_type,type,
produc890461031e_name: $tType ).
thf(list_P431515740_pi_pi_type,type,
list_P431515740_pi_pi: $tType ).
thf(set_Pr1654044726_pi_pi_type,type,
set_Pr1654044726_pi_pi: $tType ).
thf(set_Pr806375235ubject_type,type,
set_Pr806375235ubject: $tType ).
thf(set_Pr1780909331reeRes_type,type,
set_Pr1780909331reeRes: $tType ).
thf(produc1141751126_pi_pi_type,type,
produc1141751126_pi_pi: $tType ).
thf(list_l1406151091e_name_type,type,
list_l1406151091e_name: $tType ).
thf(produc1359399907ubject_type,type,
produc1359399907ubject: $tType ).
thf(produc355105483reeRes_type,type,
produc355105483reeRes: $tType ).
thf(produc214645451ubject_type,type,
produc214645451ubject: $tType ).
thf(produc1357834675reeRes_type,type,
produc1357834675reeRes: $tType ).
thf(set_Pr1131282415pi_Rep_type,type,
set_Pr1131282415pi_Rep: $tType ).
thf(produc257012921pi_Rep_type,type,
produc257012921pi_Rep: $tType ).
thf(produc1777919905pi_Rep_type,type,
produc1777919905pi_Rep: $tType ).
thf(list_P227219501e_name_type,type,
list_P227219501e_name: $tType ).
thf(set_Pr443758855e_name_type,type,
set_Pr443758855e_name: $tType ).
thf(produc1998742700t_name_type,type,
produc1998742700t_name: $tType ).
thf(produc2052722628s_name_type,type,
produc2052722628s_name: $tType ).
thf(produc865358760ubject_type,type,
produc865358760ubject: $tType ).
thf(produc2008547984reeRes_type,type,
produc2008547984reeRes: $tType ).
thf(produc140253050ect_pi_type,type,
produc140253050ect_pi: $tType ).
thf(produc992857746Res_pi_type,type,
produc992857746Res_pi: $tType ).
thf(set_Pr1834926343_pi_pi_type,type,
set_Pr1834926343_pi_pi: $tType ).
thf(produc1212344719pi_Rep_type,type,
produc1212344719pi_Rep: $tType ).
thf(produc367475239e_name_type,type,
produc367475239e_name: $tType ).
thf(product_prod_pi_pi_type,type,
product_prod_pi_pi: $tType ).
thf(list_Late_subject_type,type,
list_Late_subject: $tType ).
thf(list_Late_freeRes_type,type,
list_Late_freeRes: $tType ).
thf(set_Late_subject_type,type,
set_Late_subject: $tType ).
thf(set_Late_freeRes_type,type,
set_Late_freeRes: $tType ).
thf(list_pi_Rep_type,type,
list_pi_Rep: $tType ).
thf(late_residual_Rep_type,type,
late_residual_Rep: $tType ).
thf(late_subject_Rep_type,type,
late_subject_Rep: $tType ).
thf(late_freeRes_Rep_type,type,
late_freeRes_Rep: $tType ).
thf(set_pi_Rep_type,type,
set_pi_Rep: $tType ).
thf(list_name_type,type,
list_name: $tType ).
thf(set_name_type,type,
set_name: $tType ).
thf(list_pi_type,type,
list_pi: $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(set_pi_type,type,
set_pi: $tType ).
thf(pi_Rep_type,type,
pi_Rep: $tType ).
thf(name_type,type,
name: $tType ).
thf(pi_type,type,
pi: $tType ).
thf(input_type,type,
input: name > name > pi > pi ).
thf(res_type,type,
res: name > pi > pi ).
thf(sum_type,type,
sum: pi > pi > pi ).
thf(if_name_type,type,
if_name: $o > name > name > name ).
thf(if_pi_type,type,
if_pi: $o > pi > pi > pi ).
thf(if_pi_Rep_type,type,
if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep ).
thf(if_Late_freeRes_type,type,
if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes ).
thf(if_Late_subject_type,type,
if_Late_subject: $o > late_subject > late_subject > late_subject ).
thf(late_OutputR_type,type,
late_OutputR: name > name > 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_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(cons_name_type,type,
cons_name: name > list_name > list_name ).
thf(cons_pi_type,type,
cons_pi: pi > list_pi > list_pi ).
thf(cons_pi_Rep_type,type,
cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep ).
thf(cons_Late_freeRes_type,type,
cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes ).
thf(cons_Late_subject_type,type,
cons_Late_subject: late_subject > list_Late_subject > list_Late_subject ).
thf(cons_l798145763e_name_type,type,
cons_l798145763e_name: list_P227219501e_name > list_l1406151091e_name > list_l1406151091e_name ).
thf(cons_P1213805021e_name_type,type,
cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name ).
thf(cons_P749510156_pi_pi_type,type,
cons_P749510156_pi_pi: produc1141751126_pi_pi > list_P431515740_pi_pi > list_P431515740_pi_pi ).
thf(nil_li29751603e_name_type,type,
nil_li29751603e_name: list_l1406151091e_name ).
thf(nil_Pr743626285e_name_type,type,
nil_Pr743626285e_name: list_P227219501e_name ).
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_name_pi_Rep_type,type,
fresh_name_pi_Rep: name > pi_Rep > $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(fresh_name_list_name_type,type,
fresh_name_list_name: name > list_name > $o ).
thf(fresh_name_list_pi_type,type,
fresh_name_list_pi: name > list_pi > $o ).
thf(fresh_1981651763reeRes_type,type,
fresh_1981651763reeRes: name > list_Late_freeRes > $o ).
thf(fresh_838462539ubject_type,type,
fresh_838462539ubject: name > list_Late_subject > $o ).
thf(fresh_922791155e_name_type,type,
fresh_922791155e_name: name > list_P227219501e_name > $o ).
thf(fresh_1958133282_pi_pi_type,type,
fresh_1958133282_pi_pi: name > list_P431515740_pi_pi > $o ).
thf(fresh_441084397e_name_type,type,
fresh_441084397e_name: name > produc367475239e_name > $o ).
thf(fresh_1963366730reeRes_type,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(fresh_820177506ubject_type,type,
fresh_820177506ubject: name > produc865358760ubject > $o ).
thf(fresh_1376661020_pi_pi_type,type,
fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
thf(fresh_1627595501_pi_pi_type,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(fresh_2007541374s_name_type,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(fresh_1847501388Res_pi_type,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(fresh_493808761reeRes_type,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(fresh_1498103185ubject_type,type,
fresh_1498103185ubject: name > produc214645451ubject > $o ).
thf(fresh_1953561446t_name_type,type,
fresh_1953561446t_name: name > produc1998742700t_name > $o ).
thf(fresh_994896692ect_pi_type,type,
fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
thf(fresh_1638563217reeRes_type,type,
fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
thf(fresh_495373993ubject_type,type,
fresh_495373993ubject: name > produc1359399907ubject > $o ).
thf(perm_n382765978reeRes_type,type,
perm_n382765978reeRes: list_P227219501e_name > ( name > late_freeRes ) > name > late_freeRes ).
thf(perm_n1387060402ubject_type,type,
perm_n1387060402ubject: list_P227219501e_name > ( name > late_subject ) > name > late_subject ).
thf(perm_n1333244520reeRes_type,type,
perm_n1333244520reeRes: list_P227219501e_name > ( pi > late_freeRes ) > pi > late_freeRes ).
thf(perm_n190055296ubject_type,type,
perm_n190055296ubject: list_P227219501e_name > ( pi > late_subject ) > pi > late_subject ).
thf(perm_n1841560599reeRes_type,type,
perm_n1841560599reeRes: list_P227219501e_name > ( pi_Rep > late_freeRes ) > pi_Rep > late_freeRes ).
thf(perm_n698371375ubject_type,type,
perm_n698371375ubject: list_P227219501e_name > ( pi_Rep > late_subject ) > pi_Rep > late_subject ).
thf(perm_n1446290985reeRes_type,type,
perm_n1446290985reeRes: list_P227219501e_name > ( late_freeRes > late_freeRes ) > late_freeRes > late_freeRes ).
thf(perm_n303101761ubject_type,type,
perm_n303101761ubject: list_P227219501e_name > ( late_freeRes > late_subject ) > late_freeRes > late_subject ).
thf(perm_n443561793reeRes_type,type,
perm_n443561793reeRes: list_P227219501e_name > ( late_subject > late_freeRes ) > late_subject > late_freeRes ).
thf(perm_n1447856217ubject_type,type,
perm_n1447856217ubject: list_P227219501e_name > ( late_subject > late_subject ) > late_subject > late_subject ).
thf(perm_name_o_type,type,
perm_name_o: list_P227219501e_name > $o > $o ).
thf(perm_name_name_type,type,
perm_name_name: list_P227219501e_name > name > name ).
thf(perm_name_pi_type,type,
perm_name_pi: list_P227219501e_name > pi > pi ).
thf(perm_name_pi_Rep_type,type,
perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep ).
thf(perm_n336613537reeRes_type,type,
perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes ).
thf(perm_n1938283068es_Rep_type,type,
perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep ).
thf(perm_n414416632sidual_type,type,
perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual ).
thf(perm_n890803237al_Rep_type,type,
perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep ).
thf(perm_n1559866809ubject_type,type,
perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject ).
thf(perm_n697952036ct_Rep_type,type,
perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep ).
thf(perm_name_list_name_type,type,
perm_name_list_name: list_P227219501e_name > list_name > list_name ).
thf(perm_name_list_pi_type,type,
perm_name_list_pi: list_P227219501e_name > list_pi > list_pi ).
thf(perm_n729617823pi_Rep_type,type,
perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep ).
thf(perm_n808352945reeRes_type,type,
perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes ).
thf(perm_n1812647369ubject_type,type,
perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject ).
thf(perm_n1160739829e_name_type,type,
perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name ).
thf(perm_n1255502110_pi_pi_type,type,
perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi ).
thf(perm_n1415585007_pi_pi_type,type,
perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).
thf(perm_n258463228s_name_type,type,
perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).
thf(perm_n1211707594Res_pi_type,type,
perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).
thf(perm_n840427369pi_Rep_type,type,
perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).
thf(perm_n169932155reeRes_type,type,
perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).
thf(perm_n1174226579ubject_type,type,
perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).
thf(perm_n204483300t_name_type,type,
perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
thf(perm_n359102898ect_pi_type,type,
perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
thf(perm_n1467004033pi_Rep_type,type,
perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
thf(perm_n1314686611reeRes_type,type,
perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
thf(perm_n171497387ubject_type,type,
perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
thf(perm_name_set_name_type,type,
perm_name_set_name: list_P227219501e_name > set_name > set_name ).
thf(perm_name_set_pi_type,type,
perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
thf(perm_name_set_pi_Rep_type,type,
perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
thf(perm_n1555914327reeRes_type,type,
perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
thf(perm_n412725103ubject_type,type,
perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
thf(perm_n675238095_pi_pi_type,type,
perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
thf(swap_name_type,type,
swap_name: produc367475239e_name > name > name ).
thf(ord_le793202855e_name_type,type,
ord_le793202855e_name: set_Pr443758855e_name > set_Pr443758855e_name > $o ).
thf(ord_le797229014_pi_pi_type,type,
ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(ord_le630093991_pi_pi_type,type,
ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(produc1069608854e_name_type,type,
produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).
thf(produc1570949143e_name_type,type,
produc1570949143e_name: name > name > produc367475239e_name ).
thf(produc1531804426reeRes_type,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(produc607574050ubject_type,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
thf(produc235456326_pi_pi_type,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(product_Pair_pi_pi_type,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(produc1701355766s_name_type,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(produc1177552196Res_pi_type,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(produc216486617pi_Rep_type,type,
produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
thf(produc1244821099reeRes_type,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(produc320590723ubject_type,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(produc1647375838t_name_type,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(produc324947500ect_pi_type,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(produc843063281pi_Rep_type,type,
produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
thf(produc242091907reeRes_type,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(produc1465345179ubject_type,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(produc208131031e_name_type,type,
produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).
thf(eqvt_name_type,type,
eqvt_name: set_Pr443758855e_name > $o ).
thf(eqvt_pi_type,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(id_name_type,type,
id_name: set_Pr443758855e_name ).
thf(id_pi_type,type,
id_pi: set_Pr1834926343_pi_pi ).
thf(collec1051790738_pi_pi_type,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(strong2129052853vative_type,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(strong743114133lation_type,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(member_name_type,type,
member_name: name > set_name > $o ).
thf(member_pi_type,type,
member_pi: pi > set_pi > $o ).
thf(member_pi_Rep_type,type,
member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
thf(member_Late_freeRes_type,type,
member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
thf(member_Late_subject_type,type,
member_Late_subject: late_subject > set_Late_subject > $o ).
thf(member695284560e_name_type,type,
member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).
thf(member540268543_pi_pi_type,type,
member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(member558706512_pi_pi_type,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(p_type,type,
p: pi ).
thf(pq_type,type,
pq: pi ).
thf(p2_type,type,
p2: pi ).
thf(q_type,type,
q: pi ).
thf(rel_type,type,
rel: set_Pr1834926343_pi_pi ).
thf(a_type,type,
a: late_subject ).
thf(aa_type,type,
aa: name ).
thf(x_type,type,
x: name ).
thf(y_type,type,
y: name ).
thf(159,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_order__trans) ).
thf(892,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(346,axiom,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_name__swap__bij) ).
thf(1665,plain,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(295,axiom,
! [A: produc367475239e_name > $o,B: produc367475239e_name] :
( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_prod__cases) ).
thf(1501,plain,
! [A: produc367475239e_name > $o,B: produc367475239e_name] :
( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(334,axiom,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_1641682979reeRes @ A @ B )
=> ( ( fresh_1641682979reeRes @ C @ B )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_name__fresh__fresh) ).
thf(1633,plain,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_1641682979reeRes @ A @ B )
=> ( ( fresh_1641682979reeRes @ C @ B )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(60,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_265_pi_Ofresh_I7_J) ).
thf(555,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)],[60]) ).
thf(35,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_name__perm__compose) ).
thf(479,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(216,axiom,
! [A: produc367475239e_name] :
~ ! [B: name,C: name] :
( A
!= ( produc1570949143e_name @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_old_Oprod_Oexhaust) ).
thf(1105,plain,
! [A: produc367475239e_name] :
~ ! [B: name,C: name] :
( A
!= ( produc1570949143e_name @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(164,axiom,
! [A: produc1141751126_pi_pi] :
~ ! [B: name] :
~ ( fresh_1376661020_pi_pi @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_name__exists__fresh) ).
thf(909,plain,
! [A: produc1141751126_pi_pi] :
~ ! [B: name] :
~ ( fresh_1376661020_pi_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(81,axiom,
! [A: list_P227219501e_name,B: $o,C: pi_Rep,D: pi_Rep] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
= ( perm_name_pi_Rep @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
= ( perm_name_pi_Rep @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_if__eqvt) ).
thf(628,plain,
! [A: list_P227219501e_name,B: $o,C: pi_Rep,D: pi_Rep] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
= ( perm_name_pi_Rep @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_name_pi_Rep @ A @ ( if_pi_Rep @ B @ C @ D ) )
= ( perm_name_pi_Rep @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(184,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_322_residual_Oinducts) ).
thf(977,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)],[184]) ).
thf(243,axiom,
! [A: list_P227219501e_name,B: produc367475239e_name,C: list_P227219501e_name] :
( ( A
= ( cons_P1213805021e_name @ B @ C ) )
=> ( A != nil_Pr743626285e_name ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_list_OdiscI) ).
thf(1211,plain,
! [A: list_P227219501e_name,B: produc367475239e_name,C: list_P227219501e_name] :
( ( A
= ( cons_P1213805021e_name @ B @ C ) )
=> ( A != nil_Pr743626285e_name ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(117,axiom,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Pair__inject) ).
thf(762,plain,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(322,axiom,
! [A: list_P227219501e_name,B: name,C: name,D: pi] :
( ( perm_name_pi @ A @ ( input @ B @ C @ D ) )
= ( input @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_pi_Operm_I4_J) ).
thf(1596,plain,
! [A: list_P227219501e_name,B: name,C: name,D: pi] :
( ( perm_name_pi @ A @ ( input @ B @ C @ D ) )
= ( input @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(241,axiom,
! [A: name,B: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_name__id) ).
thf(1205,plain,
! [A: name,B: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(45,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_315_Late__Semantics1_OfreeRes_Oinject) ).
thf(511,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)],[45]) ).
thf(78,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_perm__compose) ).
thf(614,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(202,axiom,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_name__swap__bij) ).
thf(1041,plain,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(267,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Pair__inject) ).
thf(1305,plain,
! [A: name,B: name,C: name,D: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(72,axiom,
! [A: list_P227219501e_name,B: name] :
( ( perm_n1559866809ubject @ A @ ( late_InputS @ B ) )
= ( late_InputS @ ( perm_name_name @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_subject_Operm_I1_J) ).
thf(597,plain,
! [A: list_P227219501e_name,B: name] :
( ( perm_n1559866809ubject @ A @ ( late_InputS @ B ) )
= ( late_InputS @ ( perm_name_name @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(293,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062) ).
thf(1497,plain,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(348,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_subject_Ofresh_I2_J) ).
thf(1671,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(133,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: late_subject] :
( ( perm_n1174226579ubject @ A @ ( produc320590723ubject @ B @ C ) )
= ( produc320590723ubject @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_perm__prod_Osimps) ).
thf(814,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: late_subject] :
( ( perm_n1174226579ubject @ A @ ( produc320590723ubject @ B @ C ) )
= ( produc320590723ubject @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(336,axiom,
fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Bound_Ohyps_I3_J) ).
thf(1640,plain,
fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(175,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_326_resCasesF) ).
thf(945,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)],[175]) ).
thf(170,axiom,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_fresh__prod) ).
thf(930,plain,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(18,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_perm__compose) ).
thf(404,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(191,axiom,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_name__exists__fresh) ).
thf(1001,plain,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(249,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt_pi @ E )
=> ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ ( perm_n1559866809ubject @ F @ C ) @ ( perm_name_name @ F @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_derivativeEqvtI) ).
thf(1243,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt_pi @ E )
=> ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ ( perm_n1559866809ubject @ F @ C ) @ ( perm_name_name @ F @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(292,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_332_resCases_H) ).
thf(1441,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)],[292]) ).
thf(328,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_name__swap__bij) ).
thf(1613,plain,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(340,axiom,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_name__swap) ).
thf(1650,plain,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(13,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_name__perm__compose) ).
thf(389,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(206,axiom,
! [A: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_name__calc_I2_J) ).
thf(1055,plain,
! [A: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(289,axiom,
! [A: list_P227219501e_name,B: pi,C: list_pi] :
( ( perm_name_list_pi @ A @ ( cons_pi @ B @ C ) )
= ( cons_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_list_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_cons__eqvt) ).
thf(1430,plain,
! [A: list_P227219501e_name,B: pi,C: list_pi] :
( ( perm_name_list_pi @ A @ ( cons_pi @ B @ C ) )
= ( cons_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_list_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(256,axiom,
! [A: list_l1406151091e_name] :
( ( A != nil_li29751603e_name )
=> ( ! [B: list_l1406151091e_name] :
( A
!= ( cons_l798145763e_name @ nil_Pr743626285e_name @ B ) )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_l1406151091e_name] :
( A
!= ( cons_l798145763e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_transpose_Ocases) ).
thf(1264,plain,
! [A: list_l1406151091e_name] :
( ( A != nil_li29751603e_name )
=> ( ! [B: list_l1406151091e_name] :
( A
!= ( cons_l798145763e_name @ nil_Pr743626285e_name @ B ) )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_l1406151091e_name] :
( A
!= ( cons_l798145763e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(261,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
( ( perm_n414416632sidual @ A @ ( late_FreeR @ B @ C ) )
= ( late_FreeR @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_residual_Operm_I2_J) ).
thf(1279,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
( ( perm_n414416632sidual @ A @ ( late_FreeR @ B @ C ) )
= ( late_FreeR @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(315,axiom,
fresh_717452603ubject @ y @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Bound_Ohyps_I4_J) ).
thf(1577,plain,
fresh_717452603ubject @ y @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(208,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_calculation) ).
thf(1059,plain,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(32,axiom,
! [A: list_P227219501e_name,B: name,C: pi_Rep] :
( ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) )
= ( fresh_name_pi_Rep @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_fresh__bij) ).
thf(460,plain,
! [A: list_P227219501e_name,B: name,C: pi_Rep] :
( ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) )
= ( fresh_name_pi_Rep @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(69,axiom,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: pi,D: pi] :
( A
!= ( produc235456326_pi_pi @ B @ ( product_Pair_pi_pi @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_prod__cases3) ).
thf(587,plain,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: pi,D: pi] :
( A
!= ( produc235456326_pi_pi @ B @ ( product_Pair_pi_pi @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(270,axiom,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_name__swap) ).
thf(1323,plain,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(298,axiom,
! [A: name,B: name,C: name] :
( ( fresh_name_name @ A @ B )
=> ( ( fresh_name_name @ C @ B )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_name__fresh__fresh) ).
thf(1511,plain,
! [A: name,B: name,C: name] :
( ( fresh_name_name @ A @ B )
=> ( ( fresh_name_name @ C @ B )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(100,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_simE_I2_J) ).
thf(702,plain,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(146,axiom,
! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
( ( ( perm_n1559866809ubject @ A @ B )
= ( perm_n1559866809ubject @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_perm__bij) ).
thf(853,plain,
! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
( ( ( perm_n1559866809ubject @ A @ B )
= ( perm_n1559866809ubject @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(326,axiom,
fresh_name_pi @ y @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193__092_060open_062y_A_092_060sharp_062_AP_092_060close_062) ).
thf(1609,plain,
fresh_name_pi @ y @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(181,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_order__refl) ).
thf(969,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(22,axiom,
! [A: list_P227219501e_name,B: name,C: name] :
( ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) )
= ( fresh_name_name @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_fresh__bij) ).
thf(416,plain,
! [A: list_P227219501e_name,B: name,C: name] :
( ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) )
= ( fresh_name_name @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(312,axiom,
! [A: list_P227219501e_name,B: name] :
( ( perm_n1559866809ubject @ A @ ( late_BoundOutputS @ B ) )
= ( late_BoundOutputS @ ( perm_name_name @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_subject_Operm_I2_J) ).
thf(1568,plain,
! [A: list_P227219501e_name,B: name] :
( ( perm_n1559866809ubject @ A @ ( late_BoundOutputS @ B ) )
= ( late_BoundOutputS @ ( perm_name_name @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(337,axiom,
! [A: list_P227219501e_name,B: name,C: pi] :
( ( perm_name_o @ A @ ( fresh_name_pi @ B @ C ) )
= ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_fresh__eqvt) ).
thf(1641,plain,
! [A: list_P227219501e_name,B: name,C: pi] :
( ( perm_name_o @ A @ ( fresh_name_pi @ B @ C ) )
= ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(283,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_344_inputBoundOutputTrans) ).
thf(1362,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)],[283]) ).
thf(245,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_perm__compose) ).
thf(1232,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(134,axiom,
! [A: list_P227219501e_name,B: late_subject,C: late_freeRes] :
( ( perm_n1314686611reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
= ( produc242091907reeRes @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_perm__prod_Osimps) ).
thf(817,plain,
! [A: list_P227219501e_name,B: late_subject,C: late_freeRes] :
( ( perm_n1314686611reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
= ( produc242091907reeRes @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(162,axiom,
! [A: list_P227219501e_name,B: name,C: late_freeRes] :
( ( perm_name_o @ A @ ( fresh_1641682979reeRes @ B @ C ) )
= ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_fresh__eqvt) ).
thf(902,plain,
! [A: list_P227219501e_name,B: name,C: late_freeRes] :
( ( perm_name_o @ A @ ( fresh_1641682979reeRes @ B @ C ) )
= ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(266,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: late_subject,D: name] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong2129052853vative @ B @ B @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_derivativeReflexive) ).
thf(1302,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: late_subject,D: name] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong2129052853vative @ B @ B @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(125,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_316_Late__Semantics_OfreeRes_Oinject) ).
thf(789,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)],[125]) ).
thf(70,axiom,
! [A: list_P227219501e_name,B: pi_Rep > late_subject,C: pi_Rep] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n698371375ubject @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_perm__app) ).
thf(591,plain,
! [A: list_P227219501e_name,B: pi_Rep > late_subject,C: pi_Rep] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n698371375ubject @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(217,axiom,
! [A: list_P227219501e_name,B: late_subject,C: pi] :
( ( perm_n359102898ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
= ( produc324947500ect_pi @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_perm__prod_Osimps) ).
thf(1109,plain,
! [A: list_P227219501e_name,B: late_subject,C: pi] :
( ( perm_n359102898ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
= ( produc324947500ect_pi @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(46,axiom,
! [A: pi,B: pi] :
( ( if_pi @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Opi_T) ).
thf(514,plain,
! [A: pi,B: pi] :
( ( if_pi @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(197,axiom,
! [A: name,B: pi,C: list_pi] :
( ( fresh_name_list_pi @ A @ ( cons_pi @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_list_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_fresh__list__cons) ).
thf(1020,plain,
! [A: name,B: pi,C: list_pi] :
( ( fresh_name_list_pi @ A @ ( cons_pi @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_list_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(130,axiom,
( eqvt_pi
= ( ^ [A: set_Pr1834926343_pi_pi] :
! [B: product_prod_pi_pi,C: list_P227219501e_name] :
( ( member558706512_pi_pi @ B @ A )
=> ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_eqvt__def) ).
thf(806,plain,
( eqvt_pi
= ( ^ [A: set_Pr1834926343_pi_pi] :
! [B: product_prod_pi_pi,C: list_P227219501e_name] :
( ( member558706512_pi_pi @ B @ A )
=> ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(163,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_pi_Odistinct_I81_J) ).
thf(905,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(317,axiom,
! [A: name,B: name,C: list_P227219501e_name,D: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ C ) @ D )
= ( swap_name @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_name__calc_I1_J) ).
thf(1581,plain,
! [A: name,B: name,C: list_P227219501e_name,D: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ C ) @ D )
= ( swap_name @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(180,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
( ( perm_n169932155reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
= ( produc1244821099reeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_perm__prod_Osimps) ).
thf(966,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
( ( perm_n169932155reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
= ( produc1244821099reeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(74,axiom,
! [A: list_P227219501e_name,B: late_subject,C: name] :
( ( perm_n204483300t_name @ A @ ( produc1647375838t_name @ B @ C ) )
= ( produc1647375838t_name @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_perm__prod_Osimps) ).
thf(602,plain,
! [A: list_P227219501e_name,B: late_subject,C: name] :
( ( perm_n204483300t_name @ A @ ( produc1647375838t_name @ B @ C ) )
= ( produc1647375838t_name @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(96,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_294_Late__Semantics_OResB) ).
thf(687,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)],[96]) ).
thf(154,axiom,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_name__exists__fresh) ).
thf(877,plain,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(108,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_cp__name__name1) ).
thf(734,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(178,axiom,
! [A: list_P227219501e_name,B: late_subject,C: list_Late_subject] :
( ( perm_n1812647369ubject @ A @ ( cons_Late_subject @ B @ C ) )
= ( cons_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1812647369ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_cons__eqvt) ).
thf(956,plain,
! [A: list_P227219501e_name,B: late_subject,C: list_Late_subject] :
( ( perm_n1812647369ubject @ A @ ( cons_Late_subject @ B @ C ) )
= ( cons_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1812647369ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(30,axiom,
! [A: name,B: late_subject,C: late_freeRes] :
( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_fresh__prod) ).
thf(453,plain,
! [A: name,B: late_subject,C: late_freeRes] :
( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(331,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( fresh_name_pi @ C @ B )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_name__fresh__fresh) ).
thf(1622,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( fresh_name_pi @ C @ B )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(190,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_subset__antisym) ).
thf(998,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(290,axiom,
! [A: late_freeRes_Rep] :
( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_freeRes__perm__empty) ).
thf(1433,plain,
! [A: late_freeRes_Rep] :
( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(278,axiom,
! [A: list_P227219501e_name,B: pi > late_subject,C: pi] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n190055296ubject @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_perm__app) ).
thf(1345,plain,
! [A: list_P227219501e_name,B: pi > late_subject,C: pi] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n190055296ubject @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(188,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_325_resCasesF_H) ).
thf(988,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)],[188]) ).
thf(10,axiom,
! [A: name,B: name] :
( ( if_name @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Oname_T) ).
thf(380,plain,
! [A: name,B: name] :
( ( if_name @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(174,axiom,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_pair__in__Id__conv) ).
thf(942,plain,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(93,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_293_freshBoundDerivative_I1_J) ).
thf(678,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)],[93]) ).
thf(354,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(1691,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(57,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_cp__name__name1) ).
thf(546,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: name] :
( ( perm_name_name @ A @ ( perm_name_name @ B @ C ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(128,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_ord__eq__le__trans) ).
thf(798,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(121,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_sumIdempLeft) ).
thf(778,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(300,axiom,
fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_Bound_Ohyps_I2_J) ).
thf(1519,plain,
fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(281,axiom,
aa != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cOpen_Ohyps_I2_J) ).
thf(1355,plain,
aa != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(149,axiom,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_old_Oprod_Oinject) ).
thf(862,plain,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(231,axiom,
fresh_name_pi @ y @ q,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062) ).
thf(1174,plain,
fresh_name_pi @ y @ q,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(135,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ ( sum @ B @ C ) @ D ) @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_sumAssocLeft) ).
thf(820,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ ( sum @ B @ C ) @ D ) @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(14,axiom,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_old_Oprod_Oinducts) ).
thf(392,plain,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [A: list_P227219501e_name,B: name,C: list_name] :
( ( perm_name_list_name @ A @ ( cons_name @ B @ C ) )
= ( cons_name @ ( perm_name_name @ A @ B ) @ ( perm_name_list_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_cons__eqvt) ).
thf(407,plain,
! [A: list_P227219501e_name,B: name,C: list_name] :
( ( perm_name_list_name @ A @ ( cons_name @ B @ C ) )
= ( cons_name @ ( perm_name_name @ A @ B ) @ ( perm_name_list_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(330,axiom,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_name__swap) ).
thf(1619,plain,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(247,axiom,
! [A: name,B: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_name__id) ).
thf(1238,plain,
! [A: name,B: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(112,axiom,
! [A: list_P227219501e_name,B: late_subject,C: pi_Rep] :
( ( perm_n1467004033pi_Rep @ A @ ( produc843063281pi_Rep @ B @ C ) )
= ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_perm__prod_Osimps) ).
thf(746,plain,
! [A: list_P227219501e_name,B: late_subject,C: pi_Rep] :
( ( perm_n1467004033pi_Rep @ A @ ( produc843063281pi_Rep @ B @ C ) )
= ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(213,axiom,
! [A: list_P227219501e_name,B: $o,C: pi,D: pi] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
= ( perm_name_pi @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
= ( perm_name_pi @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_if__eqvt) ).
thf(1091,plain,
! [A: list_P227219501e_name,B: $o,C: pi,D: pi] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
= ( perm_name_pi @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_name_pi @ A @ ( if_pi @ B @ C @ D ) )
= ( perm_name_pi @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(324,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( fresh_name_pi @ C @ B )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_perm__fresh__fresh) ).
thf(1602,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( fresh_name_pi @ C @ B )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(233,axiom,
! [A: name,B: list_P227219501e_name,C: pi] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_name_pi @ A @ C )
=> ( fresh_name_pi @ A @ ( perm_name_pi @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_fresh__perm__app) ).
thf(1178,plain,
! [A: name,B: list_P227219501e_name,C: pi] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_name_pi @ A @ C )
=> ( fresh_name_pi @ A @ ( perm_name_pi @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(89,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_295_freshBoundDerivative_I2_J) ).
thf(665,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)],[89]) ).
thf(353,axiom,
! [A: produc890461031e_name] :
( ! [B: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
=> ( ! [B: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ B @ nil_Pr743626285e_name ) )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_shuffles_Ocases) ).
thf(1687,plain,
! [A: produc890461031e_name] :
( ! [B: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
=> ( ! [B: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ B @ nil_Pr743626285e_name ) )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(158,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_345_inputIneqTrans) ).
thf(889,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)],[158]) ).
thf(228,axiom,
! [A: name,B: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_name__id) ).
thf(1159,plain,
! [A: name,B: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(40,axiom,
! [A: pi_Rep,B: pi_Rep,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_name_pi_Rep @ C @ A )
= ( perm_name_pi_Rep @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_pt__bij3) ).
thf(493,plain,
! [A: pi_Rep,B: pi_Rep,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_name_pi_Rep @ C @ A )
= ( perm_name_pi_Rep @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(238,axiom,
! [A: produc367475239e_name,B: list_P227219501e_name,C: produc367475239e_name,D: list_P227219501e_name] :
( ( ( cons_P1213805021e_name @ A @ B )
= ( cons_P1213805021e_name @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_list_Oinject) ).
thf(1195,plain,
! [A: produc367475239e_name,B: list_P227219501e_name,C: produc367475239e_name,D: list_P227219501e_name] :
( ( ( cons_P1213805021e_name @ A @ B )
= ( cons_P1213805021e_name @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(222,axiom,
! [A: late_subject] :
( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_pt__name1) ).
thf(1128,plain,
! [A: late_subject] :
( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(183,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_sumIdempRight) ).
thf(974,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(62,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_301_freshResidual) ).
thf(566,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)],[62]) ).
thf(37,axiom,
! [A: name,B: name,C: list_name] :
( ( fresh_name_list_name @ A @ ( cons_name @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_list_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_fresh__list__cons) ).
thf(484,plain,
! [A: name,B: name,C: list_name] :
( ( fresh_name_list_name @ A @ ( cons_name @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_list_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(3,axiom,
! [A: late_freeRes,B: late_freeRes] :
( ( if_Late_freeRes @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Late____Semantics__OfreeRes_T) ).
thf(361,plain,
! [A: late_freeRes,B: late_freeRes] :
( ( if_Late_freeRes @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(284,axiom,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_perm__swap_I2_J) ).
thf(1365,plain,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(49,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_297_Sum2) ).
thf(522,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)],[49]) ).
thf(138,axiom,
! [A: list_P227219501e_name,B: name,C: late_freeRes] :
( ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) )
= ( fresh_1641682979reeRes @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_fresh__bij) ).
thf(830,plain,
! [A: list_P227219501e_name,B: name,C: late_freeRes] :
( ( fresh_1641682979reeRes @ ( perm_name_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) )
= ( fresh_1641682979reeRes @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(31,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_order__subst1) ).
thf(456,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(142,axiom,
! [A: name,B: late_subject,C: list_Late_subject] :
( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_838462539ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_fresh__list__cons) ).
thf(842,plain,
! [A: name,B: late_subject,C: list_Late_subject] :
( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_838462539ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(153,axiom,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_old_Oprod_Oinducts) ).
thf(874,plain,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(258,axiom,
! [A: produc367475239e_name] :
? [B: name,C: name] :
( A
= ( produc1570949143e_name @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_surj__pair) ).
thf(1270,plain,
! [A: produc367475239e_name] :
? [B: name,C: name] :
( A
= ( produc1570949143e_name @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(84,axiom,
! [A: list_P227219501e_name,B: name,C: name] :
( ( perm_n336613537reeRes @ A @ ( late_OutputR @ B @ C ) )
= ( late_OutputR @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_freeRes_Operm_I1_J) ).
thf(650,plain,
! [A: list_P227219501e_name,B: name,C: name] :
( ( perm_n336613537reeRes @ A @ ( late_OutputR @ B @ C ) )
= ( late_OutputR @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(196,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: set_Pr1834926343_pi_pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_le630093991_pi_pi @ B @ D )
=> ( strong743114133lation @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_monotonic) ).
thf(1017,plain,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: set_Pr1834926343_pi_pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_le630093991_pi_pi @ B @ D )
=> ( strong743114133lation @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(211,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi,F: late_subject > pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( D != A )
=> ( ( fresh_name_pi @ D @ B )
=> ( ! [G: name,H: pi] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ A ) @ H ) )
=> ( ( G != A )
=> ( ( C
= ( late_BoundOutputS @ G ) )
=> ( F @ ( late_BoundOutputS @ G ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ H ) ) ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( ( fresh_717452603ubject @ A @ C )
=> ( F @ C @ ( res @ A @ G ) ) ) )
=> ( F @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_resCasesB) ).
thf(1064,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi,F: late_subject > pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( D != A )
=> ( ( fresh_name_pi @ D @ B )
=> ( ! [G: name,H: pi] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ A ) @ H ) )
=> ( ( G != A )
=> ( ( C
= ( late_BoundOutputS @ G ) )
=> ( F @ ( late_BoundOutputS @ G ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ H ) ) ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( ( fresh_717452603ubject @ A @ C )
=> ( F @ C @ ( res @ A @ G ) ) ) )
=> ( F @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(105,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( eqvt_pi @ A )
=> ( strong743114133lation @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) @ A @ ( res @ B @ ( sum @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_sumResLeft) ).
thf(725,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( eqvt_pi @ A )
=> ( strong743114133lation @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) @ A @ ( res @ B @ ( sum @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(225,axiom,
! [A: set_Pr443758855e_name,B: list_P227219501e_name,C: name,D: name] :
( ( eqvt_name @ A )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ B @ C ) @ ( perm_name_name @ B @ D ) ) @ A )
=> ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_eqvtRelE) ).
thf(1138,plain,
! [A: set_Pr443758855e_name,B: list_P227219501e_name,C: name,D: name] :
( ( eqvt_name @ A )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ B @ C ) @ ( perm_name_name @ B @ D ) ) @ A )
=> ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(123,axiom,
! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mem__Collect__eq) ).
thf(783,plain,
! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(185,axiom,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_name__exists__fresh) ).
thf(980,plain,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
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_329_Open) ).
thf(1498,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(319,axiom,
! [A: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_pt__name1) ).
thf(1587,plain,
! [A: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(272,axiom,
! [A: list_P227219501e_name] :
( ( A != nil_Pr743626285e_name )
= ( ? [B: produc367475239e_name,C: list_P227219501e_name] :
( A
= ( cons_P1213805021e_name @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_neq__Nil__conv) ).
thf(1329,plain,
! [A: list_P227219501e_name] :
( ( A != nil_Pr743626285e_name )
= ( ? [B: produc367475239e_name,C: list_P227219501e_name] :
( A
= ( cons_P1213805021e_name @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(171,axiom,
! [A: name,B: produc1141751126_pi_pi,C: list_P431515740_pi_pi] :
( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ B @ C ) )
= ( ( fresh_1376661020_pi_pi @ A @ B )
& ( fresh_1958133282_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_fresh__list__cons) ).
thf(933,plain,
! [A: name,B: produc1141751126_pi_pi,C: list_P431515740_pi_pi] :
( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ B @ C ) )
= ( ( fresh_1376661020_pi_pi @ A @ B )
& ( fresh_1958133282_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(54,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_298_Sum1) ).
thf(537,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)],[54]) ).
thf(90,axiom,
! [A: list_P227219501e_name,B: name,C: name] :
( ( ( perm_name_name @ A @ B )
= ( perm_name_name @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_perm__bij) ).
thf(669,plain,
! [A: list_P227219501e_name,B: name,C: name] :
( ( ( perm_name_name @ A @ B )
= ( perm_name_name @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(287,axiom,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_perm__swap_I2_J) ).
thf(1424,plain,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(83,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_ord__le__eq__subst) ).
thf(642,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(318,axiom,
! [A: set_Pr443758855e_name,B: name,C: name,D: list_P227219501e_name] :
( ( eqvt_name @ A )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ B @ C ) @ A )
=> ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ D @ B ) @ ( perm_name_name @ D @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_eqvtRelI) ).
thf(1584,plain,
! [A: set_Pr443758855e_name,B: name,C: name,D: list_P227219501e_name] :
( ( eqvt_name @ A )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ B @ C ) @ A )
=> ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ D @ B ) @ ( perm_name_name @ D @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(338,axiom,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_perm__swap_I1_J) ).
thf(1644,plain,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(101,axiom,
( fresh_name_name
= ( != @ name ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_name__fresh) ).
thf(706,plain,
( fresh_name_name
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(187,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_name__perm__compose) ).
thf(985,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(251,axiom,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_name__swap__bij) ).
thf(1249,plain,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(305,axiom,
! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ B )
=> ? [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
=> ( ! [D: late_freeRes,E: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
=> ( strong743114133lation @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_simCases) ).
thf(1539,plain,
! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ B )
=> ? [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
=> ( ! [D: late_freeRes,E: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
=> ( strong743114133lation @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(223,axiom,
! [A: produc1872410278e_name] :
( ! [B: produc367475239e_name > produc367475239e_name > $o] :
( A
!= ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
=> ( ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name] :
( A
!= ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) ) )
=> ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( A
!= ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_successively_Ocases) ).
thf(1131,plain,
! [A: produc1872410278e_name] :
( ! [B: produc367475239e_name > produc367475239e_name > $o] :
( A
!= ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
=> ( ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name] :
( A
!= ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) ) )
=> ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( A
!= ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(347,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_old_Oprod_Oinject) ).
thf(1668,plain,
! [A: name,B: name,C: name,D: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(237,axiom,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_perm__swap_I1_J) ).
thf(1192,plain,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(209,axiom,
fresh_name_pi @ y @ p2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062) ).
thf(1060,plain,
fresh_name_pi @ y @ p2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(63,axiom,
! [A: list_P227219501e_name,B: name,C: set_name] :
( ( perm_name_o @ A @ ( member_name @ B @ C ) )
= ( member_name @ ( perm_name_name @ A @ B ) @ ( perm_name_set_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_in__eqvt) ).
thf(569,plain,
! [A: list_P227219501e_name,B: name,C: set_name] :
( ( perm_name_o @ A @ ( member_name @ B @ C ) )
= ( member_name @ ( perm_name_name @ A @ B ) @ ( perm_name_set_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(75,axiom,
! [A: pi,B: pi] :
( ( if_pi @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Opi_T) ).
thf(605,plain,
! [A: pi,B: pi] :
( ( if_pi @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(323,axiom,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_perm__swap_I1_J) ).
thf(1599,plain,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(250,axiom,
! [A: pi] :
( ( perm_name_pi @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_pt__name1) ).
thf(1246,plain,
! [A: pi] :
( ( perm_name_pi @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(248,axiom,
! [A: list_P227219501e_name > $o] :
( ! [B: list_P227219501e_name] : ( A @ B )
=> ( A @ nil_Pr743626285e_name ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_allE__Nil) ).
thf(1241,plain,
! [A: list_P227219501e_name > $o] :
( ! [B: list_P227219501e_name] : ( A @ B )
=> ( A @ nil_Pr743626285e_name ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1,conjecture,
strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(360,plain,
~ ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_name__exists__fresh) ).
thf(508,plain,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(61,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( A
= ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_ord__eq__le__subst) ).
thf(558,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( A
= ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(299,axiom,
! [A: list_P227219501e_name] :
( ( A != nil_Pr743626285e_name )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name] :
( A
!= ( cons_P1213805021e_name @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_list_Oexhaust) ).
thf(1515,plain,
! [A: list_P227219501e_name] :
( ( A != nil_Pr743626285e_name )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name] :
( A
!= ( cons_P1213805021e_name @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(199,axiom,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi,G: late_subject > name > pi > $o] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ( ( E != A )
=> ( ( E != B )
=> ( ( fresh_name_pi @ E @ C )
=> ( ( ( D
= ( late_InputS @ A ) )
=> ( ( F
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) )
=> ( G @ ( late_InputS @ A ) @ E @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) ) ) )
=> ( G @ D @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_inputCases) ).
thf(1026,plain,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi,G: late_subject > name > pi > $o] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ( ( E != A )
=> ( ( E != B )
=> ( ( fresh_name_pi @ E @ C )
=> ( ( ( D
= ( late_InputS @ A ) )
=> ( ( F
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) )
=> ( G @ ( late_InputS @ A ) @ E @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ E ) @ nil_Pr743626285e_name ) @ C ) ) ) )
=> ( G @ D @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(329,axiom,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_swap__simps_I2_J) ).
thf(1616,plain,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(88,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_327_freshFreeDerivative_I2_J) ).
thf(662,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)],[88]) ).
thf(240,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_prod_Oinject) ).
thf(1202,plain,
! [A: name,B: name,C: name,D: name] :
( ( ( produc1570949143e_name @ A @ B )
= ( produc1570949143e_name @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(126,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_antisym) ).
thf(792,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(263,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
( ( perm_n1211707594Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
= ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_perm__prod_Osimps) ).
thf(1286,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: pi] :
( ( perm_n1211707594Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
= ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(16,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_antisym__conv) ).
thf(398,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(177,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( sum @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_sumAssocRight) ).
thf(953,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( sum @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(235,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_name__perm__compose) ).
thf(1185,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(224,axiom,
! [A: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_pi__perm__empty) ).
thf(1135,plain,
! [A: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(259,axiom,
! [A: name,B: name] :
( ( member695284560e_name @ ( produc1570949143e_name @ A @ B ) @ id_name )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_pair__in__Id__conv) ).
thf(1273,plain,
! [A: name,B: name] :
( ( member695284560e_name @ ( produc1570949143e_name @ A @ B ) @ id_name )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(147,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_cp__name__name1) ).
thf(856,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( perm_n1559866809ubject @ B @ C ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(68,axiom,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_fresh__prodD_I1_J) ).
thf(584,plain,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(119,axiom,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_prod__cases) ).
thf(772,plain,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(111,axiom,
! [A: list_P227219501e_name,B: name,C: name] :
( ( perm_name_o @ A @ ( fresh_name_name @ B @ C ) )
= ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_fresh__eqvt) ).
thf(743,plain,
! [A: list_P227219501e_name,B: name,C: name] :
( ( perm_name_o @ A @ ( fresh_name_name @ B @ C ) )
= ( fresh_name_name @ ( perm_name_name @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(301,axiom,
! [A: produc1872410278e_name] :
( ! [B: produc367475239e_name > produc367475239e_name > $o] :
( A
!= ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
=> ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: list_P227219501e_name] :
( A
!= ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_sorted__wrt_Ocases) ).
thf(1520,plain,
! [A: produc1872410278e_name] :
( ! [B: produc367475239e_name > produc367475239e_name > $o] :
( A
!= ( produc1069608854e_name @ B @ nil_Pr743626285e_name ) )
=> ~ ! [B: produc367475239e_name > produc367475239e_name > $o,C: produc367475239e_name,D: list_P227219501e_name] :
( A
!= ( produc1069608854e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(221,axiom,
! [A: name,B: late_subject,C: name] :
( ( fresh_717452603ubject @ A @ B )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_perm__fresh__fresh) ).
thf(1124,plain,
! [A: name,B: late_subject,C: name] :
( ( fresh_717452603ubject @ A @ B )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(253,axiom,
( a
= ( late_BoundOutputS @ aa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cOpen_Ohyps_I3_J) ).
thf(1256,plain,
( a
= ( late_BoundOutputS @ aa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(21,axiom,
! [A: list_P227219501e_name,B: pi_Rep,C: set_pi_Rep] :
( ( perm_name_o @ A @ ( member_pi_Rep @ B @ C ) )
= ( member_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_name_set_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_in__eqvt) ).
thf(413,plain,
! [A: list_P227219501e_name,B: pi_Rep,C: set_pi_Rep] :
( ( perm_name_o @ A @ ( member_pi_Rep @ B @ C ) )
= ( member_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_name_set_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(193,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_321_residual_Odistinct_I1_J) ).
thf(1007,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)],[193]) ).
thf(98,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( B = C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_ord__le__eq__trans) ).
thf(694,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( B = C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(137,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_340_pi_Odistinct_I53_J) ).
thf(826,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)],[137]) ).
thf(66,axiom,
! [A: list_P227219501e_name,B: late_subject > late_subject,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n1447856217ubject @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_perm__app) ).
thf(577,plain,
! [A: list_P227219501e_name,B: late_subject > late_subject,C: late_subject] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n1447856217ubject @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(103,axiom,
! [A: $o,B: list_P227219501e_name,C: late_freeRes,D: late_freeRes] :
( ( A
=> ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
= ( perm_n336613537reeRes @ B @ C ) ) )
& ( ~ A
=> ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
= ( perm_n336613537reeRes @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_abs__fun__if) ).
thf(711,plain,
! [A: $o,B: list_P227219501e_name,C: late_freeRes,D: late_freeRes] :
( ( A
=> ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
= ( perm_n336613537reeRes @ B @ C ) ) )
& ( ~ A
=> ( ( perm_n336613537reeRes @ B @ ( if_Late_freeRes @ A @ C @ D ) )
= ( perm_n336613537reeRes @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(172,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_n336613537reeRes @ A @ B )
= ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_eq__eqvt) ).
thf(936,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_n336613537reeRes @ A @ B )
= ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(64,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ C ) @ A @ ( sum @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_sumSym) ).
thf(572,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ C ) @ A @ ( sum @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(268,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name > $o] :
( ( A != nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name] : ( B @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
=> ( ! [C: produc367475239e_name,D: list_P227219501e_name] :
( ( D != nil_Pr743626285e_name )
=> ( ( B @ D )
=> ( B @ ( cons_P1213805021e_name @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_list__nonempty__induct) ).
thf(1312,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name > $o] :
( ( A != nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name] : ( B @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
=> ( ! [C: produc367475239e_name,D: list_P227219501e_name] :
( ( D != nil_Pr743626285e_name )
=> ( ( B @ D )
=> ( B @ ( cons_P1213805021e_name @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(77,axiom,
! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
( ( perm_n171497387ubject @ A @ ( produc1465345179ubject @ B @ C ) )
= ( produc1465345179ubject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_perm__prod_Osimps) ).
thf(611,plain,
! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
( ( perm_n171497387ubject @ A @ ( produc1465345179ubject @ B @ C ) )
= ( produc1465345179ubject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(41,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: pi_Rep] :
( ( perm_n840427369pi_Rep @ A @ ( produc216486617pi_Rep @ B @ C ) )
= ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_perm__prod_Osimps) ).
thf(498,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: pi_Rep] :
( ( perm_n840427369pi_Rep @ A @ ( produc216486617pi_Rep @ B @ C ) )
= ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(207,axiom,
late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_cOpen_Ohyps_I1_J) ).
thf(1058,plain,
late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(273,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_alphaRes) ).
thf(1332,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(212,axiom,
late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_Bound_Ohyps_I1_J) ).
thf(1090,plain,
late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(167,axiom,
! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_n1559866809ubject @ A @ B )
= ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_eq__eqvt) ).
thf(919,plain,
! [A: list_P227219501e_name,B: late_subject,C: late_subject] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_n1559866809ubject @ A @ B )
= ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(254,axiom,
! [A: produc367475239e_name > $o,B: produc367475239e_name] :
( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_old_Oprod_Oinducts) ).
thf(1258,plain,
! [A: produc367475239e_name > $o,B: produc367475239e_name] :
( ! [C: name,D: name] : ( A @ ( produc1570949143e_name @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(55,axiom,
! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_name_pi_Rep @ A @ B )
= ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_eq__eqvt) ).
thf(540,plain,
! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_name_pi_Rep @ A @ B )
= ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(91,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_Strong__Late__Sim_Oreflexive) ).
thf(672,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(94,axiom,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: pi,E: pi] : ( A @ ( produc235456326_pi_pi @ C @ ( product_Pair_pi_pi @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_prod__induct3) ).
thf(681,plain,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: pi,E: pi] : ( A @ ( produc235456326_pi_pi @ C @ ( product_Pair_pi_pi @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(262,axiom,
! [A: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name > $o,C: list_P227219501e_name] :
( ! [D: produc367475239e_name > produc367475239e_name > $o] : ( A @ D @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name] : ( A @ D @ ( cons_P1213805021e_name @ E @ nil_Pr743626285e_name ) )
=> ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name,F: produc367475239e_name,G: list_P227219501e_name] :
( ( A @ D @ ( cons_P1213805021e_name @ F @ G ) )
=> ( A @ D @ ( cons_P1213805021e_name @ E @ ( cons_P1213805021e_name @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_successively_Oinduct) ).
thf(1282,plain,
! [A: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name > $o,C: list_P227219501e_name] :
( ! [D: produc367475239e_name > produc367475239e_name > $o] : ( A @ D @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name] : ( A @ D @ ( cons_P1213805021e_name @ E @ nil_Pr743626285e_name ) )
=> ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name,F: produc367475239e_name,G: list_P227219501e_name] :
( ( A @ D @ ( cons_P1213805021e_name @ F @ G ) )
=> ( A @ D @ ( cons_P1213805021e_name @ E @ ( cons_P1213805021e_name @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(302,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: set_Pr1834926343_pi_pi,E: list_P227219501e_name] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_le630093991_pi_pi @ B @ D )
=> ( ( eqvt_pi @ D )
=> ( strong743114133lation @ ( perm_name_pi @ E @ A ) @ D @ ( perm_name_pi @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_eqvtI) ).
thf(1524,plain,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: set_Pr1834926343_pi_pi,E: list_P227219501e_name] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_le630093991_pi_pi @ B @ D )
=> ( ( eqvt_pi @ D )
=> ( strong743114133lation @ ( perm_name_pi @ E @ A ) @ D @ ( perm_name_pi @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(204,axiom,
! [A: name,B: name,C: name] :
( ( A != B )
=> ( ( C != B )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_swap__simps_I3_J) ).
thf(1048,plain,
! [A: name,B: name,C: name] :
( ( A != B )
=> ( ( C != B )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(9,axiom,
! [A: pi_Rep,B: pi_Rep] :
( ( if_pi_Rep @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Opi____Rep_T) ).
thf(377,plain,
! [A: pi_Rep,B: pi_Rep] :
( ( if_pi_Rep @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(109,axiom,
! [A: list_P227219501e_name,B: late_freeRes > late_subject,C: late_freeRes] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n303101761ubject @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_perm__app) ).
thf(737,plain,
! [A: list_P227219501e_name,B: late_freeRes > late_subject,C: late_freeRes] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n303101761ubject @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(313,axiom,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_perm__swap_I2_J) ).
thf(1571,plain,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(232,axiom,
! [A: list_P227219501e_name,B: pi,C: set_pi] :
( ( perm_name_o @ A @ ( member_pi @ B @ C ) )
= ( member_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_set_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_in__eqvt) ).
thf(1175,plain,
! [A: list_P227219501e_name,B: pi,C: set_pi] :
( ( perm_name_o @ A @ ( member_pi @ B @ C ) )
= ( member_pi @ ( perm_name_pi @ A @ B ) @ ( perm_name_set_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(314,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_346_resInputBoundOutputTrans) ).
thf(1574,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)],[314]) ).
thf(194,axiom,
! [A: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Collect__mem__eq) ).
thf(1011,plain,
! [A: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(23,axiom,
! [A: list_P227219501e_name,B: product_prod_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( perm_name_o @ A @ ( member558706512_pi_pi @ B @ C ) )
= ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ A @ B ) @ ( perm_n675238095_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_in__eqvt) ).
thf(419,plain,
! [A: list_P227219501e_name,B: product_prod_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( perm_name_o @ A @ ( member558706512_pi_pi @ B @ C ) )
= ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ A @ B ) @ ( perm_n675238095_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(155,axiom,
! [A: name,B: name,C: late_subject] :
( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_fresh__prod) ).
thf(880,plain,
! [A: name,B: name,C: late_subject] :
( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(26,axiom,
! [A: list_P227219501e_name,B: pi_Rep,C: list_pi_Rep] :
( ( perm_n729617823pi_Rep @ A @ ( cons_pi_Rep @ B @ C ) )
= ( cons_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_n729617823pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_cons__eqvt) ).
thf(434,plain,
! [A: list_P227219501e_name,B: pi_Rep,C: list_pi_Rep] :
( ( perm_n729617823pi_Rep @ A @ ( cons_pi_Rep @ B @ C ) )
= ( cons_pi_Rep @ ( perm_name_pi_Rep @ A @ B ) @ ( perm_n729617823pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(132,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_323_residual_Oinject_I2_J) ).
thf(811,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)],[132]) ).
thf(53,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_299_sumCases_H) ).
thf(535,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)],[53]) ).
thf(71,axiom,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_fresh__prod) ).
thf(594,plain,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(229,axiom,
! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ ( cons_P1213805021e_name @ D @ E ) @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ D @ E ) )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
( ( A @ E @ G )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_list__induct2_H) ).
thf(1162,plain,
! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ ( cons_P1213805021e_name @ D @ E ) @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ D @ E ) )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
( ( A @ E @ G )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(80,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Pair__inject) ).
thf(621,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(160,axiom,
! [A: product_prod_pi_pi] :
~ ! [B: pi,C: pi] :
( A
!= ( product_Pair_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Oprod_Oexhaust) ).
thf(895,plain,
! [A: product_prod_pi_pi] :
~ ! [B: pi,C: pi] :
( A
!= ( product_Pair_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(277,axiom,
eqvt_pi @ rel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Eqvt) ).
thf(1344,plain,
eqvt_pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(118,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_320_residual_Ofresh_I2_J) ).
thf(769,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)],[118]) ).
thf(210,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_perm__swap_I2_J) ).
thf(1061,plain,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(218,axiom,
! [A: name,B: late_subject,C: name] :
( ( fresh_717452603ubject @ A @ B )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_name__fresh__fresh) ).
thf(1112,plain,
! [A: name,B: late_subject,C: name] :
( ( fresh_717452603ubject @ A @ B )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(59,axiom,
! [A: name,B: late_freeRes,C: late_freeRes] :
( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_fresh__prod) ).
thf(552,plain,
! [A: name,B: late_freeRes,C: late_freeRes] :
( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(5,axiom,
! [A: name,B: name] :
( ( if_name @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Agent__Oname_T) ).
thf(367,plain,
! [A: name,B: name] :
( ( if_name @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(309,axiom,
! [A: name,B: name,C: produc1141751126_pi_pi,D: name] :
( ( A != B )
=> ( ( fresh_1376661020_pi_pi @ B @ C )
=> ( ( fresh_1376661020_pi_pi @ A @ C )
=> ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_fresh__aux) ).
thf(1557,plain,
! [A: name,B: name,C: produc1141751126_pi_pi,D: name] :
( ( A != B )
=> ( ( fresh_1376661020_pi_pi @ B @ C )
=> ( ( fresh_1376661020_pi_pi @ A @ C )
=> ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(144,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_300_sumCases) ).
thf(848,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)],[144]) ).
thf(48,axiom,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_eq__iff) ).
thf(520,plain,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(165,axiom,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_IdI) ).
thf(912,plain,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(186,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_fresh__prodD_I2_J) ).
thf(983,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(239,axiom,
! [A: name,B: name,C: late_freeRes,D: name] :
( ( A != B )
=> ( ( fresh_1641682979reeRes @ B @ C )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_fresh__aux) ).
thf(1198,plain,
! [A: name,B: name,C: late_freeRes,D: name] :
( ( A != B )
=> ( ( fresh_1641682979reeRes @ B @ C )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(179,axiom,
! [A: list_P227219501e_name,B: $o,C: late_freeRes,D: late_freeRes] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
= ( perm_n336613537reeRes @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
= ( perm_n336613537reeRes @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_if__eqvt) ).
thf(959,plain,
! [A: list_P227219501e_name,B: $o,C: late_freeRes,D: late_freeRes] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
= ( perm_n336613537reeRes @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_n336613537reeRes @ A @ ( if_Late_freeRes @ B @ C @ D ) )
= ( perm_n336613537reeRes @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(203,axiom,
! [A: name,B: name,C: late_subject,D: name] :
( ( A != B )
=> ( ( fresh_717452603ubject @ B @ C )
=> ( ( fresh_717452603ubject @ A @ C )
=> ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fresh__aux) ).
thf(1044,plain,
! [A: name,B: name,C: late_subject,D: name] :
( ( A != B )
=> ( ( fresh_717452603ubject @ B @ C )
=> ( ( fresh_717452603ubject @ A @ C )
=> ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(151,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_324_ResF) ).
thf(868,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)],[151]) ).
thf(156,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_269_pi_Oinject_I6_J) ).
thf(883,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)],[156]) ).
thf(76,axiom,
! [A: list_P227219501e_name,B: name,C: late_subject] :
( ( perm_name_o @ A @ ( fresh_717452603ubject @ B @ C ) )
= ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_fresh__eqvt) ).
thf(608,plain,
! [A: list_P227219501e_name,B: name,C: late_subject] :
( ( perm_name_o @ A @ ( fresh_717452603ubject @ B @ C ) )
= ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(215,axiom,
! [A: list_P227219501e_name,B: name,C: pi] :
( ( perm_name_pi @ A @ ( res @ B @ C ) )
= ( res @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_pi_Operm_I9_J) ).
thf(1102,plain,
! [A: list_P227219501e_name,B: name,C: pi] :
( ( perm_name_pi @ A @ ( res @ B @ C ) )
= ( res @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(43,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: pi,D: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_subrelI) ).
thf(505,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: pi,D: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(25,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_old_Oprod_Oinject) ).
thf(431,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(85,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_343_resInputFreeTrans) ).
thf(653,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)],[85]) ).
thf(321,axiom,
! [A: name,B: name,C: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
=> ( fresh_name_name @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_fresh__prodD_I2_J) ).
thf(1594,plain,
! [A: name,B: name,C: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
=> ( fresh_name_name @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(356,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_perm__swap_I1_J) ).
thf(1699,plain,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(355,axiom,
! [A: pi,B: pi,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_name_pi @ C @ A )
= ( perm_name_pi @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_pt__bij3) ).
thf(1694,plain,
! [A: pi,B: pi,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_name_pi @ C @ A )
= ( perm_name_pi @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(168,axiom,
! [A: late_subject,B: late_subject,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_n1559866809ubject @ C @ A )
= ( perm_n1559866809ubject @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_pt__bij3) ).
thf(922,plain,
! [A: late_subject,B: late_subject,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_n1559866809ubject @ C @ A )
= ( perm_n1559866809ubject @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(332,axiom,
! [A: list_P227219501e_name,B: pi,C: pi] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_name_pi @ A @ B )
= ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_eq__eqvt) ).
thf(1626,plain,
! [A: list_P227219501e_name,B: pi,C: pi] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_name_pi @ A @ B )
= ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(200,axiom,
! [A: name,B: name,C: pi,D: name] :
( ( A != B )
=> ( ( fresh_name_pi @ B @ C )
=> ( ( fresh_name_pi @ A @ C )
=> ( fresh_name_pi @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_fresh__aux) ).
thf(1034,plain,
! [A: name,B: name,C: pi,D: name] :
( ( A != B )
=> ( ( fresh_name_pi @ B @ C )
=> ( ( fresh_name_pi @ A @ C )
=> ( fresh_name_pi @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(345,axiom,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_perm__swap_I2_J) ).
thf(1662,plain,
! [A: name,B: name,C: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(242,axiom,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_name__id) ).
thf(1208,plain,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(127,axiom,
! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
( ( ( perm_name_pi_Rep @ A @ B )
= ( perm_name_pi_Rep @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_perm__bij) ).
thf(795,plain,
! [A: list_P227219501e_name,B: pi_Rep,C: pi_Rep] :
( ( ( perm_name_pi_Rep @ A @ B )
= ( perm_name_pi_Rep @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(352,axiom,
! [A: set_Pr443758855e_name,B: set_Pr443758855e_name] :
( ! [C: name,D: name] :
( ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ A )
=> ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ B ) )
=> ( ord_le793202855e_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_subrelI) ).
thf(1684,plain,
! [A: set_Pr443758855e_name,B: set_Pr443758855e_name] :
( ! [C: name,D: name] :
( ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ A )
=> ( member695284560e_name @ ( produc1570949143e_name @ C @ D ) @ B ) )
=> ( ord_le793202855e_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(38,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: list_Late_freeRes] :
( ( perm_n808352945reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
= ( cons_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n808352945reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_cons__eqvt) ).
thf(487,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: list_Late_freeRes] :
( ( perm_n808352945reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
= ( cons_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n808352945reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(113,axiom,
! [A: name,B: late_freeRes,C: list_Late_freeRes] :
( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_1981651763reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_fresh__list__cons) ).
thf(749,plain,
! [A: name,B: late_freeRes,C: list_Late_freeRes] :
( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_1981651763reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(79,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_303_transitions_OResB) ).
thf(617,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)],[79]) ).
thf(227,axiom,
! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name] : ( A @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
=> ( ! [C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( ( A @ E )
=> ( ( A @ ( cons_P1213805021e_name @ D @ E ) )
=> ( A @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_induct__list012) ).
thf(1145,plain,
! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name] : ( A @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
=> ( ! [C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( ( A @ E )
=> ( ( A @ ( cons_P1213805021e_name @ D @ E ) )
=> ( A @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(140,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_subsetI) ).
thf(836,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(39,axiom,
! [A: name,B: list_P227219501e_name,C: produc1141751126_pi_pi] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_1376661020_pi_pi @ A @ C )
=> ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_fresh__perm__app) ).
thf(490,plain,
! [A: name,B: list_P227219501e_name,C: produc1141751126_pi_pi] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_1376661020_pi_pi @ A @ C )
=> ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(92,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_prod_Oinject) ).
thf(675,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(169,axiom,
! [A: name,B: late_subject,C: late_subject] :
( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_fresh__prod) ).
thf(927,plain,
! [A: name,B: late_subject,C: late_subject] :
( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(8,axiom,
! [A: late_subject,B: late_subject] :
( ( if_Late_subject @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Late____Semantics__Osubject_T) ).
thf(374,plain,
! [A: late_subject,B: late_subject] :
( ( if_Late_subject @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(173,axiom,
! [A: list_P227219501e_name,B: name > late_freeRes,C: name] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n382765978reeRes @ A @ B @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_perm__app) ).
thf(939,plain,
! [A: list_P227219501e_name,B: name > late_freeRes,C: name] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n382765978reeRes @ A @ B @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(275,axiom,
late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_cSum1_Ohyps) ).
thf(1340,plain,
late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(234,axiom,
! [A: name,B: produc1141751126_pi_pi,C: name] :
( ( fresh_1376661020_pi_pi @ A @ B )
=> ( ( fresh_1376661020_pi_pi @ C @ B )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_perm__fresh__fresh) ).
thf(1181,plain,
! [A: name,B: produc1141751126_pi_pi,C: name] :
( ( fresh_1376661020_pi_pi @ A @ B )
=> ( ( fresh_1376661020_pi_pi @ C @ B )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(136,axiom,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_prod_Oinject) ).
thf(823,plain,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(50,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_318_freeRes_Ofresh_I1_J) ).
thf(525,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)],[50]) ).
thf(67,axiom,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: product_prod_pi_pi] :
( A
!= ( produc235456326_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_old_Oprod_Oexhaust) ).
thf(580,plain,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: product_prod_pi_pi] :
( A
!= ( produc235456326_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(182,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_fresh__prodD_I1_J) ).
thf(971,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(339,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_cp__name__name1) ).
thf(1647,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi] :
( ( perm_name_pi @ A @ ( perm_name_pi @ B @ C ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(252,axiom,
! [A: produc367475239e_name,B: list_P227219501e_name] :
( nil_Pr743626285e_name
!= ( cons_P1213805021e_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_list_Odistinct_I1_J) ).
thf(1252,plain,
! [A: produc367475239e_name,B: list_P227219501e_name] :
( nil_Pr743626285e_name
!= ( cons_P1213805021e_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(285,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_331_resCasesB_H) ).
thf(1368,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)],[285]) ).
thf(214,axiom,
! [A: name,B: name,C: name,D: name] :
( ( A != B )
=> ( ( fresh_name_name @ B @ C )
=> ( ( fresh_name_name @ A @ C )
=> ( fresh_name_name @ A @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_fresh__aux) ).
thf(1098,plain,
! [A: name,B: name,C: name,D: name] :
( ( A != B )
=> ( ( fresh_name_name @ B @ C )
=> ( ( fresh_name_name @ A @ C )
=> ( fresh_name_name @ A @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(335,axiom,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_name__swap) ).
thf(1637,plain,
! [A: name,B: name,C: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(236,axiom,
! [A: name,B: pi,C: late_subject,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( late_BoundR @ C @ D @ B )
= ( late_BoundR @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_alphaBoundResidual) ).
thf(1188,plain,
! [A: name,B: pi,C: late_subject,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( late_BoundR @ C @ D @ B )
= ( late_BoundR @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(28,axiom,
! [A: $o,B: list_P227219501e_name,C: pi_Rep,D: pi_Rep] :
( ( A
=> ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
= ( perm_name_pi_Rep @ B @ C ) ) )
& ( ~ A
=> ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
= ( perm_name_pi_Rep @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_abs__fun__if) ).
thf(441,plain,
! [A: $o,B: list_P227219501e_name,C: pi_Rep,D: pi_Rep] :
( ( A
=> ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
= ( perm_name_pi_Rep @ B @ C ) ) )
& ( ~ A
=> ( ( perm_name_pi_Rep @ B @ ( if_pi_Rep @ A @ C @ D ) )
= ( perm_name_pi_Rep @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(246,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( ord_le630093991_pi_pi @ E @ F )
=> ( strong2129052853vative @ A @ B @ C @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_derivativeMonotonic) ).
thf(1235,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( ord_le630093991_pi_pi @ E @ F )
=> ( strong2129052853vative @ A @ B @ C @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(33,axiom,
! [A: list_P227219501e_name,B: $o,C: name,D: name] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
= ( perm_name_name @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
= ( perm_name_name @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_if__eqvt) ).
thf(463,plain,
! [A: list_P227219501e_name,B: $o,C: name,D: name] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
= ( perm_name_name @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_name_name @ A @ ( if_name @ B @ C @ D ) )
= ( perm_name_name @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(131,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_339_resTrans_I2_J) ).
thf(808,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)],[131]) ).
thf(274,axiom,
! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: list_P227219501e_name] :
( ( A @ F @ E )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_splice_Oinduct) ).
thf(1336,plain,
! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: list_P227219501e_name] :
( ( A @ F @ E )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(201,axiom,
! [A: list_P227219501e_name,B: pi,C: pi] :
( ( ( perm_name_pi @ A @ B )
= ( perm_name_pi @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_perm__bij) ).
thf(1038,plain,
! [A: list_P227219501e_name,B: pi,C: pi] :
( ( ( perm_name_pi @ A @ B )
= ( perm_name_pi @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(6,axiom,
! [A: late_subject,B: late_subject] :
( ( if_Late_subject @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Late____Semantics__Osubject_T) ).
thf(370,plain,
! [A: late_subject,B: late_subject] :
( ( if_Late_subject @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,axiom,
! [A: $o,B: list_P227219501e_name,C: late_subject,D: late_subject] :
( ( A
=> ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
= ( perm_n1559866809ubject @ B @ C ) ) )
& ( ~ A
=> ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
= ( perm_n1559866809ubject @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_abs__fun__if) ).
thf(470,plain,
! [A: $o,B: list_P227219501e_name,C: late_subject,D: late_subject] :
( ( A
=> ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
= ( perm_n1559866809ubject @ B @ C ) ) )
& ( ~ A
=> ( ( perm_n1559866809ubject @ B @ ( if_Late_subject @ A @ C @ D ) )
= ( perm_n1559866809ubject @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(344,axiom,
! [A: produc890461031e_name] :
( ! [B: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_splice_Ocases) ).
thf(1658,plain,
! [A: produc890461031e_name] :
( ! [B: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ nil_Pr743626285e_name @ B ) )
=> ~ ! [B: produc367475239e_name,C: list_P227219501e_name,D: list_P227219501e_name] :
( A
!= ( produc208131031e_name @ ( cons_P1213805021e_name @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(282,axiom,
! [A: ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name,C: list_P227219501e_name,D: list_P227219501e_name] :
( ! [E: produc367475239e_name > produc367475239e_name,F: list_P227219501e_name] : ( A @ E @ nil_Pr743626285e_name @ F )
=> ( ! [E: produc367475239e_name > produc367475239e_name,F: produc367475239e_name,G: list_P227219501e_name,H: list_P227219501e_name] :
( ( A @ E @ G @ ( cons_P1213805021e_name @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_P1213805021e_name @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_map__tailrec__rev_Oinduct) ).
thf(1358,plain,
! [A: ( produc367475239e_name > produc367475239e_name ) > list_P227219501e_name > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name,C: list_P227219501e_name,D: list_P227219501e_name] :
( ! [E: produc367475239e_name > produc367475239e_name,F: list_P227219501e_name] : ( A @ E @ nil_Pr743626285e_name @ F )
=> ( ! [E: produc367475239e_name > produc367475239e_name,F: produc367475239e_name,G: list_P227219501e_name,H: list_P227219501e_name] :
( ( A @ E @ G @ ( cons_P1213805021e_name @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_P1213805021e_name @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(357,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(1702,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(73,axiom,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_freshRes) ).
thf(600,plain,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(205,axiom,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_name__swap__bij) ).
thf(1052,plain,
! [A: name,B: name,C: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(288,axiom,
! [A: late_residual_Rep] :
( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_residual__perm__empty) ).
thf(1427,plain,
! [A: late_residual_Rep] :
( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(296,axiom,
! [A: list_P227219501e_name] :
( ( A != nil_Pr743626285e_name )
=> ( ! [B: produc367475239e_name] :
( A
!= ( cons_P1213805021e_name @ B @ nil_Pr743626285e_name ) )
=> ~ ! [B: produc367475239e_name,C: produc367475239e_name,D: list_P227219501e_name] :
( A
!= ( cons_P1213805021e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_remdups__adj_Ocases) ).
thf(1504,plain,
! [A: list_P227219501e_name] :
( ( A != nil_Pr743626285e_name )
=> ( ! [B: produc367475239e_name] :
( A
!= ( cons_P1213805021e_name @ B @ nil_Pr743626285e_name ) )
=> ~ ! [B: produc367475239e_name,C: produc367475239e_name,D: list_P227219501e_name] :
( A
!= ( cons_P1213805021e_name @ B @ ( cons_P1213805021e_name @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(12,axiom,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_Late__Semantics1_Osubject_Oinject_I1_J) ).
thf(386,plain,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(148,axiom,
! [A: list_P227219501e_name,B: late_subject,C: set_Late_subject] :
( ( perm_name_o @ A @ ( member_Late_subject @ B @ C ) )
= ( member_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n412725103ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_in__eqvt) ).
thf(859,plain,
! [A: list_P227219501e_name,B: late_subject,C: set_Late_subject] :
( ( perm_name_o @ A @ ( member_Late_subject @ B @ C ) )
= ( member_Late_subject @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_n412725103ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(226,axiom,
! [A: name,B: name,C: pi_Rep,D: name] :
( ( A != B )
=> ( ( fresh_name_pi_Rep @ B @ C )
=> ( ( fresh_name_pi_Rep @ A @ C )
=> ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_fresh__aux) ).
thf(1141,plain,
! [A: name,B: name,C: pi_Rep,D: name] :
( ( A != B )
=> ( ( fresh_name_pi_Rep @ B @ C )
=> ( ( fresh_name_pi_Rep @ A @ C )
=> ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ D ) @ nil_Pr743626285e_name ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(304,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: list_P227219501e_name] :
( ( eqvt_pi @ A )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ B @ C ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ D @ B ) @ ( perm_name_pi @ D @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_eqvtRelI) ).
thf(1536,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: list_P227219501e_name] :
( ( eqvt_pi @ A )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ B @ C ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ D @ B ) @ ( perm_name_pi @ D @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(86,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_328_freshFreeDerivative_I1_J) ).
thf(656,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)],[86]) ).
thf(198,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: name] :
( ( perm_n258463228s_name @ A @ ( produc1701355766s_name @ B @ C ) )
= ( produc1701355766s_name @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_perm__prod_Osimps) ).
thf(1023,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: name] :
( ( perm_n258463228s_name @ A @ ( produc1701355766s_name @ B @ C ) )
= ( produc1701355766s_name @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(143,axiom,
! [A: name,B: list_P227219501e_name,C: late_subject] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_717452603ubject @ A @ C )
=> ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_fresh__perm__app) ).
thf(845,plain,
! [A: name,B: list_P227219501e_name,C: late_subject] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_717452603ubject @ A @ C )
=> ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(286,axiom,
! [A: name,B: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_name__id) ).
thf(1421,plain,
! [A: name,B: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(29,axiom,
! [A: name,B: late_freeRes,C: late_subject] :
( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_fresh__prod) ).
thf(450,plain,
! [A: name,B: late_freeRes,C: late_subject] :
( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(308,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( input @ C @ D @ B )
= ( input @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_alphaInput) ).
thf(1553,plain,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( input @ C @ D @ B )
= ( input @ C @ A @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ D @ A ) @ nil_Pr743626285e_name ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(36,axiom,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_1627595501_pi_pi @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_fresh__prodD_I2_J) ).
thf(482,plain,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_1627595501_pi_pi @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(342,axiom,
! [A: name,B: name,C: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
=> ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_fresh__prodD_I1_J) ).
thf(1654,plain,
! [A: name,B: name,C: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ B @ C ) )
=> ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(116,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_perm__compose) ).
thf(759,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(244,axiom,
! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name] : ( A @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
=> ( ! [C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( ( ( C = D )
=> ( A @ ( cons_P1213805021e_name @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) ) )
=> ( A @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_remdups__adj_Oinduct) ).
thf(1216,plain,
! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name] : ( A @ ( cons_P1213805021e_name @ C @ nil_Pr743626285e_name ) )
=> ( ! [C: produc367475239e_name,D: produc367475239e_name,E: list_P227219501e_name] :
( ( ( C = D )
=> ( A @ ( cons_P1213805021e_name @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) ) )
=> ( A @ ( cons_P1213805021e_name @ C @ ( cons_P1213805021e_name @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(264,axiom,
! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name,D: list_P227219501e_name] :
( ( A @ D )
=> ( A @ ( cons_P1213805021e_name @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_list_Oinducts) ).
thf(1289,plain,
! [A: list_P227219501e_name > $o,B: list_P227219501e_name] :
( ( A @ nil_Pr743626285e_name )
=> ( ! [C: produc367475239e_name,D: list_P227219501e_name] :
( ( A @ D )
=> ( A @ ( cons_P1213805021e_name @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(271,axiom,
! [A: list_P227219501e_name,B: pi,C: pi] :
( ( perm_name_pi @ A @ ( sum @ B @ C ) )
= ( sum @ ( perm_name_pi @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_pi_Operm_I7_J) ).
thf(1326,plain,
! [A: list_P227219501e_name,B: pi,C: pi] :
( ( perm_name_pi @ A @ ( sum @ B @ C ) )
= ( sum @ ( perm_name_pi @ A @ B ) @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(99,axiom,
! [A: list_P227219501e_name,B: late_freeRes > late_freeRes,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n1446290985reeRes @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_perm__app) ).
thf(699,plain,
! [A: list_P227219501e_name,B: late_freeRes > late_freeRes,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n1446290985reeRes @ A @ B @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(47,axiom,
! [A: name,B: list_P227219501e_name,C: name] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_name_name @ A @ C )
=> ( fresh_name_name @ A @ ( perm_name_name @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_fresh__perm__app) ).
thf(517,plain,
! [A: name,B: list_P227219501e_name,C: name] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_name_name @ A @ C )
=> ( fresh_name_name @ A @ ( perm_name_name @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(276,axiom,
! [A: late_freeRes] :
( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_pt__name1) ).
thf(1341,plain,
! [A: late_freeRes] :
( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(349,axiom,
! [A: produc367475239e_name,B: list_P227219501e_name] :
( ( cons_P1213805021e_name @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_not__Cons__self2) ).
thf(1674,plain,
! [A: produc367475239e_name,B: list_P227219501e_name] :
( ( cons_P1213805021e_name @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(297,axiom,
y != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062) ).
thf(1508,plain,
y != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(333,axiom,
! [A: produc367475239e_name] :
( ( member695284560e_name @ A @ id_name )
=> ~ ! [B: name] :
( A
!= ( produc1570949143e_name @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_IdE) ).
thf(1629,plain,
! [A: produc367475239e_name] :
( ( member695284560e_name @ A @ id_name )
=> ~ ! [B: name] :
( A
!= ( produc1570949143e_name @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(17,axiom,
! [A: list_P227219501e_name,B: name > late_subject,C: name] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n1387060402ubject @ A @ B @ ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_perm__app) ).
thf(401,plain,
! [A: list_P227219501e_name,B: name > late_subject,C: name] :
( ( perm_n1559866809ubject @ A @ ( B @ C ) )
= ( perm_n1387060402ubject @ A @ B @ ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(122,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_dual__order_Orefl) ).
thf(781,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(189,axiom,
! [A: name,B: list_P227219501e_name,C: pi_Rep] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_name_pi_Rep @ A @ C )
=> ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_fresh__perm__app) ).
thf(995,plain,
! [A: name,B: list_P227219501e_name,C: pi_Rep] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_name_pi_Rep @ A @ C )
=> ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(260,axiom,
! [A: set_Pr1834926343_pi_pi,B: list_P227219501e_name,C: pi,D: pi] :
( ( eqvt_pi @ A )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ B @ C ) @ ( perm_name_pi @ B @ D ) ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_eqvtRelE) ).
thf(1276,plain,
! [A: set_Pr1834926343_pi_pi,B: list_P227219501e_name,C: pi,D: pi] :
( ( eqvt_pi @ A )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ B @ C ) @ ( perm_name_pi @ B @ D ) ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(320,axiom,
! [A: name,B: pi_Rep,C: name] :
( ( fresh_name_pi_Rep @ A @ B )
=> ( ( fresh_name_pi_Rep @ C @ B )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_perm__fresh__fresh) ).
thf(1590,plain,
! [A: name,B: pi_Rep,C: name] :
( ( fresh_name_pi_Rep @ A @ B )
=> ( ( fresh_name_pi_Rep @ C @ B )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(107,axiom,
! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) )
= ( fresh_1376661020_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_fresh__bij) ).
thf(731,plain,
! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) )
= ( fresh_1376661020_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(124,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_name__perm__compose) ).
thf(786,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(166,axiom,
! [A: name,B: name,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_name_name @ C @ A )
= ( perm_name_name @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_pt__bij3) ).
thf(914,plain,
! [A: name,B: name,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_name_name @ C @ A )
= ( perm_name_name @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(358,axiom,
! [A: name,B: name,C: name] :
( ( fresh_name_name @ A @ B )
=> ( ( fresh_name_name @ C @ B )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_perm__fresh__fresh) ).
thf(1706,plain,
! [A: name,B: name,C: name] :
( ( fresh_name_name @ A @ B )
=> ( ( fresh_name_name @ C @ B )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(11,axiom,
! [A: late_freeRes,B: late_freeRes] :
( ( if_Late_freeRes @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Late____Semantics__OfreeRes_T) ).
thf(383,plain,
! [A: late_freeRes,B: late_freeRes] :
( ( if_Late_freeRes @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(161,axiom,
! [A: list_P227219501e_name,B: name,C: late_subject] :
( ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) )
= ( fresh_717452603ubject @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_fresh__bij) ).
thf(899,plain,
! [A: list_P227219501e_name,B: name,C: late_subject] :
( ( fresh_717452603ubject @ ( perm_name_name @ A @ B ) @ ( perm_n1559866809ubject @ A @ C ) )
= ( fresh_717452603ubject @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(95,axiom,
! [A: list_P227219501e_name,B: late_subject > late_freeRes,C: late_subject] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n443561793reeRes @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_perm__app) ).
thf(684,plain,
! [A: list_P227219501e_name,B: late_subject > late_freeRes,C: late_subject] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n443561793reeRes @ A @ B @ ( perm_n1559866809ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(58,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_order_Otrans) ).
thf(549,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(219,axiom,
! [A: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name > $o,C: list_P227219501e_name] :
( ! [D: produc367475239e_name > produc367475239e_name > $o] : ( A @ D @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name,F: list_P227219501e_name] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_P1213805021e_name @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_sorted__wrt_Oinduct) ).
thf(1116,plain,
! [A: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,B: produc367475239e_name > produc367475239e_name > $o,C: list_P227219501e_name] :
( ! [D: produc367475239e_name > produc367475239e_name > $o] : ( A @ D @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name > produc367475239e_name > $o,E: produc367475239e_name,F: list_P227219501e_name] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_P1213805021e_name @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(279,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ A )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_simE_I1_J) ).
thf(1348,plain,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ A )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(114,axiom,
! [A: list_P227219501e_name,B: name,C: name] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_name_name @ A @ B )
= ( perm_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_eq__eqvt) ).
thf(752,plain,
! [A: list_P227219501e_name,B: name,C: name] :
( ( perm_name_o @ A @ ( B = C ) )
= ( ( perm_name_name @ A @ B )
= ( perm_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(316,axiom,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_perm__swap_I1_J) ).
thf(1578,plain,
! [A: name,B: name,C: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(350,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(1678,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(176,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_cp__name__name1) ).
thf(950,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: late_freeRes] :
( ( perm_n336613537reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_n336613537reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(306,axiom,
! [A: name,B: produc1141751126_pi_pi,C: name] :
( ( fresh_1376661020_pi_pi @ A @ B )
=> ( ( fresh_1376661020_pi_pi @ C @ B )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_name__fresh__fresh) ).
thf(1546,plain,
! [A: name,B: produc1141751126_pi_pi,C: name] :
( ( fresh_1376661020_pi_pi @ A @ B )
=> ( ( fresh_1376661020_pi_pi @ C @ B )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(303,axiom,
! [A: $o,B: list_P227219501e_name,C: pi,D: pi] :
( ( A
=> ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
= ( perm_name_pi @ B @ C ) ) )
& ( ~ A
=> ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
= ( perm_name_pi @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_abs__fun__if) ).
thf(1527,plain,
! [A: $o,B: list_P227219501e_name,C: pi,D: pi] :
( ( A
=> ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
= ( perm_name_pi @ B @ C ) ) )
& ( ~ A
=> ( ( perm_name_pi @ B @ ( if_pi @ A @ C @ D ) )
= ( perm_name_pi @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(24,axiom,
! [A: $o,B: list_P227219501e_name,C: name,D: name] :
( ( A
=> ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
= ( perm_name_name @ B @ C ) ) )
& ( ~ A
=> ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
= ( perm_name_name @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_abs__fun__if) ).
thf(422,plain,
! [A: $o,B: list_P227219501e_name,C: name,D: name] :
( ( A
=> ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
= ( perm_name_name @ B @ C ) ) )
& ( ~ A
=> ( ( perm_name_name @ B @ ( if_name @ A @ C @ D ) )
= ( perm_name_name @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(150,axiom,
! [A: set_Pr1654044726_pi_pi,B: set_Pr1654044726_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] :
( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ A )
=> ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ B ) )
=> ( ord_le797229014_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_subrelI) ).
thf(865,plain,
! [A: set_Pr1654044726_pi_pi,B: set_Pr1654044726_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] :
( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ A )
=> ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ B ) )
=> ( ord_le797229014_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(7,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Late____Semantics__Osubject_T) ).
thf(373,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(139,axiom,
! [A: list_P227219501e_name,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( perm_name_o @ A @ ( ord_le630093991_pi_pi @ B @ C ) )
= ( ord_le630093991_pi_pi @ ( perm_n675238095_pi_pi @ A @ B ) @ ( perm_n675238095_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_subseteq__eqvt) ).
thf(833,plain,
! [A: list_P227219501e_name,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( perm_name_o @ A @ ( ord_le630093991_pi_pi @ B @ C ) )
= ( ord_le630093991_pi_pi @ ( perm_n675238095_pi_pi @ A @ B ) @ ( perm_n675238095_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(20,axiom,
! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
( ( perm_name_o @ A @ ( fresh_1376661020_pi_pi @ B @ C ) )
= ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_fresh__eqvt) ).
thf(410,plain,
! [A: list_P227219501e_name,B: name,C: produc1141751126_pi_pi] :
( ( perm_name_o @ A @ ( fresh_1376661020_pi_pi @ B @ C ) )
= ( fresh_1376661020_pi_pi @ ( perm_name_name @ A @ B ) @ ( perm_n1255502110_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(291,axiom,
! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
=> ( ! [D: list_P227219501e_name] : ( A @ D @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
( ( A @ E @ ( cons_P1213805021e_name @ F @ G ) )
=> ( ( A @ ( cons_P1213805021e_name @ D @ E ) @ G )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_shuffles_Oinduct) ).
thf(1436,plain,
! [A: list_P227219501e_name > list_P227219501e_name > $o,B: list_P227219501e_name,C: list_P227219501e_name] :
( ! [D: list_P227219501e_name] : ( A @ nil_Pr743626285e_name @ D )
=> ( ! [D: list_P227219501e_name] : ( A @ D @ nil_Pr743626285e_name )
=> ( ! [D: produc367475239e_name,E: list_P227219501e_name,F: produc367475239e_name,G: list_P227219501e_name] :
( ( A @ E @ ( cons_P1213805021e_name @ F @ G ) )
=> ( ( A @ ( cons_P1213805021e_name @ D @ E ) @ G )
=> ( A @ ( cons_P1213805021e_name @ D @ E ) @ ( cons_P1213805021e_name @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(343,axiom,
ord_le630093991_pi_pi @ id_pi @ rel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Id) ).
thf(1657,plain,
ord_le630093991_pi_pi @ id_pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(27,axiom,
! [A: product_prod_pi_pi] :
( ( member558706512_pi_pi @ A @ id_pi )
=> ~ ! [B: pi] :
( A
!= ( product_Pair_pi_pi @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_IdE) ).
thf(437,plain,
! [A: product_prod_pi_pi] :
( ( member558706512_pi_pi @ A @ id_pi )
=> ~ ! [B: pi] :
( A
!= ( product_Pair_pi_pi @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(310,axiom,
! [A: name,B: pi_Rep,C: name] :
( ( fresh_name_pi_Rep @ A @ B )
=> ( ( fresh_name_pi_Rep @ C @ B )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_name__fresh__fresh) ).
thf(1561,plain,
! [A: name,B: pi_Rep,C: name] :
( ( fresh_name_pi_Rep @ A @ B )
=> ( ( fresh_name_pi_Rep @ C @ B )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(230,axiom,
( strong743114133lation
= ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
& ( fresh_name_pi @ E @ A ) )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
& ! [D: late_freeRes,E: pi] :
( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_simulation__def) ).
thf(1172,plain,
( strong743114133lation
= ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
& ( fresh_name_pi @ E @ A ) )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
& ! [D: late_freeRes,E: pi] :
( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(359,axiom,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_Bound_Ohyps_I5_J) ).
thf(1710,plain,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(82,axiom,
! [A: list_P227219501e_name,B: $o,C: late_subject,D: late_subject] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
= ( perm_n1559866809ubject @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
= ( perm_n1559866809ubject @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_if__eqvt) ).
thf(635,plain,
! [A: list_P227219501e_name,B: $o,C: late_subject,D: late_subject] :
( ( ( perm_name_o @ A @ B )
=> ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
= ( perm_n1559866809ubject @ A @ C ) ) )
& ( ~ ( perm_name_o @ A @ B )
=> ( ( perm_n1559866809ubject @ A @ ( if_Late_subject @ B @ C @ D ) )
= ( perm_n1559866809ubject @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(52,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_order__class_Oorder_Oantisym) ).
thf(532,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(104,axiom,
! [A: late_freeRes,B: late_freeRes,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_n336613537reeRes @ C @ A )
= ( perm_n336613537reeRes @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_pt__bij3) ).
thf(720,plain,
! [A: late_freeRes,B: late_freeRes,C: list_P227219501e_name] :
( ( A = B )
=> ( ( perm_n336613537reeRes @ C @ A )
= ( perm_n336613537reeRes @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(327,axiom,
! [A: late_subject_Rep] :
( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_subject__perm__empty) ).
thf(1610,plain,
! [A: late_subject_Rep] :
( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(157,axiom,
! [A: name,B: late_subject,C: name] :
( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_fresh__prod) ).
thf(886,plain,
! [A: name,B: late_subject,C: name] :
( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(280,axiom,
! [A: list_P227219501e_name,B: late_subject,C: name,D: pi] :
( ( perm_n414416632sidual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( late_BoundR @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_residual_Operm_I1_J) ).
thf(1352,plain,
! [A: list_P227219501e_name,B: late_subject,C: name,D: pi] :
( ( perm_n414416632sidual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( late_BoundR @ ( perm_n1559866809ubject @ A @ B ) @ ( perm_name_name @ A @ C ) @ ( perm_name_pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(255,axiom,
! [A: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_pt__name1) ).
thf(1261,plain,
! [A: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(51,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_order__subst2) ).
thf(528,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(307,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_name__swap) ).
thf(1550,plain,
! [A: name,B: name,C: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(145,axiom,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_perm__compose) ).
thf(850,plain,
! [A: list_P227219501e_name,B: list_P227219501e_name,C: pi_Rep] :
( ( perm_name_pi_Rep @ A @ ( perm_name_pi_Rep @ B @ C ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(192,axiom,
! [A: list_P227219501e_name,B: name,C: name] :
( ( ( perm_name_name @ A @ B )
= ( perm_name_name @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_name__bij) ).
thf(1004,plain,
! [A: list_P227219501e_name,B: name,C: name] :
( ( ( perm_name_name @ A @ B )
= ( perm_name_name @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(265,axiom,
! [A: list_P227219501e_name,B: name,C: pi] :
( ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) )
= ( fresh_name_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_fresh__bij) ).
thf(1299,plain,
! [A: list_P227219501e_name,B: name,C: pi] :
( ( fresh_name_pi @ ( perm_name_name @ A @ B ) @ ( perm_name_pi @ A @ C ) )
= ( fresh_name_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(97,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: set_Late_freeRes] :
( ( perm_name_o @ A @ ( member_Late_freeRes @ B @ C ) )
= ( member_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1555914327reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_in__eqvt) ).
thf(691,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: set_Late_freeRes] :
( ( perm_name_o @ A @ ( member_Late_freeRes @ B @ C ) )
= ( member_Late_freeRes @ ( perm_n336613537reeRes @ A @ B ) @ ( perm_n1555914327reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(152,axiom,
! [A: product_prod_pi_pi] :
? [B: pi,C: pi] :
( A
= ( product_Pair_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_surj__pair) ).
thf(871,plain,
! [A: product_prod_pi_pi] :
? [B: pi,C: pi] :
( A
= ( product_Pair_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(220,axiom,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_1641682979reeRes @ A @ B )
=> ( ( fresh_1641682979reeRes @ C @ B )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_perm__fresh__fresh) ).
thf(1120,plain,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_1641682979reeRes @ A @ B )
=> ( ( fresh_1641682979reeRes @ C @ B )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(42,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_341_pi_Odistinct_I57_J) ).
thf(501,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)],[42]) ).
thf(15,axiom,
! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
( ( ( perm_n336613537reeRes @ A @ B )
= ( perm_n336613537reeRes @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_perm__bij) ).
thf(395,plain,
! [A: list_P227219501e_name,B: late_freeRes,C: late_freeRes] :
( ( ( perm_n336613537reeRes @ A @ B )
= ( perm_n336613537reeRes @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(141,axiom,
! [A: name,B: list_P227219501e_name,C: late_freeRes] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_fresh__perm__app) ).
thf(839,plain,
! [A: name,B: list_P227219501e_name,C: late_freeRes] :
( ( fresh_922791155e_name @ A @ B )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(106,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_subject_Ofresh_I1_J) ).
thf(728,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(110,axiom,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_prod__cases) ).
thf(740,plain,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(257,axiom,
! [A: name] : ( member695284560e_name @ ( produc1570949143e_name @ A @ A ) @ id_name ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_IdI) ).
thf(1268,plain,
! [A: name] : ( member695284560e_name @ ( produc1570949143e_name @ A @ A ) @ id_name ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(65,axiom,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_order__class_Oorder_Oeq__iff) ).
thf(575,plain,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(325,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt_pi @ E )
=> ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ C @ ( perm_name_name @ F @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_derivativeEqvtI2) ).
thf(1606,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: list_P227219501e_name] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt_pi @ E )
=> ( strong2129052853vative @ ( perm_name_pi @ F @ A ) @ ( perm_name_pi @ F @ B ) @ C @ ( perm_name_name @ F @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(129,axiom,
! [A: produc1141751126_pi_pi] :
? [B: name,C: product_prod_pi_pi] :
( A
= ( produc235456326_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_surj__pair) ).
thf(803,plain,
! [A: produc1141751126_pi_pi] :
? [B: name,C: product_prod_pi_pi] :
( A
= ( produc235456326_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(269,axiom,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_swap__simps_I1_J) ).
thf(1320,plain,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(341,axiom,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062) ).
thf(1653,plain,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(351,axiom,
! [A: list_P227219501e_name,B: pi > late_freeRes,C: pi] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n1333244520reeRes @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_perm__app) ).
thf(1681,plain,
! [A: list_P227219501e_name,B: pi > late_freeRes,C: pi] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n1333244520reeRes @ A @ B @ ( perm_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(56,axiom,
! [A: list_P227219501e_name,B: pi_Rep > late_freeRes,C: pi_Rep] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n1841560599reeRes @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_perm__app) ).
thf(543,plain,
! [A: list_P227219501e_name,B: pi_Rep > late_freeRes,C: pi_Rep] :
( ( perm_n336613537reeRes @ A @ ( B @ C ) )
= ( perm_n1841560599reeRes @ A @ B @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(120,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_342_inputFreeTrans) ).
thf(775,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)],[120]) ).
thf(115,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_eq__refl) ).
thf(755,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(4,axiom,
! [A: pi_Rep,B: pi_Rep] :
( ( if_pi_Rep @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Agent__Opi____Rep_T) ).
thf(364,plain,
! [A: pi_Rep,B: pi_Rep] :
( ( if_pi_Rep @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(102,axiom,
! [A: name,B: late_subject,C: pi] :
( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_fresh__prod) ).
thf(708,plain,
! [A: name,B: late_subject,C: pi] :
( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(195,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_fresh__prod) ).
thf(1014,plain,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(87,axiom,
! [A: list_P227219501e_name,B: name,C: pi_Rep] :
( ( perm_name_o @ A @ ( fresh_name_pi_Rep @ B @ C ) )
= ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_fresh__eqvt) ).
thf(659,plain,
! [A: list_P227219501e_name,B: name,C: pi_Rep] :
( ( perm_name_o @ A @ ( fresh_name_pi_Rep @ B @ C ) )
= ( fresh_name_pi_Rep @ ( perm_name_name @ A @ B ) @ ( perm_name_pi_Rep @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(311,axiom,
! [A: pi,B: late_residual,C: list_P227219501e_name] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( perm_name_pi @ C @ A ) @ ( perm_n414416632sidual @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_eqvt) ).
thf(1565,plain,
! [A: pi,B: late_residual,C: list_P227219501e_name] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( perm_name_pi @ C @ A ) @ ( perm_n414416632sidual @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1711,plain,
$false,
inference(e,[status(thm)],[892,1665,1501,1633,555,479,1105,909,628,977,1211,762,1596,1205,511,614,1041,1305,597,1497,1671,814,1640,945,930,404,1001,1243,1441,1613,1650,389,1055,1430,1264,1279,1577,1059,460,587,1323,1511,702,853,1609,969,416,1568,1641,1362,1232,817,902,1302,789,591,1109,514,1020,806,905,1581,966,602,687,877,734,956,453,1622,998,1433,1345,988,380,942,678,1691,546,798,778,1519,1355,862,1174,820,392,407,1619,1238,746,1091,1602,1178,665,1687,889,1159,493,1195,1128,974,566,484,361,1365,522,830,456,842,874,1270,650,1017,1064,725,1138,783,980,1498,1587,1329,933,537,669,1424,642,1584,1644,706,985,1249,1539,1131,1668,1192,1060,569,605,1599,1246,1241,360,508,558,1515,1026,1616,662,1202,792,1286,398,953,1185,1135,1273,856,584,772,743,1520,1124,1256,413,1007,694,826,577,711,936,572,1312,611,498,1058,1332,1090,919,1258,540,672,681,1282,1524,1048,377,737,1571,1175,1574,1011,419,880,434,811,535,594,1162,621,895,1344,769,1061,1112,552,367,1557,848,520,912,983,1198,959,1044,868,883,608,1102,505,431,653,1594,1699,1694,922,1626,1034,1662,1208,795,1684,487,749,617,1145,836,490,675,927,374,939,1340,1181,823,525,580,971,1647,1252,1368,1098,1637,1188,441,1235,463,808,1336,1038,370,470,1658,1358,1702,600,1052,1427,1504,386,859,1141,1536,656,1023,845,1421,450,1553,482,1654,759,1216,1289,1326,699,517,1341,1674,1508,1629,401,781,995,1276,1590,731,786,914,1706,383,899,684,549,1116,1348,752,1578,1678,950,1546,1527,422,865,373,833,410,1436,1657,437,1561,1172,1710,635,532,720,1610,886,1352,1261,528,1550,850,1004,1299,691,871,1120,501,395,839,728,740,1268,575,1606,803,1320,1653,1681,543,775,755,364,708,1014,659,1565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP182^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:22:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/1.14 % [INFO] Parsing done (268ms).
% 1.95/1.15 % [INFO] Running in sequential loop mode.
% 2.68/1.36 % [INFO] eprover registered as external prover.
% 2.68/1.36 % [INFO] cvc4 registered as external prover.
% 2.68/1.36 % [INFO] Scanning for conjecture ...
% 2.89/1.47 % [INFO] Found a conjecture and 364 axioms. Running axiom selection ...
% 3.35/1.58 % [INFO] Axiom selection finished. Selected 357 axioms (removed 7 axioms).
% 4.00/1.77 % [INFO] Problem is higher-order (TPTP THF).
% 4.12/1.79 % [INFO] Type checking passed.
% 4.12/1.79 % [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 ...
% 16.74/5.14 % External prover 'e' found a proof!
% 16.74/5.14 % [INFO] Killing All external provers ...
% 16.74/5.14 % Time passed: 4605ms (effective reasoning time: 3989ms)
% 16.74/5.14 % 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)>
% 16.74/5.14 % Axioms used in derivation (357): help_If_2_1_If_001t__Agent__Opi_T, fact_175_list_Oexhaust, fact_123_cp__name__name1, help_If_1_1_If_001t__Agent__Oname_T, fact_25_pt__name1, fact_219_abs__fun__if, fact_139_perm__bij, fact_18_name__swap, fact_152_in__eqvt, fact_22_name__swap__bij, fact_77_fresh__eqvt, fact_95_fresh__aux, fact_276_antisym, fact_341_pi_Odistinct_I57_J, fact_105_old_Oprod_Oexhaust, fact_331_resCasesB_H, fact_302_eqvt, fact_115_prod__cases, fact_49_subject_Operm_I2_J, fact_19_name__swap, fact_191_fresh__prod, fact_344_inputBoundOutputTrans, fact_168_transpose_Ocases, fact_166_sorted__wrt_Oinduct, fact_10_name__id, fact_229_perm__prod_Osimps, fact_99_fresh__aux, fact_177_list_Odistinct_I1_J, fact_292_residual_Operm_I1_J, fact_37__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062, fact_284_order__trans, fact_305_Strong__Late__Sim_Oreflexive, fact_272_order__subst2, fact_92_swap__simps_I1_J, fact_212_pt__bij3, fact_72_name__exists__fresh, fact_160_eq__eqvt, fact_6_perm__swap_I1_J, fact_153_in__eqvt, fact_259_Bound_Ohyps_I3_J, fact_87_name__calc_I2_J, fact_266_pi_Operm_I7_J, fact_158_eq__eqvt, fact_119_surj__pair, fact_14_name__id, fact_338_pi_Operm_I4_J, fact_238_fresh__prodD_I1_J, fact_134_perm__compose, fact_8_perm__swap_I1_J, fact_109_prod__induct3, fact_89_sorted__wrt_Ocases, fact_200_eqvtRelI, fact_324_ResF, fact_252_IdE, fact_56_name__fresh__fresh, fact_170_induct__list012, fact_182_IdI, fact_208_if__eqvt, fact_347_inputCases, fact_218_abs__fun__if, fact_224_perm__prod_Osimps, fact_30_perm__swap_I2_J, fact_124_cp__name__name1, fact_68_fresh__perm__app, fact_316_Late__Semantics_OfreeRes_Oinject, fact_258_eqvtRelE, fact_287_calculation, fact_73_name__exists__fresh, fact_286_alphaRes, fact_112_Pair__inject, fact_227_perm__prod_Osimps, fact_54_perm__fresh__fresh, fact_343_resInputFreeTrans, fact_39_prod_Oinject, fact_310_sumSym, fact_183_fresh__prod, fact_151_in__eqvt, fact_334_simulation__def, fact_294_Late__Semantics_OResB, fact_128_name__perm__compose, fact_40_prod_Oinject, fact_121_cp__name__name1, fact_145_perm__app, fact_31_perm__swap_I2_J, fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062, fact_146_perm__app, fact_141_perm__app, fact_237_fresh__prodD_I1_J, fact_220_abs__fun__if, fact_127_name__perm__compose, fact_251_IdE, fact_299_sumCases_H, fact_211_pt__bij3, fact_349_Late__Semantics1_Osubject_Oinject_I1_J, fact_5_perm__swap_I1_J, fact_70_name__exists__fresh, fact_325_resCasesF_H, fact_111_Pair__inject, fact_332_resCases_H, fact_131_perm__compose, fact_235_cons__eqvt, fact_118_surj__pair, fact_243_fresh__list__cons, fact_269_pi_Oinject_I6_J, fact_29_pt__name1, fact_203_subject_Ofresh_I2_J, fact_179_pair__in__Id__conv, fact_328_freshFreeDerivative_I1_J, fact_335_simCases, fact_260_Bound_Ohyps_I2_J, fact_245_fresh__list__cons, fact_135_perm__compose, fact_342_inputFreeTrans, fact_261_subset__antisym, fact_193__092_060open_062y_A_092_060sharp_062_AP_092_060close_062, fact_172_list__induct2_H, fact_133_perm__compose, fact_281_ord__eq__le__trans, fact_188_fresh__prod, fact_346_resInputBoundOutputTrans, fact_129_name__perm__compose, fact_15_name__swap, fact_222_perm__prod_Osimps, fact_61_name__fresh__fresh, fact_36_Late__Semantics1_Osubject_Oinject_I2_J, fact_55_perm__fresh__fresh, fact_216_abs__fun__if, fact_250_subrelI, fact_35_Late__Semantics_Osubject_Oinject_I2_J, fact_86_fresh__bij, fact_293_freshBoundDerivative_I1_J, fact_190_fresh__prod, fact_233_cons__eqvt, fact_239_fresh__prodD_I1_J, fact_21_name__swap__bij, fact_236_cons__eqvt, fact_226_perm__prod_Osimps, help_If_1_1_If_001t__Late____Semantics__OfreeRes_T, fact_149_perm__app, fact_23_name__swap__bij, fact_263_order__refl, fact_11_name__id, fact_345_inputIneqTrans, fact_150_perm__app, fact_116_prod__cases, fact_38_list_Oinject, fact_257_eqvtRelE, fact_313_cOpen_Ohyps_I1_J, fact_280_order__class_Oorder_Oeq__iff, fact_249_subrelI, fact_132_perm__compose, fact_162_map__tailrec__rev_Oinduct, fact_221_eqvt__def, fact_28_pt__name1, help_If_2_1_If_001t__Late____Semantics__OfreeRes_T, fact_289__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062, fact_104_old_Oprod_Oexhaust, fact_138_perm__bij, fact_44_old_Oprod_Oinject, fact_169_shuffles_Oinduct, fact_189_fresh__prod, fact_253_derivativeMonotonic, fact_107_mem__Collect__eq, fact_319_residual_Operm_I2_J, help_If_1_1_If_001t__Late____Semantics__Osubject_T, fact_192_fresh__prod, help_If_1_1_If_001t__Agent__Opi____Rep_T, fact_114_prod__cases, fact_140_perm__bij, fact_178__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062, fact_154_in__eqvt, fact_230_perm__prod_Osimps, fact_278_order_Otrans, fact_63_subseteq__eqvt, fact_187_fresh__prod, help_If_2_1_If_001t__Late____Semantics__Osubject_T, fact_290_sumResLeft, fact_248_subrelI, fact_33_perm__swap_I2_J, fact_136_perm__bij, fact_147_perm__app, fact_207_if__eqvt, fact_60_name__fresh__fresh, fact_101_old_Oprod_Oinducts, fact_142_perm__app, fact_174_list_Oinducts, fact_304_monotonic, fact_24_name__swap__bij, fact_291_cSum1_Ohyps, fact_322_residual_Oinducts, fact_312_alphaBoundResidual, fact_41_prod_Oinject, fact_309_sumAssocLeft, fact_296_simE_I1_J, fact_186_fresh__prod, fact_215_pt__bij3, fact_242_fresh__prodD_I2_J, fact_209_if__eqvt, fact_156_in__eqvt, fact_34_perm__swap_I2_J, fact_79_fresh__eqvt, fact_288_Bound_Ohyps_I1_J, fact_195_derivativeEqvtI, fact_50_perm__fresh__fresh, fact_268_pi_Odistinct_I81_J, fact_47_freeRes__perm__empty, fact_165_remdups__adj_Oinduct, fact_210_if__eqvt, fact_76_fresh__eqvt, fact_339_resTrans_I2_J, fact_213_pt__bij3, fact_26_pt__name1, fact_32_perm__swap_I2_J, fact_264_name__fresh, fact_306_sumIdempRight, fact_171_splice_Oinduct, fact_164_successively_Oinduct, fact_262_subsetI, fact_93_swap__simps_I2_J, fact_17_name__swap, fact_4_Eqvt, fact_64_fresh__perm__app, fact_228_perm__prod_Osimps, fact_113_Pair__inject, fact_279_antisym__conv, fact_100_fresh__aux, fact_51_perm__fresh__fresh, fact_157_eq__eqvt, fact_225_perm__prod_Osimps, fact_318_freeRes_Ofresh_I1_J, fact_330_simE_I2_J, fact_45_residual__perm__empty, fact_317_freeRes_Operm_I1_J, fact_297_Sum2, fact_351_subject_Operm_I1_J, fact_244_fresh__list__cons, fact_96_fresh__aux, fact_159_eq__eqvt, fact_295_freshBoundDerivative_I2_J, fact_173_neq__Nil__conv, fact_52_perm__fresh__fresh, fact_247_fresh__list__cons, fact_16_name__swap, fact_194_derivativeReflexive, fact_161_eq__eqvt, fact_348_name__calc_I1_J, fact_80_fresh__eqvt, fact_98_fresh__aux, fact_27_pt__name1, fact_285_dual__order_Orefl, fact_125_cp__name__name1, fact_333_resCasesB, fact_81_fresh__bij, fact_206_if__eqvt, fact_307_sumAssocRight, fact_103_old_Oprod_Oinducts, fact_46_subject__perm__empty, fact_1_cOpen_Ohyps_I2_J, fact_117_surj__pair, fact_202_Bound_Ohyps_I5_J, fact_337_alphaInput, fact_57_name__fresh__fresh, fact_53_perm__fresh__fresh, help_If_2_1_If_001t__Agent__Opi____Rep_T, fact_62_Bound_Ohyps_I4_J, fact_340_pi_Odistinct_I53_J, fact_323_residual_Oinject_I2_J, fact_85_fresh__bij, fact_232_cons__eqvt, fact_217_abs__fun__if, fact_274_ord__le__eq__subst, fact_84_fresh__bij, fact_9_perm__swap_I1_J, fact_122_cp__name__name1, fact_176_list_OdiscI, fact_282_ord__le__eq__trans, fact_74_name__exists__fresh, fact_275_eq__iff, fact_75_fresh__eqvt, fact_267_pi_Operm_I9_J, fact_298_Sum1, fact_143_perm__app, fact_350_subject_Ofresh_I1_J, fact_130_name__perm__compose, help_If_1_1_If_001t__Agent__Opi_T, fact_196_derivativeEqvtI2, fact_42_old_Oprod_Oinject, fact_201_eqvtRelI, fact_315_Late__Semantics1_OfreeRes_Oinject, fact_144_perm__app, fact_106_old_Oprod_Oexhaust, fact_303_transitions_OResB, fact_94_swap__simps_I3_J, fact_148_perm__app, fact_88_successively_Ocases, fact_329_Open, fact_246_fresh__list__cons, fact_283_order__class_Oorder_Oantisym, fact_43_old_Oprod_Oinject, fact_185_fresh__prod, fact_277_eq__refl, help_If_3_1_If_001t__Late____Semantics__Osubject_T, fact_126_name__perm__compose, fact_59_name__fresh__fresh, fact_214_pt__bij3, fact_231_perm__prod_Osimps, fact_321_residual_Odistinct_I1_J, fact_326_resCasesF, fact_155_in__eqvt, fact_273_ord__eq__le__subst, fact_265_pi_Ofresh_I7_J, fact_13_name__id, fact_163_list__nonempty__induct, fact_0_Id, fact_90_shuffles_Ocases, fact_120_not__Cons__self2, fact_82_fresh__bij, fact_2_cOpen_Ohyps_I3_J, fact_12_name__id, fact_320_residual_Ofresh_I2_J, fact_300_sumCases, fact_102_old_Oprod_Oinducts, fact_301_freshResidual, fact_270_freshRes, fact_20_name__swap__bij, fact_58_name__fresh__fresh, fact_184_fresh__prod, fact_71_name__exists__fresh, fact_67_fresh__perm__app, fact_83_fresh__bij, fact_167_remdups__adj_Ocases, fact_180_pair__in__Id__conv, fact_97_fresh__aux, fact_205_allE__Nil, fact_181_IdI, fact_311_eqvtI, fact_314__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062, fact_65_fresh__perm__app, fact_234_cons__eqvt, fact_137_perm__bij, fact_69_fresh__perm__app, fact_241_fresh__prodD_I2_J, fact_223_perm__prod_Osimps, fact_308_sumIdempLeft, fact_240_fresh__prodD_I2_J, fact_91_splice_Ocases, fact_110_prod__cases3, fact_327_freshFreeDerivative_I2_J, fact_204_name__bij, fact_78_fresh__eqvt, fact_271_order__subst1, fact_108_Collect__mem__eq, fact_66_fresh__perm__app, fact_48_pi__perm__empty, fact_7_perm__swap_I1_J, help_If_2_1_If_001t__Agent__Oname_T, fact_352_Late__Semantics_Osubject_Odistinct_I1_J
% 16.74/5.14 % No. of inferences in proof: 718
% 16.74/5.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4605 ms resp. 3989 ms w/o parsing
% 17.80/5.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.80/5.33 % [INFO] Killing All external provers ...
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