TSTP Solution File: SWW874+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW874+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Thu Sep 29 21:00:08 EDT 2022
% Result : Theorem 0.17s 0.51s
% Output : Proof 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWW874+1 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Sep 4 22:37:55 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.17/0.51 % SZS status Theorem
% 0.17/0.51 % SZS output start Proof
% 0.17/0.51 tff(s__02_type, type, (
% 0.17/0.51 s__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2etypeSystem_2eunion__decls_27__02_type, type, (
% 0.17/0.51 c_27const_2etypeSystem_2eunion__decls_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2eenvRel_2econvert__decls_27__01_type, type, (
% 0.17/0.51 c_27const_2eenvRel_2econvert__decls_27__01: $i > $i)).
% 0.17/0.51 tff(tptp_fun_V_27decls2_27_1_type, type, (
% 0.17/0.51 tptp_fun_V_27decls2_27_1: $i)).
% 0.17/0.51 tff(c_27type_2einfer_2einf__decls_27__00_type, type, (
% 0.17/0.51 c_27type_2einfer_2einf__decls_27__00: $i)).
% 0.17/0.51 tff(c_27type_2etypeSystem_2edecls_27__00_type, type, (
% 0.17/0.51 c_27type_2etypeSystem_2edecls_27__00: $i)).
% 0.17/0.51 tff(tptp_fun_V_27decls1_27_2_type, type, (
% 0.17/0.51 tptp_fun_V_27decls1_27_2: $i)).
% 0.17/0.51 tff(c_27const_2einfer_2eappend__decls_27__02_type, type, (
% 0.17/0.51 c_27const_2einfer_2eappend__decls_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02_type, type, (
% 0.17/0.51 c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02_type, type, (
% 0.17/0.51 c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02_type, type, (
% 0.17/0.51 c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2ebool_2eARB_27__00_type, type, (
% 0.17/0.51 c_27const_2ebool_2eARB_27__00: $i)).
% 0.17/0.51 tff(c_27const_2ecombin_2eK_27__01_type, type, (
% 0.17/0.51 c_27const_2ecombin_2eK_27__01: $i > $i)).
% 0.17/0.51 tff(c_27const_2epred__set_2eUNION_27__02_type, type, (
% 0.17/0.51 c_27const_2epred__set_2eUNION_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2etypeSystem_2edecls__defined__exns_27__01_type, type, (
% 0.17/0.51 c_27const_2etypeSystem_2edecls__defined__exns_27__01: $i > $i)).
% 0.17/0.51 tff(cfun__02_type, type, (
% 0.17/0.51 cfun__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(cbool__00_type, type, (
% 0.17/0.51 cbool__00: $i)).
% 0.17/0.51 tff(c_27type_2enamespace_2eid_27__02_type, type, (
% 0.17/0.51 c_27type_2enamespace_2eid_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27type_2elist_2elist_27__01_type, type, (
% 0.17/0.51 c_27type_2elist_2elist_27__01: $i > $i)).
% 0.17/0.51 tff(c_27type_2estring_2echar_27__00_type, type, (
% 0.17/0.51 c_27type_2estring_2echar_27__00: $i)).
% 0.17/0.51 tff(c_27const_2etypeSystem_2edecls__defined__types_27__01_type, type, (
% 0.17/0.51 c_27const_2etypeSystem_2edecls__defined__types_27__01: $i > $i)).
% 0.17/0.51 tff(c_27const_2etypeSystem_2edecls__defined__mods_27__01_type, type, (
% 0.17/0.51 c_27const_2etypeSystem_2edecls__defined__mods_27__01: $i > $i)).
% 0.17/0.51 tff(c_27const_2elist_2eLIST__TO__SET_27__01_type, type, (
% 0.17/0.51 c_27const_2elist_2eLIST__TO__SET_27__01: $i > $i)).
% 0.17/0.51 tff(c_27const_2einfer_2einf__decls__inf__defined__exns_27__01_type, type, (
% 0.17/0.51 c_27const_2einfer_2einf__decls__inf__defined__exns_27__01: $i > $i)).
% 0.17/0.51 tff(c_27const_2einfer_2einf__decls__inf__defined__types_27__01_type, type, (
% 0.17/0.51 c_27const_2einfer_2einf__decls__inf__defined__types_27__01: $i > $i)).
% 0.17/0.51 tff(c_27const_2einfer_2einf__decls__inf__defined__mods_27__01_type, type, (
% 0.17/0.51 c_27const_2einfer_2einf__decls__inf__defined__mods_27__01: $i > $i)).
% 0.17/0.51 tff(c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02_type, type, (
% 0.17/0.51 c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02_type, type, (
% 0.17/0.51 c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2elist_2eAPPEND_27__02_type, type, (
% 0.17/0.51 c_27const_2elist_2eAPPEND_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02_type, type, (
% 0.17/0.51 c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(chapp__02_type, type, (
% 0.17/0.51 chapp__02: ( $i * $i ) > $i)).
% 0.17/0.51 tff(1,plain,
% 0.17/0.51 (^[V_27d1_27: $i, V_27d2_27: $i] : refl((s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.17/0.52 inference(bind,[status(th)],[])).
% 0.17/0.52 tff(2,plain,
% 0.17/0.52 (![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> ![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.17/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.52 tff(3,plain,
% 0.17/0.52 (![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> ![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.17/0.52 inference(rewrite,[status(thm)],[])).
% 0.17/0.52 tff(4,axiom,(![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''thm.typeSystem.union_decls_def'')).
% 0.17/0.52 tff(5,plain,
% 0.17/0.52 (![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.17/0.52 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.17/0.52 tff(6,plain,(
% 0.17/0.52 ![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.17/0.52 inference(skolemize,[status(sab)],[5])).
% 0.17/0.52 tff(7,plain,
% 0.17/0.52 (![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.17/0.53 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.17/0.53 tff(8,plain,
% 0.17/0.53 ((~![V_27d1_27: $i, V_27d2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d1_27))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d2_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) | (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.17/0.53 inference(quant_inst,[status(thm)],[])).
% 0.17/0.53 tff(9,plain,
% 0.17/0.53 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.17/0.53 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.17/0.53 tff(10,plain,
% 0.17/0.53 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.17/0.53 inference(symmetry,[status(thm)],[9])).
% 0.17/0.53 tff(11,plain,
% 0.17/0.53 (^[V_27i_27: $i, V_27f_27: $i] : refl((s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))),
% 0.17/0.53 inference(bind,[status(th)],[])).
% 0.17/0.53 tff(12,plain,
% 0.17/0.53 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.53 inference(quant_intro,[status(thm)],[11])).
% 0.17/0.53 tff(13,plain,
% 0.17/0.53 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.53 inference(rewrite,[status(thm)],[])).
% 0.17/0.53 tff(14,axiom,((((((((![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''thm.infer.inf_decls_accfupds'')).
% 0.17/0.54 tff(15,plain,
% 0.17/0.54 (((((((![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.17/0.54 inference(and_elim,[status(thm)],[14])).
% 0.17/0.54 tff(16,plain,
% 0.17/0.54 ((((((![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.17/0.54 inference(and_elim,[status(thm)],[15])).
% 0.17/0.54 tff(17,plain,
% 0.17/0.54 (((((![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.54 inference(and_elim,[status(thm)],[16])).
% 0.17/0.54 tff(18,plain,
% 0.17/0.54 ((((![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.55 inference(and_elim,[status(thm)],[17])).
% 0.17/0.55 tff(19,plain,
% 0.17/0.55 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.55 inference(and_elim,[status(thm)],[18])).
% 0.17/0.55 tff(20,plain,
% 0.17/0.55 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.55 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.17/0.55 tff(21,plain,(
% 0.17/0.55 ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.55 inference(skolemize,[status(sab)],[20])).
% 0.17/0.55 tff(22,plain,
% 0.17/0.55 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.17/0.55 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.17/0.55 tff(23,plain,
% 0.17/0.55 ((~![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.17/0.55 inference(quant_inst,[status(thm)],[])).
% 0.17/0.55 tff(24,plain,
% 0.17/0.55 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.17/0.55 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.17/0.55 tff(25,plain,
% 0.17/0.55 (^[V_27idecls1_27: $i, V_27idecls2_27: $i] : refl((s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.49/0.55 inference(bind,[status(th)],[])).
% 0.49/0.55 tff(26,plain,
% 0.49/0.55 (![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> ![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.56 inference(quant_intro,[status(thm)],[25])).
% 0.49/0.56 tff(27,plain,
% 0.49/0.56 (![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> ![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.56 inference(rewrite,[status(thm)],[])).
% 0.49/0.56 tff(28,axiom,(![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''thm.infer.append_decls_def'')).
% 0.49/0.56 tff(29,plain,
% 0.49/0.56 (![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.56 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.49/0.56 tff(30,plain,(
% 0.49/0.56 ![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.56 inference(skolemize,[status(sab)],[29])).
% 0.49/0.56 tff(31,plain,
% 0.49/0.56 (![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.56 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.49/0.56 tff(32,plain,
% 0.49/0.56 ((~![V_27idecls1_27: $i, V_27idecls2_27: $i] : (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls1_27))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls2_27))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) | (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.57 inference(quant_inst,[status(thm)],[])).
% 0.49/0.57 tff(33,plain,
% 0.49/0.57 (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.49/0.57 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.49/0.57 tff(34,plain,
% 0.49/0.57 (s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))),
% 0.49/0.57 inference(symmetry,[status(thm)],[33])).
% 0.49/0.57 tff(35,plain,
% 0.49/0.57 (c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[34])).
% 0.49/0.57 tff(36,plain,
% 0.49/0.57 (c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))) = c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.57 inference(symmetry,[status(thm)],[35])).
% 0.49/0.57 tff(37,plain,
% 0.49/0.57 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[36])).
% 0.49/0.57 tff(38,plain,
% 0.49/0.57 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.49/0.57 inference(transitivity,[status(thm)],[37, 24])).
% 0.49/0.57 tff(39,plain,
% 0.49/0.57 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.49/0.57 inference(monotonicity,[status(thm)],[38])).
% 0.49/0.57 tff(40,plain,
% 0.49/0.57 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[39])).
% 0.52/0.58 tff(41,plain,
% 0.52/0.58 (c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))) = c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[40])).
% 0.52/0.58 tff(42,plain,
% 0.52/0.58 (s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))) = s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[41])).
% 0.52/0.58 tff(43,plain,
% 0.52/0.58 (c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)) = c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[42])).
% 0.52/0.58 tff(44,plain,
% 0.52/0.58 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[43])).
% 0.52/0.58 tff(45,plain,
% 0.52/0.58 (^[V_27i_27: $i, V_27f_27: $i] : refl((s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(46,plain,
% 0.52/0.58 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[45])).
% 0.52/0.58 tff(47,plain,
% 0.52/0.58 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(48,plain,
% 0.52/0.58 (((![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.58 inference(and_elim,[status(thm)],[18])).
% 0.52/0.59 tff(49,plain,
% 0.52/0.59 ((![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) & ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.59 inference(and_elim,[status(thm)],[48])).
% 0.52/0.59 tff(50,plain,
% 0.52/0.59 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.59 inference(and_elim,[status(thm)],[49])).
% 0.52/0.59 tff(51,plain,
% 0.52/0.59 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.52/0.59 tff(52,plain,(
% 0.52/0.59 ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.59 inference(skolemize,[status(sab)],[51])).
% 0.52/0.59 tff(53,plain,
% 0.52/0.59 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[52, 46])).
% 0.52/0.59 tff(54,plain,
% 0.52/0.59 ((~![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.59 inference(quant_inst,[status(thm)],[])).
% 0.52/0.59 tff(55,plain,
% 0.52/0.59 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.52/0.59 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.52/0.59 tff(56,plain,
% 0.52/0.59 (c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))),
% 0.52/0.59 inference(monotonicity,[status(thm)],[34])).
% 0.52/0.59 tff(57,plain,
% 0.52/0.59 (c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))) = c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.59 inference(symmetry,[status(thm)],[56])).
% 0.52/0.59 tff(58,plain,
% 0.52/0.59 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[57])).
% 0.52/0.60 tff(59,plain,
% 0.52/0.60 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.52/0.60 inference(transitivity,[status(thm)],[58, 55])).
% 0.52/0.60 tff(60,plain,
% 0.52/0.60 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[59])).
% 0.52/0.60 tff(61,plain,
% 0.52/0.60 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[60])).
% 0.52/0.60 tff(62,plain,
% 0.52/0.60 (c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))) = c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[61])).
% 0.52/0.60 tff(63,plain,
% 0.52/0.60 (s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))) = s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[62])).
% 0.52/0.60 tff(64,plain,
% 0.52/0.60 (c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))) = c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[63, 44])).
% 0.52/0.61 tff(65,plain,
% 0.52/0.61 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[64])).
% 0.52/0.61 tff(66,plain,
% 0.52/0.61 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.52/0.61 inference(symmetry,[status(thm)],[65])).
% 0.52/0.61 tff(67,plain,
% 0.52/0.61 (^[V_27idecls_27: $i] : refl((s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(68,plain,
% 0.52/0.61 (![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> ![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[67])).
% 0.52/0.61 tff(69,plain,
% 0.52/0.61 (![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) <=> ![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(70,axiom,(![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''thm.envRel.convert_decls_def'')).
% 0.52/0.62 tff(71,plain,
% 0.52/0.62 (![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.52/0.62 tff(72,plain,(
% 0.52/0.62 ![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.62 inference(skolemize,[status(sab)],[71])).
% 0.52/0.62 tff(73,plain,
% 0.52/0.62 (![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.52/0.62 tff(74,plain,
% 0.52/0.62 ((~![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) | (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.62 inference(quant_inst,[status(thm)],[])).
% 0.52/0.62 tff(75,plain,
% 0.52/0.62 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.52/0.62 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.52/0.62 tff(76,plain,
% 0.52/0.62 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))),
% 0.52/0.62 inference(symmetry,[status(thm)],[75])).
% 0.52/0.62 tff(77,plain,
% 0.52/0.62 (c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))),
% 0.52/0.63 inference(monotonicity,[status(thm)],[76])).
% 0.52/0.63 tff(78,plain,
% 0.52/0.63 (c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))) = c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.52/0.63 inference(symmetry,[status(thm)],[77])).
% 0.52/0.63 tff(79,plain,
% 0.52/0.63 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.52/0.63 inference(monotonicity,[status(thm)],[78])).
% 0.52/0.63 tff(80,plain,
% 0.52/0.63 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.52/0.63 inference(symmetry,[status(thm)],[79])).
% 0.52/0.63 tff(81,plain,
% 0.52/0.63 (^[V_27f_27: $i, V_27d_27: $i] : refl((s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))))),
% 0.52/0.63 inference(bind,[status(th)],[])).
% 0.52/0.63 tff(82,plain,
% 0.52/0.63 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.52/0.63 inference(quant_intro,[status(thm)],[81])).
% 0.52/0.63 tff(83,plain,
% 0.52/0.63 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.52/0.63 inference(rewrite,[status(thm)],[])).
% 0.52/0.63 tff(84,axiom,((((((((![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''thm.typeSystem.decls_accfupds'')).
% 0.58/0.64 tff(85,plain,
% 0.58/0.64 (((((((![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.58/0.64 inference(and_elim,[status(thm)],[84])).
% 0.58/0.64 tff(86,plain,
% 0.58/0.64 ((((((![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.58/0.64 inference(and_elim,[status(thm)],[85])).
% 0.58/0.64 tff(87,plain,
% 0.58/0.64 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.58/0.64 inference(and_elim,[status(thm)],[86])).
% 0.58/0.64 tff(88,plain,
% 0.58/0.64 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.58/0.64 tff(89,plain,(
% 0.58/0.64 ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.58/0.64 inference(skolemize,[status(sab)],[88])).
% 0.58/0.64 tff(90,plain,
% 0.58/0.64 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.58/0.64 tff(91,plain,
% 0.58/0.64 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) | (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(92,plain,
% 0.58/0.65 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.58/0.65 tff(93,plain,
% 0.58/0.65 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.58/0.65 inference(symmetry,[status(thm)],[92])).
% 0.58/0.65 tff(94,plain,
% 0.58/0.65 (^[V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : refl((s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27)) <=> (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27)))),
% 0.58/0.65 inference(bind,[status(th)],[])).
% 0.58/0.65 tff(95,plain,
% 0.58/0.65 (![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27)) <=> ![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))),
% 0.58/0.65 inference(quant_intro,[status(thm)],[94])).
% 0.58/0.65 tff(96,plain,
% 0.58/0.65 (![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27)) <=> ![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))),
% 0.58/0.65 inference(rewrite,[status(thm)],[])).
% 0.58/0.65 tff(97,axiom,(![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''thm.combin.K_THM'')).
% 0.58/0.65 tff(98,plain,
% 0.58/0.65 (![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.58/0.65 tff(99,plain,(
% 0.58/0.65 ![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))),
% 0.58/0.65 inference(skolemize,[status(sab)],[98])).
% 0.58/0.65 tff(100,plain,
% 0.58/0.65 (![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))),
% 0.58/0.65 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.58/0.65 tff(101,plain,
% 0.58/0.65 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.58/0.65 inference(quant_inst,[status(thm)],[])).
% 0.58/0.65 tff(102,plain,
% 0.58/0.65 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.58/0.65 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.58/0.65 tff(103,plain,
% 0.58/0.65 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.58/0.66 inference(symmetry,[status(thm)],[102])).
% 0.58/0.66 tff(104,plain,
% 0.58/0.66 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.58/0.66 inference(transitivity,[status(thm)],[103, 93, 80])).
% 0.58/0.66 tff(105,plain,
% 0.58/0.66 ((~![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) | (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(106,plain,
% 0.60/0.66 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[105, 73])).
% 0.60/0.66 tff(107,plain,
% 0.60/0.66 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))),
% 0.60/0.66 inference(symmetry,[status(thm)],[106])).
% 0.60/0.66 tff(108,plain,
% 0.60/0.66 (c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[107])).
% 0.60/0.66 tff(109,plain,
% 0.60/0.66 (c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))) = c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.60/0.66 inference(symmetry,[status(thm)],[108])).
% 0.60/0.66 tff(110,plain,
% 0.60/0.66 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[109])).
% 0.60/0.66 tff(111,plain,
% 0.60/0.66 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.60/0.66 inference(symmetry,[status(thm)],[110])).
% 0.60/0.66 tff(112,plain,
% 0.60/0.66 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) | (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(113,plain,
% 0.60/0.67 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[112, 90])).
% 0.60/0.67 tff(114,plain,
% 0.60/0.67 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.67 inference(symmetry,[status(thm)],[113])).
% 0.60/0.67 tff(115,plain,
% 0.60/0.67 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(116,plain,
% 0.60/0.67 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[115, 100])).
% 0.60/0.67 tff(117,plain,
% 0.60/0.67 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.67 inference(symmetry,[status(thm)],[116])).
% 0.60/0.67 tff(118,plain,
% 0.60/0.67 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.60/0.67 inference(transitivity,[status(thm)],[117, 114, 111])).
% 0.60/0.67 tff(119,plain,
% 0.60/0.67 (c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[118, 104])).
% 0.60/0.67 tff(120,plain,
% 0.60/0.67 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.60/0.68 inference(monotonicity,[status(thm)],[119])).
% 0.60/0.68 tff(121,plain,
% 0.60/0.68 (^[V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : refl((s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27)))))) <=> (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27)))))))),
% 0.60/0.68 inference(bind,[status(th)],[])).
% 0.60/0.68 tff(122,plain,
% 0.60/0.68 (![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27)))))) <=> ![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))),
% 0.60/0.68 inference(quant_intro,[status(thm)],[121])).
% 0.60/0.68 tff(123,plain,
% 0.60/0.68 (![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27)))))) <=> ![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(124,axiom,(![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''thm.list.LIST_TO_SET_APPEND'')).
% 0.60/0.68 tff(125,plain,
% 0.60/0.68 (![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.60/0.68 tff(126,plain,(
% 0.60/0.68 ![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))),
% 0.60/0.68 inference(skolemize,[status(sab)],[125])).
% 0.60/0.68 tff(127,plain,
% 0.60/0.68 (![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.60/0.68 tff(128,plain,
% 0.60/0.68 ((~![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))) | (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))),
% 0.60/0.68 inference(quant_inst,[status(thm)],[])).
% 0.60/0.68 tff(129,plain,
% 0.60/0.68 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.60/0.68 tff(130,plain,
% 0.60/0.68 (c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))),
% 0.60/0.68 inference(monotonicity,[status(thm)],[34])).
% 0.60/0.68 tff(131,plain,
% 0.60/0.68 (c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))) = c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.60/0.68 inference(symmetry,[status(thm)],[130])).
% 0.60/0.68 tff(132,plain,
% 0.60/0.68 (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.68 inference(monotonicity,[status(thm)],[131])).
% 0.60/0.68 tff(133,plain,
% 0.60/0.68 (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.60/0.68 inference(symmetry,[status(thm)],[132])).
% 0.60/0.68 tff(134,plain,
% 0.60/0.68 (^[V_27i_27: $i, V_27f_27: $i] : refl((s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))))),
% 0.60/0.69 inference(bind,[status(th)],[])).
% 0.60/0.69 tff(135,plain,
% 0.60/0.69 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.60/0.69 inference(quant_intro,[status(thm)],[134])).
% 0.60/0.69 tff(136,plain,
% 0.60/0.69 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.60/0.69 inference(rewrite,[status(thm)],[])).
% 0.60/0.69 tff(137,plain,
% 0.60/0.69 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.60/0.69 inference(and_elim,[status(thm)],[16])).
% 0.60/0.69 tff(138,plain,
% 0.60/0.69 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.60/0.69 tff(139,plain,(
% 0.60/0.69 ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.60/0.69 inference(skolemize,[status(sab)],[138])).
% 0.60/0.69 tff(140,plain,
% 0.60/0.69 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.60/0.69 tff(141,plain,
% 0.60/0.69 ((~![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))),
% 0.60/0.69 inference(quant_inst,[status(thm)],[])).
% 0.60/0.69 tff(142,plain,
% 0.60/0.69 (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.69 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.60/0.69 tff(143,plain,
% 0.60/0.69 (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.70 inference(symmetry,[status(thm)],[142])).
% 0.60/0.70 tff(144,plain,
% 0.60/0.70 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.60/0.70 inference(quant_inst,[status(thm)],[])).
% 0.60/0.70 tff(145,plain,
% 0.60/0.70 (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.60/0.70 inference(unit_resolution,[status(thm)],[144, 100])).
% 0.60/0.70 tff(146,plain,
% 0.60/0.70 (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.70 inference(symmetry,[status(thm)],[145])).
% 0.60/0.70 tff(147,plain,
% 0.60/0.70 (s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.60/0.70 inference(transitivity,[status(thm)],[146, 143, 133])).
% 0.60/0.70 tff(148,plain,
% 0.60/0.70 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.60/0.70 inference(monotonicity,[status(thm)],[147])).
% 0.60/0.70 tff(149,plain,
% 0.60/0.70 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.60/0.70 inference(symmetry,[status(thm)],[148])).
% 0.60/0.70 tff(150,plain,
% 0.60/0.70 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.60/0.70 inference(monotonicity,[status(thm)],[149])).
% 0.60/0.70 tff(151,plain,
% 0.60/0.70 (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.60/0.70 inference(transitivity,[status(thm)],[150, 129, 120])).
% 0.60/0.70 tff(152,plain,
% 0.60/0.70 (c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))) = c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))),
% 0.60/0.70 inference(monotonicity,[status(thm)],[151])).
% 0.60/0.70 tff(153,plain,
% 0.60/0.70 (s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))) = s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))))),
% 0.60/0.70 inference(monotonicity,[status(thm)],[152])).
% 0.60/0.70 tff(154,plain,
% 0.60/0.70 (s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))) = s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))))),
% 0.60/0.70 inference(symmetry,[status(thm)],[153])).
% 0.60/0.70 tff(155,plain,
% 0.60/0.70 (c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))) = c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.60/0.71 inference(monotonicity,[status(thm)],[154, 66])).
% 0.60/0.71 tff(156,plain,
% 0.60/0.71 (c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))),
% 0.60/0.71 inference(monotonicity,[status(thm)],[76])).
% 0.60/0.71 tff(157,plain,
% 0.60/0.71 (c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))) = c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.60/0.71 inference(symmetry,[status(thm)],[156])).
% 0.60/0.71 tff(158,plain,
% 0.60/0.71 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.60/0.71 inference(monotonicity,[status(thm)],[157])).
% 0.60/0.71 tff(159,plain,
% 0.60/0.71 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.60/0.71 inference(symmetry,[status(thm)],[158])).
% 0.60/0.71 tff(160,plain,
% 0.60/0.71 (^[V_27f_27: $i, V_27d_27: $i] : refl((s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))),
% 0.60/0.71 inference(bind,[status(th)],[])).
% 0.60/0.71 tff(161,plain,
% 0.60/0.71 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.60/0.71 inference(quant_intro,[status(thm)],[160])).
% 0.60/0.71 tff(162,plain,
% 0.60/0.71 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.60/0.71 inference(rewrite,[status(thm)],[])).
% 0.60/0.71 tff(163,plain,
% 0.60/0.71 (((((![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.60/0.72 inference(and_elim,[status(thm)],[86])).
% 0.60/0.72 tff(164,plain,
% 0.60/0.72 ((((![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.72 inference(and_elim,[status(thm)],[163])).
% 0.65/0.72 tff(165,plain,
% 0.65/0.72 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.72 inference(and_elim,[status(thm)],[164])).
% 0.65/0.72 tff(166,plain,
% 0.65/0.72 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[165, 162])).
% 0.65/0.72 tff(167,plain,(
% 0.65/0.72 ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.72 inference(skolemize,[status(sab)],[166])).
% 0.65/0.72 tff(168,plain,
% 0.65/0.72 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.72 inference(modus_ponens,[status(thm)],[167, 161])).
% 0.65/0.72 tff(169,plain,
% 0.65/0.72 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.65/0.72 inference(quant_inst,[status(thm)],[])).
% 0.65/0.72 tff(170,plain,
% 0.65/0.72 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.65/0.72 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.65/0.72 tff(171,plain,
% 0.65/0.72 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.65/0.72 inference(symmetry,[status(thm)],[170])).
% 0.65/0.72 tff(172,plain,
% 0.65/0.72 (^[V_27f_27: $i, V_27d_27: $i] : refl((s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))),
% 0.65/0.72 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(173,plain,
% 0.65/0.73 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.73 inference(quant_intro,[status(thm)],[172])).
% 0.65/0.73 tff(174,plain,
% 0.65/0.73 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.73 inference(rewrite,[status(thm)],[])).
% 0.65/0.73 tff(175,plain,
% 0.65/0.73 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.73 inference(and_elim,[status(thm)],[163])).
% 0.65/0.73 tff(176,plain,
% 0.65/0.73 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.65/0.73 tff(177,plain,(
% 0.65/0.73 ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.73 inference(skolemize,[status(sab)],[176])).
% 0.65/0.73 tff(178,plain,
% 0.65/0.73 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.65/0.73 tff(179,plain,
% 0.65/0.73 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.65/0.73 inference(quant_inst,[status(thm)],[])).
% 0.65/0.73 tff(180,plain,
% 0.65/0.73 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.65/0.73 tff(181,plain,
% 0.65/0.73 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.65/0.73 inference(symmetry,[status(thm)],[180])).
% 0.65/0.73 tff(182,plain,
% 0.65/0.73 (^[V_27f_27: $i, V_27d_27: $i] : refl((s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))))),
% 0.65/0.73 inference(bind,[status(th)],[])).
% 0.65/0.73 tff(183,plain,
% 0.65/0.73 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.65/0.74 inference(quant_intro,[status(thm)],[182])).
% 0.65/0.74 tff(184,plain,
% 0.65/0.74 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.65/0.74 inference(rewrite,[status(thm)],[])).
% 0.65/0.74 tff(185,plain,
% 0.65/0.74 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.65/0.74 inference(and_elim,[status(thm)],[84])).
% 0.65/0.74 tff(186,plain,
% 0.65/0.74 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.65/0.74 tff(187,plain,(
% 0.65/0.74 ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.65/0.74 inference(skolemize,[status(sab)],[186])).
% 0.65/0.74 tff(188,plain,
% 0.65/0.74 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.65/0.74 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.65/0.74 tff(189,plain,
% 0.65/0.74 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.65/0.74 inference(quant_inst,[status(thm)],[])).
% 0.65/0.74 tff(190,plain,
% 0.65/0.74 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.65/0.74 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.65/0.74 tff(191,plain,
% 0.65/0.74 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.65/0.74 inference(symmetry,[status(thm)],[190])).
% 0.65/0.74 tff(192,plain,
% 0.65/0.74 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.65/0.74 inference(quant_inst,[status(thm)],[])).
% 0.65/0.74 tff(193,plain,
% 0.65/0.74 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.65/0.74 inference(unit_resolution,[status(thm)],[192, 100])).
% 0.65/0.74 tff(194,plain,
% 0.65/0.74 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.65/0.74 inference(symmetry,[status(thm)],[193])).
% 0.65/0.74 tff(195,plain,
% 0.65/0.74 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.65/0.74 inference(transitivity,[status(thm)],[194, 191, 181, 171, 159])).
% 0.65/0.74 tff(196,plain,
% 0.65/0.74 (c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))),
% 0.65/0.75 inference(monotonicity,[status(thm)],[107])).
% 0.65/0.75 tff(197,plain,
% 0.65/0.75 (c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))) = c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.65/0.75 inference(symmetry,[status(thm)],[196])).
% 0.65/0.75 tff(198,plain,
% 0.65/0.75 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.65/0.75 inference(monotonicity,[status(thm)],[197])).
% 0.65/0.75 tff(199,plain,
% 0.65/0.75 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.65/0.75 inference(symmetry,[status(thm)],[198])).
% 0.65/0.75 tff(200,plain,
% 0.65/0.75 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.65/0.75 inference(quant_inst,[status(thm)],[])).
% 0.65/0.75 tff(201,plain,
% 0.65/0.75 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.65/0.75 inference(unit_resolution,[status(thm)],[200, 168])).
% 0.65/0.75 tff(202,plain,
% 0.65/0.75 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.65/0.75 inference(symmetry,[status(thm)],[201])).
% 0.65/0.75 tff(203,plain,
% 0.65/0.75 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.69/0.76 inference(quant_inst,[status(thm)],[])).
% 0.69/0.76 tff(204,plain,
% 0.69/0.76 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.76 inference(unit_resolution,[status(thm)],[203, 178])).
% 0.69/0.76 tff(205,plain,
% 0.69/0.76 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.69/0.76 inference(symmetry,[status(thm)],[204])).
% 0.69/0.76 tff(206,plain,
% 0.69/0.76 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.69/0.76 inference(quant_inst,[status(thm)],[])).
% 0.69/0.76 tff(207,plain,
% 0.69/0.76 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.76 inference(unit_resolution,[status(thm)],[206, 188])).
% 0.69/0.76 tff(208,plain,
% 0.69/0.76 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.76 inference(symmetry,[status(thm)],[207])).
% 0.69/0.76 tff(209,plain,
% 0.69/0.76 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))),
% 0.69/0.76 inference(quant_inst,[status(thm)],[])).
% 0.69/0.76 tff(210,plain,
% 0.69/0.76 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.69/0.76 inference(unit_resolution,[status(thm)],[209, 100])).
% 0.69/0.76 tff(211,plain,
% 0.69/0.76 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.76 inference(symmetry,[status(thm)],[210])).
% 0.69/0.76 tff(212,plain,
% 0.69/0.76 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.69/0.76 inference(transitivity,[status(thm)],[211, 208, 205, 202, 199])).
% 0.69/0.76 tff(213,plain,
% 0.69/0.76 (c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.69/0.77 inference(monotonicity,[status(thm)],[212, 195])).
% 0.69/0.77 tff(214,plain,
% 0.69/0.77 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.69/0.77 inference(monotonicity,[status(thm)],[213])).
% 0.69/0.77 tff(215,plain,
% 0.69/0.77 ((~![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))),
% 0.69/0.77 inference(quant_inst,[status(thm)],[])).
% 0.69/0.77 tff(216,plain,
% 0.69/0.77 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.69/0.77 inference(unit_resolution,[status(thm)],[215, 127])).
% 0.69/0.77 tff(217,plain,
% 0.69/0.77 (^[V_27i_27: $i, V_27f_27: $i] : refl((s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))),
% 0.69/0.77 inference(bind,[status(th)],[])).
% 0.69/0.77 tff(218,plain,
% 0.69/0.77 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.69/0.77 inference(quant_intro,[status(thm)],[217])).
% 0.69/0.77 tff(219,plain,
% 0.69/0.77 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.69/0.77 inference(rewrite,[status(thm)],[])).
% 0.69/0.77 tff(220,plain,
% 0.69/0.77 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.69/0.77 inference(and_elim,[status(thm)],[17])).
% 0.69/0.77 tff(221,plain,
% 0.69/0.77 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.69/0.77 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.69/0.77 tff(222,plain,(
% 0.69/0.77 ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.69/0.77 inference(skolemize,[status(sab)],[221])).
% 0.69/0.77 tff(223,plain,
% 0.69/0.77 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))),
% 0.69/0.77 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.69/0.77 tff(224,plain,
% 0.69/0.77 ((~![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.69/0.77 inference(quant_inst,[status(thm)],[])).
% 0.69/0.77 tff(225,plain,
% 0.69/0.77 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.77 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.69/0.77 tff(226,plain,
% 0.69/0.77 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.69/0.78 inference(symmetry,[status(thm)],[225])).
% 0.69/0.78 tff(227,plain,
% 0.69/0.78 (^[V_27i_27: $i, V_27f_27: $i] : refl((s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))))),
% 0.69/0.78 inference(bind,[status(th)],[])).
% 0.69/0.78 tff(228,plain,
% 0.69/0.78 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.69/0.78 inference(quant_intro,[status(thm)],[227])).
% 0.69/0.78 tff(229,plain,
% 0.69/0.78 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.69/0.78 inference(rewrite,[status(thm)],[])).
% 0.69/0.78 tff(230,plain,
% 0.69/0.78 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.69/0.78 inference(and_elim,[status(thm)],[14])).
% 0.69/0.78 tff(231,plain,
% 0.69/0.78 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.69/0.78 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.69/0.78 tff(232,plain,(
% 0.69/0.78 ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.69/0.78 inference(skolemize,[status(sab)],[231])).
% 0.69/0.78 tff(233,plain,
% 0.69/0.78 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.69/0.78 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.69/0.78 tff(234,plain,
% 0.69/0.78 ((~![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.69/0.78 inference(quant_inst,[status(thm)],[])).
% 0.69/0.78 tff(235,plain,
% 0.69/0.78 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.78 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.69/0.78 tff(236,plain,
% 0.69/0.78 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.78 inference(symmetry,[status(thm)],[235])).
% 0.69/0.78 tff(237,plain,
% 0.69/0.78 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.69/0.78 inference(quant_inst,[status(thm)],[])).
% 0.69/0.78 tff(238,plain,
% 0.69/0.78 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.69/0.78 inference(unit_resolution,[status(thm)],[237, 100])).
% 0.69/0.78 tff(239,plain,
% 0.69/0.78 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.69/0.79 inference(symmetry,[status(thm)],[238])).
% 0.69/0.79 tff(240,plain,
% 0.69/0.79 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.69/0.79 inference(transitivity,[status(thm)],[239, 236, 226])).
% 0.69/0.79 tff(241,plain,
% 0.69/0.79 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.69/0.79 inference(monotonicity,[status(thm)],[240])).
% 0.69/0.79 tff(242,plain,
% 0.69/0.79 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.69/0.79 inference(symmetry,[status(thm)],[241])).
% 0.69/0.79 tff(243,plain,
% 0.69/0.79 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.69/0.79 inference(monotonicity,[status(thm)],[242])).
% 0.69/0.79 tff(244,plain,
% 0.69/0.79 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.69/0.79 inference(transitivity,[status(thm)],[243, 216, 214])).
% 0.69/0.79 tff(245,plain,
% 0.69/0.79 (c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))) = c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))),
% 0.69/0.79 inference(monotonicity,[status(thm)],[244])).
% 0.69/0.79 tff(246,plain,
% 0.69/0.79 (s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))) = s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))))),
% 0.69/0.79 inference(monotonicity,[status(thm)],[245])).
% 0.69/0.79 tff(247,plain,
% 0.69/0.79 (c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)) = c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))),
% 0.69/0.80 inference(monotonicity,[status(thm)],[246])).
% 0.69/0.80 tff(248,plain,
% 0.69/0.80 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))),
% 0.69/0.80 inference(monotonicity,[status(thm)],[247])).
% 0.69/0.80 tff(249,plain,
% 0.69/0.80 (c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))) = c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))),
% 0.69/0.80 inference(monotonicity,[status(thm)],[248])).
% 0.69/0.80 tff(250,plain,
% 0.69/0.80 (c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))),
% 0.69/0.80 inference(monotonicity,[status(thm)],[76])).
% 0.69/0.80 tff(251,plain,
% 0.69/0.80 (c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))) = c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.69/0.80 inference(symmetry,[status(thm)],[250])).
% 0.69/0.80 tff(252,plain,
% 0.69/0.80 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.69/0.80 inference(monotonicity,[status(thm)],[251])).
% 0.69/0.80 tff(253,plain,
% 0.69/0.80 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.69/0.81 inference(symmetry,[status(thm)],[252])).
% 0.69/0.81 tff(254,plain,
% 0.69/0.81 (^[V_27f_27: $i, V_27d_27: $i] : refl((s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))),
% 0.69/0.81 inference(bind,[status(th)],[])).
% 0.69/0.81 tff(255,plain,
% 0.69/0.81 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(quant_intro,[status(thm)],[254])).
% 0.69/0.81 tff(256,plain,
% 0.69/0.81 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(rewrite,[status(thm)],[])).
% 0.69/0.81 tff(257,plain,
% 0.69/0.81 (((![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(and_elim,[status(thm)],[164])).
% 0.69/0.81 tff(258,plain,
% 0.69/0.81 ((![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) & ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(and_elim,[status(thm)],[257])).
% 0.69/0.81 tff(259,plain,
% 0.69/0.81 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(and_elim,[status(thm)],[258])).
% 0.69/0.81 tff(260,plain,
% 0.69/0.81 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(modus_ponens,[status(thm)],[259, 256])).
% 0.69/0.81 tff(261,plain,(
% 0.69/0.81 ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(skolemize,[status(sab)],[260])).
% 0.69/0.81 tff(262,plain,
% 0.69/0.81 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))),
% 0.69/0.81 inference(modus_ponens,[status(thm)],[261, 255])).
% 0.69/0.81 tff(263,plain,
% 0.69/0.81 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.69/0.81 inference(quant_inst,[status(thm)],[])).
% 0.69/0.81 tff(264,plain,
% 0.69/0.81 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.69/0.81 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.69/0.81 tff(265,plain,
% 0.69/0.81 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.69/0.82 inference(symmetry,[status(thm)],[264])).
% 0.69/0.82 tff(266,plain,
% 0.69/0.82 (^[V_27f_27: $i, V_27d_27: $i] : refl((s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))))),
% 0.69/0.82 inference(bind,[status(th)],[])).
% 0.69/0.82 tff(267,plain,
% 0.69/0.82 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.69/0.82 inference(quant_intro,[status(thm)],[266])).
% 0.69/0.82 tff(268,plain,
% 0.69/0.82 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27)))))) <=> ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.69/0.82 inference(rewrite,[status(thm)],[])).
% 0.69/0.82 tff(269,plain,
% 0.69/0.82 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.69/0.82 inference(and_elim,[status(thm)],[85])).
% 0.69/0.82 tff(270,plain,
% 0.69/0.82 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.69/0.82 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.69/0.82 tff(271,plain,(
% 0.69/0.82 ![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.69/0.82 inference(skolemize,[status(sab)],[270])).
% 0.69/0.82 tff(272,plain,
% 0.69/0.82 (![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))),
% 0.69/0.82 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.69/0.82 tff(273,plain,
% 0.69/0.82 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.69/0.82 inference(quant_inst,[status(thm)],[])).
% 0.69/0.82 tff(274,plain,
% 0.69/0.82 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.69/0.83 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.69/0.83 tff(275,plain,
% 0.69/0.83 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.69/0.83 inference(symmetry,[status(thm)],[274])).
% 0.69/0.83 tff(276,plain,
% 0.69/0.83 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.69/0.83 inference(quant_inst,[status(thm)],[])).
% 0.69/0.83 tff(277,plain,
% 0.69/0.83 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.69/0.83 inference(unit_resolution,[status(thm)],[276, 100])).
% 0.69/0.83 tff(278,plain,
% 0.69/0.83 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.69/0.83 inference(symmetry,[status(thm)],[277])).
% 0.69/0.83 tff(279,plain,
% 0.69/0.83 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.69/0.83 inference(transitivity,[status(thm)],[278, 275, 265, 253])).
% 0.69/0.83 tff(280,plain,
% 0.69/0.83 (c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))),
% 0.69/0.83 inference(monotonicity,[status(thm)],[107])).
% 0.69/0.83 tff(281,plain,
% 0.69/0.83 (c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))) = c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.69/0.83 inference(symmetry,[status(thm)],[280])).
% 0.69/0.83 tff(282,plain,
% 0.69/0.83 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.69/0.83 inference(monotonicity,[status(thm)],[281])).
% 0.69/0.83 tff(283,plain,
% 0.69/0.83 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.77/0.84 inference(symmetry,[status(thm)],[282])).
% 0.77/0.84 tff(284,plain,
% 0.77/0.84 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.77/0.84 inference(quant_inst,[status(thm)],[])).
% 0.77/0.84 tff(285,plain,
% 0.77/0.84 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.84 inference(unit_resolution,[status(thm)],[284, 262])).
% 0.77/0.84 tff(286,plain,
% 0.77/0.84 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))))),
% 0.77/0.84 inference(symmetry,[status(thm)],[285])).
% 0.77/0.84 tff(287,plain,
% 0.77/0.84 ((~![V_27f_27: $i, V_27d_27: $i] : (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), V_27f_27), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, V_27d_27))))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.77/0.84 inference(quant_inst,[status(thm)],[])).
% 0.77/0.84 tff(288,plain,
% 0.77/0.84 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.84 inference(unit_resolution,[status(thm)],[287, 272])).
% 0.77/0.84 tff(289,plain,
% 0.77/0.84 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.85 inference(symmetry,[status(thm)],[288])).
% 0.77/0.85 tff(290,plain,
% 0.77/0.85 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))),
% 0.77/0.85 inference(quant_inst,[status(thm)],[])).
% 0.77/0.85 tff(291,plain,
% 0.77/0.85 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.77/0.85 inference(unit_resolution,[status(thm)],[290, 100])).
% 0.77/0.85 tff(292,plain,
% 0.77/0.85 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), chapp__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.85 inference(symmetry,[status(thm)],[291])).
% 0.77/0.85 tff(293,plain,
% 0.77/0.85 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2)))))),
% 0.77/0.85 inference(transitivity,[status(thm)],[292, 289, 286, 283])).
% 0.77/0.85 tff(294,plain,
% 0.77/0.85 (c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.77/0.85 inference(monotonicity,[status(thm)],[293, 279])).
% 0.77/0.85 tff(295,plain,
% 0.77/0.85 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.77/0.85 inference(monotonicity,[status(thm)],[294])).
% 0.77/0.85 tff(296,plain,
% 0.77/0.85 ((~![V_27A_27: $i, V_27l1_27: $i, V_27l2_27: $i] : (s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27), s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))) = s__02(cfun__02(V_27A_27, cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l1_27))), s__02(cfun__02(V_27A_27, cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27), V_27l2_27))))))) | (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))),
% 0.77/0.85 inference(quant_inst,[status(thm)],[])).
% 0.77/0.85 tff(297,plain,
% 0.77/0.85 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.77/0.85 inference(unit_resolution,[status(thm)],[296, 127])).
% 0.77/0.85 tff(298,plain,
% 0.77/0.85 (^[V_27i_27: $i, V_27f_27: $i] : refl((s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))))),
% 0.77/0.85 inference(bind,[status(th)],[])).
% 0.77/0.85 tff(299,plain,
% 0.77/0.85 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.77/0.85 inference(quant_intro,[status(thm)],[298])).
% 0.77/0.85 tff(300,plain,
% 0.77/0.85 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27)))))) <=> ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.77/0.85 inference(rewrite,[status(thm)],[])).
% 0.77/0.85 tff(301,plain,
% 0.77/0.85 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.77/0.86 inference(and_elim,[status(thm)],[15])).
% 0.77/0.86 tff(302,plain,
% 0.77/0.86 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.77/0.86 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.77/0.86 tff(303,plain,(
% 0.77/0.86 ![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.77/0.86 inference(skolemize,[status(sab)],[302])).
% 0.77/0.86 tff(304,plain,
% 0.77/0.86 (![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))),
% 0.77/0.86 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.77/0.86 tff(305,plain,
% 0.77/0.86 ((~![V_27i_27: $i, V_27f_27: $i] : (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), V_27f_27), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27i_27))))))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.77/0.86 inference(quant_inst,[status(thm)],[])).
% 0.77/0.86 tff(306,plain,
% 0.77/0.86 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.86 inference(unit_resolution,[status(thm)],[305, 304])).
% 0.77/0.86 tff(307,plain,
% 0.77/0.86 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.86 inference(symmetry,[status(thm)],[306])).
% 0.77/0.86 tff(308,plain,
% 0.77/0.86 ((~![V_27B_27: $i, V_27A_27: $i, V_27x_27: $i, V_27y_27: $i] : (s__02(V_27A_27, chapp__02(s__02(cfun__02(V_27B_27, V_27A_27), c_27const_2ecombin_2eK_27__01(s__02(V_27A_27, V_27x_27))), s__02(V_27B_27, V_27y_27))) = s__02(V_27A_27, V_27x_27))) | (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.77/0.86 inference(quant_inst,[status(thm)],[])).
% 0.77/0.86 tff(309,plain,
% 0.77/0.86 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.77/0.87 inference(unit_resolution,[status(thm)],[308, 100])).
% 0.77/0.87 tff(310,plain,
% 0.77/0.87 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.87 inference(symmetry,[status(thm)],[309])).
% 0.77/0.87 tff(311,plain,
% 0.77/0.87 (s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.77/0.87 inference(transitivity,[status(thm)],[310, 307])).
% 0.77/0.87 tff(312,plain,
% 0.77/0.87 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.77/0.87 inference(monotonicity,[status(thm)],[311])).
% 0.77/0.87 tff(313,plain,
% 0.77/0.87 (c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))) = c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.77/0.87 inference(symmetry,[status(thm)],[312])).
% 0.77/0.87 tff(314,plain,
% 0.77/0.87 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.77/0.87 inference(monotonicity,[status(thm)],[313])).
% 0.77/0.87 tff(315,plain,
% 0.77/0.87 (s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))) = s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))),
% 0.77/0.87 inference(transitivity,[status(thm)],[314, 297, 295])).
% 0.77/0.87 tff(316,plain,
% 0.77/0.87 (c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00)))))))))) = c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))),
% 0.77/0.87 inference(monotonicity,[status(thm)],[315])).
% 0.77/0.87 tff(317,plain,
% 0.77/0.87 (s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))) = s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))))))),
% 0.77/0.87 inference(monotonicity,[status(thm)],[316])).
% 0.77/0.87 tff(318,plain,
% 0.77/0.87 (c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))) = c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))),
% 0.81/0.88 inference(monotonicity,[status(thm)],[317])).
% 0.81/0.88 tff(319,plain,
% 0.81/0.88 (c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))) = c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))),
% 0.81/0.88 inference(transitivity,[status(thm)],[318, 249])).
% 0.81/0.88 tff(320,plain,
% 0.81/0.88 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.81/0.88 inference(monotonicity,[status(thm)],[319])).
% 0.81/0.88 tff(321,plain,
% 0.81/0.88 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))),
% 0.81/0.89 inference(symmetry,[status(thm)],[320])).
% 0.81/0.89 tff(322,plain,
% 0.81/0.89 (c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))) = c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)))), c_27const_2ecombin_2eK_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2elist_2eAPPEND_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))), s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2ebool_2eARB_27__00))))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.81/0.89 inference(monotonicity,[status(thm)],[321])).
% 0.81/0.89 tff(323,plain,
% 0.81/0.89 (c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))) = c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))),
% 0.81/0.89 inference(transitivity,[status(thm)],[322, 155])).
% 0.81/0.89 tff(324,plain,
% 0.81/0.89 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.81/0.90 inference(monotonicity,[status(thm)],[323])).
% 0.81/0.90 tff(325,plain,
% 0.81/0.90 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__mods_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__types_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2epred__set_2eUNION_27__02(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))))), s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2etypeSystem_2edecls__defined__exns_27__01(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.81/0.90 inference(symmetry,[status(thm)],[324])).
% 0.81/0.90 tff(326,plain,
% 0.81/0.90 ((~![V_27idecls_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27idecls_27))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))) | (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00))))))))),
% 0.81/0.90 inference(quant_inst,[status(thm)],[])).
% 0.81/0.90 tff(327,plain,
% 0.81/0.90 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__mods_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__types_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02(s__02(cfun__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00)), c_27const_2ecombin_2eK_27__01(s__02(cfun__02(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00)), cbool__00), c_27const_2elist_2eLIST__TO__SET_27__01(s__02(c_27type_2elist_2elist_27__01(c_27type_2enamespace_2eid_27__02(c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00), c_27type_2elist_2elist_27__01(c_27type_2estring_2echar_27__00))), c_27const_2einfer_2einf__decls__inf__defined__exns_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2ebool_2eARB_27__00)))))))),
% 0.81/0.90 inference(unit_resolution,[status(thm)],[326, 73])).
% 0.81/0.90 tff(328,plain,
% 0.81/0.90 (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1)))))),
% 0.81/0.90 inference(transitivity,[status(thm)],[327, 325, 10])).
% 0.81/0.90 tff(329,plain,
% 0.81/0.90 ((~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))) <=> (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27)))))))),
% 0.81/0.90 inference(rewrite,[status(thm)],[])).
% 0.81/0.90 tff(330,axiom,(~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture')).
% 0.81/0.90 tff(331,plain,
% 0.81/0.90 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.90 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.81/0.90 tff(332,plain,
% 0.81/0.90 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.90 inference(modus_ponens,[status(thm)],[331, 329])).
% 0.81/0.90 tff(333,plain,
% 0.81/0.90 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.90 inference(modus_ponens,[status(thm)],[332, 329])).
% 0.81/0.90 tff(334,plain,
% 0.81/0.90 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.90 inference(modus_ponens,[status(thm)],[333, 329])).
% 0.81/0.90 tff(335,plain,
% 0.81/0.90 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.90 inference(modus_ponens,[status(thm)],[334, 329])).
% 0.81/0.90 tff(336,plain,
% 0.81/0.90 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.90 inference(modus_ponens,[status(thm)],[335, 329])).
% 0.81/0.90 tff(337,plain,
% 0.81/0.90 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.91 inference(modus_ponens,[status(thm)],[336, 329])).
% 0.81/0.91 tff(338,plain,
% 0.81/0.91 (~![V_27decls1_27: $i, V_27decls2_27: $i] : (s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27))))))),
% 0.81/0.91 inference(modus_ponens,[status(thm)],[337, 329])).
% 0.81/0.91 tff(339,plain,(
% 0.81/0.91 ~(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, c_27const_2einfer_2eappend__decls_27__02(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2), s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))) = s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2etypeSystem_2eunion__decls_27__02(s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls1_27!2))), s__02(c_27type_2etypeSystem_2edecls_27__00, c_27const_2eenvRel_2econvert__decls_27__01(s__02(c_27type_2einfer_2einf__decls_27__00, V_27decls2_27!1))))))),
% 0.81/0.91 inference(skolemize,[status(sab)],[338])).
% 0.81/0.91 tff(340,plain,
% 0.81/0.91 ($false),
% 0.81/0.91 inference(unit_resolution,[status(thm)],[339, 328])).
% 0.81/0.91 % SZS output end Proof
%------------------------------------------------------------------------------