TSTP Solution File: SWW874+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW874+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:25:26 EDT 2023
% Result : Theorem 43.90s 22.69s
% Output : Refutation 44.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 48
% Syntax : Number of formulae : 66 ( 21 unt; 32 typ; 0 def)
% Number of atoms : 118 ( 70 equ; 0 cnn)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 3574 ( 4 ~; 2 |; 63 &;3486 @)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 8 con; 0-2 aty)
% Number of variables : 130 ( 0 ^; 130 !; 0 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(s__02_type,type,
s__02: $i > $i > $i ).
thf(c_27type_2etypeSystem_2edecls_27__00_type,type,
c_27type_2etypeSystem_2edecls_27__00: $i ).
thf(c_27const_2eenvRel_2econvert__decls_27__01_type,type,
c_27const_2eenvRel_2econvert__decls_27__01: $i > $i ).
thf(c_27type_2einfer_2einf__decls_27__00_type,type,
c_27type_2einfer_2einf__decls_27__00: $i ).
thf(c_27const_2einfer_2eappend__decls_27__02_type,type,
c_27const_2einfer_2eappend__decls_27__02: $i > $i > $i ).
thf(c_27const_2etypeSystem_2eunion__decls_27__02_type,type,
c_27const_2etypeSystem_2eunion__decls_27__02: $i > $i > $i ).
thf(cfun__02_type,type,
cfun__02: $i > $i > $i ).
thf(cbool__00_type,type,
cbool__00: $i ).
thf(c_27const_2elist_2eLIST__TO__SET_27__01_type,type,
c_27const_2elist_2eLIST__TO__SET_27__01: $i > $i ).
thf(c_27type_2elist_2elist_27__01_type,type,
c_27type_2elist_2elist_27__01: $i > $i ).
thf(c_27const_2elist_2eAPPEND_27__02_type,type,
c_27const_2elist_2eAPPEND_27__02: $i > $i > $i ).
thf(c_27const_2epred__set_2eUNION_27__02_type,type,
c_27const_2epred__set_2eUNION_27__02: $i > $i > $i ).
thf(c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02_type,type,
c_27const_2etypeSystem_2edecls__defined__mods__fupd_27__02: $i > $i > $i ).
thf(c_27type_2estring_2echar_27__00_type,type,
c_27type_2estring_2echar_27__00: $i ).
thf(c_27const_2ecombin_2eK_27__01_type,type,
c_27const_2ecombin_2eK_27__01: $i > $i ).
thf(c_27const_2etypeSystem_2edecls__defined__mods_27__01_type,type,
c_27const_2etypeSystem_2edecls__defined__mods_27__01: $i > $i ).
thf(c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02_type,type,
c_27const_2etypeSystem_2edecls__defined__types__fupd_27__02: $i > $i > $i ).
thf(c_27type_2enamespace_2eid_27__02_type,type,
c_27type_2enamespace_2eid_27__02: $i > $i > $i ).
thf(c_27const_2etypeSystem_2edecls__defined__types_27__01_type,type,
c_27const_2etypeSystem_2edecls__defined__types_27__01: $i > $i ).
thf(c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02_type,type,
c_27const_2etypeSystem_2edecls__defined__exns__fupd_27__02: $i > $i > $i ).
thf(c_27const_2etypeSystem_2edecls__defined__exns_27__01_type,type,
c_27const_2etypeSystem_2edecls__defined__exns_27__01: $i > $i ).
thf(c_27const_2ebool_2eARB_27__00_type,type,
c_27const_2ebool_2eARB_27__00: $i ).
thf(p__01_type,type,
p__01: $i > $o ).
thf(cT__00_type,type,
cT__00: $i ).
thf(cF__00_type,type,
cF__00: $i ).
thf(c_27const_2einfer_2einf__decls__inf__defined__mods_27__01_type,type,
c_27const_2einfer_2einf__decls__inf__defined__mods_27__01: $i > $i ).
thf(c_27const_2einfer_2einf__decls__inf__defined__types_27__01_type,type,
c_27const_2einfer_2einf__decls__inf__defined__types_27__01: $i > $i ).
thf(c_27const_2einfer_2einf__decls__inf__defined__exns_27__01_type,type,
c_27const_2einfer_2einf__decls__inf__defined__exns_27__01: $i > $i ).
thf(chapp__02_type,type,
chapp__02: $i > $i > $i ).
thf(c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02_type,type,
c_27const_2einfer_2einf__decls__inf__defined__types__fupd_27__02: $i > $i > $i ).
thf(c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02_type,type,
c_27const_2einfer_2einf__decls__inf__defined__exns__fupd_27__02: $i > $i > $i ).
thf(c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02_type,type,
c_27const_2einfer_2einf__decls__inf__defined__mods__fupd_27__02: $i > $i > $i ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ ( c_27const_2etypeSystem_2eunion__decls_27__02 @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) )
= ( 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 @ A ) ) ) @ ( s__02 @ ( 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 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ c_27const_2ebool_2eARB_27__00 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.typeSystem.union_decls_def') ).
thf(24,plain,
! [A: $i,B: $i] :
( ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ ( c_27const_2etypeSystem_2eunion__decls_27__02 @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) )
= ( 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 @ A ) ) ) @ ( s__02 @ ( 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 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ c_27const_2ebool_2eARB_27__00 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
~ ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','HL_FALSITY') ).
thf(52,plain,
~ ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( ( s__02 @ cbool__00 @ A )
= ( s__02 @ cbool__00 @ cT__00 ) )
| ( ( s__02 @ cbool__00 @ A )
= ( s__02 @ cbool__00 @ cF__00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','HL_BOOL_CASES') ).
thf(57,plain,
! [A: $i] :
( ( ( s__02 @ cbool__00 @ A )
= ( s__02 @ cbool__00 @ cT__00 ) )
| ( ( s__02 @ cbool__00 @ A )
= ( s__02 @ cbool__00 @ cF__00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( 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 ) @ A ) ) ) @ ( 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 ) @ B ) ) ) @ ( 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 ) ) ) @ ( 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 ) @ D ) ) ) @ ( 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 ) @ E ) ) ) @ ( 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 ) @ F ) ) ) @ ( 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 ) @ A )
= ( s__02 @ ( cfun__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ D ) )
& ( ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ B )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ E ) )
& ( ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ C )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.typeSystem.decls_literal_11') ).
thf(60,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( 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 ) @ A ) ) ) @ ( 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 ) @ B ) ) ) @ ( 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 ) ) ) @ ( 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 ) @ D ) ) ) @ ( 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 ) @ E ) ) ) @ ( 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 ) @ F ) ) ) @ ( 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 ) @ A )
= ( s__02 @ ( cfun__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ D ) )
& ( ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ B )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ E ) )
& ( ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ C )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ F ) ) ) )
& ( ( ( ( s__02 @ ( cfun__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ A )
= ( s__02 @ ( cfun__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ D ) )
& ( ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ B )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ E ) )
& ( ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ C )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) @ cbool__00 ) @ F ) ) )
=> ( ( 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 ) @ A ) ) ) @ ( 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 ) @ B ) ) ) @ ( 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 ) ) ) @ ( 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 ) @ D ) ) ) @ ( 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 ) @ E ) ) ) @ ( 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 ) @ F ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ c_27const_2ebool_2eARB_27__00 ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2elist_2eLIST__TO__SET_27__01 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ ( c_27const_2elist_2eAPPEND_27__02 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ C ) ) ) ) )
= ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2epred__set_2eUNION_27__02 @ ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2elist_2eLIST__TO__SET_27__01 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ B ) ) ) @ ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2elist_2eLIST__TO__SET_27__01 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.list.LIST_TO_SET_APPEND') ).
thf(21,plain,
! [A: $i,B: $i,C: $i] :
( ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2elist_2eLIST__TO__SET_27__01 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ ( c_27const_2elist_2eAPPEND_27__02 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ C ) ) ) ) )
= ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2epred__set_2eUNION_27__02 @ ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2elist_2eLIST__TO__SET_27__01 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ B ) ) ) @ ( s__02 @ ( cfun__02 @ A @ cbool__00 ) @ ( c_27const_2elist_2eLIST__TO__SET_27__01 @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( s__02 @ B @ ( chapp__02 @ ( s__02 @ ( cfun__02 @ A @ B ) @ C ) @ ( s__02 @ A @ E ) ) )
= ( s__02 @ B @ ( chapp__02 @ ( s__02 @ ( cfun__02 @ A @ B ) @ D ) @ ( s__02 @ A @ E ) ) ) )
=> ( ( s__02 @ ( cfun__02 @ A @ B ) @ C )
= ( s__02 @ ( cfun__02 @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','HL_EXT') ).
thf(73,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( s__02 @ B @ ( chapp__02 @ ( s__02 @ ( cfun__02 @ A @ B ) @ C ) @ ( s__02 @ A @ E ) ) )
= ( s__02 @ B @ ( chapp__02 @ ( s__02 @ ( cfun__02 @ A @ B ) @ D ) @ ( s__02 @ A @ E ) ) ) )
=> ( ( s__02 @ ( cfun__02 @ A @ B ) @ C )
= ( s__02 @ ( cfun__02 @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( ( ( p__01 @ ( s__02 @ cbool__00 @ cT__00 ) )
& ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
<=> ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
& ( ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
& ( p__01 @ ( s__02 @ cbool__00 @ cT__00 ) ) )
<=> ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
& ( ( ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) )
& ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
<=> ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ) )
& ( ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
& ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ) )
<=> ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ) )
& ( ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
& ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
<=> ( p__01 @ ( s__02 @ cbool__00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.bool.AND_CLAUSES') ).
thf(27,plain,
! [A: $i] :
( ( ( ( p__01 @ ( s__02 @ cbool__00 @ cT__00 ) )
& ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
=> ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
& ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
=> ( ( p__01 @ ( s__02 @ cbool__00 @ cT__00 ) )
& ( p__01 @ ( s__02 @ cbool__00 @ A ) ) ) )
& ( ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
& ( p__01 @ ( s__02 @ cbool__00 @ cT__00 ) ) )
=> ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
& ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
=> ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
& ( p__01 @ ( s__02 @ cbool__00 @ cT__00 ) ) ) )
& ( ( ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) )
& ( p__01 @ ( s__02 @ cbool__00 @ A ) ) )
=> ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ) )
& ( ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) )
=> ( ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) )
& ( p__01 @ ( s__02 @ cbool__00 @ A ) ) ) )
& ( ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
& ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ) )
=> ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ) )
& ( ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) )
=> ( ( p__01 @ ( s__02 @ cbool__00 @ A ) )
& ( p__01 @ ( s__02 @ cbool__00 @ cF__00 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
( ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( 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 ) ) ) ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( 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 ) ) ) ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( 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 ) ) ) ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.infer.inf_decls_accfupds') ).
thf(76,plain,
( ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( 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 ) ) ) ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( 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 ) ) ) ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) ) ) @ B ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) )
= ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( 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 ) ) ) ) @ B ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
( ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( 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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( 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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( 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 ) ) @ A ) @ ( s__02 @ ( 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 @ B ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_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 ) ) @ A ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_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 ) ) @ A ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.typeSystem.decls_accfupds') ).
thf(103,plain,
( ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( 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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( 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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( 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 ) ) @ A ) @ ( s__02 @ ( 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 @ B ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_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 ) ) @ A ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) )
& ! [A: $i,B: $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 ) ) @ A ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ B ) ) ) ) )
= ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_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 ) ) @ A ) @ ( s__02 @ ( cfun__02 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_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 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( s__02 @ A @ B )
= ( s__02 @ A @ B ) )
<=> ( p__01 @ ( s__02 @ cbool__00 @ cT__00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.bool.REFL_CLAUSE') ).
thf(130,plain,
p__01 @ ( s__02 @ cbool__00 @ cT__00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
! [A: $i,B: $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 @ A ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) )
= ( 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 @ A ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ ( c_27const_2eenvRel_2econvert__decls_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $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 @ A ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) )
= ( 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 @ A ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ ( c_27const_2eenvRel_2econvert__decls_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: $i,B: $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 @ A ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) )
= ( 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 @ A ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ ( c_27const_2eenvRel_2econvert__decls_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
p__01 @ ( s__02 @ cbool__00 @ cT__00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.bool.TRUTH') ).
thf(72,plain,
p__01 @ ( s__02 @ cbool__00 @ cT__00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $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 @ A ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) )
= ( 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 @ A ) ) ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ) ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ c_27const_2ebool_2eARB_27__00 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.infer.append_decls_def') ).
thf(131,plain,
! [A: $i,B: $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 @ A ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) )
= ( 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 @ A ) ) ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__mods_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__types_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) @ ( s__02 @ ( c_27type_2elist_2elist_27__01 @ ( c_27type_2enamespace_2eid_27__02 @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) @ ( c_27type_2elist_2elist_27__01 @ c_27type_2estring_2echar_27__00 ) ) ) @ ( c_27const_2einfer_2einf__decls__inf__defined__exns_27__01 @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ B ) ) ) ) ) ) ) @ ( s__02 @ c_27type_2einfer_2einf__decls_27__00 @ c_27const_2ebool_2eARB_27__00 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
p__01 @ ( s__02 @ cbool__00 @ cT__00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','HL_TRUTH') ).
thf(71,plain,
p__01 @ ( s__02 @ cbool__00 @ cT__00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s__02 @ B @ ( chapp__02 @ ( s__02 @ ( cfun__02 @ A @ B ) @ ( c_27const_2ecombin_2eK_27__01 @ ( s__02 @ B @ C ) ) ) @ ( s__02 @ A @ D ) ) )
= ( s__02 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.combin.K_THM') ).
thf(54,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s__02 @ B @ ( chapp__02 @ ( s__02 @ ( cfun__02 @ A @ B ) @ ( c_27const_2ecombin_2eK_27__01 @ ( s__02 @ B @ C ) ) ) @ ( s__02 @ A @ D ) ) )
= ( s__02 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $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 @ A ) ) )
= ( 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 @ A ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) ) ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ c_27const_2ebool_2eARB_27__00 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm.envRel.convert_decls_def') ).
thf(49,plain,
! [A: $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 @ A ) ) )
= ( 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 @ A ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) ) ) ) ) @ ( 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 @ A ) ) ) ) ) ) ) @ ( s__02 @ c_27type_2etypeSystem_2edecls_27__00 @ c_27const_2ebool_2eARB_27__00 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1052,plain,
$false,
inference(e,[status(thm)],[24,52,57,60,21,73,27,76,103,130,18,72,131,71,54,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW874+1 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 23:09:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.02 % [INFO] Parsing done (169ms).
% 1.28/1.03 % [INFO] Running in sequential loop mode.
% 1.75/1.23 % [INFO] eprover registered as external prover.
% 1.98/1.23 % [INFO] cvc4 registered as external prover.
% 1.98/1.24 % [INFO] Scanning for conjecture ...
% 2.20/1.33 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 2.41/1.38 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.41/1.47 % [INFO] Problem is first-order (TPTP FOF).
% 2.41/1.48 % [INFO] Type checking passed.
% 2.87/1.48 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 43.90/22.69 % External prover 'e' found a proof!
% 43.90/22.69 % [INFO] Killing All external provers ...
% 43.90/22.69 % Time passed: 22170ms (effective reasoning time: 21657ms)
% 43.90/22.69 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 43.90/22.69 % Axioms used in derivation (15): thm.typeSystem.decls_literal_11, HL_BOOL_CASES, thm.bool.TRUTH, thm.bool.REFL_CLAUSE, thm.infer.inf_decls_accfupds, HL_FALSITY, HL_EXT, thm.infer.append_decls_def, thm.typeSystem.union_decls_def, HL_TRUTH, thm.list.LIST_TO_SET_APPEND, thm.bool.AND_CLAUSES, thm.combin.K_THM, thm.typeSystem.decls_accfupds, thm.envRel.convert_decls_def
% 43.90/22.69 % No. of inferences in proof: 34
% 43.90/22.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22170 ms resp. 21657 ms w/o parsing
% 44.46/22.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.46/22.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------