%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SCT149+1 : TPTP v9.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6gBQZRYbPo true
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:50:52 PM UTC 2025
% Result : Theorem 0.58s 0.96s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 3459 ( 21 ~; 20 |; 0 &;3412 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 27 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 18 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_member_type,type,
c_member: $i > $i ).
thf(v_c_____type,type,
v_c____: $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(v_P_____type,type,
v_P____: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(v_b_____type,type,
v_b____: $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(v_P_H_____type,type,
v_P_H____: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(v_F_type,type,
v_F: $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(fact_bc,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) ) ) ).
thf(zip_derived_cl42,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) ) ),
inference(cnf,[status(esa)],[fact_bc]) ).
thf('0',plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl42]) ).
thf(fact_ac,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) ) ) ).
thf(zip_derived_cl44,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) ) ),
inference(cnf,[status(esa)],[fact_ac]) ).
thf('1',plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl44]) ).
thf(conj_0,conjecture,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl806,plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('2',plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl806]) ).
thf(zip_derived_cl45,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) ) ),
inference(cnf,[status(esa)],[fact_ac]) ).
thf('3',plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl45]) ).
thf(fact_ba,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ) ).
thf(zip_derived_cl39,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) ) ),
inference(cnf,[status(esa)],[fact_ba]) ).
thf('4',plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl39]) ).
thf(zip_derived_cl43,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) ) ),
inference(cnf,[status(esa)],[fact_bc]) ).
thf('5',plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl43]) ).
thf(fact_ab,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) ) ) ).
thf(zip_derived_cl47,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) ) ),
inference(cnf,[status(esa)],[fact_ab]) ).
thf('6',plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl47]) ).
thf(zip_derived_cl40,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
inference(cnf,[status(esa)],[fact_ba]) ).
thf('7',plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) @ v_b____ ) ) @ v_a____ ) ) ) @ v_a____ ) ) @ v_c____ ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl40]) ).
thf(zip_derived_cl805,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf('8',plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_b____ ) @ v_a____ ) ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl805]) ).
thf(zip_derived_cl46,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) ) ),
inference(cnf,[status(esa)],[fact_ab]) ).
thf('9',plain,
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_c____ ) ) @ ( hAPP @ v_F @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_Obelow ) @ v_P____ ) ) @ v_c____ ) ) @ v_b____ ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl46]) ).
thf(zip_derived_cl827,plain,
$false,
inference('sat_resolution*',[status(thm)],['0','1','2','3','4','5','6','7','8','9']) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT149+1 : TPTP v9.2.0. Released v5.2.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6gBQZRYbPo true
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 15:14:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.55/0.64 % Total configuration time : 435
% 0.55/0.64 % Estimated wc time : 1092
% 0.55/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.56/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.58/0.96 % Solved by fo/fo1_av.sh.
% 0.58/0.96 % done 0 iterations in 0.188s
% 0.58/0.96 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/0.96 % SZS output start Refutation
% See solution above
% 0.58/0.97
% 0.58/0.97
% 0.58/0.97 % Terminating...
% 0.62/1.05 % Runner terminated.
% 0.62/1.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------