TSTP Solution File: SCT135+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SCT135+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjCiWc7k98 true
% Computer : n007.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 Aug 31 14:27:18 EDT 2023
% Result : Theorem 0.57s 0.87s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 97 ( 40 unt; 17 typ; 0 def)
% Number of atoms : 278 ( 117 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2282 ( 86 ~; 186 |; 0 &;1998 @)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 12 con; 0-6 aty)
% Number of variables : 72 ( 0 ^; 72 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_b_H_____type,type,
v_b_H____: $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_Arrow__Order__Mirabelle_OProf_type,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(v_P_H_____type,type,
v_P_H____: $i ).
thf(c_member_type,type,
c_member: $i > $i > $i > $o ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(v_P_____type,type,
v_P____: $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_prod_type,type,
tc_prod: $i > $i > $i ).
thf(sk__1_type,type,
sk__1: $i > $i > $i > $i > $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i > $i > $i ).
thf(v_a_H_____type,type,
v_a_H____: $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(v_F_type,type,
v_F: $i ).
thf(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_096,axiom,
! [B_i: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ B_i ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ B_i ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ X0 ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ X0 ) ) ),
inference(cnf,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_096]) ).
thf(zip_derived_cl7,plain,
! [X0: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ X0 ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ X0 ) ) ),
inference(cnf,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_096]) ).
thf(fact__096P_A_058_AProf_096,axiom,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf ).
thf(zip_derived_cl9,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_A_058_AProf_096]) ).
thf(fact__096P_H_A_058_AProf_096,axiom,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf ).
thf(zip_derived_cl10,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_H_A_058_AProf_096]) ).
thf(conj_0,conjecture,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl28,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( 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(fact__C1_C,axiom,
! [V_P_Ha_2: $i,V_Pa_2: $i,V_b_Ha_2: $i,V_a_Ha_2: $i,V_ba_2: $i,V_aa_2: $i] :
( ( V_aa_2 != V_ba_2 )
=> ( ( V_a_Ha_2 != V_b_Ha_2 )
=> ( ( V_aa_2 != V_b_Ha_2 )
=> ( ( V_ba_2 != V_a_Ha_2 )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ V_Pa_2 @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ V_P_Ha_2 @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [B_i: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ V_aa_2 @ V_ba_2 ) @ ( hAPP @ V_Pa_2 @ B_i ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ V_a_Ha_2 @ V_b_Ha_2 ) @ ( hAPP @ V_P_Ha_2 @ B_i ) ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ V_aa_2 @ V_ba_2 ) @ ( hAPP @ v_F @ V_Pa_2 ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ V_a_Ha_2 @ V_b_Ha_2 ) @ ( hAPP @ v_F @ V_P_Ha_2 ) ) ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl16,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X0 )
| ( X2 = X1 )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X3 @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ v_F @ X3 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X4 @ c_Arrow__Order__Mirabelle_OProf )
| ( X5 = X2 )
| ( X5 = X0 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ X4 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ X3 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ v_F @ X4 ) ) ),
inference(cnf,[status(esa)],[fact__C1_C]) ).
thf(zip_derived_cl56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( v_a____ = X1 )
| ( v_a____ = v_b____ )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b____ = X2 )
| ( X2 = X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl16]) ).
thf(zip_derived_cl9_001,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_A_058_AProf_096]) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( v_a____ = X1 )
| ( v_a____ = v_b____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b____ = X2 )
| ( X2 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl56,zip_derived_cl9]) ).
thf(fact__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____ ).
thf(zip_derived_cl3,plain,
v_a____ != v_b____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_096]) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( v_a____ = X1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b____ = X2 )
| ( X2 = X1 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl57,zip_derived_cl3]) ).
thf(zip_derived_cl61,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( v_b____ = X0 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X0 @ X1 ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( v_a____ = X1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a____ @ v_b____ @ X0 @ X1 @ v_P____ @ v_P_H____ ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X0 @ X1 ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ X0 @ X1 @ v_P____ @ v_P_H____ ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl58]) ).
thf(zip_derived_cl7_002,plain,
! [X0: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ X0 ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ X0 ) ) ),
inference(cnf,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_096]) ).
thf(zip_derived_cl104,plain,
! [X0: $i,X1: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ X1 @ X0 @ v_P____ @ v_P_H____ ) ) )
| ( v_a____ = X0 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( v_b____ = X1 )
| ( X1 = X0 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ X1 @ X0 @ v_P____ @ v_P_H____ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl7]) ).
thf(zip_derived_cl140,plain,
( ( v_a_H____ = v_b_H____ )
| ( v_b____ = v_a_H____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( v_a____ = v_b_H____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ v_a_H____ @ v_b_H____ @ v_P____ @ v_P_H____ ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl142,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ v_a_H____ @ v_b_H____ @ v_P____ @ v_P_H____ ) ) )
| ( v_a____ = v_b_H____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( v_b____ = v_a_H____ )
| ( v_a_H____ = v_b_H____ ) ),
inference(simplify,[status(thm)],[zip_derived_cl140]) ).
thf(fact__096a_H_A_126_061_Ab_H_096,axiom,
v_a_H____ != v_b_H____ ).
thf(zip_derived_cl6,plain,
v_a_H____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_H_A_126_061_Ab_H_096]) ).
thf(fact__096b_A_126_061_Aa_H_096,axiom,
v_b____ != v_a_H____ ).
thf(zip_derived_cl5,plain,
v_b____ != v_a_H____,
inference(cnf,[status(esa)],[fact__096b_A_126_061_Aa_H_096]) ).
thf(fact__096a_A_126_061_Ab_H_096,axiom,
v_a____ != v_b_H____ ).
thf(zip_derived_cl4,plain,
v_a____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_H_096]) ).
thf(zip_derived_cl143,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ v_a_H____ @ v_b_H____ @ v_P____ @ v_P_H____ ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl142,zip_derived_cl6,zip_derived_cl5,zip_derived_cl4]) ).
thf(zip_derived_cl28_003,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( 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(zip_derived_cl8_004,plain,
! [X0: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ X0 ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ X0 ) ) ),
inference(cnf,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_096]) ).
thf(zip_derived_cl17,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X0 )
| ( X2 = X1 )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X3 @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ v_F @ X3 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X4 @ c_Arrow__Order__Mirabelle_OProf )
| ( X5 = X2 )
| ( X5 = X0 )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ X4 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ X3 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ v_F @ X4 ) ) ),
inference(cnf,[status(esa)],[fact__C1_C]) ).
thf(zip_derived_cl40,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( v_a____ = X1 )
| ( v_a____ = v_b____ )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b____ = X2 )
| ( X2 = X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl17]) ).
thf(zip_derived_cl9_005,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_A_058_AProf_096]) ).
thf(zip_derived_cl43,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( v_a____ = X1 )
| ( v_a____ = v_b____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b____ = X2 )
| ( X2 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl9]) ).
thf(zip_derived_cl3_006,plain,
v_a____ != v_b____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_096]) ).
thf(zip_derived_cl44,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a____ @ v_b____ @ X2 @ X1 @ v_P____ @ X0 ) ) )
| ( v_a____ = X1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b____ = X2 )
| ( X2 = X1 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl43,zip_derived_cl3]) ).
thf(zip_derived_cl47,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( X0 = X1 )
| ( v_b____ = X0 )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X2 @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X0 @ X1 ) @ ( hAPP @ v_F @ X2 ) )
| ( v_a____ = X1 )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X0 @ X1 ) @ ( hAPP @ X2 @ ( sk__1 @ v_a____ @ v_b____ @ X0 @ X1 @ v_P____ @ X2 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ X0 @ X1 @ v_P____ @ X2 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl44]) ).
thf(zip_derived_cl49,plain,
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ v_a_H____ @ v_b_H____ @ v_P____ @ v_P_H____ ) ) )
| ( v_a____ = v_b_H____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b____ = v_a_H____ )
| ( v_a_H____ = v_b_H____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl50,plain,
( ( v_a_H____ = v_b_H____ )
| ( v_b____ = v_a_H____ )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( v_a____ = v_b_H____ )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ v_a_H____ @ v_b_H____ @ v_P____ @ v_P_H____ ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl10_007,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_H_A_058_AProf_096]) ).
thf(zip_derived_cl51,plain,
( ( v_a_H____ = v_b_H____ )
| ( v_b____ = v_a_H____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( v_a____ = v_b_H____ )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ v_a_H____ @ v_b_H____ @ v_P____ @ v_P_H____ ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl10]) ).
thf(zip_derived_cl4_008,plain,
v_a____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_H_096]) ).
thf(zip_derived_cl5_009,plain,
v_b____ != v_a_H____,
inference(cnf,[status(esa)],[fact__096b_A_126_061_Aa_H_096]) ).
thf(zip_derived_cl6_010,plain,
v_a_H____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_H_A_126_061_Ab_H_096]) ).
thf(zip_derived_cl52,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a____ @ v_b____ @ v_a_H____ @ v_b_H____ @ v_P____ @ v_P_H____ ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl51,zip_derived_cl4,zip_derived_cl5,zip_derived_cl6]) ).
thf(zip_derived_cl158,plain,
c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ),
inference(clc,[status(thm)],[zip_derived_cl143,zip_derived_cl52]) ).
thf(zip_derived_cl16_011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X0 )
| ( X2 = X1 )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X3 @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ v_F @ X3 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X4 @ c_Arrow__Order__Mirabelle_OProf )
| ( X5 = X2 )
| ( X5 = X0 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ X4 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ X3 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ v_F @ X4 ) ) ),
inference(cnf,[status(esa)],[fact__C1_C]) ).
thf(zip_derived_cl160,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X2 @ X1 @ v_P_H____ @ X0 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X2 @ X1 @ v_P_H____ @ X0 ) ) )
| ( v_a_H____ = X1 )
| ( v_a_H____ = v_b_H____ )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b_H____ = X2 )
| ( X2 = X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl158,zip_derived_cl16]) ).
thf(zip_derived_cl10_012,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_H_A_058_AProf_096]) ).
thf(zip_derived_cl161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X2 @ X1 @ v_P_H____ @ X0 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X2 @ X1 @ v_P_H____ @ X0 ) ) )
| ( v_a_H____ = X1 )
| ( v_a_H____ = v_b_H____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b_H____ = X2 )
| ( X2 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl10]) ).
thf(zip_derived_cl6_013,plain,
v_a_H____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_H_A_126_061_Ab_H_096]) ).
thf(zip_derived_cl162,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ X0 @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X2 @ X1 @ v_P_H____ @ X0 ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X2 @ X1 @ v_P_H____ @ X0 ) ) )
| ( v_a_H____ = X1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X2 @ X1 ) @ ( hAPP @ v_F @ X0 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X0 @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b_H____ = X2 )
| ( X2 = X1 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl161,zip_derived_cl6]) ).
thf(zip_derived_cl168,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( v_b_H____ = X0 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X0 @ X1 ) @ ( hAPP @ v_F @ v_P____ ) )
| ( v_a_H____ = X1 )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X0 @ X1 @ v_P_H____ @ v_P____ ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X0 @ X1 ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ X0 @ X1 @ v_P_H____ @ v_P____ ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl162]) ).
thf(zip_derived_cl172,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) )
| ( v_a_H____ = v_b____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ( v_b_H____ = v_a____ )
| ( v_a____ = v_b____ ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl168]) ).
thf(zip_derived_cl29,plain,
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( 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(zip_derived_cl158_014,plain,
c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ),
inference(clc,[status(thm)],[zip_derived_cl143,zip_derived_cl52]) ).
thf(zip_derived_cl159,plain,
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl158]) ).
thf(zip_derived_cl173,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) )
| ( v_a_H____ = v_b____ )
| ( v_b_H____ = v_a____ )
| ( v_a____ = v_b____ ) ),
inference(demod,[status(thm)],[zip_derived_cl172,zip_derived_cl159]) ).
thf(zip_derived_cl174,plain,
( ( v_a____ = v_b____ )
| ( v_b_H____ = v_a____ )
| ( v_a_H____ = v_b____ )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl173]) ).
thf(zip_derived_cl5_015,plain,
v_b____ != v_a_H____,
inference(cnf,[status(esa)],[fact__096b_A_126_061_Aa_H_096]) ).
thf(zip_derived_cl4_016,plain,
v_a____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_H_096]) ).
thf(zip_derived_cl3_017,plain,
v_a____ != v_b____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_096]) ).
thf(zip_derived_cl175,plain,
c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl174,zip_derived_cl5,zip_derived_cl4,zip_derived_cl3]) ).
thf(zip_derived_cl17_018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X0 )
| ( X2 = X1 )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X3 @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ v_F @ X3 ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ X4 @ c_Arrow__Order__Mirabelle_OProf )
| ( X5 = X2 )
| ( X5 = X0 )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ X4 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X1 @ X0 ) @ ( hAPP @ X3 @ ( sk__1 @ X5 @ X2 @ X1 @ X0 @ X4 @ X3 ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ X5 @ X2 ) @ ( hAPP @ v_F @ X4 ) ) ),
inference(cnf,[status(esa)],[fact__C1_C]) ).
thf(zip_derived_cl182,plain,
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) )
| ( v_a_H____ = v_b____ )
| ( v_a_H____ = v_b_H____ )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ~ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf )
| ( v_b_H____ = v_a____ )
| ( v_a____ = v_b____ ) ),
inference('sup-',[status(thm)],[zip_derived_cl175,zip_derived_cl17]) ).
thf(zip_derived_cl158_019,plain,
c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ),
inference(clc,[status(thm)],[zip_derived_cl143,zip_derived_cl52]) ).
thf(zip_derived_cl10_020,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_H_A_058_AProf_096]) ).
thf(zip_derived_cl159_021,plain,
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ),
inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl158]) ).
thf(zip_derived_cl9_022,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf,
inference(cnf,[status(esa)],[fact__096P_A_058_AProf_096]) ).
thf(zip_derived_cl183,plain,
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) )
| ( v_a_H____ = v_b____ )
| ( v_a_H____ = v_b_H____ )
| ( v_b_H____ = v_a____ )
| ( v_a____ = v_b____ ) ),
inference(demod,[status(thm)],[zip_derived_cl182,zip_derived_cl158,zip_derived_cl10,zip_derived_cl159,zip_derived_cl9]) ).
thf(zip_derived_cl3_023,plain,
v_a____ != v_b____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_096]) ).
thf(zip_derived_cl4_024,plain,
v_a____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_A_126_061_Ab_H_096]) ).
thf(zip_derived_cl6_025,plain,
v_a_H____ != v_b_H____,
inference(cnf,[status(esa)],[fact__096a_H_A_126_061_Ab_H_096]) ).
thf(zip_derived_cl5_026,plain,
v_b____ != v_a_H____,
inference(cnf,[status(esa)],[fact__096b_A_126_061_Aa_H_096]) ).
thf(zip_derived_cl184,plain,
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl183,zip_derived_cl3,zip_derived_cl4,zip_derived_cl6,zip_derived_cl5]) ).
thf(zip_derived_cl185,plain,
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl184]) ).
thf(zip_derived_cl175_027,plain,
c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ ( sk__1 @ v_a_H____ @ v_b_H____ @ v_a____ @ v_b____ @ v_P_H____ @ v_P____ ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl174,zip_derived_cl5,zip_derived_cl4,zip_derived_cl3]) ).
thf(zip_derived_cl187,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl185,zip_derived_cl175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT135+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjCiWc7k98 true
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 15:30:25 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.35 % Running in FO mode
% 0.49/0.64 % Total configuration time : 435
% 0.49/0.64 % Estimated wc time : 1092
% 0.49/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.49/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.49/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.56/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.56/0.75 % /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
% 0.57/0.87 % Solved by fo/fo4.sh.
% 0.57/0.87 % done 64 iterations in 0.087s
% 0.57/0.87 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.57/0.87 % SZS output start Refutation
% See solution above
% 0.57/0.87
% 0.57/0.87
% 0.57/0.87 % Terminating...
% 1.49/0.95 % Runner terminated.
% 1.49/0.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------