TPTP Problem File: ITP007+4.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP007+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ebool_2ETRUTH.p [Gau20]
% : HL403001+4.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 7072 (3716 unt; 0 def)
% Number of atoms : 18852 (9911 equ)
% Maximal formula atoms : 912 ( 2 avg)
% Number of connectives : 12474 ( 694 ~; 471 |;4566 &)
% (3311 <=>;3432 =>; 0 <=; 0 <~>)
% Maximal formula depth : 360 ( 6 avg)
% Maximal term depth : 53 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 1232 (1232 usr; 569 con; 0-6 aty)
% Number of variables : 39451 (26933 !;12518 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002+4.ax').
include('Axioms/ITP001/ITP003+4.ax').
include('Axioms/ITP001/ITP004+4.ax').
include('Axioms/ITP001/ITP005+4.ax').
include('Axioms/ITP001/ITP006+4.ax').
include('Axioms/ITP001/ITP007+4.ax').
include('Axioms/ITP001/ITP008+4.ax').
include('Axioms/ITP001/ITP009+4.ax').
include('Axioms/ITP001/ITP010+4.ax').
include('Axioms/ITP001/ITP011+4.ax').
include('Axioms/ITP001/ITP012+4.ax').
include('Axioms/ITP001/ITP013+4.ax').
include('Axioms/ITP001/ITP014+4.ax').
include('Axioms/ITP001/ITP015+4.ax').
include('Axioms/ITP001/ITP016+4.ax').
include('Axioms/ITP001/ITP017+4.ax').
include('Axioms/ITP001/ITP018+4.ax').
include('Axioms/ITP001/ITP019+4.ax').
include('Axioms/ITP001/ITP020+4.ax').
include('Axioms/ITP001/ITP021+4.ax').
include('Axioms/ITP001/ITP022+4.ax').
include('Axioms/ITP001/ITP023+4.ax').
include('Axioms/ITP001/ITP024+4.ax').
include('Axioms/ITP001/ITP025+4.ax').
include('Axioms/ITP001/ITP026+4.ax').
include('Axioms/ITP001/ITP027+4.ax').
include('Axioms/ITP001/ITP028+4.ax').
include('Axioms/ITP001/ITP029+4.ax').
include('Axioms/ITP001/ITP030+4.ax').
include('Axioms/ITP001/ITP031+4.ax').
include('Axioms/ITP001/ITP032+4.ax').
include('Axioms/ITP001/ITP033+4.ax').
include('Axioms/ITP001/ITP034+4.ax').
include('Axioms/ITP001/ITP035+4.ax').
include('Axioms/ITP001/ITP036+4.ax').
include('Axioms/ITP001/ITP037+4.ax').
include('Axioms/ITP001/ITP038+4.ax').
include('Axioms/ITP001/ITP039+4.ax').
include('Axioms/ITP001/ITP040+4.ax').
include('Axioms/ITP001/ITP041+4.ax').
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
( ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))
=> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ).
fof(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).
fof(reserved_2Eho_2Etruth,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(reserved_2Eho_2Ei__thm,axiom,
! [A_27a,V0x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ).
fof(reserved_2Eho_2Es__thm,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ).
fof(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
& p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).
fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
=> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).
fof(reserved_2Elogic_2E_3D,axiom,
! [A_27a,V0_2E0,V1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0))))
<=> s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ).
fof(reserved_2Equant_2E_21,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(reserved_2Equant_2E_3F,axiom,
! [A_27a,V0f_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
<=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
& p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
| p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0,X1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
=> p(s(tyop_2Emin_2Ebool,X1_2E0)) )
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] :
( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X3_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
! [X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(A_27b,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27b),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2ESOME_2E0),s(A_27c,X0_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0] : s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool)),c_2Eoption_2Esome_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27c),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)))),c_2Elist_2EFILTER_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),X0_2E0))) ).
fof(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ).
fof(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2Esome_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),A_27b)),c_2EpatternMatches_2EPMATCH_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X2_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),A_27c)),c_2EpatternMatches_2EPMATCH_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),A_27a)),c_2EpatternMatches_2EPMATCH_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))))),c_2Elist_2ESNOC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),A_27c)),c_2EpatternMatches_2EPMATCH_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2ESNOC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),A_27a)),c_2EpatternMatches_2EPMATCH_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)),c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool)),c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Ebool)),c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28A_27d_29_29,axiom,
! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),X1_2E0))) ).
fof(arityeq2_2Ec_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27d,axiom,
! [A_27d,X0_2E0] : s(A_27d,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),A_27d),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0,X1_2E0,X2_2E0] : s(A_27c,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27c,X1_2E0),s(A_27c,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27c))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27c,X1_2E0))),s(A_27c,X2_2E0))) ).
fof(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Elist_2EMAP2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27d),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) ).
fof(arityeq3_2Ec_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))) ).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X3_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Elist_2ESNOC_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))))),c_2Elist_2ESNOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X1_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X2_2E0),s(A_27c,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))))),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X2_2E0))),s(A_27c,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27c),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))),s(A_27b,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27c),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0),s(A_27c,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0))),s(A_27c,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27d),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27d),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))),s(A_27b,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27e_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b,A_27c,A_27e,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27e),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27e),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27e))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27e),X2_2E0))),s(A_27b,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27e_20mono_2EA_27d_20mono_2EA_27a,axiom,
! [A_27a,A_27d,A_27e,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27d,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27e))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27f_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27b,A_27d,A_27f,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27f),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27f),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27f),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27f),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27f)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27f),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27f))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27f),X2_2E0))),s(A_27b,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW_2E4_2Emono_2EA_27f_20mono_2EA_27e_20mono_2EA_27a,axiom,
! [A_27a,A_27e,A_27f,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Eoption_2Eoption(A_27f),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27e,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Eoption_2Eoption(A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27f)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27f))))),c_2EpatternMatches_2EPMATCH__ROW_2E0),s(tyop_2Emin_2Efun(A_27e,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2EpatternMatches_2EPMATCH__ROW__COND_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))),s(A_27a,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2EpatternMatches_2EPMATCH__ROW__COND_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27c,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2EpatternMatches_2EPMATCH__ROW__COND_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27c,X2_2E0))),s(A_27b,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27c,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),c_2EpatternMatches_2EPMATCH__ROW__COND_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27c,X3_2E0))) ).
fof(arityeq4_2Ec_2EpatternMatches_2EPMATCH__ROW__COND_2E4_2Emono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27b,A_27d,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0),s(A_27d,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)))),c_2EpatternMatches_2EPMATCH__ROW__COND_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))),s(A_27d,X3_2E0))) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__COND__def,axiom,
! [A_27a,A_27b,V0pat_2E0,V1guard_2E0,V2inp_2E0,V3v_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0pat_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1guard_2E0),s(A_27b,V2inp_2E0),s(A_27a,V3v_2E0))))
<=> ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0pat_2E0),s(A_27a,V3v_2E0))) = s(A_27b,V2inp_2E0)
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1guard_2E0),s(A_27a,V3v_2E0)))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__def,axiom,
! [A_27a,A_27b,A_27c,F0_2E0] :
( ! [V0pat_2E0,V1guard_2E0,V3i_2E0,V4v_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0pat_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1guard_2E0))),s(A_27c,V3i_2E0))),s(A_27b,V4v_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V0pat_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1guard_2E0),s(A_27c,V3i_2E0),s(A_27b,V4v_2E0)))
=> ! [V0pat_2E0,V1guard_2E0,V2rhs_2E0,V3i_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V0pat_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1guard_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rhs_2E0),s(A_27c,V3i_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rhs_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0pat_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1guard_2E0))),s(A_27c,V3i_2E0))))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__INCOMPLETE__def,axiom,
! [A_27a] : s(A_27a,c_2EpatternMatches_2EPMATCH__INCOMPLETE_2E0) = s(A_27a,c_2Ebool_2EARB_2E0) ).
fof(thm_2EpatternMatches_2EPMATCH__def,axiom,
! [A_27a,A_27b] :
( ! [V0v_2E0] : s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ENIL_2E0))) = s(A_27a,c_2EpatternMatches_2EPMATCH__INCOMPLETE_2E0)
& ! [V1v_2E0,V2r_2E0,V3rs_2E0] : s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V1v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V3rs_2E0))))) = s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2r_2E0),s(A_27b,V1v_2E0))),s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V1v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V3rs_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__def,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows1_2E0,V2rows2_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0))))
<=> ( s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0)))
& ( ? [V3r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0),s(A_27a,V0v_2E0)))))) )
<=> ? [V4r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V0v_2E0)))))) ) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__def,axiom,
! [A_27a,A_27b,V0v_2E0,V1rs_2E0,V2i_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0),s(tyop_2Enum_2Enum,V2i_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0))))))
& ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0))),s(A_27a,V0v_2E0))))))
=> ? [V3j_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3j_2E0),s(tyop_2Enum_2Enum,V2i_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3j_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0))),s(A_27a,V0v_2E0)))))) ) ) ) ) ).
fof(thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__def,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V5r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V5r_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V5r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1rows_2E0,V2c_2E0,V3infos_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
<=> ( s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0)))
& ! [V4i_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Enum_2Enum,V4i_2E0)))) ) )
& ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))
=> p(s(tyop_2Emin_2Ebool,V2c_2E0)) ) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__def,axiom,
! [A_27a,A_27b,V0i_2E0,V1p_2E0,V2g_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V0i_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))))
<=> ? [V3x_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(A_27a,V0i_2E0),s(A_27b,V3x_2E0)))) ) ).
fof(thm_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO__def,axiom,
! [A_27a,F0_2E0] :
( ! [V2x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),V2x_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),V2x_2E0)))) )
=> ! [V0is_2E0,V1xs_2E0] : s(tyop_2Elist_2Elist(A_27a),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0is_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0is_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))))))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__def,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V2r_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0),s(A_27a,V0v_2E0)))))
=> ! [V0v_2E0,V1rs_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0))) ) ).
fof(thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ__def,axiom,
! [F0_2E0] :
( ! [V2i1_2E0,V3i2_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V2i1_2E0))),s(tyop_2Emin_2Ebool,V3i2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V2i1_2E0))
& p(s(tyop_2Emin_2Ebool,V3i2_2E0)) ) )
=> ! [V0ip1_2E0,V1ip2_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0ip1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1ip2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0ip1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1ip2_2E0))) ) ).
fof(thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ__def,axiom,
! [F0_2E0] :
( ! [V2i1_2E0,V3i2_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V2i1_2E0))),s(tyop_2Emin_2Ebool,V3i2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V2i1_2E0))
| p(s(tyop_2Emin_2Ebool,V3i2_2E0)) ) )
=> ! [V0ip1_2E0,V1ip2_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0ip1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1ip2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0ip1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1ip2_2E0))) ) ).
fof(thm_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX__def,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0] :
( ! [V6p_2E0,V4r_2E0,V3v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Ebool,V6p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0))),s(A_27a,V3v_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V6p_2E0))
=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) )
=> ( ! [V6p_2E0,V4r_2E0,V3v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Ebool,V6p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0))),s(A_27a,V3v_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V6p_2E0))
& s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) )
=> ( ! [V0v_2E0,V1p_2E0,V2infos_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Ebool,V1p_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2infos_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Ebool,V1p_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2infos_2E0)))
& ! [V3v_2E0,V4r_2E0,V5rows_2E0,V6p_2E0,V7infos_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V3v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V5rows_2E0))),s(tyop_2Emin_2Ebool,V6p_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V7infos_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V3v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V5rows_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Ebool,V6p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0))),s(A_27a,V3v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Ebool,V6p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0))),s(A_27a,V3v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V7infos_2E0))))) ) ) ) ).
fof(thm_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__def,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0] : s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0))))) ).
fof(thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__def,axiom,
! [A_27a,A_27b,A_27c,F1_2E0,F0_2E0] :
( ! [V2row_2E0,V5x_2E0] : s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V2row_2E0))),s(A_27b,V5x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V2row_2E0),s(A_27b,V5x_2E0))),s(A_27b,V5x_2E0)))
=> ( ! [V0p_2E0,V1g_2E0,V3v_2E0,V4x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1g_2E0))),s(A_27c,V3v_2E0))),s(A_27b,V4x_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V0p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1g_2E0),s(A_27c,V3v_2E0),s(A_27b,V4x_2E0)))
=> ! [V0p_2E0,V1g_2E0,V2row_2E0,V3v_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V0p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V2row_2E0),s(A_27c,V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1g_2E0))),s(A_27c,V3v_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V2row_2E0))))) ) ) ).
fof(thm_2EpatternMatches_2ELENGTH__STRONGEST__REDUNDANT__ROWS__INFO,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))) ).
fof(thm_2EpatternMatches_2EEL2__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V5r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V5r_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V5r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1rows_2E0,V2p_2E0,V3infos_2E0,V4i_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0)))))))) )
=> ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2p_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))))))
<=> ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
& p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0)))))) )
=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) ) ) ).
fof(thm_2EpatternMatches_2EEL1__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2p_2E0,V3infos_2E0,V4i_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))))
=> s(tyop_2Emin_2Ebool,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2p_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))) ) ).
fof(thm_2EpatternMatches_2Esome__var__bool__T,axiom,
! [F0_2E0] :
( ! [V0x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,V0x_2E0))) = s(tyop_2Emin_2Ebool,V0x_2E0)
=> s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) ) ).
fof(thm_2EpatternMatches_2Esome__var__bool__F,axiom,
! [F0_2E0] :
( ! [V0x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Ebool,V0x_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0x_2E0)) )
=> s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__CONG,axiom,
! [A_27a,A_27b,A_27c,V0p_2E0,V1p_27_2E0,V2g_2E0,V3g_27_2E0,V4r_2E0,V5r_27_2E0,V6v_2E0,V7v_27_2E0] :
( ( s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1p_27_2E0)
& s(A_27b,V6v_2E0) = s(A_27b,V7v_27_2E0)
& ! [V8x_2E0] :
( s(A_27b,V6v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V8x_2E0)))
=> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0),s(A_27a,V8x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3g_27_2E0),s(A_27a,V8x_2E0))) )
& ! [V9x_2E0] :
( ( s(A_27b,V6v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V9x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0),s(A_27a,V9x_2E0)))) )
=> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V4r_2E0),s(A_27a,V9x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V5r_27_2E0),s(A_27a,V9x_2E0))) ) )
=> s(tyop_2Eoption_2Eoption(A_27c),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V4r_2E0),s(A_27b,V6v_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V1p_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3g_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V5r_27_2E0),s(A_27b,V7v_27_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__CONG,axiom,
! [A_27a,A_27b,V0v_2E0,V1v_27_2E0,V2rows_2E0,V3rows_27_2E0,V4r_2E0,V5r_27_2E0] :
( ( s(A_27a,V0v_2E0) = s(A_27a,V1v_27_2E0)
& s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V1v_27_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V5r_27_2E0),s(A_27a,V1v_27_2E0)))
& s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V1v_27_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V1v_27_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows_27_2E0))) )
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0))))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V1v_27_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V5r_27_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows_27_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__EQ__AUX,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0r_27_2E0,V1r_2E0,V2p_27_2E0,V3p_2E0,V4g_27_2E0,V5g_2E0] :
( ( ! [V6i_2E0] :
( ? [V7x_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27a),V3p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5g_2E0),s(A_27a,V6i_2E0),s(A_27b,V7x_2E0))))
<=> ? [V8x_27_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_27_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_27_2E0),s(A_27a,V6i_2E0),s(A_27c,V8x_27_2E0)))) )
& ! [V9x_2E0,V10x_27_2E0] :
( ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3p_2E0),s(A_27b,V9x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_27_2E0),s(A_27c,V10x_27_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5g_2E0),s(A_27b,V9x_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_27_2E0),s(A_27c,V10x_27_2E0)))) )
=> s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1r_2E0),s(A_27b,V9x_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0r_27_2E0),s(A_27c,V10x_27_2E0))) ) )
=> s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_27_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_27_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0r_27_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__EQ__NONE,axiom,
! [A_27a,A_27b,A_27c,V0r_2E0,V1p_2E0,V2i_2E0,V3g_2E0] :
( s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V0r_2E0),s(A_27c,V2i_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)
<=> ! [V4x_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0),s(A_27c,V2i_2E0),s(A_27b,V4x_2E0)))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__EQ__SOME,axiom,
! [A_27a,A_27b,A_27c,V0y_2E0,V1r_2E0,V2p_2E0,V3i_2E0,V4g_2E0] :
( s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V2p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1r_2E0),s(A_27c,V3i_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0)))
=> ? [V5x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V2p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4g_2E0),s(A_27c,V3i_2E0),s(A_27b,V5x_2E0))))
& s(A_27a,V0y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1r_2E0),s(A_27b,V5x_2E0))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__COND__SELECT__UNIQUE,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0p_2E0,V1g_2E0,V2i_2E0,V6y_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0))),s(A_27b,V2i_2E0))),s(A_27a,V6y_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27b,V2i_2E0),s(A_27a,V6y_2E0)))
=> ! [V0p_2E0,V1g_2E0,V2i_2E0] :
( ! [V3x1_2E0,V4x2_2E0] :
( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27a,V3x1_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27a,V4x2_2E0))))
& s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V3x1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V4x2_2E0))) )
=> s(A_27a,V3x1_2E0) = s(A_27a,V4x2_2E0) )
=> ! [V5x_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27b,V2i_2E0),s(A_27a,V5x_2E0))))
=> s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0))),s(A_27b,V2i_2E0))))) = s(A_27a,V5x_2E0) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__COND__DEF__GSYM,axiom,
! [A_27a,A_27b,V0v_2E0,V1pat_2E0,V2inp_2E0,V3guard_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V1pat_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3guard_2E0),s(A_27b,V2inp_2E0),s(A_27a,V0v_2E0))))
<=> ( s(A_27b,V2inp_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1pat_2E0),s(A_27a,V0v_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3guard_2E0),s(A_27a,V0v_2E0)))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EVAL,axiom,
! [A_27a,A_27b,A_27c,A_27d,F0_2E0,F1_2E0] :
( ! [V3p_2E0,V4g_2E0,V0v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(A_27b,V0v_2E0))))
<=> ? [V5x_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0),s(A_27b,V0v_2E0),s(A_27d,V5x_2E0)))) )
=> ( ! [V3p_2E0,V4g_2E0,V0v_2E0,V6x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(A_27b,V0v_2E0))),s(A_27d,V6x_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0),s(A_27b,V0v_2E0),s(A_27d,V6x_2E0)))
=> ! [V0v_2E0,V1rs_2E0,V2r_2E0,V3p_2E0,V4g_2E0] :
( s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ENIL_2E0))) = s(A_27a,c_2EpatternMatches_2EPMATCH__INCOMPLETE_2E0)
& s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V1rs_2E0))))) = s(A_27c,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(A_27b,V0v_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),V2r_2E0),s(A_27d,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(A_27b,V0v_2E0))))))),s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V1rs_2E0))))) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EVAL__MATCH,axiom,
! [A_27a,A_27b,A_27c,F0_2E0] :
( ! [V3p_2E0,V4g_2E0,V0v_2E0,V5x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V3p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4g_2E0))),s(A_27c,V0v_2E0))),s(A_27b,V5x_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V3p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4g_2E0),s(A_27c,V0v_2E0),s(A_27b,V5x_2E0)))
=> ! [V0v_2E0,V1rs_2E0,V2r_2E0,V3p_2E0,V4g_2E0] :
( s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V3p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2r_2E0),s(A_27c,V0v_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)
=> s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27c,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V3p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),V1rs_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2r_2E0),s(A_27b,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V3p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4g_2E0))),s(A_27c,V0v_2E0))))))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EXTEND__BASE,axiom,
! [A_27a,A_27b,A_27c,V0v__old_2E0,V1v__new_2E0] : s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v__old_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ENIL_2E0))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V1v__new_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ENIL_2E0))) ).
fof(thm_2EpatternMatches_2EPMATCH__EXTEND__BOTH,axiom,
! [A_27a,A_27b,A_27c,V0v__old_2E0,V1v__new_2E0,V2rows__old_2E0,V3rows__new_2E0,V4r__old_2E0,V5r__new_2E0] :
( s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),V4r__old_2E0),s(A_27a,V0v__old_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),V5r__new_2E0),s(A_27b,V1v__new_2E0)))
=> ( s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v__old_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V2rows__old_2E0))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V1v__new_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V3rows__new_2E0)))
=> s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v__old_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),V4r__old_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V2rows__old_2E0))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V1v__new_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),V5r__new_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V3rows__new_2E0))))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EXTEND__BOTH__ID,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows__old_2E0,V2rows__new_2E0,V3r_2E0] :
( s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows__old_2E0))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows__new_2E0)))
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows__old_2E0))))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows__new_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EXTEND__OLD,axiom,
! [A_27a,A_27b,A_27c,V0v__old_2E0,V1v__new_2E0,V2rows__old_2E0,V3rows__new_2E0,V4r__old_2E0] :
( s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),V4r__old_2E0),s(A_27a,V0v__old_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0)
=> ( s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v__old_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V2rows__old_2E0))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V1v__new_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V3rows__new_2E0)))
=> s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v__old_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),V4r__old_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V2rows__old_2E0))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V1v__new_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V3rows__new_2E0))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REMOVE__FUN,axiom,
! [A_27a,A_27b,A_27c,A_27d,F1_2E0,F0_2E0] :
( ! [V2p_2E0,V8x_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),F1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_2E0))),s(A_27c,V8x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_2E0),s(A_27c,V8x_2E0)))
=> ( ! [V0ff_2E0,V2p_2E0,V7x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0ff_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_2E0))),s(A_27c,V7x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0ff_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_2E0),s(A_27c,V7x_2E0)))))
=> ! [V0ff_2E0,V1v_2E0,V2p_2E0,V3g_2E0,V4r_2E0] :
( ! [V5x_2E0,V6y_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0ff_2E0),s(A_27a,V5x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0ff_2E0),s(A_27a,V6y_2E0)))
=> s(A_27a,V5x_2E0) = s(A_27a,V6y_2E0) )
=> s(tyop_2Eoption_2Eoption(A_27d),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0ff_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V4r_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0ff_2E0),s(A_27a,V1v_2E0))))) = s(tyop_2Eoption_2Eoption(A_27d),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),F1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2p_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V4r_2E0),s(A_27a,V1v_2E0))) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__EXTEND__INPUT,axiom,
! [A_27a,A_27b,A_27c,A_27d,A_27e,A_27f,F0_2E0,F1_2E0] :
( ! [V5g_2E0,V2f_27_2E0,V7p_27_2E0,V3f_2E0,V13x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),V5g_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),V3f_2E0))),s(A_27d,V13x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),V5g_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0),s(A_27d,V13x_2E0))))))),s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V3f_2E0),s(A_27d,V13x_2E0)))))
=> ( ! [V6r_2E0,V2f_27_2E0,V7p_27_2E0,V3f_2E0,V14x_2E0] : s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f))))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,A_27f)),V6r_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),V3f_2E0))),s(A_27d,V14x_2E0))) = s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,A_27f)),V6r_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0),s(A_27d,V14x_2E0))))))),s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V3f_2E0),s(A_27d,V14x_2E0)))))
=> ! [V0v_2E0,V1v_27_2E0,V2f_27_2E0,V3f_2E0,V4p_2E0,V5g_2E0,V6r_2E0,V7p_27_2E0] :
( ( ! [V8x_27_2E0] :
( s(A_27b,V1v_27_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0),s(A_27d,V8x_27_2E0)))
=> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27a),V4p_2E0),s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V3f_2E0),s(A_27d,V8x_27_2E0))))) = s(A_27a,V0v_2E0) )
& ! [V9x_2E0] :
( s(A_27a,V0v_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27a),V4p_2E0),s(A_27e,V9x_2E0)))
=> ? [V10x_27_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0),s(A_27d,V10x_27_2E0))) = s(A_27b,V1v_27_2E0) )
& ! [V11x_2E0,V12y_2E0] :
( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27a),V4p_2E0),s(A_27e,V11x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27a),V4p_2E0),s(A_27e,V12y_2E0)))
=> s(A_27e,V11x_2E0) = s(A_27e,V12y_2E0) ) )
=> s(tyop_2Eoption_2Eoption(A_27f),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27e,A_27a),V4p_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),V5g_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0),s(A_27b,V1v_27_2E0))))),s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,A_27f)),V6r_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0),s(A_27b,V1v_27_2E0))))),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27f),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool))))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),V5g_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),V3f_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f))))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27e,A_27f)),V6r_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),V2f_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),V7p_27_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),V3f_2E0))),s(A_27b,V1v_27_2E0))) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REMOVE__FUN__VAR,axiom,
! [A_27a,A_27b,A_27c,A_27d,A_27e,F0_2E0,F1_2E0] :
( ! [V4g_2E0,V2f_2E0,V12x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(A_27c,V12x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V12x_2E0)))))
=> ( ! [V5r_2E0,V2f_2E0,V13x_2E0] : s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(A_27c,V13x_2E0))) = s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V13x_2E0)))))
=> ! [V0v_2E0,V1v_27_2E0,V2f_2E0,V3p_2E0,V4g_2E0,V5r_2E0,V6p_27_2E0] :
( ( ! [V7x_27_2E0] :
( s(A_27b,V1v_27_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V6p_27_2E0),s(A_27c,V7x_27_2E0)))
<=> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V7x_27_2E0))))) = s(A_27a,V0v_2E0) )
& ! [V8x_2E0] :
( s(A_27a,V0v_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,V8x_2E0)))
=> ? [V9x_27_2E0] : s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0),s(A_27c,V9x_27_2E0))) = s(A_27d,V8x_2E0) )
& ! [V10x_2E0,V11y_2E0] :
( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,V10x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(A_27d,V11y_2E0)))
=> s(A_27d,V10x_2E0) = s(A_27d,V11y_2E0) ) )
=> s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27d,A_27a),V3p_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27e),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27c,A_27b),V6p_27_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27e))),F1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V5r_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V2f_2E0))),s(A_27b,V1v_27_2E0))) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__EQUIV__EXPAND,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows2_2E0,V2rows1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows2_2E0))))
<=> s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows2_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__1,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0)))) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__2,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows1_2E0,V2rows2_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0))) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__is__equiv__3,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows1_2E0,V2rows2_2E0,V3rows3_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows3_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows3_2E0)))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__MATCH,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows2_2E0,V2rows1_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows2_2E0))))
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows2_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__APPEND__SEM,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V1rows1_2E0,V0v_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0))),s(A_27a,V0v_2E0))))
<=> ? [V3r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0),s(A_27a,V0v_2E0)))))) ) )
=> ! [V0v_2E0,V1rows1_2E0,V2rows2_2E0] : s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0))))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0))),s(A_27a,V0v_2E0))),s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1_2E0))),s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows2_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__APPEND,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows1a_2E0,V2rows1b_2E0,V3rows2a_2E0,V4rows2b_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1a_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1b_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows2a_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V4rows2b_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows1a_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows2a_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1b_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V4rows2b_2E0)))))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__EQUIV__ROWS__CONS__NONE,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2row_2E0] :
( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2row_2E0),s(A_27b,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)
=> s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2row_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V1rows_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V1rows_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__TRIVIAL__SOUNDNESS__EQUIV,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2n_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(A_27a,V0v_2E0)))))) )
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0)))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__TRIVIAL__SOUNDNESS,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2n_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))))
& p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(A_27a,V0v_2E0)))))) )
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT,axiom,
! [A_27a,A_27b,V0r1_2E0,V1r2_2E0,V2rows1_2E0,V3rows2_2E0,V4rows3_2E0,V5v_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1r2_2E0),s(A_27a,V5v_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0r1_2E0),s(A_27a,V5v_2E0)))))) )
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V5v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0r1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1r2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V4rows3_2E0))))))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V5v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0r1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V4rows3_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__PMATCH__ROWS,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0p_2E0,V1g_2E0,V2r_2E0,V3p_27_2E0,V4g_27_2E0,V5r_27_2E0,V6rows1_2E0,V7rows2_2E0,V8rows3_2E0,V9v_2E0] :
( ! [V10x_27_2E0] :
( ( s(A_27b,V9v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(A_27d,V10x_27_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(A_27d,V10x_27_2E0)))) )
=> ? [V11x_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(A_27d,V10x_27_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V11x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27a,V11x_2E0)))) ) )
=> s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V9v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V6rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7rows2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V5r_27_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8rows3_2E0))))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V9v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V6rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7rows2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8rows3_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROWS__DROP__SUBSUMED,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V5v_2E0,V7row_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V5v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V7row_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V7row_2E0),s(A_27a,V5v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0r1_2E0,V1r2_2E0,V2rows1_2E0,V3rows2_2E0,V4rows3_2E0,V5v_2E0] :
( ( ! [V6x_2E0] :
( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0r1_2E0),s(A_27a,V5v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V6x_2E0)))
=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1r2_2E0),s(A_27a,V5v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V6x_2E0))) )
& ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0r1_2E0),s(A_27a,V5v_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V5v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows2_2E0)))) ) )
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V5v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0r1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1r2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V4rows3_2E0))))))))))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V5v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V3rows2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1r2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V4rows3_2E0))))))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROWS__DROP__SUBSUMED__PMATCH__ROWS,axiom,
! [A_27a,A_27b,A_27c,A_27d,F0_2E0] :
( ! [V0p_2E0,V14x_2E0,V15row_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0))),s(A_27a,V14x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),V15row_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),V15row_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V14x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0) )
=> ! [V0p_2E0,V1g_2E0,V2r_2E0,V3p_27_2E0,V4g_27_2E0,V5r_27_2E0,V6rows1_2E0,V7rows2_2E0,V8rows3_2E0,V9v_2E0] :
( ( ! [V10x_2E0] :
( ( s(A_27b,V9v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V10x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27a,V10x_2E0)))) )
=> ? [V11x_27_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V10x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(A_27d,V11x_27_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(A_27d,V11x_27_2E0)))) ) )
& ! [V12x_2E0,V13x_27_2E0] :
( ( s(A_27b,V9v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V12x_2E0)))
& s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V12x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(A_27d,V13x_27_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27a,V12x_2E0))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(A_27d,V13x_27_2E0)))) )
=> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0),s(A_27a,V12x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),V5r_27_2E0),s(A_27d,V13x_27_2E0))) )
& ! [V14x_2E0] :
( ( s(A_27b,V9v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V14x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(A_27a,V14x_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0))),s(A_27a,V14x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7rows2_2E0)))) ) )
=> s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V9v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V6rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7rows2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V5r_27_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8rows3_2E0))))))))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V9v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V6rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7rows2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27d,A_27b),V3p_27_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V4g_27_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V5r_27_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8rows3_2E0))))))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__REMOVE__ARB,axiom,
! [A_27a,A_27b,A_27c,V0p_2E0,V1g_2E0,V2r_2E0,V3v_2E0,V4rows_2E0] :
( ! [V5x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0),s(A_27a,V5x_2E0))) = s(A_27c,c_2Ebool_2EARB_2E0)
=> s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V3v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V2r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V4rows_2E0))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V3v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V4rows_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__INTRO__CATCHALL,axiom,
! [A_27a,A_27b,F1_2E0,F0_2E0,F2_2E0] :
( ! [V3__0_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F1_2E0),s(A_27b,V3__0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
=> ( ! [V2__0_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0),s(A_27b,V2__0_2E0))) = s(A_27b,V2__0_2E0)
=> ( ! [V4__0_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),F2_2E0),s(A_27b,V4__0_2E0))) = s(A_27a,c_2Ebool_2EARB_2E0)
=> ! [V0v_2E0,V1rows_2E0] : s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V1rows_2E0))) = s(A_27a,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),F2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),V1rows_2E0))))) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__REMOVE__ARB__NO__OVERLAP,axiom,
! [A_27a,A_27b,A_27c,F0_2E0] :
( ! [V1p_2E0,V7x_2E0,V8row_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(A_27b,V7x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),V8row_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),V8row_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(A_27b,V7x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1p_2E0,V2g_2E0,V3r_2E0,V4rows1_2E0,V5rows2_2E0] :
( ( ! [V6x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V3r_2E0),s(A_27b,V6x_2E0))) = s(A_27c,c_2Ebool_2EARB_2E0)
& ! [V7x_2E0] :
( ( s(A_27a,V0v_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(A_27b,V7x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(A_27b,V7x_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(A_27b,V7x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V5rows2_2E0)))) ) )
=> s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V4rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V3r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V5rows2_2E0))))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V4rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V5rows2_2E0))))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__NIL,axiom,
! [A_27a,A_27b,V0v_2E0,V1i_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ENIL_2E0),s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__0,axiom,
! [A_27a,A_27b,V0v_2E0,V1rs_2E0,V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__SUC,axiom,
! [A_27a,A_27b,V0v_2E0,V1r_2E0,V2rs_2E0,V3i_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3i_2E0))))))
<=> ( ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1r_2E0),s(A_27a,V0v_2E0))) != s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs_2E0)))))) )
| p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__APPEND__LT,axiom,
! [A_27a,A_27b,V0v_2E0,V1rs1_2E0,V2rs2_2E0,V3i_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0))))))
=> s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0))),s(tyop_2Enum_2Enum,V3i_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0),s(tyop_2Enum_2Enum,V3i_2E0))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REDUNDANT__APPEND__GE,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V4r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1rs1_2E0,V2rs2_2E0,V3i_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0))),s(tyop_2Enum_2Enum,V3i_2E0))))
<=> ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0)))))))) )
| p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__REDUNDANT_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0)))))))) ) ) ) ) ).
fof(thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__NIL,axiom,
! [A_27a,A_27b,V0v_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0)))) ).
fof(thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__SNOC,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2c_2E0,V3infos_2E0,V4r_2E0,V5i_2E0,V6c_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> ( ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)
=> ( p(s(tyop_2Emin_2Ebool,V2c_2E0))
=> p(s(tyop_2Emin_2Ebool,V6c_27_2E0)) ) )
=> ( ( p(s(tyop_2Emin_2Ebool,V2c_2E0))
=> ( p(s(tyop_2Emin_2Ebool,V5i_2E0))
=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) )
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(tyop_2Emin_2Ebool,V6c_27_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Ebool,V5i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0)))))) ) ) ) ).
fof(thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__SNOC__PMATCH__ROW,axiom,
! [A_27a,A_27b,A_27c,F0_2E0] :
( ! [V2c_2E0,V0v_2E0,V4p_2E0,V5g_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Ebool,V2c_2E0))),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5g_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V2c_2E0))
=> ~ p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V0v_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5g_2E0)))) ) )
=> ! [V0v_2E0,V1rows_2E0,V2c_2E0,V3infos_2E0,V4p_2E0,V5g_2E0,V6r_2E0,V7c_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> ( ( ~ p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V0v_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5g_2E0))))
=> s(tyop_2Emin_2Ebool,V2c_2E0) = s(tyop_2Emin_2Ebool,V7c_27_2E0) )
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V6r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(tyop_2Emin_2Ebool,V7c_27_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ESNOC_2E2(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Ebool,V2c_2E0))),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V5g_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0)))))) ) ) ) ).
fof(thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__CONS,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2row_2E0,V3infos_27_2E0,V4i_2E0,V5c_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2row_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(tyop_2Emin_2Ebool,V5c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,V4i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_27_2E0))))))
<=> ( s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_27_2E0)))
& ( p(s(tyop_2Emin_2Ebool,V4i_2E0))
=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2row_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
& ( s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2row_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V5c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_27_2E0)))) ) ) ) ).
fof(thm_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO__THMS,axiom,
! [A_27a,A_27b,A_27c] :
( s(tyop_2Elist_2Elist(A_27a),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)
& ! [V0is_2E0,V1x_2E0,V2xs_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0is_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1x_2E0),s(tyop_2Elist_2Elist(A_27b),V2xs_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0is_2E0),s(tyop_2Elist_2Elist(A_27b),V2xs_2E0)))
& ! [V3is_2E0,V4x_2E0,V5xs_2E0] : s(tyop_2Elist_2Elist(A_27c),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3is_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4x_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4x_2E0),s(tyop_2Elist_2Elist(A_27c),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3is_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROWS__DROP__REDUNDANT__ROWS__INFO__EQUIV,axiom,
! [A_27a,A_27b,V0v_2E0,V1c_2E0,V2rows_2E0,V3infos_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0),s(tyop_2Emin_2Ebool,V1c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0)))))) ) ).
fof(thm_2EpatternMatches_2EREDUNDANT__ROWS__INFO__TO__PMATCH__EQ,axiom,
! [A_27a,A_27b,V0v_2E0,V1c_2E0,V2rows_2E0,V3infos_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0),s(tyop_2Emin_2Ebool,V1c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2EpatternMatches_2EAPPLY__REDUNDANT__ROWS__INFO_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rows_2E0))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__REWRITES,axiom,
! [A_27a,A_27b,A_27c,A_27d] :
( ! [V0v_2E0] : s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
& ! [V1v_2E0,V2r_2E0,V3rs_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27c,V1v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V2r_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),V3rs_2E0))))))
<=> ( s(tyop_2Eoption_2Eoption(A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V2r_2E0),s(A_27c,V1v_2E0))) != s(tyop_2Eoption_2Eoption(A_27d),c_2Eoption_2ENONE_2E0)
| p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27c,V1v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),V3rs_2E0)))) ) ) ) ).
fof(thm_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO__EXTRACT__IS__EXHAUSTIVE,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2c_2E0,V3infos_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> ( ~ p(s(tyop_2Emin_2Ebool,V2c_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0)))) ) ) ).
fof(thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ__REWRITE,axiom,
! [F0_2E0] :
( ! [V3i1_2E0,V2i2_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V3i1_2E0))),s(tyop_2Emin_2Ebool,V2i2_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V3i1_2E0))
& p(s(tyop_2Emin_2Ebool,V2i2_2E0)) ) )
=> ! [V0is2_2E0,V1is1_2E0,V2i2_2E0,V3i1_2E0] :
( s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ENIL_2E0)
& s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,V3i1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1is1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,V2i2_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0is2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V3i1_2E0))),s(tyop_2Emin_2Ebool,V2i2_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1is1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0is2_2E0))))) ) ) ).
fof(thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ__THM,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V2c_2E0,V4c_27_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V2c_2E0))),s(tyop_2Emin_2Ebool,V4c_27_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V2c_2E0))
| p(s(tyop_2Emin_2Ebool,V4c_27_2E0)) ) )
=> ! [V0v_2E0,V1rows_2E0,V2c_2E0,V3infos_2E0,V4c_27_2E0,V5infos_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> ( s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5infos_27_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0)))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V2c_2E0))),s(tyop_2Emin_2Ebool,V4c_27_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__CONJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5infos_27_2E0)))))) ) ) ) ).
fof(thm_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ__THM,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V2c_2E0,V4c_27_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V2c_2E0))),s(tyop_2Emin_2Ebool,V4c_27_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,V2c_2E0))
& p(s(tyop_2Emin_2Ebool,V4c_27_2E0)) ) )
=> ! [V0v_2E0,V1rows_2E0,V2c_2E0,V3infos_2E0,V4c_27_2E0,V5infos_27_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2c_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))
=> ( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V4c_27_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5infos_27_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Ebool,V2c_2E0))),s(tyop_2Emin_2Ebool,V4c_27_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2EREDUNDANT__ROWS__INFOS__DISJ_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V5infos_27_2E0)))))) ) ) ) ).
fof(thm_2EpatternMatches_2ELENGTH__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a,A_27b,V0v_2E0,V1rows_2E0,V2p_2E0,V3infos_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2p_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))) ).
fof(thm_2EpatternMatches_2EFST__STRONGEST__REDUNDANT__ROWS__INFO__AUX,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V4r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V4r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1rows_2E0,V2p_2E0,V3infos_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__AUX_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,V2p_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3infos_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,V2p_2E0))
& p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0)))) ) ) ) ).
fof(thm_2EpatternMatches_2EEL__STRONGEST__REDUNDANT__ROWS__INFO,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V3r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1rows_2E0,V2i_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))))
=> ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))))))
=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) ) ) ) ) ).
fof(thm_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO__OK,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1rows_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EIS__REDUNDANT__ROWS__INFO_2E4(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0),s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2EpatternMatches_2ESTRONGEST__REDUNDANT__ROWS__INFO_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rows_2E0)))))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__FULL__DEF,axiom,
! [A_27a,A_27b,V0p_2E0,V1i_2E0,V2g_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V0p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))))
<=> ? [V3x_2E0] :
( s(A_27a,V1i_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0p_2E0),s(A_27b,V3x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(A_27b,V3x_2E0)))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__WEAKEN,axiom,
! [A_27a,A_27b,A_27c,F0_2E0] :
( ! [V5g_27_2E0,V3g_2E0,V0f_2E0,V7x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5g_27_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27a,V7x_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5g_27_2E0),s(A_27a,V7x_2E0))))
& ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V7x_2E0)))))) ) )
=> ! [V0f_2E0,V1v_2E0,V2p_2E0,V3g_2E0,V4p_27_2E0,V5g_27_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27c,V1v_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V2p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0))))
=> ( ! [V6x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V4p_27_2E0),s(A_27a,V6x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V2p_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6x_2E0)))))
=> s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27c,V1v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V4p_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5g_27_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27c,V1v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V4p_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5g_27_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__FALSE,axiom,
! [A_27a,A_27b,V0v_2E0,V1p_2E0,V2g_2E0] :
( ! [V3x_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(A_27b,V3x_2E0))))
=> s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V0v_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__COND__EX__IMP__REWRITE,axiom,
! [A_27a,A_27b,A_27c,V0v_2E0,V1p_2E0,V2g_2E0,V3p_27_2E0,V4g_27_2E0,V5RES_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V0v_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))))
=> ( ! [V6x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(A_27b,V6x_2E0))))
=> ( ? [V7x_27_2E0] :
( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_27_2E0),s(A_27c,V7x_27_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(A_27b,V6x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_27_2E0),s(A_27c,V7x_27_2E0)))) )
<=> p(s(tyop_2Emin_2Ebool,V5RES_2E0)) ) )
=> s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V0v_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_27_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_27_2E0))) = s(tyop_2Emin_2Ebool,V5RES_2E0) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE__CONTRADICT,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V0v_2E0,V2r_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0))))
<=> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2r_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) )
=> ! [V0v_2E0,V1rs_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V0v_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs_2E0)))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__EVAL__COND__EX,axiom,
! [A_27a,A_27b,A_27c,F0_2E0] :
( ! [V1p_2E0,V3g_2E0,V2i_2E0,V4x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0))),s(A_27a,V2i_2E0))),s(A_27b,V4x_2E0))) = s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND_2E4(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0),s(A_27a,V2i_2E0),s(A_27b,V4x_2E0)))
=> ! [V0r_2E0,V1p_2E0,V2i_2E0,V3g_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0))))
=> s(tyop_2Eoption_2Eoption(A_27c),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0r_2E0),s(A_27a,V2i_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0r_2E0),s(A_27b,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0))),s(A_27a,V2i_2E0))))))))) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__NEQ__NONE,axiom,
! [A_27a,A_27b,A_27c,V0r_2E0,V1p_2E0,V2i_2E0,V3g_2E0] :
( s(tyop_2Eoption_2Eoption(A_27a),c_2EpatternMatches_2EPMATCH__ROW_2E4(s(tyop_2Emin_2Efun(A_27b,A_27c),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V0r_2E0),s(A_27c,V2i_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)
<=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__ROW__COND__EX_2E3(s(A_27c,V2i_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3g_2E0)))) ) ).
fof(thm_2EpatternMatches_2EPMATCH__ROW__REMOVE__DOUBLE__BINDS__THM,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0g_2E0,V1p1_2E0,V2g1_2E0,V3r1_2E0,V4p2_2E0,V5g2_2E0,V6r2_2E0] :
( ( ! [V7x_2E0,V8y_2E0] :
( s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1p1_2E0),s(A_27a,V7x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1p1_2E0),s(A_27a,V8y_2E0)))
=> s(A_27a,V7x_2E0) = s(A_27a,V8y_2E0) )
& ! [V9x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V4p2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0),s(A_27a,V9x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1p1_2E0),s(A_27a,V9x_2E0)))
& ! [V10x_27_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5g2_2E0),s(A_27b,V10x_27_2E0))))
<=> ? [V11x_2E0] :
( s(A_27b,V10x_27_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0),s(A_27a,V11x_2E0)))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g1_2E0),s(A_27a,V11x_2E0)))) ) )
& ! [V12x_2E0] : s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V6r2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0),s(A_27a,V12x_2E0))))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27d),V3r1_2E0),s(A_27a,V12x_2E0))) )
=> s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1p1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V3r1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V4p2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5g2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V6r2_2E0))) ) ).
fof(thm_2EpatternMatches_2EGUARDS__ELIM__THM,axiom,
! [A_27a,A_27b,A_27c,F1_2E0,F0_2E0] :
( ! [V4g_2E0,V5r_2E0,V3p_2E0,V2rs2_2E0,V9x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b))))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V5r_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0))),s(A_27c,V9x_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_2E0),s(A_27c,V9x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V5r_2E0),s(A_27c,V9x_2E0))),s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_2E0),s(A_27c,V9x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0)))))
=> ( ! [V8x_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),F0_2E0),s(A_27c,V8x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
=> ! [V0v_2E0,V1rs1_2E0,V2rs2_2E0,V3p_2E0,V4g_2E0,V5r_2E0] :
( ! [V6x1_2E0,V7x2_2E0] :
( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_2E0),s(A_27c,V6x1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_2E0),s(A_27c,V7x2_2E0)))
=> s(A_27c,V6x1_2E0) = s(A_27c,V7x2_2E0) )
=> s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V5r_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0))))))) = s(A_27b,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V1rs1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Efun(A_27c,A_27b))))),F1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),V5r_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V3p_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),V2rs2_2E0))))))) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__FLATTEN__THM__SINGLE,axiom,
! [A_27a,A_27b,A_27c,F3_2E0,F1_2E0,F2_2E0,F0_2E0] :
( ! [V6x_2E0,V7r_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F3_2E0),s(A_27b,V6x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7r_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7r_2E0),s(A_27b,V6x_2E0)))
=> ( ! [V3rows_2E0,V6x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(A_27b,A_27c)),F1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V3rows_2E0))),s(A_27b,V6x_2E0))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V6x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F3_2E0),s(A_27b,V6x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V3rows_2E0)))))
=> ( ! [V1p_2E0,V2g_2E0,V8r_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V8r_2E0)))
=> ( ! [V4x_2E0,V5r_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F0_2E0),s(A_27b,V4x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V5r_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V5r_2E0),s(A_27b,V4x_2E0)))
=> ! [V0v_2E0,V1p_2E0,V2g_2E0,V3rows_2E0] :
( ! [V4x_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27b,V4x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F0_2E0),s(A_27b,V4x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V3rows_2E0))))))
=> p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__EQUIV__ROWS_2E3(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(A_27b,A_27c)),F1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V3rows_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V3rows_2E0)))))) ) ) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__FLATTEN__THM,axiom,
! [A_27a,A_27b,A_27c,F3_2E0,F1_2E0,F2_2E0,F0_2E0] :
( ! [V8x_2E0,V9r_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F3_2E0),s(A_27b,V8x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V9r_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V9r_2E0),s(A_27b,V8x_2E0)))
=> ( ! [V5rows_2E0,V8x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(A_27b,A_27c)),F1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V5rows_2E0))),s(A_27b,V8x_2E0))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27b,V8x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F3_2E0),s(A_27b,V8x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V5rows_2E0)))))
=> ( ! [V1p_2E0,V2g_2E0,V10r_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V10r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V10r_2E0)))
=> ( ! [V6x_2E0,V7r_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F0_2E0),s(A_27b,V6x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7r_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V7r_2E0),s(A_27b,V6x_2E0)))
=> ! [V0v_2E0,V1p_2E0,V2g_2E0,V3rows1_2E0,V4rows2_2E0,V5rows_2E0] :
( ! [V6x_2E0] : p(s(tyop_2Emin_2Ebool,c_2EpatternMatches_2EPMATCH__IS__EXHAUSTIVE_2E2(s(A_27b,V6x_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F0_2E0),s(A_27b,V6x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V5rows_2E0))))))
=> s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V3rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(A_27b,A_27c)),F1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V5rows_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V4rows2_2E0))))))) = s(A_27c,c_2EpatternMatches_2EPMATCH_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V3rows1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))))),F2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2g_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),V5rows_2E0))))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),V4rows2_2E0))))) ) ) ) ) ) ).
fof(thm_2EpatternMatches_2EPMATCH__FLATTEN__FUN__PMATCH__ROW,conjecture,
! [A_27a,A_27b,A_27c,A_27d,F0_2E0,F3_2E0,F2_2E0,F1_2E0] :
( ! [V4p_27_2E0,V5g_27_2E0,V6r_27_2E0,V7x_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V5g_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V6r_27_2E0))),s(A_27a,V7x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V5g_27_2E0),s(A_27a,V7x_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V6r_27_2E0),s(A_27a,V7x_2E0)))))
=> ( ! [V6r_27_2E0,V4p_27_2E0,V10x_2E0] : s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V6r_27_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))),s(A_27c,V10x_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V6r_27_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0),s(A_27c,V10x_2E0))))),s(A_27c,V10x_2E0)))
=> ( ! [V3g_2E0,V4p_27_2E0,V5g_27_2E0,V9x_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V5g_27_2E0))),s(A_27c,V9x_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3g_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0),s(A_27c,V9x_2E0))))))
& p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V5g_27_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0),s(A_27c,V9x_2E0))))),s(A_27c,V9x_2E0)))) ) )
=> ( ! [V0p_2E0,V4p_27_2E0,V8x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))),s(A_27c,V8x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0),s(A_27c,V8x_2E0)))))
=> ! [V0p_2E0] :
( ! [V1x1_2E0,V2x2_2E0] :
( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V1x1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(A_27a,V2x2_2E0)))
=> s(A_27a,V1x1_2E0) = s(A_27a,V2x2_2E0) )
=> ! [V3g_2E0,V4p_27_2E0,V5g_27_2E0,V6r_27_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__FLATTEN__FUN_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V5g_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V6r_27_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),c_2EpatternMatches_2EPMATCH__ROW_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0p_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V5g_27_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27d))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27d)),V6r_27_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),V4p_27_2E0))))) ) ) ) ) ) ).
%------------------------------------------------------------------------------